https://www.math.wisc.edu/wiki/api.php?action=feedcontributions&user=Arinkin&feedformat=atomUW-Math Wiki - User contributions [en]2019-09-23T03:06:39ZUser contributionsMediaWiki 1.30.1https://www.math.wisc.edu/wiki/index.php?title=File:Math763hw2.pdf&diff=17969File:Math763hw2.pdf2019-09-19T23:23:26Z<p>Arinkin: </p>
<hr />
<div></div>Arinkinhttps://www.math.wisc.edu/wiki/index.php?title=Math_763_--_Algebraic_Geometry_I&diff=17968Math 763 -- Algebraic Geometry I2019-09-19T23:23:16Z<p>Arinkin: /* Homework assignments */</p>
<hr />
<div><br />
=Fall 2019=<br />
<br />
== Homework assignments ==<br />
<br />
* [[Media:math763hw1.pdf|Homework 1]], due Thursday, September 19th.<br />
* [[Media:math763hw2.pdf|Homework 2]], due Thursday, September 26th.<br />
<br />
== Course description ==<br />
<br />
This is a first course in algebraic geometry. While there are no formal prerequisites beyond a knowledge of the material covered in the first-year algebra and geometry sequence, familiarity with some basic commutative algebra will be helpful. The rough outline of the course is as follows (subject to change):<br />
<br />
* Affine and projective varieties.<br />
* Morphisms and rational maps.<br />
* Local properties: smoothness and dimension. Tangent space.<br />
* Divisors.<br />
* Low-dimensional varieties: curves and surfaces. Blow-ups.<br />
* The Riemann-Roch Theorem.<br />
<br />
Here is a more detailed lecture-by-lecture [[Math 763 -- Algebraic Geometry I -- Detailed list of topics|list of topics]] that I covered in the past, of course, this is all subject to change.<br />
<br />
== Handouts ==<br />
<br />
* [[Media:IV.pdf | Correspondence between sets and ideals]]<br />
* [[Media:Nullstellensatz.pdf|Proof of the Nullstellensatz]]<br />
<br />
== References ==<br />
* Shafarevich, Basic Algebraic Geometry.<br />
* [http://www.jmilne.org/math/CourseNotes/ag.html Algebraic Geometry] (online notes) by Milne.<br />
* Hartshorne, Algebraic Geometry, Chapter I (this is more advanced, so does not quite match the content).<br />
* Here is a [https://mathoverflow.net/questions/2446/best-algebraic-geometry-text-book-other-than-hartshorne discussion] on MathOverflow with more books on algebraic geometry, but most of them are going to be too advanced.<br />
* Here are [[Media:notes.pdf | notes]] from the last time I taught this course. These were taken in class, so<br />
there are probably typos.<br />
<br />
== Information for students ==<br />
<br />
* '''Instructor''': Dima Arinkin<br />
* '''Office Hours''': Tuesday 3-4pm, Wednesday 2-2:45pm, and by appointment in VV 603<br />
* '''Lectures''': TuTh 11am-12:15pm, VV B129<br />
* '''Grade''': There will be weekly [[Math 763 -- Algebraic Geometry I -- Homeworks|homework assignments]], but no exams in this course.</div>Arinkinhttps://www.math.wisc.edu/wiki/index.php?title=Math_763_--_Algebraic_Geometry_I&diff=17849Math 763 -- Algebraic Geometry I2019-09-13T00:15:29Z<p>Arinkin: /* Fall 2019 */</p>
<hr />
<div><br />
=Fall 2019=<br />
<br />
== Homework assignments ==<br />
<br />
* [[Media:math763hw1.pdf|Homework 1]], due Thursday, September 18th.<br />
<br />
== Course description ==<br />
<br />
This is a first course in algebraic geometry. While there are no formal prerequisites beyond a knowledge of the material covered in the first-year algebra and geometry sequence, familiarity with some basic commutative algebra will be helpful. The rough outline of the course is as follows (subject to change):<br />
<br />
* Affine and projective varieties.<br />
* Morphisms and rational maps.<br />
* Local properties: smoothness and dimension. Tangent space.<br />
* Divisors.<br />
* Low-dimensional varieties: curves and surfaces. Blow-ups.<br />
* The Riemann-Roch Theorem.<br />
<br />
Here is a more detailed lecture-by-lecture [[Math 763 -- Algebraic Geometry I -- Detailed list of topics|list of topics]] that I covered in the past, of course, this is all subject to change.<br />
<br />
== Handouts ==<br />
<br />
* [[Media:IV.pdf | Correspondence between sets and ideals]]<br />
* [[Media:Nullstellensatz.pdf|Proof of the Nullstellensatz]]<br />
<br />
== References ==<br />
* Shafarevich, Basic Algebraic Geometry.<br />
* [http://www.jmilne.org/math/CourseNotes/ag.html Algebraic Geometry] (online notes) by Milne.<br />
* Hartshorne, Algebraic Geometry, Chapter I (this is more advanced, so does not quite match the content).<br />
* Here is a [https://mathoverflow.net/questions/2446/best-algebraic-geometry-text-book-other-than-hartshorne discussion] on MathOverflow with more books on algebraic geometry, but most of them are going to be too advanced.<br />
* Here are [[Media:notes.pdf | notes]] from the last time I taught this course. These were taken in class, so<br />
there are probably typos.<br />
<br />
== Information for students ==<br />
<br />
* '''Instructor''': Dima Arinkin<br />
* '''Office Hours''': Tuesday 3-4pm, Wednesday 2-2:45pm, and by appointment in VV 603<br />
* '''Lectures''': TuTh 11am-12:15pm, VV B129<br />
* '''Grade''': There will be weekly [[Math 763 -- Algebraic Geometry I -- Homeworks|homework assignments]], but no exams in this course.</div>Arinkinhttps://www.math.wisc.edu/wiki/index.php?title=Math_763_--_Algebraic_Geometry_I&diff=17848Math 763 -- Algebraic Geometry I2019-09-13T00:15:19Z<p>Arinkin: /* Fall 2019 */</p>
<hr />
<div><br />
=Fall 2019=<br />
<br />
== Homework assignments]]<br />
<br />
* [[Media:math763hw1.pdf|Homework 1]], due Thursday, September 18th.<br />
<br />
== Course description ==<br />
<br />
This is a first course in algebraic geometry. While there are no formal prerequisites beyond a knowledge of the material covered in the first-year algebra and geometry sequence, familiarity with some basic commutative algebra will be helpful. The rough outline of the course is as follows (subject to change):<br />
<br />
* Affine and projective varieties.<br />
* Morphisms and rational maps.<br />
* Local properties: smoothness and dimension. Tangent space.<br />
* Divisors.<br />
* Low-dimensional varieties: curves and surfaces. Blow-ups.<br />
* The Riemann-Roch Theorem.<br />
<br />
Here is a more detailed lecture-by-lecture [[Math 763 -- Algebraic Geometry I -- Detailed list of topics|list of topics]] that I covered in the past, of course, this is all subject to change.<br />
<br />
== Handouts ==<br />
<br />
* [[Media:IV.pdf | Correspondence between sets and ideals]]<br />
* [[Media:Nullstellensatz.pdf|Proof of the Nullstellensatz]]<br />
<br />
== References ==<br />
* Shafarevich, Basic Algebraic Geometry.<br />
* [http://www.jmilne.org/math/CourseNotes/ag.html Algebraic Geometry] (online notes) by Milne.<br />
* Hartshorne, Algebraic Geometry, Chapter I (this is more advanced, so does not quite match the content).<br />
* Here is a [https://mathoverflow.net/questions/2446/best-algebraic-geometry-text-book-other-than-hartshorne discussion] on MathOverflow with more books on algebraic geometry, but most of them are going to be too advanced.<br />
* Here are [[Media:notes.pdf | notes]] from the last time I taught this course. These were taken in class, so<br />
there are probably typos.<br />
<br />
== Information for students ==<br />
<br />
* '''Instructor''': Dima Arinkin<br />
* '''Office Hours''': Tuesday 3-4pm, Wednesday 2-2:45pm, and by appointment in VV 603<br />
* '''Lectures''': TuTh 11am-12:15pm, VV B129<br />
* '''Grade''': There will be weekly [[Math 763 -- Algebraic Geometry I -- Homeworks|homework assignments]], but no exams in this course.</div>Arinkinhttps://www.math.wisc.edu/wiki/index.php?title=Math_763_--_Algebraic_Geometry_I_--_Homeworks&diff=17847Math 763 -- Algebraic Geometry I -- Homeworks2019-09-13T00:14:01Z<p>Arinkin: </p>
<hr />
<div>* [[Media:math763hw1.pdf|Homework 1]], due Thursday, September 18th.<br />
<br />
[[Math 763 -- Algebraic Geometry I|Back to the main Math 763 page]]</div>Arinkinhttps://www.math.wisc.edu/wiki/index.php?title=Math_763_--_Algebraic_Geometry_I_--_Homeworks&diff=17846Math 763 -- Algebraic Geometry I -- Homeworks2019-09-13T00:12:40Z<p>Arinkin: </p>
<hr />
<div>* [[Media:math763hw1.pdf|Homework 1]], due Thursday, September 18th.<br />
<br />
[[Math763 -- Algebraic Geometry I|Back to the main Math 763 page]]</div>Arinkinhttps://www.math.wisc.edu/wiki/index.php?title=File:Math763hw1.pdf&diff=17845File:Math763hw1.pdf2019-09-13T00:11:28Z<p>Arinkin: Arinkin uploaded a new version of File:Math763hw1.pdf</p>
<hr />
<div></div>Arinkinhttps://www.math.wisc.edu/wiki/index.php?title=File:Math763hw1.pdf&diff=17827File:Math763hw1.pdf2019-09-11T23:37:17Z<p>Arinkin: </p>
<hr />
<div></div>Arinkinhttps://www.math.wisc.edu/wiki/index.php?title=Math_763_--_Algebraic_Geometry_I_--_Homeworks&diff=17826Math 763 -- Algebraic Geometry I -- Homeworks2019-09-11T23:37:04Z<p>Arinkin: </p>
<hr />
<div>* [[Media:math763hw1.pdf|Homework 1]], due Thursday, September 18th.</div>Arinkinhttps://www.math.wisc.edu/wiki/index.php?title=File:Notes.pdf&diff=17825File:Notes.pdf2019-09-11T21:33:09Z<p>Arinkin: </p>
<hr />
<div></div>Arinkinhttps://www.math.wisc.edu/wiki/index.php?title=File:Nullstellensatz.pdf&diff=17824File:Nullstellensatz.pdf2019-09-11T21:32:13Z<p>Arinkin: </p>
<hr />
<div></div>Arinkinhttps://www.math.wisc.edu/wiki/index.php?title=Math_763_--_Algebraic_Geometry_I&diff=17823Math 763 -- Algebraic Geometry I2019-09-11T21:31:59Z<p>Arinkin: /* Handouts */</p>
<hr />
<div><br />
=Fall 2019=<br />
<br />
[[Math 763 -- Algebraic Geometry I -- Homeworks|Homework assignments]]<br />
<br />
== Course description ==<br />
<br />
This is a first course in algebraic geometry. While there are no formal prerequisites beyond a knowledge of the material covered in the first-year algebra and geometry sequence, familiarity with some basic commutative algebra will be helpful. The rough outline of the course is as follows (subject to change):<br />
<br />
* Affine and projective varieties.<br />
* Morphisms and rational maps.<br />
* Local properties: smoothness and dimension. Tangent space.<br />
* Divisors.<br />
* Low-dimensional varieties: curves and surfaces. Blow-ups.<br />
* The Riemann-Roch Theorem.<br />
<br />
Here is a more detailed lecture-by-lecture [[Math 763 -- Algebraic Geometry I -- Detailed list of topics|list of topics]] that I covered in the past, of course, this is all subject to change.<br />
<br />
== Handouts ==<br />
<br />
* [[Media:IV.pdf | Correspondence between sets and ideals]]<br />
* [[Media:Nullstellensatz.pdf|Proof of the Nullstellensatz]]<br />
<br />
== References ==<br />
* Shafarevich, Basic Algebraic Geometry.<br />
* [http://www.jmilne.org/math/CourseNotes/ag.html Algebraic Geometry] (online notes) by Milne.<br />
* Hartshorne, Algebraic Geometry, Chapter I (this is more advanced, so does not quite match the content).<br />
* Here is a [https://mathoverflow.net/questions/2446/best-algebraic-geometry-text-book-other-than-hartshorne discussion] on MathOverflow with more books on algebraic geometry, but most of them are going to be too advanced.<br />
* Here are [[Media:notes.pdf | notes]] from the last time I taught this course. These were taken in class, so<br />
there are probably typos.<br />
<br />
== Information for students ==<br />
<br />
* '''Instructor''': Dima Arinkin<br />
* '''Office Hours''': Tuesday 3-4pm, Wednesday 2-2:45pm, and by appointment in VV 603<br />
* '''Lectures''': TuTh 11am-12:15pm, VV B129<br />
* '''Grade''': There will be weekly [[Math 763 -- Algebraic Geometry I -- Homeworks|homework assignments]], but no exams in this course.</div>Arinkinhttps://www.math.wisc.edu/wiki/index.php?title=Math_763_--_Algebraic_Geometry_I&diff=17822Math 763 -- Algebraic Geometry I2019-09-11T21:30:28Z<p>Arinkin: /* Handouts */</p>
<hr />
<div><br />
=Fall 2019=<br />
<br />
[[Math 763 -- Algebraic Geometry I -- Homeworks|Homework assignments]]<br />
<br />
== Course description ==<br />
<br />
This is a first course in algebraic geometry. While there are no formal prerequisites beyond a knowledge of the material covered in the first-year algebra and geometry sequence, familiarity with some basic commutative algebra will be helpful. The rough outline of the course is as follows (subject to change):<br />
<br />
* Affine and projective varieties.<br />
* Morphisms and rational maps.<br />
* Local properties: smoothness and dimension. Tangent space.<br />
* Divisors.<br />
* Low-dimensional varieties: curves and surfaces. Blow-ups.<br />
* The Riemann-Roch Theorem.<br />
<br />
Here is a more detailed lecture-by-lecture [[Math 763 -- Algebraic Geometry I -- Detailed list of topics|list of topics]] that I covered in the past, of course, this is all subject to change.<br />
<br />
== Handouts ==<br />
<br />
* [[File:IV.pdf | Correspondence between sets and ideals]]<br />
* [[File:Nullstellensatz.pdf|Proof of the Nullstellensatz]]<br />
<br />
== References ==<br />
* Shafarevich, Basic Algebraic Geometry.<br />
* [http://www.jmilne.org/math/CourseNotes/ag.html Algebraic Geometry] (online notes) by Milne.<br />
* Hartshorne, Algebraic Geometry, Chapter I (this is more advanced, so does not quite match the content).<br />
* Here is a [https://mathoverflow.net/questions/2446/best-algebraic-geometry-text-book-other-than-hartshorne discussion] on MathOverflow with more books on algebraic geometry, but most of them are going to be too advanced.<br />
* Here are [[Media:notes.pdf | notes]] from the last time I taught this course. These were taken in class, so<br />
there are probably typos.<br />
<br />
== Information for students ==<br />
<br />
* '''Instructor''': Dima Arinkin<br />
* '''Office Hours''': Tuesday 3-4pm, Wednesday 2-2:45pm, and by appointment in VV 603<br />
* '''Lectures''': TuTh 11am-12:15pm, VV B129<br />
* '''Grade''': There will be weekly [[Math 763 -- Algebraic Geometry I -- Homeworks|homework assignments]], but no exams in this course.</div>Arinkinhttps://www.math.wisc.edu/wiki/index.php?title=File:IV.pdf&diff=17821File:IV.pdf2019-09-11T21:29:46Z<p>Arinkin: </p>
<hr />
<div></div>Arinkinhttps://www.math.wisc.edu/wiki/index.php?title=Math_763_--_Algebraic_Geometry_I&diff=17806Math 763 -- Algebraic Geometry I2019-09-10T14:35:44Z<p>Arinkin: /* References */</p>
<hr />
<div><br />
=Fall 2019=<br />
<br />
[[Math 763 -- Algebraic Geometry I -- Homeworks|Homework assignments]]<br />
<br />
== Course description ==<br />
<br />
This is a first course in algebraic geometry. While there are no formal prerequisites beyond a knowledge of the material covered in the first-year algebra and geometry sequence, familiarity with some basic commutative algebra will be helpful. The rough outline of the course is as follows (subject to change):<br />
<br />
* Affine and projective varieties.<br />
* Morphisms and rational maps.<br />
* Local properties: smoothness and dimension. Tangent space.<br />
* Divisors.<br />
* Low-dimensional varieties: curves and surfaces. Blow-ups.<br />
* The Riemann-Roch Theorem.<br />
<br />
Here is a more detailed lecture-by-lecture [[Math 763 -- Algebraic Geometry I -- Detailed list of topics|list of topics]] that I covered in the past, of course, this is all subject to change.<br />
<br />
== Handouts ==<br />
<br />
* [[File:IV.pdf|Correspondence between sets and ideals]]<br />
* [[File:Nullstellensatz.pdf|Proof of the Nullstellensatz]]<br />
<br />
== References ==<br />
* Shafarevich, Basic Algebraic Geometry.<br />
* [http://www.jmilne.org/math/CourseNotes/ag.html Algebraic Geometry] (online notes) by Milne.<br />
* Hartshorne, Algebraic Geometry, Chapter I (this is more advanced, so does not quite match the content).<br />
* Here is a [https://mathoverflow.net/questions/2446/best-algebraic-geometry-text-book-other-than-hartshorne discussion] on MathOverflow with more books on algebraic geometry, but most of them are going to be too advanced.<br />
* Here are [[Media:notes.pdf | notes]] from the last time I taught this course. These were taken in class, so<br />
there are probably typos.<br />
<br />
== Information for students ==<br />
<br />
* '''Instructor''': Dima Arinkin<br />
* '''Office Hours''': Tuesday 3-4pm, Wednesday 2-2:45pm, and by appointment in VV 603<br />
* '''Lectures''': TuTh 11am-12:15pm, VV B129<br />
* '''Grade''': There will be weekly [[Math 763 -- Algebraic Geometry I -- Homeworks|homework assignments]], but no exams in this course.</div>Arinkinhttps://www.math.wisc.edu/wiki/index.php?title=Math_763_--_Algebraic_Geometry_I&diff=17805Math 763 -- Algebraic Geometry I2019-09-10T14:31:59Z<p>Arinkin: /* Handouts */</p>
<hr />
<div><br />
=Fall 2019=<br />
<br />
[[Math 763 -- Algebraic Geometry I -- Homeworks|Homework assignments]]<br />
<br />
== Course description ==<br />
<br />
This is a first course in algebraic geometry. While there are no formal prerequisites beyond a knowledge of the material covered in the first-year algebra and geometry sequence, familiarity with some basic commutative algebra will be helpful. The rough outline of the course is as follows (subject to change):<br />
<br />
* Affine and projective varieties.<br />
* Morphisms and rational maps.<br />
* Local properties: smoothness and dimension. Tangent space.<br />
* Divisors.<br />
* Low-dimensional varieties: curves and surfaces. Blow-ups.<br />
* The Riemann-Roch Theorem.<br />
<br />
Here is a more detailed lecture-by-lecture [[Math 763 -- Algebraic Geometry I -- Detailed list of topics|list of topics]] that I covered in the past, of course, this is all subject to change.<br />
<br />
== Handouts ==<br />
<br />
* [[File:IV.pdf|Correspondence between sets and ideals]]<br />
* [[File:Nullstellensatz.pdf|Proof of the Nullstellensatz]]<br />
<br />
== References ==<br />
* Shafarevich, Basic Algebraic Geometry.<br />
* [http://www.jmilne.org/math/CourseNotes/ag.html Algebraic Geometry] (online notes) by Milne.<br />
* Hartshorne, Algebraic Geometry, Chapter I (this is more advanced, so does not quite match the content).<br />
* Here is a [https://mathoverflow.net/questions/2446/best-algebraic-geometry-text-book-other-than-hartshorne discussion] on MathOverflow with more books on algebraic geometry, but most of them are going to be too advanced.<br />
* Here are [[Media:notes.pdf|notes]] from the last time I taught this course. These were taken in class, so<br />
there are probably typos.<br />
<br />
== Information for students ==<br />
<br />
* '''Instructor''': Dima Arinkin<br />
* '''Office Hours''': Tuesday 3-4pm, Wednesday 2-2:45pm, and by appointment in VV 603<br />
* '''Lectures''': TuTh 11am-12:15pm, VV B129<br />
* '''Grade''': There will be weekly [[Math 763 -- Algebraic Geometry I -- Homeworks|homework assignments]], but no exams in this course.</div>Arinkinhttps://www.math.wisc.edu/wiki/index.php?title=Math_763_--_Algebraic_Geometry_I&diff=17804Math 763 -- Algebraic Geometry I2019-09-10T14:30:39Z<p>Arinkin: </p>
<hr />
<div><br />
=Fall 2019=<br />
<br />
[[Math 763 -- Algebraic Geometry I -- Homeworks|Homework assignments]]<br />
<br />
== Course description ==<br />
<br />
This is a first course in algebraic geometry. While there are no formal prerequisites beyond a knowledge of the material covered in the first-year algebra and geometry sequence, familiarity with some basic commutative algebra will be helpful. The rough outline of the course is as follows (subject to change):<br />
<br />
* Affine and projective varieties.<br />
* Morphisms and rational maps.<br />
* Local properties: smoothness and dimension. Tangent space.<br />
* Divisors.<br />
* Low-dimensional varieties: curves and surfaces. Blow-ups.<br />
* The Riemann-Roch Theorem.<br />
<br />
Here is a more detailed lecture-by-lecture [[Math 763 -- Algebraic Geometry I -- Detailed list of topics|list of topics]] that I covered in the past, of course, this is all subject to change.<br />
<br />
== Handouts ==<br />
<br />
* [[Media:IV.pdf|Correspondence between sets and ideals]]<br />
* [[Media:Nullstellensatz.pdf|Proof of the Nullstellensatz]]<br />
<br />
== References ==<br />
* Shafarevich, Basic Algebraic Geometry.<br />
* [http://www.jmilne.org/math/CourseNotes/ag.html Algebraic Geometry] (online notes) by Milne.<br />
* Hartshorne, Algebraic Geometry, Chapter I (this is more advanced, so does not quite match the content).<br />
* Here is a [https://mathoverflow.net/questions/2446/best-algebraic-geometry-text-book-other-than-hartshorne discussion] on MathOverflow with more books on algebraic geometry, but most of them are going to be too advanced.<br />
* Here are [[Media:notes.pdf|notes]] from the last time I taught this course. These were taken in class, so<br />
there are probably typos.<br />
<br />
== Information for students ==<br />
<br />
* '''Instructor''': Dima Arinkin<br />
* '''Office Hours''': Tuesday 3-4pm, Wednesday 2-2:45pm, and by appointment in VV 603<br />
* '''Lectures''': TuTh 11am-12:15pm, VV B129<br />
* '''Grade''': There will be weekly [[Math 763 -- Algebraic Geometry I -- Homeworks|homework assignments]], but no exams in this course.</div>Arinkinhttps://www.math.wisc.edu/wiki/index.php?title=Math_763_--_Algebraic_Geometry_I_--_Detailed_list_of_topics&diff=17749Math 763 -- Algebraic Geometry I -- Detailed list of topics2019-09-05T15:28:07Z<p>Arinkin: Created page with "Here is a detailed list of topics that I have covered in the past, based on 29 75-minute-classes. (To tell the truth, it seems very optimistic now... but who knows?) # What i..."</p>
<hr />
<div>Here is a detailed list of topics that I have covered in the past, based on 29 75-minute-classes. (To tell the truth, it seems very optimistic now... but who knows?)<br />
<br />
# What is AG? Algebraic sets vs ideals. Statement of the Nullstellensatz.<br />
# Proof of the Nullstellensatz. Zariski topology on $k^n$.<br />
# Regular functions and regular maps. Coordinate rings.<br />
# Zariski topology on algebraic varieties. Noetherian topological spaces. Principal open sets.<br />
# Locally defined regular functions. Regularity of a function is local.<br />
# Subvarieties of ${\mathbb A}^n$. <br />
# Abstract algebraic varieties. Separated varieties.<br />
# Subvarieties and products of varieties.<br />
# Rational functions and rational maps.<br />
# Dimension.<br />
# Dimension of hypersurface.<br />
# Complete intersections. Dimensions of fibers. ${\mathbb P}^n$.<br />
# Projective varieties. Projective Nullstellensatz.<br />
# Projective varieties are complete. Segre embedding.<br />
# Grassmannians. Incidence variety.<br />
# Dimension of fibers of projective maps.<br />
# Chevalley's Theorem. Tangent space.<br />
# Differential of a map. Smoothness. Local parameters.<br />
# Taylor decomposition at a smooth point. Completed local ring.<br />
# Regular local ring is a UFD.<br />
# Smooth subvariety is lci. Birational vs biregular classification.<br />
# Blow-ups.<br />
# Resolution of singularities. Castelnuovo's criterion. Minimal surfaces.<br />
# Divisors on smooth varieties. Weil divisors vs Cartier divisors.<br />
# Pricipal divisors and the Picard group.<br />
# Divisors on an affine variety as (fractional) ideals. Divisor classes as invertible modules.<br />
# Algebraic vector bundles and line bundles.<br />
# Linear systems and sections of line bundles. <br />
# The Riemann-Roch Theorem.</div>Arinkinhttps://www.math.wisc.edu/wiki/index.php?title=Math_763_--_Algebraic_Geometry_I_--_Homeworks&diff=17748Math 763 -- Algebraic Geometry I -- Homeworks2019-09-05T15:22:51Z<p>Arinkin: Created page with "None so far!"</p>
<hr />
<div>None so far!</div>Arinkinhttps://www.math.wisc.edu/wiki/index.php?title=Math_763_--_Algebraic_Geometry_I&diff=17747Math 763 -- Algebraic Geometry I2019-09-05T15:22:42Z<p>Arinkin: Created page with " =Fall 2019= Homework assignments == Course description == This is a first course in algebraic geometry. While there are n..."</p>
<hr />
<div><br />
=Fall 2019=<br />
<br />
[[Math 763 -- Algebraic Geometry I -- Homeworks|Homework assignments]]<br />
<br />
== Course description ==<br />
<br />
This is a first course in algebraic geometry. While there are no formal prerequisites beyond a knowledge of the material covered in the first-year algebra and geometry sequence, familiarity with some basic commutative algebra will be helpful. The rough outline of the course is as follows (subject to change):<br />
<br />
* Affine and projective varieties.<br />
* Morphisms and rational maps.<br />
* Local properties: smoothness and dimension. Tangent space.<br />
* Divisors.<br />
* Low-dimensional varieties: curves and surfaces. Blow-ups.<br />
* The Riemann-Roch Theorem.<br />
<br />
Here is a more detailed lecture-by-lecture [[Math 763 -- Algebraic Geometry I -- Detailed list of topics|list of topics]] that I covered in the past, of course, this is all subject to change.<br />
<br />
<br />
== References ==<br />
* Shafarevich, Basic Algebraic Geometry.<br />
* [http://www.jmilne.org/math/CourseNotes/ag.html Algebraic Geometry] (online notes) by Milne.<br />
* Hartshorne, Algebraic Geometry, Chapter I (this is more advanced, so does not quite match the content).<br />
* Here is a [https://mathoverflow.net/questions/2446/best-algebraic-geometry-text-book-other-than-hartshorne discussion] on MathOverflow with more books on algebraic geometry, but most of them are going to be too advanced.<br />
<br />
== Information for students ==<br />
<br />
* '''Instructor''': Dima Arinkin<br />
* '''Office Hours''': Tuesday 3-4pm, Wednesday 2-2:45pm, and by appointment in VV 603<br />
* '''Lectures''': TuTh 11am-12:15pm, VV B129<br />
* '''Grade''': There will be weekly [[Math 763 -- Algebraic Geometry I -- Homeworks|homework assignments]], but no exams in this course.</div>Arinkinhttps://www.math.wisc.edu/wiki/index.php?title=Algebra_and_Algebraic_Geometry_Seminar_Fall_2019&diff=17703Algebra and Algebraic Geometry Seminar Fall 20192019-08-29T21:25:19Z<p>Arinkin: </p>
<hr />
<div>The seminar meets on Fridays at 2:25 pm in room B235 Van Vleck.<br />
<br />
Here is the schedule for [[Algebra and Algebraic Geometry Seminar Spring 2019 | the previous semester]], for [[Algebra and Algebraic Geometry Seminar Spring 2020 | the next semester]], and for [[Algebra and Algebraic Geometry Seminar | this semester]].<br />
<br />
==Algebra and Algebraic Geometry Mailing List==<br />
*Please join the [https://admin.lists.wisc.edu/index.php?p=11&l=ags AGS Mailing List] to hear about upcoming seminars, lunches, and other algebraic geometry events in the department (it is possible you must be on a math department computer to use this link).<br />
<br />
<br />
== Fall 2019 Schedule ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s) <br />
|-<br />
|September 6<br />
|Yuki Matsubara<br />
|[[#Yuki Matsubara|On the cohomology of the moduli space of parabolic connections]]<br />
|Dima<br />
|-<br />
|September 13<br />
|<br />
|<br />
| Reserved (Juliette)<br />
|-<br />
|September 20<br />
|<br />
|<br />
|<br />
|-<br />
|September 27<br />
|<br />
|<br />
|<br />
|-<br />
|October 4<br />
|<br />
|<br />
|<br />
|-<br />
|October 11<br />
|<br />
|<br />
|<br />
|-<br />
|October 18<br />
|Kevin Tucker (UIC)<br />
|<br />
|<br />
|-<br />
|October 25<br />
|<br />
|<br />
|<br />
|-<br />
|November 1<br />
|<br />
|<br />
|<br />
|-<br />
|November 8<br />
|Patricia Klein<br />
|<br />
|<br />
|-<br />
|November 15<br />
|<br />
|<br />
|<br />
|-<br />
|November 22<br />
|<br />
|<br />
|<br />
|-<br />
|November 29<br />
|<br />
| Thanksgiving Break<br />
|<br />
|-<br />
|December 6<br />
|<br />
|<br />
| Reserved (Matroids Day)<br />
|-<br />
|December 13<br />
|<br />
|<br />
|<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===Yuki Matsubara===<br />
'''On the cohomology of the moduli space of parabolic connections'''<br />
<br />
We consider the moduli space of logarithmic connections of rank 2<br />
on the projective line minus 5 points with fixed spectral data.<br />
We compute the cohomology of such moduli space, <br />
and this computation will be used to extend the results of <br />
Geometric Langlands correspondence due to D. Arinkin <br />
to the case where the this type of connections have five simple poles on ${\mathbb P}^1$.<br />
<br />
In this talk, I will review the Geometric Langlands Correspondence <br />
in the tamely ramified cases, and after that, <br />
I will explain how the cohomology of above moduli space will be used.</div>Arinkinhttps://www.math.wisc.edu/wiki/index.php?title=Algebra_and_Algebraic_Geometry_Seminar_Fall_2019&diff=17702Algebra and Algebraic Geometry Seminar Fall 20192019-08-29T21:23:32Z<p>Arinkin: </p>
<hr />
<div>The seminar meets on Fridays at 2:25 pm in room B235 Van Vleck.<br />
<br />
Here is the schedule for [[Algebra and Algebraic Geometry Seminar Spring 2019 | the previous semester]], for [[Algebra and Algebraic Geometry Seminar Spring 2020 | the next semester]], and for [[Algebra and Algebraic Geometry Seminar | this semester]].<br />
<br />
==Algebra and Algebraic Geometry Mailing List==<br />
*Please join the [https://admin.lists.wisc.edu/index.php?p=11&l=ags AGS Mailing List] to hear about upcoming seminars, lunches, and other algebraic geometry events in the department (it is possible you must be on a math department computer to use this link).<br />
<br />
<br />
== Fall 2019 Schedule ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s) <br />
|-<br />
|September 6<br />
|Yuki Matsubara<br />
|On the cohomology of the moduli space of parabolic connections<br />
|Dima<br />
|-<br />
|September 13<br />
|<br />
|<br />
| Reserved (Juliette)<br />
|-<br />
|September 20<br />
|<br />
|<br />
|<br />
|-<br />
|September 27<br />
|<br />
|<br />
|<br />
|-<br />
|October 4<br />
|<br />
|<br />
|<br />
|-<br />
|October 11<br />
|<br />
|<br />
|<br />
|-<br />
|October 18<br />
|Kevin Tucker (UIC)<br />
|<br />
|<br />
|-<br />
|October 25<br />
|<br />
|<br />
|<br />
|-<br />
|November 1<br />
|<br />
|<br />
|<br />
|-<br />
|November 8<br />
|Patricia Klein<br />
|<br />
|<br />
|-<br />
|November 15<br />
|<br />
|<br />
|<br />
|-<br />
|November 22<br />
|<br />
|<br />
|<br />
|-<br />
|November 29<br />
|<br />
| Thanksgiving Break<br />
|<br />
|-<br />
|December 6<br />
|<br />
|<br />
| Reserved (Matroids Day)<br />
|-<br />
|December 13<br />
|<br />
|<br />
|<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===Yuki Matsubara===<br />
'''On the cohomology of the moduli space of parabolic connections'''<br />
<br />
Abstract:<br />
We consider the moduli space of logarithmic connections of rank 2<br />
on the projective line minus 5 points with fixed spectral data.<br />
We compute the cohomology of such moduli space, <br />
and this computation will be used to extend the results of <br />
Geometric Langlands correspondence due to D. Arinkin <br />
to the case where the this type of connections have five simple poles on ${\mathbb P}^1$.<br />
<br />
In this talk, I will review the Geometric Langlands Correspondence <br />
in the tamely ramified cases, and after that, <br />
I will explain how the cohomology of above moduli space will be used.</div>Arinkinhttps://www.math.wisc.edu/wiki/index.php?title=Algebra_and_Algebraic_Geometry_Seminar_Fall_2019&diff=17701Algebra and Algebraic Geometry Seminar Fall 20192019-08-29T21:19:26Z<p>Arinkin: /* Fall 2019 Schedule */</p>
<hr />
<div>The seminar meets on Fridays at 2:25 pm in room TBA.<br />
<br />
Here is the schedule for [[Algebra and Algebraic Geometry Seminar Spring 2019 | the previous semester]], for [[Algebra and Algebraic Geometry Seminar Spring 2020 | the next semester]], and for [[Algebra and Algebraic Geometry Seminar | this semester]].<br />
<br />
==Algebra and Algebraic Geometry Mailing List==<br />
*Please join the [https://admin.lists.wisc.edu/index.php?p=11&l=ags AGS Mailing List] to hear about upcoming seminars, lunches, and other algebraic geometry events in the department (it is possible you must be on a math department computer to use this link).<br />
<br />
<br />
== Fall 2019 Schedule ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s) <br />
|-<br />
|September 6<br />
|Yuki Matsubara<br />
|On the cohomology of the moduli space of parabolic connections<br />
|Dima<br />
|-<br />
|September 13<br />
|<br />
|<br />
| Reserved (Juliette)<br />
|-<br />
|September 20<br />
|<br />
|<br />
|<br />
|-<br />
|September 27<br />
|<br />
|<br />
|<br />
|-<br />
|October 4<br />
|<br />
|<br />
|<br />
|-<br />
|October 11<br />
|<br />
|<br />
|<br />
|-<br />
|October 18<br />
|Kevin Tucker (UIC)<br />
|<br />
|<br />
|-<br />
|October 25<br />
|<br />
|<br />
|<br />
|-<br />
|November 1<br />
|<br />
|<br />
|<br />
|-<br />
|November 8<br />
|Patricia Klein<br />
|<br />
|<br />
|-<br />
|November 15<br />
|<br />
|<br />
|<br />
|-<br />
|November 22<br />
|<br />
|<br />
|<br />
|-<br />
|November 29<br />
|<br />
| Thanksgiving Break<br />
|<br />
|-<br />
|December 6<br />
|<br />
|<br />
| Reserved (Matroids Day)<br />
|-<br />
|December 13<br />
|<br />
|<br />
|<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===Speaker===<br />
'''Title: '''<br />
Abstract:</div>Arinkinhttps://www.math.wisc.edu/wiki/index.php?title=Algebra_and_Algebraic_Geometry_Seminar&diff=17695Algebra and Algebraic Geometry Seminar2019-08-29T17:40:33Z<p>Arinkin: Redirected page to Algebra and Algebraic Geometry Seminar Fall 2019</p>
<hr />
<div>#REDIRECT [[Algebra and Algebraic Geometry Seminar Fall 2019]]</div>Arinkinhttps://www.math.wisc.edu/wiki/index.php?title=Algebra_and_Algebraic_Geometry_Seminar_Fall_2019&diff=17664Algebra and Algebraic Geometry Seminar Fall 20192019-08-21T19:09:44Z<p>Arinkin: /* Fall 2019 Schedule */</p>
<hr />
<div>The seminar meets on Fridays at 2:25 pm in room TBA.<br />
<br />
Here is the schedule for [[Algebra and Algebraic Geometry Seminar Spring 2019 | the previous semester]], for [[Algebra and Algebraic Geometry Seminar Spring 2020 | the next semester]], and for [[Algebra and Algebraic Geometry Seminar | this semester]].<br />
<br />
==Algebra and Algebraic Geometry Mailing List==<br />
*Please join the [https://admin.lists.wisc.edu/index.php?p=11&l=ags AGS Mailing List] to hear about upcoming seminars, lunches, and other algebraic geometry events in the department (it is possible you must be on a math department computer to use this link).<br />
<br />
<br />
== Fall 2019 Schedule ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s) <br />
|-<br />
|September 6<br />
|<br />
|<br />
| Reserved (Dima)<br />
|-<br />
|September 13<br />
|<br />
|<br />
| Reserved (Juliette)<br />
|-<br />
|September 20<br />
|<br />
|<br />
|<br />
|-<br />
|September 27<br />
|<br />
|<br />
|<br />
|-<br />
|October 4<br />
|<br />
|<br />
|<br />
|-<br />
|October 11<br />
|<br />
|<br />
|<br />
|-<br />
|October 18<br />
|Kevin Tucker (UIC)<br />
|<br />
|<br />
|-<br />
|October 25<br />
|<br />
|<br />
|<br />
|-<br />
|November 1<br />
|<br />
|<br />
|<br />
|-<br />
|November 8<br />
|Patricia Klein<br />
|<br />
|<br />
|-<br />
|November 15<br />
|<br />
|<br />
|<br />
|-<br />
|November 22<br />
|<br />
|<br />
|<br />
|-<br />
|November 29<br />
|<br />
| Thanksgiving Break<br />
|<br />
|-<br />
|December 6<br />
|<br />
|<br />
| Reserved (Matroids Day)<br />
|-<br />
|December 13<br />
|<br />
|<br />
|<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===Speaker===<br />
'''Title: '''<br />
Abstract:</div>Arinkinhttps://www.math.wisc.edu/wiki/index.php?title=File:Aug_2018_Algebra_Quals_solution.pdf&diff=15778File:Aug 2018 Algebra Quals solution.pdf2018-08-27T19:27:40Z<p>Arinkin: </p>
<hr />
<div></div>Arinkinhttps://www.math.wisc.edu/wiki/index.php?title=File:Aug_2018_Algebra_Quals.pdf&diff=15777File:Aug 2018 Algebra Quals.pdf2018-08-27T19:27:23Z<p>Arinkin: </p>
<hr />
<div></div>Arinkinhttps://www.math.wisc.edu/wiki/index.php?title=Algebra_Qualifying_Exam&diff=15776Algebra Qualifying Exam2018-08-27T19:26:57Z<p>Arinkin: /* Past Qualifying Exams */</p>
<hr />
<div>Here is some assorted material related to the Algebra Qualifying Exam. This page has been created by graduate students, so, as always, you should consult the [http://www.math.wisc.edu/graduate/ official graduate program page] for official information.<br />
<br />
= Past Qualifying Exams =<br />
<br />
* [[Media:Aug 2018 Algebra Quals.pdf | Summer 2018]] ([[Media:Aug 2018 Algebra Quals solution.pdf | Solutions]])<br />
* [[Media:Jan 2018 Algebra Quals.pdf | Winter 2018]] ([[Media:Jan 2018 Algebra Quals solution.pdf | Solutions]])<br />
* [[Media:Aug 2017 Algebra Quals.pdf | Summer 2017]] ([[Media:Aug 2017 Algebra Quals solution.pdf | Solutions]])<br />
* [[Media:Jan 2017 Algebra Quals.pdf | Winter 2017]] ([[Media:Jan 2017 Algebra Quals solution.pdf | Solutions]])<br />
* [[Media:Aug 2016 Algebra Quals.pdf | Summer 2016]]<br />
* [[Media:Jan 2016 Algebra Quals.pdf | Winter 2016]]<br />
* [[Media:Aug 2015 Algebra Quals.pdf | Summer 2015]]<br />
* [[Media:Jan 2015 Algebra Quals.pdf | Winter 2015]]<br />
* [[Media:Aug 2014 Algebra Quals.pdf | Summer 2014]]<br />
* [[Media:Jan 2014 Algebra Quals.pdf | Winter 2014]]<br />
* Pre-2014 exams are available [http://www.math.wisc.edu/~passman/algquals.html here], there is also a file with 1991-2013 quals on Atrium.<br />
<br />
= Guillermo Mantilla's SEP Notes =<br />
In the summers of 2008, 2009, 2010 Guillermo Mantilla ran a well-regarded summer enchancement program in algebra preparing for the qualifying examination. Guillermo wrote up a set of notes covering the material that appears on the qualifying exam. Links appear in the order presented in class, not the order of the respective problems on the exam.<br />
<br />
Note: the links below are broken. The files themselves are available on Atrium, there are also 2016 SEP [https://www.math.wisc.edu/~eramos/teaching/SEP.html notes by Eric Ramos]. <br />
<br />
<br />
* Linear Algebra<br />
** [http://www.math.wisc.edu/~dynerman/content/mantilla/linear/Linear.pdf Linear Algebra I]<br />
** [http://www.math.wisc.edu/~dynerman/content/mantilla/linear/inner.pdf Linear Algebra II (inner products)]<br />
** [http://www.math.wisc.edu/~dynerman/content/mantilla/linear/Jform.pdf Linear Algebra III (Jordan Form)]<br />
<br />
* Group Theory<br />
** [http://www.math.wisc.edu/~dynerman/content/mantilla/group/BasicGroups.pdf Group Theory I]<br />
** [http://www.math.wisc.edu/~dynerman/content/mantilla/group/MoreGroups.pdf Group Theory II (group actions)]<br />
** [http://www.math.wisc.edu/~dynerman/content/mantilla/group/SolNil.pdf Solvable & Nilpotent Groups]<br />
** [http://www.math.wisc.edu/~dynerman/content/mantilla/group/ThmsGroups.pdf Theorems for non-simplicity]<br />
*** [http://www.math.wisc.edu/~dynerman/content/mantilla/group/less1000.pdf Non-simplicity proofs for groups of order < 1000]<br />
<br />
* Field Theory<br />
** [http://www.math.wisc.edu/~dynerman/content/mantilla/galois/BasicFields.pdf Field Theory I]<br />
** [http://www.math.wisc.edu/~dynerman/content/mantilla/galois/Fields2.pdf Field Theory II]<br />
<br />
* Ring Theory<br />
** [http://www.math.wisc.edu/~dynerman/content/mantilla/ring/Modules.pdf Modules]<br />
** [http://www.math.wisc.edu/~dynerman/content/mantilla/commute/CommutativeAlg.pdf Commutative Rings]</div>Arinkinhttps://www.math.wisc.edu/wiki/index.php?title=File:Jan_2018_Algebra_Quals_solution.pdf&diff=15622File:Jan 2018 Algebra Quals solution.pdf2018-07-18T10:32:01Z<p>Arinkin: </p>
<hr />
<div></div>Arinkinhttps://www.math.wisc.edu/wiki/index.php?title=File:Jan_2018_Algebra_Quals.pdf&diff=15621File:Jan 2018 Algebra Quals.pdf2018-07-18T10:31:35Z<p>Arinkin: </p>
<hr />
<div></div>Arinkinhttps://www.math.wisc.edu/wiki/index.php?title=Algebra_Qualifying_Exam&diff=15620Algebra Qualifying Exam2018-07-18T10:30:52Z<p>Arinkin: /* Past Qualifying Exams */</p>
<hr />
<div>Here is some assorted material related to the Algebra Qualifying Exam. This page has been created by graduate students, so, as always, you should consult the [http://www.math.wisc.edu/graduate/ official graduate program page] for official information.<br />
<br />
= Past Qualifying Exams =<br />
<br />
* [[Media:Jan 2018 Algebra Quals.pdf | Winter 2018]] ([[Media:Jan 2018 Algebra Quals solution.pdf | Solutions]])<br />
* [[Media:Aug 2017 Algebra Quals.pdf | Summer 2017]] ([[Media:Aug 2017 Algebra Quals solution.pdf | Solutions]])<br />
* [[Media:Jan 2017 Algebra Quals.pdf | Winter 2017]] ([[Media:Jan 2017 Algebra Quals solution.pdf | Solutions]])<br />
* [[Media:Aug 2016 Algebra Quals.pdf | Summer 2016]]<br />
* [[Media:Jan 2016 Algebra Quals.pdf | Winter 2016]]<br />
* [[Media:Aug 2015 Algebra Quals.pdf | Summer 2015]]<br />
* [[Media:Jan 2015 Algebra Quals.pdf | Winter 2015]]<br />
* [[Media:Aug 2014 Algebra Quals.pdf | Summer 2014]]<br />
* [[Media:Jan 2014 Algebra Quals.pdf | Winter 2014]]<br />
* Pre-2014 exams are available [http://www.math.wisc.edu/~passman/algquals.html here], there is also a file with 1991-2013 quals on Atrium.<br />
<br />
= Guillermo Mantilla's SEP Notes =<br />
In the summers of 2008, 2009, 2010 Guillermo Mantilla ran a well-regarded summer enchancement program in algebra preparing for the qualifying examination. Guillermo wrote up a set of notes covering the material that appears on the qualifying exam. Links appear in the order presented in class, not the order of the respective problems on the exam.<br />
<br />
Note: the links below are broken. The files themselves are available on Atrium, there are also 2016 SEP [https://www.math.wisc.edu/~eramos/teaching/SEP.html notes by Eric Ramos]. <br />
<br />
<br />
* Linear Algebra<br />
** [http://www.math.wisc.edu/~dynerman/content/mantilla/linear/Linear.pdf Linear Algebra I]<br />
** [http://www.math.wisc.edu/~dynerman/content/mantilla/linear/inner.pdf Linear Algebra II (inner products)]<br />
** [http://www.math.wisc.edu/~dynerman/content/mantilla/linear/Jform.pdf Linear Algebra III (Jordan Form)]<br />
<br />
* Group Theory<br />
** [http://www.math.wisc.edu/~dynerman/content/mantilla/group/BasicGroups.pdf Group Theory I]<br />
** [http://www.math.wisc.edu/~dynerman/content/mantilla/group/MoreGroups.pdf Group Theory II (group actions)]<br />
** [http://www.math.wisc.edu/~dynerman/content/mantilla/group/SolNil.pdf Solvable & Nilpotent Groups]<br />
** [http://www.math.wisc.edu/~dynerman/content/mantilla/group/ThmsGroups.pdf Theorems for non-simplicity]<br />
*** [http://www.math.wisc.edu/~dynerman/content/mantilla/group/less1000.pdf Non-simplicity proofs for groups of order < 1000]<br />
<br />
* Field Theory<br />
** [http://www.math.wisc.edu/~dynerman/content/mantilla/galois/BasicFields.pdf Field Theory I]<br />
** [http://www.math.wisc.edu/~dynerman/content/mantilla/galois/Fields2.pdf Field Theory II]<br />
<br />
* Ring Theory<br />
** [http://www.math.wisc.edu/~dynerman/content/mantilla/ring/Modules.pdf Modules]<br />
** [http://www.math.wisc.edu/~dynerman/content/mantilla/commute/CommutativeAlg.pdf Commutative Rings]</div>Arinkinhttps://www.math.wisc.edu/wiki/index.php?title=File:UWUMC2018.pdf&diff=15504File:UWUMC2018.pdf2018-05-04T18:23:05Z<p>Arinkin: </p>
<hr />
<div></div>Arinkinhttps://www.math.wisc.edu/wiki/index.php?title=File:UWUMC2015.pdf&diff=15502File:UWUMC2015.pdf2018-05-04T18:22:32Z<p>Arinkin: Arinkin moved page File:UWUMC15.pdf to File:UWUMC2015.pdf</p>
<hr />
<div></div>Arinkinhttps://www.math.wisc.edu/wiki/index.php?title=File:UWUMC15.pdf&diff=15503File:UWUMC15.pdf2018-05-04T18:22:32Z<p>Arinkin: Arinkin moved page File:UWUMC15.pdf to File:UWUMC2015.pdf</p>
<hr />
<div>#REDIRECT [[File:UWUMC2015.pdf]]</div>Arinkinhttps://www.math.wisc.edu/wiki/index.php?title=Putnam_Club&diff=15501Putnam Club2018-05-04T16:56:28Z<p>Arinkin: /* Fall 2015 */</p>
<hr />
<div><br />
''Organizers: Dima Arinkin, Gheorghe Craciun, Mihaela Ifrim''<br />
<br />
The Putnam Exam, offered by the Mathematical Association of America, is the premier American math competition for undergraduate students. It is given each year on the first Saturday in December. The exam consists of 12 problems, 6 in the 3 hour morning session and 6 in the 3 hour afternoon session. Each problem is worth 10 points, so the maximum score is 120. National winners usually get around 100 points. The median score is generally around 0-2 points. This is a difficult exam with many interesting and fun problems.<br />
<br />
[http://kskedlaya.org/putnam-archive/ Old exams and more information on the Putnam competition.]<br />
<br />
The UW is also participating in the Virginia Tech Regional Mathematics Contest. This is an individual competition with seven problems in 2.5 hours. Many schools use it as a kind of rehearsal for the Putnam. You can find more information [http://www.math.vt.edu/people/plinnell/Vtregional/ over here.]<br />
<br />
We hold our own UW Madison [[Undergraduate Math Competition]] in the spring; this year, it is on '''April 24th, 2018'''.<br />
<br />
==Spring 2017==<br />
<br />
The Putnam Club does not meet in the spring, but we had the fourth annual UW [[Undergraduate Math Competition]] on '''April 24th''', 2018, 5:30-8pm in VV B239.<br />
<br />
==Fall 2017==<br />
<br />
The Putnam Club will help you prepare for the exam by practicing on problems from previous years and other olympiad-style problems. The meeting time is 5pm on Wednesdays in VV B139.<br />
<br />
* September 20: [[Media:Putnam092017.pdf | Introductory meeting]] by D.Arinkin<br />
* September 27: [[Media:Putnam092717.pdf | Equations with functions as unknowns]] by M.Ifrim (by request: here is [[Media:Putnam092717sol6.pdf | a solution to problem 6]]; problem 7 is problem B5 of 2016 Putnam exam; you can see the solution [http://kskedlaya.org/putnam-archive/2016s.pdf here]).<br />
* October 4: [[Media:Putnam100417.pdf | Inequalities ]] by G.Craciun.<br />
* October 11: [[Media:Putnam101117.pdf | Polynomials ]] by D.Arinkin.<br />
* October 18: [[Media:Putnam1(2)..pdf | Equations ]] by M. Ifrim<br />
* October 21: Virginia Tech Math Contest: 9-11:30am in VV B203.<br />
* October 25: Review of this year's [[Media:VTRMC2017.pdf | Virginia Tech Contest]] by G.Craciun.<br />
* November 1: [[Media:Putnam110117.pdf | Functions and calculus]] by D.Arinkin.<br />
* November 8: [[Media:Putnam1.pdf | Past Competitions]] by M.Ifrim<br />
* November 15: [[Media:Putnam111517.pdf | Recurrences]] by G.Craciun.<br />
* November 22: '''No meeting''': Happy Thanksgiving!<br />
* November 29: [[Media:Putnam112917.pdf | Complex numbers]] by D.Arinkin.<br />
* December 2: '''Putnam Exam''' in VVB115. Morning session: 9-12pm; Afternoon session: 2-5pm.<br />
<br />
==Spring 2016==<br />
<br />
The Putnam Club does not meet in the spring, but we had the third annual UW [[Undergraduate Math Competition]] on April 19th, 2017.<br />
<br />
==Fall 2016==<br />
<br />
* September 20: [[Media:Putnam092016.pdf | Introductory meeting]]<br />
* September 27: [[Media:Putnam092716.pdf | Calculus and analysis]]<br />
* October 4: [[Media:Putnam100416.pdf | Generating functions]] (by Vlad Matei) <br />
* October 11: [[Media:UWUMC2016.pdf | Review of last year's UW Math competition]]<br />
* October 18: [[Media:Putnam101816.pdf | Functional equations]]<br />
* October 22: Virginia Tech Math Contest<br />
* October 25: Review of this year's [[Media:vtrmc16.pdf | VT contest]]<br />
* November 1: [[Media:Putnam110116.pdf | Matrices]] (by Vlad Matei)<br />
* November 15: [[Media:Putnam111516.pdf | Two algebra problems]]<br />
* November 22: No meeting: Happy Thanksgiving!<br />
* November 29: [[Media:Putnam112916.pdf | Assorted problems]]<br />
* December 3: Putnam Exam: Morning session: 9am-noon, Afternoon session: 2-5pm in VV B135.<br />
<br />
==Spring 2016==<br />
<br />
The Putnam Club does not meet in the spring, but we had the second annual UW [[Undergraduate Math Competition]] on April 12th, 2016.<br />
<br />
==Fall 2015==<br />
. <br />
* September 23rd: [[Media:Putnam092315.pdf | Introductory meeting]]<br />
* September 30th: [[Media:Putnam093015.pdf | Pigeonhole principle]]<br />
* October 7th: Review of [[Media:UWUMC2015.pdf | 2015 UW math competition]]<br />
* October 14th: [[Media:Putnam101415.pdf | Matrices and determinants]]<br />
* October 21st: [[Media:Putnam102115.pdf | Virginia Tech practice]]<br />
* October 24th: Virginia Tech Regional Mathematics Contest: 9-11:30 am<br />
* October 28th: Review of the 2015 Virginia Tech contest.<br />
* November 4th: [[Media:PutnamProblemsOct12.pdf | Polynomials]]<br />
* November 11th: [[Media:PutnamProblemsNov11.pdf | Assorted problems]]<br />
* November 18th: [[Media:PutnamProblemsNov18.pdf | Assorted problems]]<br />
* No meeting on November 25th<br />
* December 2nd: TBA<br />
* December 5th: Putnam competition: Morning session: 9am-12pm, afternoon session: 2-5pm in VV B115.<br />
<br />
==Spring 2015==<br />
<br />
The Putnam Club does not meet in the spring, but we had our first UW [[Undergraduate Math Competition]]!<br />
<br />
==Fall 2014==<br />
<br />
* September 17: [[Media:Putnam091714.pdf | Introductory meeting]]<br />
* September 22: [[Media:Putnam092214.pdf | Coloring and pigeonhole principle]]<br />
* October 1st: Went through HW problems from last time<br />
* October 8th: [[Media:Putnam100814.pdf | Number theory]]<br />
* October 15th: [[Media:Putnam101514.pdf | Games]]<br />
* October 22nd: [[Media:VTRMC13.pdf | Problems from last year's Virginia Tech contest]]<br />
* October 25th: Virginia Tech Regional Mathematics Contest<br />
* October 29th: Review of this year's Virginia Tech contest<br />
* November 5th: [http://www.math.cmu.edu/~lohp/docs/math/2014-295/06-inequalities.pdf Inequalities] and [http://www.math.cmu.edu/~lohp/docs/math/2014-295/05-functional.pdf functional equations]<br />
* November 12th: [http://www.math.cmu.edu/~lohp/docs/math/2014-295/02-polynomials.pdf Polynomials]<br />
* November 19th: [http://www.math.cmu.edu/~lohp/docs/math/2014-295/10-combinatorics.pdf Combinatorics]<br />
* December 3rd: [http://www.math.cmu.edu/~lohp/docs/math/2014-295/08-recursions.pdf Recursions]<br />
* December 6th: Putnam competition: Morning session: 9am-12pm, Afternoon session: 2pm-5pm in Van Vleck B119<br />
* December 10th: Review of [http://www.artofproblemsolving.com/Forum/resources/files/undergraduate_competitions/Undergraduate_Competitions-Putnam-2014-23 this year's Putnam]<br />
<br />
==Fall 2013==<br />
<br />
<br />
* September 11: [[Media:Putnam091113.pdf | Introductory Meeting]]<br />
* September 18: [[Media:Putnam091813.pdf | Assorted Problems]] (by Yihe Dong) <br />
* September 25: [[Media:Putnam092513.pdf | Combinatorics]]<br />
* October 2: [[Media:Putnam100213.pdf | Matrices and Linear Algebra]]<br />
* October 9: [[Media:Putnam100913.pdf | Number Theory]]<br />
* October 16: [[Media:Putnam101613.pdf | Functions and Calculus]]<br />
* October 23: [[Media:Putnam102313.pdf | Polynomials]]<br />
* October 26: Virginia Tech Regional Mathematics Contest<br />
* October 30: [[Media:VTRMC13.pdf | Problems from this year's Virginia Tech contest]]<br />
* November 6: [[Media:Putnam110413.pdf | Games]]<br />
* November 13: [[Media:Putnam111113.pdf | Pigeonhole Principle]]<br />
* November 20: [[Media:Putnam112013.pdf | Extreme Principle]]<br />
* November 27: No meeting (Thanksgiving)<br />
* December 4: TBA<br />
* December 7: Putnam competition Morning session: 9am-12pm, afternoon session: 2-5pm in VV B239.<br />
<br />
==Fall 2012==<br />
<br />
* September 11: Introduction [[Media:Putnam2012IntroProblems.pdf | Problems]]<br />
* September 18: Some Basic Techniques [[Media:Putnam2012Week1Problems.pdf | Problems]]<br />
* September 25: Polynomials and Algebra [[Media:Putnam2012Week2Problems.pdf | Problems]]<br />
* October 2: Number Theory [[Media:Putnam2012Week3Problems.pdf | Problems]]<br />
* October 9: Calculus [[Media:Putnam2012Week4Problems.pdf | Problems]]<br />
* October 16: Games and Algorithms [[Media:Putnam2012Week5Problems.pdf | Problems]]<br />
* October 23: Combinatorics [[Media:Putnam2012Week6Problems.pdf | Problems]]<br />
* October 30: Probability [[Media:Putnam2012Week7Problems.pdf | Problems]]<br />
* November 6: Linear Algebra [[Media:Putnam2012Week8Problems.pdf | Problems]]<br />
* November 13: Grab Bag [[Media:Putnam2012Week9Problems.pdf | Problems]]<br />
* November 27: Grab Bag 2 [[Media:Putnam2012Week10Problems.pdf | Problems]]<br />
<br />
==Fall 2011==<br />
<br />
* September 21: Pigeonhole Principle (Brian Rice) [[Media:PutnamProblemsSept21.pdf | Problems]]<br />
* September 28: Introduction to Counting (Brian Rice) [[Media:PutnamProblemsSept28.pdf | Problems]]<br />
* October 5: Elementary Number Theory (Brian Rice) [[Media:PutnamProblemsOct5.pdf | Problems]], [[Media:PutnamProblemsOct5Hard.pdf | Problems (Hardcore)]]<br />
* October 12: Polynomials (Brian Rice) [[Media:PutnamProblemsOct12.pdf | Problems]], [[Media:PutnamProblemsOct12Hard.pdf | Problems (Hardcore)]]<br />
* October 19: A Grab Bag of Discrete Math (Brian Rice) [[Media:PutnamProblemsOct19.pdf | Problems]]<br />
* October 26: Calculus, Week 1 (Brian Rice) [[Media:PutnamProblemsOct26.pdf | Problems]]<br />
* November 2: Calculus, Week 2 (Brian Rice) [[Media:PutnamProblemsNov2.pdf | Problems]]<br />
* November 9: Linear and Abstract Algebra (Brian Rice) [[Media: PutnamProblemsNov9.pdf | Problems]]<br />
* November 16: Mock Putnam [[Media: MockPutnamProblems.pdf | Problems]], [[Media: MockPutnamSolutions.pdf | Solutions]]</div>Arinkinhttps://www.math.wisc.edu/wiki/index.php?title=Undergraduate_Math_Competition&diff=15500Undergraduate Math Competition2018-05-04T16:54:03Z<p>Arinkin: </p>
<hr />
<div><br />
The fifth annual<br />
<br />
===UW Madison Undergraduate Math Competition (2019)===<br />
<br />
is tentatively scheduled for April, 2019.<br />
<br />
<br />
If you have any questions, please contact [mailto:arinkin@math.wisc.edu Dima Arinkin].<br />
<br />
----<br />
<br />
===Past competitions===<br />
<br />
{| class="wikitable"<br />
|+ Past Competitions<br />
|-<br />
! <br />
! Information<br />
! First place<br />
! Second place<br />
! Third place<br />
! Honorable mention<br />
|-<br />
! [[Media:UWUMC2018.pdf | Fourth UW Math Competition]] <br />
| April 24, 2018; 19 participants || Sivakorn Sanguanmoo || Yeqin Liu, Liding Yao || Daotong Ge, Xiaxin Li || Yifan Gao, James Tautges, Suyan Qu, Jikai Zhang<br />
|-<br />
! [[Media:UWUMC2017.pdf | Third UW Math Competition]] <br />
| April 19, 2017; 12 participants || Shouwei Hui, Hasan Eid || Xiaxin Li || Daotong Ge, Thomas Hameister || -<br />
|-<br />
! [[Media:UWUMC2016.pdf | Second UW Math Competition]] <br />
| April 19, 2016; 17 participants || Thomas Hameister || Chenwei Ruan, Yongzhe Zhang || Daotong Ge || -<br />
|-<br />
! [[Media:UWUMC2015.pdf | First UW Math Competition]] <br />
| April 22, 2015; 20 participants || Enkhzaya Enkhtaivan, Killian Kvalvik || - || - || Yida Ding, Thomas Hameister, Yan Chen<br />
|}</div>Arinkinhttps://www.math.wisc.edu/wiki/index.php?title=Putnam_Club&diff=15436Putnam Club2018-04-19T23:03:01Z<p>Arinkin: </p>
<hr />
<div><br />
''Organizers: Dima Arinkin, Gheorghe Craciun, Mihaela Ifrim''<br />
<br />
The Putnam Exam, offered by the Mathematical Association of America, is the premier American math competition for undergraduate students. It is given each year on the first Saturday in December. The exam consists of 12 problems, 6 in the 3 hour morning session and 6 in the 3 hour afternoon session. Each problem is worth 10 points, so the maximum score is 120. National winners usually get around 100 points. The median score is generally around 0-2 points. This is a difficult exam with many interesting and fun problems.<br />
<br />
[http://kskedlaya.org/putnam-archive/ Old exams and more information on the Putnam competition.]<br />
<br />
The UW is also participating in the Virginia Tech Regional Mathematics Contest. This is an individual competition with seven problems in 2.5 hours. Many schools use it as a kind of rehearsal for the Putnam. You can find more information [http://www.math.vt.edu/people/plinnell/Vtregional/ over here.]<br />
<br />
We hold our own UW Madison [[Undergraduate Math Competition]] in the spring; this year, it is on '''April 24th, 2018'''.<br />
<br />
==Spring 2017==<br />
<br />
The Putnam Club does not meet in the spring, but we had the fourth annual UW [[Undergraduate Math Competition]] on '''April 24th''', 2018, 5:30-8pm in VV B239.<br />
<br />
==Fall 2017==<br />
<br />
The Putnam Club will help you prepare for the exam by practicing on problems from previous years and other olympiad-style problems. The meeting time is 5pm on Wednesdays in VV B139.<br />
<br />
* September 20: [[Media:Putnam092017.pdf | Introductory meeting]] by D.Arinkin<br />
* September 27: [[Media:Putnam092717.pdf | Equations with functions as unknowns]] by M.Ifrim (by request: here is [[Media:Putnam092717sol6.pdf | a solution to problem 6]]; problem 7 is problem B5 of 2016 Putnam exam; you can see the solution [http://kskedlaya.org/putnam-archive/2016s.pdf here]).<br />
* October 4: [[Media:Putnam100417.pdf | Inequalities ]] by G.Craciun.<br />
* October 11: [[Media:Putnam101117.pdf | Polynomials ]] by D.Arinkin.<br />
* October 18: [[Media:Putnam1(2)..pdf | Equations ]] by M. Ifrim<br />
* October 21: Virginia Tech Math Contest: 9-11:30am in VV B203.<br />
* October 25: Review of this year's [[Media:VTRMC2017.pdf | Virginia Tech Contest]] by G.Craciun.<br />
* November 1: [[Media:Putnam110117.pdf | Functions and calculus]] by D.Arinkin.<br />
* November 8: [[Media:Putnam1.pdf | Past Competitions]] by M.Ifrim<br />
* November 15: [[Media:Putnam111517.pdf | Recurrences]] by G.Craciun.<br />
* November 22: '''No meeting''': Happy Thanksgiving!<br />
* November 29: [[Media:Putnam112917.pdf | Complex numbers]] by D.Arinkin.<br />
* December 2: '''Putnam Exam''' in VVB115. Morning session: 9-12pm; Afternoon session: 2-5pm.<br />
<br />
==Spring 2016==<br />
<br />
The Putnam Club does not meet in the spring, but we had the third annual UW [[Undergraduate Math Competition]] on April 19th, 2017.<br />
<br />
==Fall 2016==<br />
<br />
* September 20: [[Media:Putnam092016.pdf | Introductory meeting]]<br />
* September 27: [[Media:Putnam092716.pdf | Calculus and analysis]]<br />
* October 4: [[Media:Putnam100416.pdf | Generating functions]] (by Vlad Matei) <br />
* October 11: [[Media:UWUMC2016.pdf | Review of last year's UW Math competition]]<br />
* October 18: [[Media:Putnam101816.pdf | Functional equations]]<br />
* October 22: Virginia Tech Math Contest<br />
* October 25: Review of this year's [[Media:vtrmc16.pdf | VT contest]]<br />
* November 1: [[Media:Putnam110116.pdf | Matrices]] (by Vlad Matei)<br />
* November 15: [[Media:Putnam111516.pdf | Two algebra problems]]<br />
* November 22: No meeting: Happy Thanksgiving!<br />
* November 29: [[Media:Putnam112916.pdf | Assorted problems]]<br />
* December 3: Putnam Exam: Morning session: 9am-noon, Afternoon session: 2-5pm in VV B135.<br />
<br />
==Spring 2016==<br />
<br />
The Putnam Club does not meet in the spring, but we had the second annual UW [[Undergraduate Math Competition]] on April 12th, 2016.<br />
<br />
==Fall 2015==<br />
. <br />
* September 23rd: [[Media:Putnam092315.pdf | Introductory meeting]]<br />
* September 30th: [[Media:Putnam093015.pdf | Pigeonhole principle]]<br />
* October 7th: Review of [[Media:UWUMC15.pdf | 2015 UW math competition]]<br />
* October 14th: [[Media:Putnam101415.pdf | Matrices and determinants]]<br />
* October 21st: [[Media:Putnam102115.pdf | Virginia Tech practice]]<br />
* October 24th: Virginia Tech Regional Mathematics Contest: 9-11:30 am<br />
* October 28th: Review of the 2015 Virginia Tech contest.<br />
* November 4th: [[Media:PutnamProblemsOct12.pdf | Polynomials]]<br />
* November 11th: [[Media:PutnamProblemsNov11.pdf | Assorted problems]]<br />
* November 18th: [[Media:PutnamProblemsNov18.pdf | Assorted problems]]<br />
* No meeting on November 25th<br />
* December 2nd: TBA<br />
* December 5th: Putnam competition: Morning session: 9am-12pm, afternoon session: 2-5pm in VV B115.<br />
<br />
==Spring 2015==<br />
<br />
The Putnam Club does not meet in the spring, but we had our first UW [[Undergraduate Math Competition]]!<br />
<br />
==Fall 2014==<br />
<br />
* September 17: [[Media:Putnam091714.pdf | Introductory meeting]]<br />
* September 22: [[Media:Putnam092214.pdf | Coloring and pigeonhole principle]]<br />
* October 1st: Went through HW problems from last time<br />
* October 8th: [[Media:Putnam100814.pdf | Number theory]]<br />
* October 15th: [[Media:Putnam101514.pdf | Games]]<br />
* October 22nd: [[Media:VTRMC13.pdf | Problems from last year's Virginia Tech contest]]<br />
* October 25th: Virginia Tech Regional Mathematics Contest<br />
* October 29th: Review of this year's Virginia Tech contest<br />
* November 5th: [http://www.math.cmu.edu/~lohp/docs/math/2014-295/06-inequalities.pdf Inequalities] and [http://www.math.cmu.edu/~lohp/docs/math/2014-295/05-functional.pdf functional equations]<br />
* November 12th: [http://www.math.cmu.edu/~lohp/docs/math/2014-295/02-polynomials.pdf Polynomials]<br />
* November 19th: [http://www.math.cmu.edu/~lohp/docs/math/2014-295/10-combinatorics.pdf Combinatorics]<br />
* December 3rd: [http://www.math.cmu.edu/~lohp/docs/math/2014-295/08-recursions.pdf Recursions]<br />
* December 6th: Putnam competition: Morning session: 9am-12pm, Afternoon session: 2pm-5pm in Van Vleck B119<br />
* December 10th: Review of [http://www.artofproblemsolving.com/Forum/resources/files/undergraduate_competitions/Undergraduate_Competitions-Putnam-2014-23 this year's Putnam]<br />
<br />
==Fall 2013==<br />
<br />
<br />
* September 11: [[Media:Putnam091113.pdf | Introductory Meeting]]<br />
* September 18: [[Media:Putnam091813.pdf | Assorted Problems]] (by Yihe Dong) <br />
* September 25: [[Media:Putnam092513.pdf | Combinatorics]]<br />
* October 2: [[Media:Putnam100213.pdf | Matrices and Linear Algebra]]<br />
* October 9: [[Media:Putnam100913.pdf | Number Theory]]<br />
* October 16: [[Media:Putnam101613.pdf | Functions and Calculus]]<br />
* October 23: [[Media:Putnam102313.pdf | Polynomials]]<br />
* October 26: Virginia Tech Regional Mathematics Contest<br />
* October 30: [[Media:VTRMC13.pdf | Problems from this year's Virginia Tech contest]]<br />
* November 6: [[Media:Putnam110413.pdf | Games]]<br />
* November 13: [[Media:Putnam111113.pdf | Pigeonhole Principle]]<br />
* November 20: [[Media:Putnam112013.pdf | Extreme Principle]]<br />
* November 27: No meeting (Thanksgiving)<br />
* December 4: TBA<br />
* December 7: Putnam competition Morning session: 9am-12pm, afternoon session: 2-5pm in VV B239.<br />
<br />
==Fall 2012==<br />
<br />
* September 11: Introduction [[Media:Putnam2012IntroProblems.pdf | Problems]]<br />
* September 18: Some Basic Techniques [[Media:Putnam2012Week1Problems.pdf | Problems]]<br />
* September 25: Polynomials and Algebra [[Media:Putnam2012Week2Problems.pdf | Problems]]<br />
* October 2: Number Theory [[Media:Putnam2012Week3Problems.pdf | Problems]]<br />
* October 9: Calculus [[Media:Putnam2012Week4Problems.pdf | Problems]]<br />
* October 16: Games and Algorithms [[Media:Putnam2012Week5Problems.pdf | Problems]]<br />
* October 23: Combinatorics [[Media:Putnam2012Week6Problems.pdf | Problems]]<br />
* October 30: Probability [[Media:Putnam2012Week7Problems.pdf | Problems]]<br />
* November 6: Linear Algebra [[Media:Putnam2012Week8Problems.pdf | Problems]]<br />
* November 13: Grab Bag [[Media:Putnam2012Week9Problems.pdf | Problems]]<br />
* November 27: Grab Bag 2 [[Media:Putnam2012Week10Problems.pdf | Problems]]<br />
<br />
==Fall 2011==<br />
<br />
* September 21: Pigeonhole Principle (Brian Rice) [[Media:PutnamProblemsSept21.pdf | Problems]]<br />
* September 28: Introduction to Counting (Brian Rice) [[Media:PutnamProblemsSept28.pdf | Problems]]<br />
* October 5: Elementary Number Theory (Brian Rice) [[Media:PutnamProblemsOct5.pdf | Problems]], [[Media:PutnamProblemsOct5Hard.pdf | Problems (Hardcore)]]<br />
* October 12: Polynomials (Brian Rice) [[Media:PutnamProblemsOct12.pdf | Problems]], [[Media:PutnamProblemsOct12Hard.pdf | Problems (Hardcore)]]<br />
* October 19: A Grab Bag of Discrete Math (Brian Rice) [[Media:PutnamProblemsOct19.pdf | Problems]]<br />
* October 26: Calculus, Week 1 (Brian Rice) [[Media:PutnamProblemsOct26.pdf | Problems]]<br />
* November 2: Calculus, Week 2 (Brian Rice) [[Media:PutnamProblemsNov2.pdf | Problems]]<br />
* November 9: Linear and Abstract Algebra (Brian Rice) [[Media: PutnamProblemsNov9.pdf | Problems]]<br />
* November 16: Mock Putnam [[Media: MockPutnamProblems.pdf | Problems]], [[Media: MockPutnamSolutions.pdf | Solutions]]</div>Arinkinhttps://www.math.wisc.edu/wiki/index.php?title=Undergraduate_Math_Competition&diff=15435Undergraduate Math Competition2018-04-19T23:02:05Z<p>Arinkin: </p>
<hr />
<div><br />
The fourth annual<br />
<br />
===UW Madison Undergraduate Math Competition (2018)===<br />
<br />
with '''prizes''' for top performers!<br />
<br />
----<br />
<br />
* ''When?'' '''Tuesday, April 24''', 2018, 5:30-8pm. <br />
* ''Where?'' '''VV B239'''<br />
* ''What?'' There will be seven problems from various areas of mathematics (such as algebra, number theory, calculus, combinatorics, and others). We would like it to be challenging, but probably easier than, say, the Virginia Tech competition, and much easier than the Putnam Exam. You can take a look at our [[Putnam Club|Putnam Club page]] to see what type of problems we have in mind.<br />
<br />
If you are interested in the competition, please fill this short '''[https://goo.gl/forms/MhWb0n20YnFKKpVi2 registration form]'''! It is not actually required (so do not worry if something goes wrong), but it lets us see how many people are interested.<br />
<br />
<br />
If you have any questions, please contact [mailto:arinkin@math.wisc.edu Dima Arinkin].<br />
<br />
----<br />
<br />
===Past competitions===<br />
<br />
The third UW Madison Undergraduate Math Competition took place on April 19th, 2017. <br />
<br />
'''Problems''': [[Media:UWUMC2017.pdf | 2017 UW math competition]]<br />
<br />
'''Results''': 12 students took part in the competition. Congratulations to the winners:<br />
<br />
* ''First place'': Shouwei Hui, Hasan Eid <br />
* ''Second place'': Xiaxin Li <br />
* ''Third place'': Daotong Ge, Thomas Hameister<br />
<br />
The second UW Madison Undergraduate Math Competition took place on April 19th, 2016. <br />
<br />
'''Problems''': [[Media:UWUMC2016.pdf | 2016 UW math competition]]<br />
<br />
'''Results''': 17 students took part in the competition. Congratulations to the winners:<br />
<br />
* ''First place'': Thomas Hameister<br />
* ''Second place'': Chenwei Ruan, Yongzhe Zhang<br />
* ''Third place'': Daotong Ge<br />
<br />
The first (ever?) UW Madison Undergraduate Math Competition took place on April 22nd, 2015. <br />
<br />
'''Problems''': [[Media:UWUMC15.pdf | 2015 UW math competition]]<br />
<br />
'''Results''': 20 students took part in the competition. Congratulations to the winners:<br />
<br />
* ''First place'': Enkhzaya Enkhtaivan, Killian Kvalvik<br />
* ''Honorable mention'': Yida Ding, Thomas Hameister, Yan Chen</div>Arinkinhttps://www.math.wisc.edu/wiki/index.php?title=Undergraduate_Math_Competition&diff=15341Undergraduate Math Competition2018-04-04T23:31:00Z<p>Arinkin: /* UW Madison Undergraduate Math Competition (2018) */</p>
<hr />
<div><br />
The fourth annual<br />
<br />
===UW Madison Undergraduate Math Competition (2018)===<br />
<br />
with '''prizes''' for top performers!<br />
<br />
----<br />
<br />
* ''When?'' '''Tuesday, April 24''', 2018. <br />
* ''Where?'' '''VV B239'''<br />
* ''What?'' There will be seven problems from various areas of mathematics (such as algebra, number theory, calculus, combinatorics, and others). We would like it to be challenging, but probably easier than, say, the Virginia Tech competition, and much easier than the Putnam Exam. You can take a look at our [[Putnam Club|Putnam Club page]] to see what type of problems we have in mind.<br />
<br />
If you are interested in the competition, please fill this short '''[https://goo.gl/forms/MhWb0n20YnFKKpVi2 registration form]'''! It is not actually required (so do not worry if something goes wrong), but it lets us see how many people are interested.<br />
<br />
<br />
If you have any questions, please contact [mailto:arinkin@math.wisc.edu Dima Arinkin].<br />
<br />
----<br />
<br />
===Past competitions===<br />
<br />
The third UW Madison Undergraduate Math Competition took place on April 19th, 2017. <br />
<br />
'''Problems''': [[Media:UWUMC2017.pdf | 2017 UW math competition]]<br />
<br />
'''Results''': 12 students took part in the competition. Congratulations to the winners:<br />
<br />
* ''First place'': Shouwei Hui, Hasan Eid <br />
* ''Second place'': Xiaxin Li <br />
* ''Third place'': Daotong Ge, Thomas Hameister<br />
<br />
The second UW Madison Undergraduate Math Competition took place on April 19th, 2016. <br />
<br />
'''Problems''': [[Media:UWUMC2016.pdf | 2016 UW math competition]]<br />
<br />
'''Results''': 17 students took part in the competition. Congratulations to the winners:<br />
<br />
* ''First place'': Thomas Hameister<br />
* ''Second place'': Chenwei Ruan, Yongzhe Zhang<br />
* ''Third place'': Daotong Ge<br />
<br />
The first (ever?) UW Madison Undergraduate Math Competition took place on April 22nd, 2015. <br />
<br />
'''Problems''': [[Media:UWUMC15.pdf | 2015 UW math competition]]<br />
<br />
'''Results''': 20 students took part in the competition. Congratulations to the winners:<br />
<br />
* ''First place'': Enkhzaya Enkhtaivan, Killian Kvalvik<br />
* ''Honorable mention'': Yida Ding, Thomas Hameister, Yan Chen</div>Arinkinhttps://www.math.wisc.edu/wiki/index.php?title=Undergraduate_Math_Competition&diff=15340Undergraduate Math Competition2018-04-04T23:27:17Z<p>Arinkin: /* UW Madison Undergraduate Math Competition (2018) */</p>
<hr />
<div><br />
The fourth annual<br />
<br />
===UW Madison Undergraduate Math Competition (2018)===<br />
<br />
with '''prizes''' for top performers!<br />
<br />
----<br />
<br />
* ''When?'' '''Tuesday, April 24''', 2018. <br />
* ''Where?'' '''VV B239'''<br />
* ''What?'' There will be seven problems from various areas of mathematics (such as algebra, number theory, calculus, combinatorics, and others). We would like it to be challenging, but probably easier than, say, the Virginia Tech competition, and much easier than the Putnam Exam. You can take a look at our [[Putnam Club|Putnam Club page]] to see what type of problems we have in mind.<br />
<br />
If you are interested in the competition, please fill this short [https://goo.gl/forms/MhWb0n20YnFKKpVi2 registration form]! It is not actually required (so do not worry if something goes wrong), but it lets us see how many people are interested.<br />
<br />
<br />
If you have any questions, please contact [mailto:arinkin@math.wisc.edu Dima Arinkin].<br />
<br />
----<br />
<br />
===Past competitions===<br />
<br />
The third UW Madison Undergraduate Math Competition took place on April 19th, 2017. <br />
<br />
'''Problems''': [[Media:UWUMC2017.pdf | 2017 UW math competition]]<br />
<br />
'''Results''': 12 students took part in the competition. Congratulations to the winners:<br />
<br />
* ''First place'': Shouwei Hui, Hasan Eid <br />
* ''Second place'': Xiaxin Li <br />
* ''Third place'': Daotong Ge, Thomas Hameister<br />
<br />
The second UW Madison Undergraduate Math Competition took place on April 19th, 2016. <br />
<br />
'''Problems''': [[Media:UWUMC2016.pdf | 2016 UW math competition]]<br />
<br />
'''Results''': 17 students took part in the competition. Congratulations to the winners:<br />
<br />
* ''First place'': Thomas Hameister<br />
* ''Second place'': Chenwei Ruan, Yongzhe Zhang<br />
* ''Third place'': Daotong Ge<br />
<br />
The first (ever?) UW Madison Undergraduate Math Competition took place on April 22nd, 2015. <br />
<br />
'''Problems''': [[Media:UWUMC15.pdf | 2015 UW math competition]]<br />
<br />
'''Results''': 20 students took part in the competition. Congratulations to the winners:<br />
<br />
* ''First place'': Enkhzaya Enkhtaivan, Killian Kvalvik<br />
* ''Honorable mention'': Yida Ding, Thomas Hameister, Yan Chen</div>Arinkinhttps://www.math.wisc.edu/wiki/index.php?title=Putnam_Club&diff=15339Putnam Club2018-04-04T23:10:09Z<p>Arinkin: </p>
<hr />
<div><br />
''Organizers: Dima Arinkin, Gheorghe Craciun, Mihaela Ifrim''<br />
<br />
The Putnam Exam, offered by the Mathematical Association of America, is the premier American math competition for undergraduate students. It is given each year on the first Saturday in December. The exam consists of 12 problems, 6 in the 3 hour morning session and 6 in the 3 hour afternoon session. Each problem is worth 10 points, so the maximum score is 120. National winners usually get around 100 points. The median score is generally around 0-2 points. This is a difficult exam with many interesting and fun problems.<br />
<br />
[http://kskedlaya.org/putnam-archive/ Old exams and more information on the Putnam competition.]<br />
<br />
The UW is also participating in the Virginia Tech Regional Mathematics Contest. This is an individual competition with seven problems in 2.5 hours. Many schools use it as a kind of rehearsal for the Putnam. You can find more information [http://www.math.vt.edu/people/plinnell/Vtregional/ over here.]<br />
<br />
We hold our own UW Madison [[Undergraduate Math Competition]] in the spring; this year, it is on '''April 24th, 2018'''.<br />
<br />
==Spring 2017==<br />
<br />
The Putnam Club does not meet in the spring, but we had the fourth annual UW [[Undergraduate Math Competition]] on '''April 24th''', 2018.<br />
<br />
==Fall 2017==<br />
<br />
The Putnam Club will help you prepare for the exam by practicing on problems from previous years and other olympiad-style problems. The meeting time is 5pm on Wednesdays in VV B139.<br />
<br />
* September 20: [[Media:Putnam092017.pdf | Introductory meeting]] by D.Arinkin<br />
* September 27: [[Media:Putnam092717.pdf | Equations with functions as unknowns]] by M.Ifrim (by request: here is [[Media:Putnam092717sol6.pdf | a solution to problem 6]]; problem 7 is problem B5 of 2016 Putnam exam; you can see the solution [http://kskedlaya.org/putnam-archive/2016s.pdf here]).<br />
* October 4: [[Media:Putnam100417.pdf | Inequalities ]] by G.Craciun.<br />
* October 11: [[Media:Putnam101117.pdf | Polynomials ]] by D.Arinkin.<br />
* October 18: [[Media:Putnam1(2)..pdf | Equations ]] by M. Ifrim<br />
* October 21: Virginia Tech Math Contest: 9-11:30am in VV B203.<br />
* October 25: Review of this year's [[Media:VTRMC2017.pdf | Virginia Tech Contest]] by G.Craciun.<br />
* November 1: [[Media:Putnam110117.pdf | Functions and calculus]] by D.Arinkin.<br />
* November 8: [[Media:Putnam1.pdf | Past Competitions]] by M.Ifrim<br />
* November 15: [[Media:Putnam111517.pdf | Recurrences]] by G.Craciun.<br />
* November 22: '''No meeting''': Happy Thanksgiving!<br />
* November 29: [[Media:Putnam112917.pdf | Complex numbers]] by D.Arinkin.<br />
* December 2: '''Putnam Exam''' in VVB115. Morning session: 9-12pm; Afternoon session: 2-5pm.<br />
<br />
==Spring 2016==<br />
<br />
The Putnam Club does not meet in the spring, but we had the third annual UW [[Undergraduate Math Competition]] on April 19th, 2017.<br />
<br />
==Fall 2016==<br />
<br />
* September 20: [[Media:Putnam092016.pdf | Introductory meeting]]<br />
* September 27: [[Media:Putnam092716.pdf | Calculus and analysis]]<br />
* October 4: [[Media:Putnam100416.pdf | Generating functions]] (by Vlad Matei) <br />
* October 11: [[Media:UWUMC2016.pdf | Review of last year's UW Math competition]]<br />
* October 18: [[Media:Putnam101816.pdf | Functional equations]]<br />
* October 22: Virginia Tech Math Contest<br />
* October 25: Review of this year's [[Media:vtrmc16.pdf | VT contest]]<br />
* November 1: [[Media:Putnam110116.pdf | Matrices]] (by Vlad Matei)<br />
* November 15: [[Media:Putnam111516.pdf | Two algebra problems]]<br />
* November 22: No meeting: Happy Thanksgiving!<br />
* November 29: [[Media:Putnam112916.pdf | Assorted problems]]<br />
* December 3: Putnam Exam: Morning session: 9am-noon, Afternoon session: 2-5pm in VV B135.<br />
<br />
==Spring 2016==<br />
<br />
The Putnam Club does not meet in the spring, but we had the second annual UW [[Undergraduate Math Competition]] on April 12th, 2016.<br />
<br />
==Fall 2015==<br />
. <br />
* September 23rd: [[Media:Putnam092315.pdf | Introductory meeting]]<br />
* September 30th: [[Media:Putnam093015.pdf | Pigeonhole principle]]<br />
* October 7th: Review of [[Media:UWUMC15.pdf | 2015 UW math competition]]<br />
* October 14th: [[Media:Putnam101415.pdf | Matrices and determinants]]<br />
* October 21st: [[Media:Putnam102115.pdf | Virginia Tech practice]]<br />
* October 24th: Virginia Tech Regional Mathematics Contest: 9-11:30 am<br />
* October 28th: Review of the 2015 Virginia Tech contest.<br />
* November 4th: [[Media:PutnamProblemsOct12.pdf | Polynomials]]<br />
* November 11th: [[Media:PutnamProblemsNov11.pdf | Assorted problems]]<br />
* November 18th: [[Media:PutnamProblemsNov18.pdf | Assorted problems]]<br />
* No meeting on November 25th<br />
* December 2nd: TBA<br />
* December 5th: Putnam competition: Morning session: 9am-12pm, afternoon session: 2-5pm in VV B115.<br />
<br />
==Spring 2015==<br />
<br />
The Putnam Club does not meet in the spring, but we had our first UW [[Undergraduate Math Competition]]!<br />
<br />
==Fall 2014==<br />
<br />
* September 17: [[Media:Putnam091714.pdf | Introductory meeting]]<br />
* September 22: [[Media:Putnam092214.pdf | Coloring and pigeonhole principle]]<br />
* October 1st: Went through HW problems from last time<br />
* October 8th: [[Media:Putnam100814.pdf | Number theory]]<br />
* October 15th: [[Media:Putnam101514.pdf | Games]]<br />
* October 22nd: [[Media:VTRMC13.pdf | Problems from last year's Virginia Tech contest]]<br />
* October 25th: Virginia Tech Regional Mathematics Contest<br />
* October 29th: Review of this year's Virginia Tech contest<br />
* November 5th: [http://www.math.cmu.edu/~lohp/docs/math/2014-295/06-inequalities.pdf Inequalities] and [http://www.math.cmu.edu/~lohp/docs/math/2014-295/05-functional.pdf functional equations]<br />
* November 12th: [http://www.math.cmu.edu/~lohp/docs/math/2014-295/02-polynomials.pdf Polynomials]<br />
* November 19th: [http://www.math.cmu.edu/~lohp/docs/math/2014-295/10-combinatorics.pdf Combinatorics]<br />
* December 3rd: [http://www.math.cmu.edu/~lohp/docs/math/2014-295/08-recursions.pdf Recursions]<br />
* December 6th: Putnam competition: Morning session: 9am-12pm, Afternoon session: 2pm-5pm in Van Vleck B119<br />
* December 10th: Review of [http://www.artofproblemsolving.com/Forum/resources/files/undergraduate_competitions/Undergraduate_Competitions-Putnam-2014-23 this year's Putnam]<br />
<br />
==Fall 2013==<br />
<br />
<br />
* September 11: [[Media:Putnam091113.pdf | Introductory Meeting]]<br />
* September 18: [[Media:Putnam091813.pdf | Assorted Problems]] (by Yihe Dong) <br />
* September 25: [[Media:Putnam092513.pdf | Combinatorics]]<br />
* October 2: [[Media:Putnam100213.pdf | Matrices and Linear Algebra]]<br />
* October 9: [[Media:Putnam100913.pdf | Number Theory]]<br />
* October 16: [[Media:Putnam101613.pdf | Functions and Calculus]]<br />
* October 23: [[Media:Putnam102313.pdf | Polynomials]]<br />
* October 26: Virginia Tech Regional Mathematics Contest<br />
* October 30: [[Media:VTRMC13.pdf | Problems from this year's Virginia Tech contest]]<br />
* November 6: [[Media:Putnam110413.pdf | Games]]<br />
* November 13: [[Media:Putnam111113.pdf | Pigeonhole Principle]]<br />
* November 20: [[Media:Putnam112013.pdf | Extreme Principle]]<br />
* November 27: No meeting (Thanksgiving)<br />
* December 4: TBA<br />
* December 7: Putnam competition Morning session: 9am-12pm, afternoon session: 2-5pm in VV B239.<br />
<br />
==Fall 2012==<br />
<br />
* September 11: Introduction [[Media:Putnam2012IntroProblems.pdf | Problems]]<br />
* September 18: Some Basic Techniques [[Media:Putnam2012Week1Problems.pdf | Problems]]<br />
* September 25: Polynomials and Algebra [[Media:Putnam2012Week2Problems.pdf | Problems]]<br />
* October 2: Number Theory [[Media:Putnam2012Week3Problems.pdf | Problems]]<br />
* October 9: Calculus [[Media:Putnam2012Week4Problems.pdf | Problems]]<br />
* October 16: Games and Algorithms [[Media:Putnam2012Week5Problems.pdf | Problems]]<br />
* October 23: Combinatorics [[Media:Putnam2012Week6Problems.pdf | Problems]]<br />
* October 30: Probability [[Media:Putnam2012Week7Problems.pdf | Problems]]<br />
* November 6: Linear Algebra [[Media:Putnam2012Week8Problems.pdf | Problems]]<br />
* November 13: Grab Bag [[Media:Putnam2012Week9Problems.pdf | Problems]]<br />
* November 27: Grab Bag 2 [[Media:Putnam2012Week10Problems.pdf | Problems]]<br />
<br />
==Fall 2011==<br />
<br />
* September 21: Pigeonhole Principle (Brian Rice) [[Media:PutnamProblemsSept21.pdf | Problems]]<br />
* September 28: Introduction to Counting (Brian Rice) [[Media:PutnamProblemsSept28.pdf | Problems]]<br />
* October 5: Elementary Number Theory (Brian Rice) [[Media:PutnamProblemsOct5.pdf | Problems]], [[Media:PutnamProblemsOct5Hard.pdf | Problems (Hardcore)]]<br />
* October 12: Polynomials (Brian Rice) [[Media:PutnamProblemsOct12.pdf | Problems]], [[Media:PutnamProblemsOct12Hard.pdf | Problems (Hardcore)]]<br />
* October 19: A Grab Bag of Discrete Math (Brian Rice) [[Media:PutnamProblemsOct19.pdf | Problems]]<br />
* October 26: Calculus, Week 1 (Brian Rice) [[Media:PutnamProblemsOct26.pdf | Problems]]<br />
* November 2: Calculus, Week 2 (Brian Rice) [[Media:PutnamProblemsNov2.pdf | Problems]]<br />
* November 9: Linear and Abstract Algebra (Brian Rice) [[Media: PutnamProblemsNov9.pdf | Problems]]<br />
* November 16: Mock Putnam [[Media: MockPutnamProblems.pdf | Problems]], [[Media: MockPutnamSolutions.pdf | Solutions]]</div>Arinkinhttps://www.math.wisc.edu/wiki/index.php?title=Putnam_Club&diff=15338Putnam Club2018-04-04T23:09:27Z<p>Arinkin: </p>
<hr />
<div><br />
''Organizers: Dima Arinkin, Gheorghe Craciun, Mihaela Ifrim''<br />
<br />
The Putnam Exam, offered by the Mathematical Association of America, is the premier American math competition for undergraduate students. It is given each year on the first Saturday in December. The exam consists of 12 problems, 6 in the 3 hour morning session and 6 in the 3 hour afternoon session. Each problem is worth 10 points, so the maximum score is 120. National winners usually get around 100 points. The median score is generally around 0-2 points. This is a difficult exam with many interesting and fun problems.<br />
<br />
[http://kskedlaya.org/putnam-archive/ Old exams and more information on the Putnam competition.]<br />
<br />
The UW is also participating in the Virginia Tech Regional Mathematics Contest. This is an individual competition with seven problems in 2.5 hours. Many schools use it as a kind of rehearsal for the Putnam. You can find more information [http://www.math.vt.edu/people/plinnell/Vtregional/ over here.]<br />
<br />
We hold our own UW Madison [[Undergraduate Math Competition]] in the spring.<br />
<br />
==Spring 2017==<br />
<br />
The Putnam Club does not meet in the spring, but we had the fourth annual UW [[Undergraduate Math Competition]] on '''April 24th''', 2018.<br />
<br />
==Fall 2017==<br />
<br />
The Putnam Club will help you prepare for the exam by practicing on problems from previous years and other olympiad-style problems. The meeting time is 5pm on Wednesdays in VV B139.<br />
<br />
* September 20: [[Media:Putnam092017.pdf | Introductory meeting]] by D.Arinkin<br />
* September 27: [[Media:Putnam092717.pdf | Equations with functions as unknowns]] by M.Ifrim (by request: here is [[Media:Putnam092717sol6.pdf | a solution to problem 6]]; problem 7 is problem B5 of 2016 Putnam exam; you can see the solution [http://kskedlaya.org/putnam-archive/2016s.pdf here]).<br />
* October 4: [[Media:Putnam100417.pdf | Inequalities ]] by G.Craciun.<br />
* October 11: [[Media:Putnam101117.pdf | Polynomials ]] by D.Arinkin.<br />
* October 18: [[Media:Putnam1(2)..pdf | Equations ]] by M. Ifrim<br />
* October 21: Virginia Tech Math Contest: 9-11:30am in VV B203.<br />
* October 25: Review of this year's [[Media:VTRMC2017.pdf | Virginia Tech Contest]] by G.Craciun.<br />
* November 1: [[Media:Putnam110117.pdf | Functions and calculus]] by D.Arinkin.<br />
* November 8: [[Media:Putnam1.pdf | Past Competitions]] by M.Ifrim<br />
* November 15: [[Media:Putnam111517.pdf | Recurrences]] by G.Craciun.<br />
* November 22: '''No meeting''': Happy Thanksgiving!<br />
* November 29: [[Media:Putnam112917.pdf | Complex numbers]] by D.Arinkin.<br />
* December 2: '''Putnam Exam''' in VVB115. Morning session: 9-12pm; Afternoon session: 2-5pm.<br />
<br />
==Spring 2016==<br />
<br />
The Putnam Club does not meet in the spring, but we had the third annual UW [[Undergraduate Math Competition]] on April 19th, 2017.<br />
<br />
==Fall 2016==<br />
<br />
* September 20: [[Media:Putnam092016.pdf | Introductory meeting]]<br />
* September 27: [[Media:Putnam092716.pdf | Calculus and analysis]]<br />
* October 4: [[Media:Putnam100416.pdf | Generating functions]] (by Vlad Matei) <br />
* October 11: [[Media:UWUMC2016.pdf | Review of last year's UW Math competition]]<br />
* October 18: [[Media:Putnam101816.pdf | Functional equations]]<br />
* October 22: Virginia Tech Math Contest<br />
* October 25: Review of this year's [[Media:vtrmc16.pdf | VT contest]]<br />
* November 1: [[Media:Putnam110116.pdf | Matrices]] (by Vlad Matei)<br />
* November 15: [[Media:Putnam111516.pdf | Two algebra problems]]<br />
* November 22: No meeting: Happy Thanksgiving!<br />
* November 29: [[Media:Putnam112916.pdf | Assorted problems]]<br />
* December 3: Putnam Exam: Morning session: 9am-noon, Afternoon session: 2-5pm in VV B135.<br />
<br />
==Spring 2016==<br />
<br />
The Putnam Club does not meet in the spring, but we had the second annual UW [[Undergraduate Math Competition]] on April 12th, 2016.<br />
<br />
==Fall 2015==<br />
. <br />
* September 23rd: [[Media:Putnam092315.pdf | Introductory meeting]]<br />
* September 30th: [[Media:Putnam093015.pdf | Pigeonhole principle]]<br />
* October 7th: Review of [[Media:UWUMC15.pdf | 2015 UW math competition]]<br />
* October 14th: [[Media:Putnam101415.pdf | Matrices and determinants]]<br />
* October 21st: [[Media:Putnam102115.pdf | Virginia Tech practice]]<br />
* October 24th: Virginia Tech Regional Mathematics Contest: 9-11:30 am<br />
* October 28th: Review of the 2015 Virginia Tech contest.<br />
* November 4th: [[Media:PutnamProblemsOct12.pdf | Polynomials]]<br />
* November 11th: [[Media:PutnamProblemsNov11.pdf | Assorted problems]]<br />
* November 18th: [[Media:PutnamProblemsNov18.pdf | Assorted problems]]<br />
* No meeting on November 25th<br />
* December 2nd: TBA<br />
* December 5th: Putnam competition: Morning session: 9am-12pm, afternoon session: 2-5pm in VV B115.<br />
<br />
==Spring 2015==<br />
<br />
The Putnam Club does not meet in the spring, but we had our first UW [[Undergraduate Math Competition]]!<br />
<br />
==Fall 2014==<br />
<br />
* September 17: [[Media:Putnam091714.pdf | Introductory meeting]]<br />
* September 22: [[Media:Putnam092214.pdf | Coloring and pigeonhole principle]]<br />
* October 1st: Went through HW problems from last time<br />
* October 8th: [[Media:Putnam100814.pdf | Number theory]]<br />
* October 15th: [[Media:Putnam101514.pdf | Games]]<br />
* October 22nd: [[Media:VTRMC13.pdf | Problems from last year's Virginia Tech contest]]<br />
* October 25th: Virginia Tech Regional Mathematics Contest<br />
* October 29th: Review of this year's Virginia Tech contest<br />
* November 5th: [http://www.math.cmu.edu/~lohp/docs/math/2014-295/06-inequalities.pdf Inequalities] and [http://www.math.cmu.edu/~lohp/docs/math/2014-295/05-functional.pdf functional equations]<br />
* November 12th: [http://www.math.cmu.edu/~lohp/docs/math/2014-295/02-polynomials.pdf Polynomials]<br />
* November 19th: [http://www.math.cmu.edu/~lohp/docs/math/2014-295/10-combinatorics.pdf Combinatorics]<br />
* December 3rd: [http://www.math.cmu.edu/~lohp/docs/math/2014-295/08-recursions.pdf Recursions]<br />
* December 6th: Putnam competition: Morning session: 9am-12pm, Afternoon session: 2pm-5pm in Van Vleck B119<br />
* December 10th: Review of [http://www.artofproblemsolving.com/Forum/resources/files/undergraduate_competitions/Undergraduate_Competitions-Putnam-2014-23 this year's Putnam]<br />
<br />
==Fall 2013==<br />
<br />
<br />
* September 11: [[Media:Putnam091113.pdf | Introductory Meeting]]<br />
* September 18: [[Media:Putnam091813.pdf | Assorted Problems]] (by Yihe Dong) <br />
* September 25: [[Media:Putnam092513.pdf | Combinatorics]]<br />
* October 2: [[Media:Putnam100213.pdf | Matrices and Linear Algebra]]<br />
* October 9: [[Media:Putnam100913.pdf | Number Theory]]<br />
* October 16: [[Media:Putnam101613.pdf | Functions and Calculus]]<br />
* October 23: [[Media:Putnam102313.pdf | Polynomials]]<br />
* October 26: Virginia Tech Regional Mathematics Contest<br />
* October 30: [[Media:VTRMC13.pdf | Problems from this year's Virginia Tech contest]]<br />
* November 6: [[Media:Putnam110413.pdf | Games]]<br />
* November 13: [[Media:Putnam111113.pdf | Pigeonhole Principle]]<br />
* November 20: [[Media:Putnam112013.pdf | Extreme Principle]]<br />
* November 27: No meeting (Thanksgiving)<br />
* December 4: TBA<br />
* December 7: Putnam competition Morning session: 9am-12pm, afternoon session: 2-5pm in VV B239.<br />
<br />
==Fall 2012==<br />
<br />
* September 11: Introduction [[Media:Putnam2012IntroProblems.pdf | Problems]]<br />
* September 18: Some Basic Techniques [[Media:Putnam2012Week1Problems.pdf | Problems]]<br />
* September 25: Polynomials and Algebra [[Media:Putnam2012Week2Problems.pdf | Problems]]<br />
* October 2: Number Theory [[Media:Putnam2012Week3Problems.pdf | Problems]]<br />
* October 9: Calculus [[Media:Putnam2012Week4Problems.pdf | Problems]]<br />
* October 16: Games and Algorithms [[Media:Putnam2012Week5Problems.pdf | Problems]]<br />
* October 23: Combinatorics [[Media:Putnam2012Week6Problems.pdf | Problems]]<br />
* October 30: Probability [[Media:Putnam2012Week7Problems.pdf | Problems]]<br />
* November 6: Linear Algebra [[Media:Putnam2012Week8Problems.pdf | Problems]]<br />
* November 13: Grab Bag [[Media:Putnam2012Week9Problems.pdf | Problems]]<br />
* November 27: Grab Bag 2 [[Media:Putnam2012Week10Problems.pdf | Problems]]<br />
<br />
==Fall 2011==<br />
<br />
* September 21: Pigeonhole Principle (Brian Rice) [[Media:PutnamProblemsSept21.pdf | Problems]]<br />
* September 28: Introduction to Counting (Brian Rice) [[Media:PutnamProblemsSept28.pdf | Problems]]<br />
* October 5: Elementary Number Theory (Brian Rice) [[Media:PutnamProblemsOct5.pdf | Problems]], [[Media:PutnamProblemsOct5Hard.pdf | Problems (Hardcore)]]<br />
* October 12: Polynomials (Brian Rice) [[Media:PutnamProblemsOct12.pdf | Problems]], [[Media:PutnamProblemsOct12Hard.pdf | Problems (Hardcore)]]<br />
* October 19: A Grab Bag of Discrete Math (Brian Rice) [[Media:PutnamProblemsOct19.pdf | Problems]]<br />
* October 26: Calculus, Week 1 (Brian Rice) [[Media:PutnamProblemsOct26.pdf | Problems]]<br />
* November 2: Calculus, Week 2 (Brian Rice) [[Media:PutnamProblemsNov2.pdf | Problems]]<br />
* November 9: Linear and Abstract Algebra (Brian Rice) [[Media: PutnamProblemsNov9.pdf | Problems]]<br />
* November 16: Mock Putnam [[Media: MockPutnamProblems.pdf | Problems]], [[Media: MockPutnamSolutions.pdf | Solutions]]</div>Arinkinhttps://www.math.wisc.edu/wiki/index.php?title=Undergraduate_Math_Competition&diff=15337Undergraduate Math Competition2018-04-04T23:06:36Z<p>Arinkin: </p>
<hr />
<div><br />
The fourth annual<br />
<br />
===UW Madison Undergraduate Math Competition (2018)===<br />
<br />
with '''prizes''' for top performers!<br />
<br />
----<br />
<br />
* ''When?'' '''Tuesday, April 24''', 2018. <br />
* ''Where?'' '''VV B239'''<br />
* ''What?'' There will be seven problems from various areas of mathematics (such as algebra, number theory, calculus, combinatorics, and others). We would like it to be challenging, but probably easier than, say, the Virginia Tech competition, and much easier than the Putnam Exam. You can take a look at our [[Putnam Club|Putnam Club page]] to see what type of problems we have in mind.<br />
<br />
<br />
If you have any questions, please contact [mailto:arinkin@math.wisc.edu Dima Arinkin].<br />
<br />
----<br />
<br />
===Past competitions===<br />
<br />
The third UW Madison Undergraduate Math Competition took place on April 19th, 2017. <br />
<br />
'''Problems''': [[Media:UWUMC2017.pdf | 2017 UW math competition]]<br />
<br />
'''Results''': 12 students took part in the competition. Congratulations to the winners:<br />
<br />
* ''First place'': Shouwei Hui, Hasan Eid <br />
* ''Second place'': Xiaxin Li <br />
* ''Third place'': Daotong Ge, Thomas Hameister<br />
<br />
The second UW Madison Undergraduate Math Competition took place on April 19th, 2016. <br />
<br />
'''Problems''': [[Media:UWUMC2016.pdf | 2016 UW math competition]]<br />
<br />
'''Results''': 17 students took part in the competition. Congratulations to the winners:<br />
<br />
* ''First place'': Thomas Hameister<br />
* ''Second place'': Chenwei Ruan, Yongzhe Zhang<br />
* ''Third place'': Daotong Ge<br />
<br />
The first (ever?) UW Madison Undergraduate Math Competition took place on April 22nd, 2015. <br />
<br />
'''Problems''': [[Media:UWUMC15.pdf | 2015 UW math competition]]<br />
<br />
'''Results''': 20 students took part in the competition. Congratulations to the winners:<br />
<br />
* ''First place'': Enkhzaya Enkhtaivan, Killian Kvalvik<br />
* ''Honorable mention'': Yida Ding, Thomas Hameister, Yan Chen</div>Arinkinhttps://www.math.wisc.edu/wiki/index.php?title=Algebra_and_Algebraic_Geometry_Seminar_Spring_2018&diff=15258Algebra and Algebraic Geometry Seminar Spring 20182018-03-15T17:10:12Z<p>Arinkin: /* Alexander Yom Din */</p>
<hr />
<div>The seminar meets on Fridays at 2:25 pm in room B113.<br />
<br />
Here is the schedule for [[Algebraic Geometry Seminar Spring 2017 | the previous semester]].<br />
<!--, [[Algebraic Geometry Seminar Spring 2018 | the next semester]], and for [[Algebraic Geometry Seminar | this semester]]. --><br />
<br />
==Algebra and Algebraic Geometry Mailing List==<br />
<br />
<br />
*Please join the [https://admin.lists.wisc.edu/index.php?p=11&l=ags AGS Mailing List] to hear about upcoming seminars, lunches, and other algebraic geometry events in the department (it is possible you must be on a math department computer to use this link).<br />
<br />
== Spring 2018 Schedule ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s) <br />
<br />
|-<br />
|January 26<br />
|[http://homepages.math.uic.edu/~tmoulinos/ Tasos Moulinos (UIC)] <br />
|[[#Tasos Moulinos|Derived Azumaya Algebras and Twisted K-theory]]<br />
|Michael<br />
|-<br />
|February 2<br />
|Daniel Erman (Wisconsin) <br />
|[[#Daniel Erman|TBA]]<br />
|Local<br />
|-<br />
|'''February 8''' 2:30-3:30 in VV B113<br />
|[http://www.mathematics.pitt.edu/person/roman-fedorov/ Roman Fedorov (University of Pittsburgh)]<br />
|[[#Roman Fedorov|A conjecture of Grothendieck and Serre on principal bundles in mixed characteristic]]<br />
|Dima<br />
|-<br />
|February 9<br />
|Juliette Bruce (Wisconsin) <br />
|[[#Juliette Bruce|Asymptotic Syzygies in the Semi-Ample Setting ]]<br />
|Local<br />
|-<br />
|February 16<br />
|[http://www.math.wisc.edu/~andreic/ Andrei Caldararu (Wisconsin)]<br />
|[[#Andrei Caldararu|Computing a categorical Gromov-Witten invariant]]<br />
|Local<br />
|-<br />
|February 23<br />
|Aron Heleodoro (Northwestern) <br />
|[[#Aron Heleodoro|Normally ordered tensor product of Tate objects and decomposition of higher adeles]]<br />
|Dima<br />
|-<br />
|March 2<br />
|Moisés Herradón Cueto (Wisconsin)<br />
|[[#Moisés Herradón Cueto|Local type of difference equations]]<br />
|Local<br />
|-<br />
|March 9<br />
|Eva Elduque (Wisconsin)<br />
|[[#Eva Elduque|On the signed Euler characteristic property for subvarieties of Abelian varieties]]<br />
|Local<br />
|-<br />
|March 16<br />
|[https://math.berkeley.edu/~chenhi/ Harrison Chen (Berkeley)]<br />
|[[#Harrison Chen|Equivariant localization for periodic cyclic homology and derived loop spaces]]<br />
|Andrei<br />
|-<br />
|March 23<br />
|[http://www-personal.umich.edu/~ptoste/ Phil Tosteson (Michigan)]<br />
|[[#Phil Tosteson|TBA]]<br />
|Steven<br />
|-<br />
|-<br />
|April 6<br />
|Wei Ho<br />
|TBA<br />
|Daniel/Wanlin<br />
|-<br />
|-<br />
|April 13<br />
|Reserved<br />
|<br />
|Daniel<br />
|-<br />
|April 20<br />
|Alena Pirutka (NYU)<br />
|[[#Alena Pirutka|TBA]]<br />
|Jordan<br />
|-<br />
|April 27<br />
|Alexander Yom Din (Caltech) <br />
|[[#Alexander Yom Din|Drinfeld-Gaitsgory functor and contragradient duality for (g,K)-modules]]<br />
|Dima<br />
|-<br />
|May 4<br />
|John Lesieutre (UIC) <br />
|[[#John Lesieutre|TBA]]<br />
|Daniel<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===Tasos Moulinos===<br />
<br />
'''Derived Azumaya Algebras and Twisted K-theory'''<br />
<br />
Topological K-theory of dg-categories is a localizing invariant of dg-categories over <math> \mathbb{C} </math><br />
taking values in the <math> \infty </math>-category of <math> KU </math>-modules. In this talk I describe a relative version<br />
of this construction; namely for <math>X</math> a quasi-compact, quasi-separated <math> \mathbb{C} </math>-scheme I construct a<br />
functor valued in the <math> \infty </math>-category of sheaves of spectra on <math> X(\mathbb{C}) </math>, the complex points of <math>X</math>. For inputs<br />
of the form <math>\operatorname{Perf}(X, A)</math> where <math>A</math> is an Azumaya algebra over <math>X</math>, I characterize the values<br />
of this functor in terms of the twisted topological K-theory of <math> X(\mathbb{C}) </math>. From this I deduce<br />
a certain decomposition, for <math> X </math> a finite CW-complex equipped with a bundle <math> P </math> of projective<br />
spaces over <math> X </math>, of <math> KU(P) </math> in terms of the twisted topological K-theory of <math> X </math> ; this is<br />
a topological analogue of a result of Quillen’s on the algebraic K-theory of Severi-Brauer<br />
schemes.<br />
<br />
===Roman Fedorov===<br />
<br />
'''A conjecture of Grothendieck and Serre on principal bundles in mixed<br />
characteristic'''<br />
<br />
Let G be a reductive group scheme over a regular local ring R. An old<br />
conjecture of Grothendieck and Serre predicts that such a principal<br />
bundle is trivial, if it is trivial over the fraction field of R. The<br />
conjecture has recently been proved in the "geometric" case, that is,<br />
when R contains a field. In the remaining case, the difficulty comes<br />
from the fact, that the situation is more rigid, so that a certain<br />
general position argument does not go through. I will discuss this<br />
difficulty and a way to circumvent it to obtain some partial results.<br />
<br />
===Juliette Bruce===<br />
<br />
'''Asymptotic Syzygies in the Semi-Ample Setting'''<br />
<br />
In recent years numerous conjectures have been made describing the asymptotic Betti numbers of a projective variety as the embedding line bundle becomes more ample. I will discuss recent work attempting to generalize these conjectures to the case when the embedding line bundle becomes more semi-ample. (Recall a line bundle is semi-ample if a sufficiently large multiple is base point free.) In particular, I will discuss how the monomial methods of Ein, Erman, and Lazarsfeld used to prove non-vanishing results on projective space can be extended to prove non-vanishing results for products of projective space.<br />
<br />
===Andrei Caldararu===<br />
<br />
'''Computing a categorical Gromov-Witten invariant'''<br />
<br />
In his 2005 paper "The Gromov-Witten potential associated to a TCFT" Kevin Costello described a procedure for recovering an analogue of the Gromov-Witten potential directly out of a cyclic A-inifinity algebra or category. Applying his construction to the derived category of sheaves of a complex projective variety provides a definition of higher genus B-model Gromov-Witten invariants, independent of the BCOV formalism. This has several advantages. Due to the categorical invariance of these invariants, categorical mirror symmetry automatically implies classical mirror symmetry to all genera. Also, the construction can be applied to other categories like categories of matrix factorization, giving a direct definition of FJRW invariants, for example.<br />
<br />
In my talk I shall describe the details of the computation (joint with Junwu Tu) of the invariant, at g=1, n=1, for elliptic curves. The result agrees with the predictions of mirror symmetry, matching classical calculations of Dijkgraaf. It is the first non-trivial computation of a categorical Gromov-Witten invariant.<br />
<br />
===Aron Heleodoro===<br />
<br />
'''Normally ordered tensor product of Tate objects and decomposition of higher adeles'''<br />
<br />
In this talk I will introduce the different tensor products that exist on Tate objects over vector spaces (or more generally coherent sheaves on a given scheme). As an application, I will explain how these can be used to describe higher adeles on an n-dimensional smooth scheme. Both Tate objects and higher adeles would be introduced in the talk. (This is based on joint work with Braunling, Groechenig and Wolfson.)<br />
<br />
===Moisés Herradón Cueto===<br />
<br />
'''Local type of difference equations'''<br />
<br />
The theory of algebraic differential equations on the affine line is very well-understood. In particular, there is a well-defined notion of restricting a D-module to a formal neighborhood of a point, and these restrictions are completely described by two vector spaces, called vanishing cycles and nearby cycles, and some maps between them. We give an analogous notion of "restriction to a formal disk" for difference equations that satisfies several desirable properties: first of all, a difference module can be recovered uniquely from its restriction to the complement of a point and its restriction to a formal disk around this point. Secondly, it gives rise to a local Mellin transform, which relates vanishing cycles of a difference module to nearby cycles of its Mellin transform. Since the Mellin transform of a difference module is a D-module, the Mellin transform brings us back to the familiar world of D-modules.<br />
<br />
===Eva Elduque===<br />
<br />
'''On the signed Euler characteristic property for subvarieties of Abelian varieties'''<br />
<br />
Franecki and Kapranov proved that the Euler characteristic of a perverse sheaf on a semi-abelian variety is non-negative. This result has several purely topological consequences regarding the sign of the (topological and intersection homology) Euler characteristic of a subvariety of an abelian variety, and it is natural to attempt to justify them by more elementary methods. In this talk, we'll explore the geometric tools used recently in the proof of the signed Euler<br />
characteristic property. Joint work with Christian Geske and Laurentiu Maxim.<br />
<br />
===Harrison Chen===<br />
<br />
'''Equivariant localization for periodic cyclic homology and derived loop spaces'''<br />
<br />
There is a close relationship between derived loop spaces, a geometric object, and (periodic) cyclic homology, a categorical invariant. In this talk we will discuss this relationship and how it leads to an equivariant localization result, which has an intuitive interpretation using the language of derived loop spaces. We discuss ongoing generalizations and potential applications in computing the periodic cyclic homology of categories of equivariant (coherent) sheaves on algebraic varieties.<br />
<br />
===Alexander Yom Din===<br />
<br />
'''Drinfeld-Gaitsgory functor and contragradient duality for (g,K)-modules'''<br />
<br />
Drinfeld suggested the definition of a certain endo-functor, called the pseudo-identity functor (or the Drinfeld-Gaitsgory functor), on the category of D-modules on an algebraic stack. We extend this definition to an arbitrary DG category, and show that if certain finiteness conditions are satisfied, this functor is the inverse of the Serre functor. We show that the pseudo-identity functor for (g,K)-modules is isomorphic to the composition of cohomological and contragredient dualities, which is parallel to an analogous assertion for p-adic groups.<br />
<br />
In this talk I will try to discuss some of these results and around them. This is joint work with Dennis Gaitsgory.</div>Arinkinhttps://www.math.wisc.edu/wiki/index.php?title=Algebra_and_Algebraic_Geometry_Seminar_Spring_2018&diff=15257Algebra and Algebraic Geometry Seminar Spring 20182018-03-15T17:09:33Z<p>Arinkin: </p>
<hr />
<div>The seminar meets on Fridays at 2:25 pm in room B113.<br />
<br />
Here is the schedule for [[Algebraic Geometry Seminar Spring 2017 | the previous semester]].<br />
<!--, [[Algebraic Geometry Seminar Spring 2018 | the next semester]], and for [[Algebraic Geometry Seminar | this semester]]. --><br />
<br />
==Algebra and Algebraic Geometry Mailing List==<br />
<br />
<br />
*Please join the [https://admin.lists.wisc.edu/index.php?p=11&l=ags AGS Mailing List] to hear about upcoming seminars, lunches, and other algebraic geometry events in the department (it is possible you must be on a math department computer to use this link).<br />
<br />
== Spring 2018 Schedule ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s) <br />
<br />
|-<br />
|January 26<br />
|[http://homepages.math.uic.edu/~tmoulinos/ Tasos Moulinos (UIC)] <br />
|[[#Tasos Moulinos|Derived Azumaya Algebras and Twisted K-theory]]<br />
|Michael<br />
|-<br />
|February 2<br />
|Daniel Erman (Wisconsin) <br />
|[[#Daniel Erman|TBA]]<br />
|Local<br />
|-<br />
|'''February 8''' 2:30-3:30 in VV B113<br />
|[http://www.mathematics.pitt.edu/person/roman-fedorov/ Roman Fedorov (University of Pittsburgh)]<br />
|[[#Roman Fedorov|A conjecture of Grothendieck and Serre on principal bundles in mixed characteristic]]<br />
|Dima<br />
|-<br />
|February 9<br />
|Juliette Bruce (Wisconsin) <br />
|[[#Juliette Bruce|Asymptotic Syzygies in the Semi-Ample Setting ]]<br />
|Local<br />
|-<br />
|February 16<br />
|[http://www.math.wisc.edu/~andreic/ Andrei Caldararu (Wisconsin)]<br />
|[[#Andrei Caldararu|Computing a categorical Gromov-Witten invariant]]<br />
|Local<br />
|-<br />
|February 23<br />
|Aron Heleodoro (Northwestern) <br />
|[[#Aron Heleodoro|Normally ordered tensor product of Tate objects and decomposition of higher adeles]]<br />
|Dima<br />
|-<br />
|March 2<br />
|Moisés Herradón Cueto (Wisconsin)<br />
|[[#Moisés Herradón Cueto|Local type of difference equations]]<br />
|Local<br />
|-<br />
|March 9<br />
|Eva Elduque (Wisconsin)<br />
|[[#Eva Elduque|On the signed Euler characteristic property for subvarieties of Abelian varieties]]<br />
|Local<br />
|-<br />
|March 16<br />
|[https://math.berkeley.edu/~chenhi/ Harrison Chen (Berkeley)]<br />
|[[#Harrison Chen|Equivariant localization for periodic cyclic homology and derived loop spaces]]<br />
|Andrei<br />
|-<br />
|March 23<br />
|[http://www-personal.umich.edu/~ptoste/ Phil Tosteson (Michigan)]<br />
|[[#Phil Tosteson|TBA]]<br />
|Steven<br />
|-<br />
|-<br />
|April 6<br />
|Wei Ho<br />
|TBA<br />
|Daniel/Wanlin<br />
|-<br />
|-<br />
|April 13<br />
|Reserved<br />
|<br />
|Daniel<br />
|-<br />
|April 20<br />
|Alena Pirutka (NYU)<br />
|[[#Alena Pirutka|TBA]]<br />
|Jordan<br />
|-<br />
|April 27<br />
|Alexander Yom Din (Caltech) <br />
|[[#Alexander Yom Din|Drinfeld-Gaitsgory functor and contragradient duality for (g,K)-modules]]<br />
|Dima<br />
|-<br />
|May 4<br />
|John Lesieutre (UIC) <br />
|[[#John Lesieutre|TBA]]<br />
|Daniel<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===Tasos Moulinos===<br />
<br />
'''Derived Azumaya Algebras and Twisted K-theory'''<br />
<br />
Topological K-theory of dg-categories is a localizing invariant of dg-categories over <math> \mathbb{C} </math><br />
taking values in the <math> \infty </math>-category of <math> KU </math>-modules. In this talk I describe a relative version<br />
of this construction; namely for <math>X</math> a quasi-compact, quasi-separated <math> \mathbb{C} </math>-scheme I construct a<br />
functor valued in the <math> \infty </math>-category of sheaves of spectra on <math> X(\mathbb{C}) </math>, the complex points of <math>X</math>. For inputs<br />
of the form <math>\operatorname{Perf}(X, A)</math> where <math>A</math> is an Azumaya algebra over <math>X</math>, I characterize the values<br />
of this functor in terms of the twisted topological K-theory of <math> X(\mathbb{C}) </math>. From this I deduce<br />
a certain decomposition, for <math> X </math> a finite CW-complex equipped with a bundle <math> P </math> of projective<br />
spaces over <math> X </math>, of <math> KU(P) </math> in terms of the twisted topological K-theory of <math> X </math> ; this is<br />
a topological analogue of a result of Quillen’s on the algebraic K-theory of Severi-Brauer<br />
schemes.<br />
<br />
===Roman Fedorov===<br />
<br />
'''A conjecture of Grothendieck and Serre on principal bundles in mixed<br />
characteristic'''<br />
<br />
Let G be a reductive group scheme over a regular local ring R. An old<br />
conjecture of Grothendieck and Serre predicts that such a principal<br />
bundle is trivial, if it is trivial over the fraction field of R. The<br />
conjecture has recently been proved in the "geometric" case, that is,<br />
when R contains a field. In the remaining case, the difficulty comes<br />
from the fact, that the situation is more rigid, so that a certain<br />
general position argument does not go through. I will discuss this<br />
difficulty and a way to circumvent it to obtain some partial results.<br />
<br />
===Juliette Bruce===<br />
<br />
'''Asymptotic Syzygies in the Semi-Ample Setting'''<br />
<br />
In recent years numerous conjectures have been made describing the asymptotic Betti numbers of a projective variety as the embedding line bundle becomes more ample. I will discuss recent work attempting to generalize these conjectures to the case when the embedding line bundle becomes more semi-ample. (Recall a line bundle is semi-ample if a sufficiently large multiple is base point free.) In particular, I will discuss how the monomial methods of Ein, Erman, and Lazarsfeld used to prove non-vanishing results on projective space can be extended to prove non-vanishing results for products of projective space.<br />
<br />
===Andrei Caldararu===<br />
<br />
'''Computing a categorical Gromov-Witten invariant'''<br />
<br />
In his 2005 paper "The Gromov-Witten potential associated to a TCFT" Kevin Costello described a procedure for recovering an analogue of the Gromov-Witten potential directly out of a cyclic A-inifinity algebra or category. Applying his construction to the derived category of sheaves of a complex projective variety provides a definition of higher genus B-model Gromov-Witten invariants, independent of the BCOV formalism. This has several advantages. Due to the categorical invariance of these invariants, categorical mirror symmetry automatically implies classical mirror symmetry to all genera. Also, the construction can be applied to other categories like categories of matrix factorization, giving a direct definition of FJRW invariants, for example.<br />
<br />
In my talk I shall describe the details of the computation (joint with Junwu Tu) of the invariant, at g=1, n=1, for elliptic curves. The result agrees with the predictions of mirror symmetry, matching classical calculations of Dijkgraaf. It is the first non-trivial computation of a categorical Gromov-Witten invariant.<br />
<br />
===Aron Heleodoro===<br />
<br />
'''Normally ordered tensor product of Tate objects and decomposition of higher adeles'''<br />
<br />
In this talk I will introduce the different tensor products that exist on Tate objects over vector spaces (or more generally coherent sheaves on a given scheme). As an application, I will explain how these can be used to describe higher adeles on an n-dimensional smooth scheme. Both Tate objects and higher adeles would be introduced in the talk. (This is based on joint work with Braunling, Groechenig and Wolfson.)<br />
<br />
===Moisés Herradón Cueto===<br />
<br />
'''Local type of difference equations'''<br />
<br />
The theory of algebraic differential equations on the affine line is very well-understood. In particular, there is a well-defined notion of restricting a D-module to a formal neighborhood of a point, and these restrictions are completely described by two vector spaces, called vanishing cycles and nearby cycles, and some maps between them. We give an analogous notion of "restriction to a formal disk" for difference equations that satisfies several desirable properties: first of all, a difference module can be recovered uniquely from its restriction to the complement of a point and its restriction to a formal disk around this point. Secondly, it gives rise to a local Mellin transform, which relates vanishing cycles of a difference module to nearby cycles of its Mellin transform. Since the Mellin transform of a difference module is a D-module, the Mellin transform brings us back to the familiar world of D-modules.<br />
<br />
===Eva Elduque===<br />
<br />
'''On the signed Euler characteristic property for subvarieties of Abelian varieties'''<br />
<br />
Franecki and Kapranov proved that the Euler characteristic of a perverse sheaf on a semi-abelian variety is non-negative. This result has several purely topological consequences regarding the sign of the (topological and intersection homology) Euler characteristic of a subvariety of an abelian variety, and it is natural to attempt to justify them by more elementary methods. In this talk, we'll explore the geometric tools used recently in the proof of the signed Euler<br />
characteristic property. Joint work with Christian Geske and Laurentiu Maxim.<br />
<br />
===Harrison Chen===<br />
<br />
'''Equivariant localization for periodic cyclic homology and derived loop spaces'''<br />
<br />
There is a close relationship between derived loop spaces, a geometric object, and (periodic) cyclic homology, a categorical invariant. In this talk we will discuss this relationship and how it leads to an equivariant localization result, which has an intuitive interpretation using the language of derived loop spaces. We discuss ongoing generalizations and potential applications in computing the periodic cyclic homology of categories of equivariant (coherent) sheaves on algebraic varieties.<br />
<br />
===Alexander Yom Din===<br />
<br />
'''Drinfeld-Gaitsgory functor and contragradient duality for (g,K)-modules'''<br />
<br />
Drinfeld suggested the definition of a certain endo-functor, called the pseudo-identity functor (or the Drinfeld-Gaitsgory functor), on the category of D-modules on an algebraic stack. We extend this definition to an arbitrary DG category, and show that if certain finiteness conditions are satisfied, this functor is the inverse of the Serre functor. We show that the pseudo-identity functor for $(\mathfrak{g},K)$-modules is isomorphic to the composition of cohomological and contragredient dualities, which is parallel to an analogous assertion for p-adic groups.<br />
<br />
In this talk I will try to discuss some of these results and around them. This is joint work with Dennis Gaitsgory.</div>Arinkinhttps://www.math.wisc.edu/wiki/index.php?title=Graduate_Algebraic_Geometry_Seminar_Spring_2018&diff=15193Graduate Algebraic Geometry Seminar Spring 20182018-02-27T16:50:45Z<p>Arinkin: /* February 28 */</p>
<hr />
<div>'''<br />
'''When:''' Wednesdays 3:40pm<br />
<br />
'''Where:'''Van Vleck B321 (Spring 2018)<br />
[[Image:cat.jpg|thumb|220px| | Lizzie the OFFICIAL mascot of GAGS!!]]<br />
<br />
'''Who:''' All undergraduate and graduate students interested in algebraic geometry, commutative algebra, and related fields are welcome to attend.<br />
<br />
'''Why:''' The purpose of this seminar is to learn algebraic geometry and commutative algebra by giving and listening to talks in a informal setting. Talks are typically accessible to beginning graduate students and take many different forms. Sometimes people present an interesting paper they find. Other times people give a prep talk for the Friday Algebraic Geometry Seminar. Other times people give a series of talks on a topic they have been studying in-depth. Regardless the goal of GAGS is to provide a supportive and inclusive place for all to learn more about algebraic geometry and commutative algebra.<br />
<br />
'''How:'''If you want to get emails regarding time, place, and talk topics ('''which are often assigned quite last minute''') add yourself to the gags mailing list: gags@lists.wisc.edu. The list registration page is [https://admin.lists.wisc.edu/index.php?p=11&l=gags here].<br />
'''<br />
<br />
== Give a talk! ==<br />
We need volunteers to give talks this semester. If you're interested contact [mailto:juliette.bruce@math.wisc.edu Juliette] or [mailto:moises@math.wisc.edu Moisés], or just add yourself to the list (though in that case we might move your talk later without your permission). Beginning graduate students are particularly encouraged to give a talk, since it's a great way to get your feet wet with the material.<br />
<br />
== Being an audience member ==<br />
The goal of GAGS is to create a safe and comfortable space inclusive of all who wish to expand their knowledge of algebraic geometry and commutative algebra. In order to promote such an environment in addition to the standard expectations of respect/kindness all participants are asked to following the following guidelines:<br />
* Do Not Speak For/Over the Speaker: <br />
* Ask Questions Appropriately: <br />
<br />
<br />
== Wish List ==<br />
Here are the topics we're '''DYING''' to learn about! Please consider looking into one of these topics and giving one or two GAGS talks.<br />
<br />
===Specifically Vague Topics===<br />
* D-modules 101: basics of D-modules, equivalence between left and right D-modules, pullbacks, pushforwards, maybe the Gauss-Manin Connection. Claude Sabbah's introduction to the subject could be a good place to start.<br />
<br />
* Sheaf operations on D-modules (the point is that then you can get a Fourier-Mukai transform between certain O-modules and certain D-modules, which is more or less how geometric Langlands is supposed to work)<br />
<br />
===Famous Theorems===<br />
<br />
===Interesting Papers & Books===<br />
* ''Symplectic structure of the moduli space of sheaves on an abelian or K3 surface'' - Shigeru Mukai.<br />
<br />
* ''Residues and Duality'' - Robin Hatshorne.<br />
** Have you heard of Serre Duality? Would you like to really understand the nuts and bolts of it and its generalizations? If so this book is for you. (You wouldn't need to read the whole book to give a talk ;).)<br />
<br />
* ''Coherent sheaves on P^n and problems in linear algebra'' - A. A. Beilinson.<br />
** In this two page paper constructs the semi-orthogonal decomposition of the derived category of coherent sheaves on projective space. (This topic is very important, and there are a ton of other resources for this result and the general theory of derived categories.)<br />
<br />
* ''Frobenius splitting and cohomology vanishing for Schubert varieties'' - V.B. Mehta and A. Ramanathan.<br />
** In characteristic p the fact that (x+y)^p=x^p+y^p means that one has the Frobenius morphism, which sends f to f^p. In this paper the authors introduce the notion of what it means for a variety to be Frobenius split, and use this to prove certain cohomologcal vanishing results for Schubert varieties. Since then Frobenius splitting -- and its related cousins (F-regularity, strong F-regularity, F-purity, etc.) have played large roles in geometry and algebra in characteristic p. This is a good place to get a sense for what kicked all this stuff off! <br />
<br />
* ''Schubert Calculus'' - S. L. Kleiman and Dan Laksov.<br />
** An introduction to Schubert calculus suitable for those of all ages. I am told the paper essentially only uses linear algebra!<br />
<br />
* ''Rational Isogenies of Prime Degree'' - Barry Mazur.<br />
** In this paper Mazur classifies all isogenies of rational elliptic curves of prime order. As a result of this he deduces his famous result that the torsion subgroup of an elliptic curve (over Q) is one of 15 abelian groups. This definitely stares into the land of number theory, but certainly would still be of interest to many.<br />
<br />
* ''Esquisse d’une programme'' - Alexander Grothendieck.<br />
** Originating from a grant proposal in the mid 1980's this famous paper outlines a tantalizing research program, which seeks to tie numerous different areas of math (algebraic geometry, Teichmuller theory, Galois theory, etc.) together. This is where Grothendieck introduced his famous Lego game and dessin d'enfant. While just a research proposal this paper has seemingly inspired a ton of cool math, and will allow you to "blow peoples’ minds". (The original paper is in French, but there are English translations out there.)<br />
<br />
* ''Géométrie algébraique et géométrie analytique'' - J.P. Serre.<br />
** A projective variety X over the complex numbers has two lives, an algebraic and an analytic, depending on which topology one wishes to work with. That is one can think about X as a complex manifold and work with holomorphic functions or as an algebraic variety and work with regular functions. Hence to any complex projective variety we have two sheaf theories and as a result two cohomology theories. In this famous paper Serre compares these two and shows they are in fact the same. (''Note: This is a super fundamental result that is used all the time; normally in the following way: Uhh... What do you mean by cohomology? Well by GAGA or something it doesn't really mater.) (The original paper is in French, but there are English translations out there.)<br />
<br />
* ''Limit linear series: Basic theory''- David Eisenbud and Joe Harris.<br />
** One of the more profitable tools -- especially when studying moduli spaces -- in a geometers tool box is the theory of degenerations. However, sometimes we care about more than just the variety we are degenerating and want to keep track of things like vector/line bundles. In this paper Eisenbud and Harris develop the theory of degenerating a curve together with a linear series. From this they prove a ton of cool results: M_g is of general type for g>24, Brill-Noether theory, etc.<br />
<br />
* ''Picard Groups of Moduli Problems'' - David Mumford.<br />
** This paper is essentially the origin of algebraic stacks.<br />
<br />
* ''The Structure of Algebraic Threefolds: An Introduction to Mori's Program'' - Janos Kollar<br />
** This paper is an introduction to Mori's famous ``minimal model'' program, which is a far reaching program seeking to understand the birational geometry of higher dimensional varieties. <br />
<br />
* ''Cayley-Bacharach Formulas'' - Qingchun Ren, Jürgen Richter-Gebert, Bernd Sturmfels.<br />
** A classical result we all learn in a first semester of algebraic geometry is that 5 points in the plane (in general position) determine a unique plane conic. One can similarly show that 9 (general) points in the plane determine a unique plane cubic curve. This paper tries to answer the question: ``What is equation for this cubic curve?''.<br />
<br />
* ''On Varieties of Minimal Degree (A Centennial Approach)'' - David Eisenbud and Joe Harris.<br />
** Suppose X is a projective variety embedded in projective space so that X is not contained in any hyperplane. By projecting from general points one can see that the degree of X is at least codim(X)+1. This paper discusses the classification of varieties that achieve this lower degree bound i.e. varieties of minimal degree. This topic is quite classical and the paper seems to contain a nice mixture of classical and modern geometry.<br />
<br />
* ''The Gromov-Witten potential associated to a TCFT'' - Kevin J. Costello.<br />
** This seems incredibly interesting, but fairing warning this paper has been described as ''highly technical'', which considering it uses A-infinity algebras and the derived category of a Calabi-Yau seems like a reasonable description. (This paper may be covered in Caldararu's Spring 2017 topics course.)<br />
__NOTOC__<br />
<br />
== Spring 2017 ==<br />
<br />
<center><br />
{| style="color:black; font-size:120%" border="0" cellpadding="14" cellspacing="5"<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|'''Date'''<br />
| bgcolor="#A6B658" width="300" align="center"|'''Speaker'''<br />
| bgcolor="#BCD2EE" width="300" align="center"|'''Title (click to see abstract)'''<br />
|-<br />
| bgcolor="#E0E0E0"| February 14<br />
| bgcolor="#C6D46E"| Moisés Herradón Cueto<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#February 14| Fun with commutative groups]]<br />
|-<br />
| bgcolor="#E0E0E0"| February 21<br />
| bgcolor="#C6D46E"| Moisés Herradón Cueto<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#February 21| <math>\mathcal F</math>un with commutative groups]]<br />
|-<br />
| bgcolor="#E0E0E0"| February 28<br />
| bgcolor="#C6D46E"| Dima Arinkin<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#February 28| ODEs: algebraic vs analytic vs formal]]<br />
|-<br />
| bgcolor="#E0E0E0"| March 7<br />
| bgcolor="#C6D46E"| Vladimir Sotirov<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#March 7| TBD]]<br />
|-<br />
| bgcolor="#E0E0E0"| March 14<br />
| bgcolor="#C6D46E"| David Wagner<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#March 14| TBD]]<br />
|-<br />
| bgcolor="#E0E0E0"| March 21<br />
| bgcolor="#C6D46E"| TBD<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#March 21| TBD]]<br />
|-<br />
| bgcolor="#E0E0E0"| March 28<br />
| bgcolor="#C6D46E"| Spring break<br />
| bgcolor="#BCE2FE"| Whoo!<br />
|-<br />
| bgcolor="#E0E0E0"| April 4<br />
| bgcolor="#C6D46E"| Rachel Davis<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#April 4| TBD]]<br />
|-<br />
| bgcolor="#E0E0E0"| April 11<br />
| bgcolor="#C6D46E"| Brandon Boggess<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#April 11| TBD]]<br />
|-<br />
| bgcolor="#E0E0E0"| April 18<br />
| bgcolor="#C6D46E"| Soumya Sankar<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#April 18| TBD]]<br />
|-<br />
| bgcolor="#E0E0E0"| April 25<br />
| bgcolor="#C6D46E"| Solly Parenti<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#April 25| TBD]]<br />
|-<br />
| bgcolor="#E0E0E0"| May 2<br />
| bgcolor="#C6D46E"| TBD<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#May 2| TBD]]<br />
|}<br />
</center><br />
<br />
== February 14 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Moisés Herradón Cueto'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Fun with commutative groups<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: <br />
<br />
My goal is to next week talk about Gerard Laumon's preprint ''Transformation de Fourier généralisée'', which will encapsulate all the Fourier transforms I can name (which for me includes the Fourier transform for D-modules on affine space, the Mellin transform, the Fourier-Mukai transform for abelian varieties and the rare John Mahoney transform between modules on the punctured line and vector spaces with a Z-action) into one crazy package.<br />
<br />
In order to achieve this altered mental state, we will have to rethink all our preconceptions, and rediscover algebraic groups, make sense of Cartier duality for them, define formal groups along the way, and see how duality of Abelian varieties relates to Cartier duality. If you come to the talk in an already in this altered mental state, then hopefully I'll do some examples that you've been too lazy to work out for yourself.<br />
<br />
|} <br />
</center><br />
<br />
== February 21 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''<math>\mathcal F</math>un with commutative groups'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: <math>\mathcal F</math>un with commutative groups<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: <br />
<br />
I will talk about how last week's Cartier duality relates to duality for abelian varieties. Then we will see how this allows us to take certain complexes of groups which are self dual, going back to altered mental states which are now derived.<br />
<br />
If we're going to Fourier transform something, it should be a sheaf, but what is even a sheaf on a complex of groups? Once we see what it should be, I will handwave what the Fourier transform is and give a bunch of concrete examples.<br />
<br />
|} <br />
</center><br />
<br />
== February 28 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Dima Arinkin'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: ODEs: algebraic vs analytic vs formal<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: <br />
<br />
Linear ordinary differential equations (or, as they are known geometrically, bundles with connections on Riemann surfaces) can be studied from many directions. In algebraic geometry, the goal is ''to classify'' equations rather than ''to solve'' them. The classification can be<br />
done in different settings: algebraic, analytic, or formal; each setting has its advantages and disadvantages. However, for one of the most<br />
important class of equations (equations with regular singularities aka Fuchsian equations) the three approaches agree, leading to a rich <br />
and beautiful picture. <br />
<br />
In my talk, I will sketch the algebraic theory of differential equations, focusing on equations with regular singularities. (I do not expect to have time<br />
for irregular singularities.) The talk is related to my topics course on D-modules, but it does not rely on the topics course.<br />
|} <br />
</center><br />
<br />
== March 7 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''TBD'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: TBD<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: <br />
<br />
TBD<br />
<br />
|} <br />
</center><br />
<br />
== March 14 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''TBD'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: TBD<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: <br />
<br />
TBD<br />
<br />
|} <br />
</center><br />
<br />
== March 21 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''TBD'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: TBD<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: <br />
<br />
TBD<br />
<br />
|} <br />
</center><br />
<br />
== April 4 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''TBD'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: TBD<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: <br />
<br />
TBD<br />
<br />
|} <br />
</center><br />
<br />
== April 11 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''TBD'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: TBD<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: <br />
<br />
TBD<br />
<br />
|} <br />
</center><br />
<br />
== April 18 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''TBD'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: TBD<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: <br />
<br />
TBD<br />
<br />
|} <br />
</center><br />
<br />
== April 25 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''TBD'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: TBD<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: <br />
<br />
TBD<br />
<br />
|} <br />
</center><br />
<br />
== May 2 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''TBD'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: TBD<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: <br />
<br />
TBD<br />
<br />
|} <br />
</center><br />
<br />
<br />
== Organizers' Contact Info ==<br />
[http://www.math.wisc.edu/~juliettebruce Juliette Bruce]<br />
<br />
[http://www.math.wisc.edu/~clement Nathan Clement]<br />
<br />
[https://www.math.wisc.edu/~moises Moisés Herradón Cueto]<br />
<br />
== Past Semesters ==<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2017 Fall 2017]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2017 Spring 2017]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2016 Fall 2016]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2016 Spring 2016]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_(Fall_2015) Fall 2015]</div>Arinkinhttps://www.math.wisc.edu/wiki/index.php?title=Graduate_Algebraic_Geometry_Seminar_Spring_2018&diff=15192Graduate Algebraic Geometry Seminar Spring 20182018-02-27T16:34:45Z<p>Arinkin: /* Spring 2017 */</p>
<hr />
<div>'''<br />
'''When:''' Wednesdays 3:40pm<br />
<br />
'''Where:'''Van Vleck B321 (Spring 2018)<br />
[[Image:cat.jpg|thumb|220px| | Lizzie the OFFICIAL mascot of GAGS!!]]<br />
<br />
'''Who:''' All undergraduate and graduate students interested in algebraic geometry, commutative algebra, and related fields are welcome to attend.<br />
<br />
'''Why:''' The purpose of this seminar is to learn algebraic geometry and commutative algebra by giving and listening to talks in a informal setting. Talks are typically accessible to beginning graduate students and take many different forms. Sometimes people present an interesting paper they find. Other times people give a prep talk for the Friday Algebraic Geometry Seminar. Other times people give a series of talks on a topic they have been studying in-depth. Regardless the goal of GAGS is to provide a supportive and inclusive place for all to learn more about algebraic geometry and commutative algebra.<br />
<br />
'''How:'''If you want to get emails regarding time, place, and talk topics ('''which are often assigned quite last minute''') add yourself to the gags mailing list: gags@lists.wisc.edu. The list registration page is [https://admin.lists.wisc.edu/index.php?p=11&l=gags here].<br />
'''<br />
<br />
== Give a talk! ==<br />
We need volunteers to give talks this semester. If you're interested contact [mailto:juliette.bruce@math.wisc.edu Juliette] or [mailto:moises@math.wisc.edu Moisés], or just add yourself to the list (though in that case we might move your talk later without your permission). Beginning graduate students are particularly encouraged to give a talk, since it's a great way to get your feet wet with the material.<br />
<br />
== Being an audience member ==<br />
The goal of GAGS is to create a safe and comfortable space inclusive of all who wish to expand their knowledge of algebraic geometry and commutative algebra. In order to promote such an environment in addition to the standard expectations of respect/kindness all participants are asked to following the following guidelines:<br />
* Do Not Speak For/Over the Speaker: <br />
* Ask Questions Appropriately: <br />
<br />
<br />
== Wish List ==<br />
Here are the topics we're '''DYING''' to learn about! Please consider looking into one of these topics and giving one or two GAGS talks.<br />
<br />
===Specifically Vague Topics===<br />
* D-modules 101: basics of D-modules, equivalence between left and right D-modules, pullbacks, pushforwards, maybe the Gauss-Manin Connection. Claude Sabbah's introduction to the subject could be a good place to start.<br />
<br />
* Sheaf operations on D-modules (the point is that then you can get a Fourier-Mukai transform between certain O-modules and certain D-modules, which is more or less how geometric Langlands is supposed to work)<br />
<br />
===Famous Theorems===<br />
<br />
===Interesting Papers & Books===<br />
* ''Symplectic structure of the moduli space of sheaves on an abelian or K3 surface'' - Shigeru Mukai.<br />
<br />
* ''Residues and Duality'' - Robin Hatshorne.<br />
** Have you heard of Serre Duality? Would you like to really understand the nuts and bolts of it and its generalizations? If so this book is for you. (You wouldn't need to read the whole book to give a talk ;).)<br />
<br />
* ''Coherent sheaves on P^n and problems in linear algebra'' - A. A. Beilinson.<br />
** In this two page paper constructs the semi-orthogonal decomposition of the derived category of coherent sheaves on projective space. (This topic is very important, and there are a ton of other resources for this result and the general theory of derived categories.)<br />
<br />
* ''Frobenius splitting and cohomology vanishing for Schubert varieties'' - V.B. Mehta and A. Ramanathan.<br />
** In characteristic p the fact that (x+y)^p=x^p+y^p means that one has the Frobenius morphism, which sends f to f^p. In this paper the authors introduce the notion of what it means for a variety to be Frobenius split, and use this to prove certain cohomologcal vanishing results for Schubert varieties. Since then Frobenius splitting -- and its related cousins (F-regularity, strong F-regularity, F-purity, etc.) have played large roles in geometry and algebra in characteristic p. This is a good place to get a sense for what kicked all this stuff off! <br />
<br />
* ''Schubert Calculus'' - S. L. Kleiman and Dan Laksov.<br />
** An introduction to Schubert calculus suitable for those of all ages. I am told the paper essentially only uses linear algebra!<br />
<br />
* ''Rational Isogenies of Prime Degree'' - Barry Mazur.<br />
** In this paper Mazur classifies all isogenies of rational elliptic curves of prime order. As a result of this he deduces his famous result that the torsion subgroup of an elliptic curve (over Q) is one of 15 abelian groups. This definitely stares into the land of number theory, but certainly would still be of interest to many.<br />
<br />
* ''Esquisse d’une programme'' - Alexander Grothendieck.<br />
** Originating from a grant proposal in the mid 1980's this famous paper outlines a tantalizing research program, which seeks to tie numerous different areas of math (algebraic geometry, Teichmuller theory, Galois theory, etc.) together. This is where Grothendieck introduced his famous Lego game and dessin d'enfant. While just a research proposal this paper has seemingly inspired a ton of cool math, and will allow you to "blow peoples’ minds". (The original paper is in French, but there are English translations out there.)<br />
<br />
* ''Géométrie algébraique et géométrie analytique'' - J.P. Serre.<br />
** A projective variety X over the complex numbers has two lives, an algebraic and an analytic, depending on which topology one wishes to work with. That is one can think about X as a complex manifold and work with holomorphic functions or as an algebraic variety and work with regular functions. Hence to any complex projective variety we have two sheaf theories and as a result two cohomology theories. In this famous paper Serre compares these two and shows they are in fact the same. (''Note: This is a super fundamental result that is used all the time; normally in the following way: Uhh... What do you mean by cohomology? Well by GAGA or something it doesn't really mater.) (The original paper is in French, but there are English translations out there.)<br />
<br />
* ''Limit linear series: Basic theory''- David Eisenbud and Joe Harris.<br />
** One of the more profitable tools -- especially when studying moduli spaces -- in a geometers tool box is the theory of degenerations. However, sometimes we care about more than just the variety we are degenerating and want to keep track of things like vector/line bundles. In this paper Eisenbud and Harris develop the theory of degenerating a curve together with a linear series. From this they prove a ton of cool results: M_g is of general type for g>24, Brill-Noether theory, etc.<br />
<br />
* ''Picard Groups of Moduli Problems'' - David Mumford.<br />
** This paper is essentially the origin of algebraic stacks.<br />
<br />
* ''The Structure of Algebraic Threefolds: An Introduction to Mori's Program'' - Janos Kollar<br />
** This paper is an introduction to Mori's famous ``minimal model'' program, which is a far reaching program seeking to understand the birational geometry of higher dimensional varieties. <br />
<br />
* ''Cayley-Bacharach Formulas'' - Qingchun Ren, Jürgen Richter-Gebert, Bernd Sturmfels.<br />
** A classical result we all learn in a first semester of algebraic geometry is that 5 points in the plane (in general position) determine a unique plane conic. One can similarly show that 9 (general) points in the plane determine a unique plane cubic curve. This paper tries to answer the question: ``What is equation for this cubic curve?''.<br />
<br />
* ''On Varieties of Minimal Degree (A Centennial Approach)'' - David Eisenbud and Joe Harris.<br />
** Suppose X is a projective variety embedded in projective space so that X is not contained in any hyperplane. By projecting from general points one can see that the degree of X is at least codim(X)+1. This paper discusses the classification of varieties that achieve this lower degree bound i.e. varieties of minimal degree. This topic is quite classical and the paper seems to contain a nice mixture of classical and modern geometry.<br />
<br />
* ''The Gromov-Witten potential associated to a TCFT'' - Kevin J. Costello.<br />
** This seems incredibly interesting, but fairing warning this paper has been described as ''highly technical'', which considering it uses A-infinity algebras and the derived category of a Calabi-Yau seems like a reasonable description. (This paper may be covered in Caldararu's Spring 2017 topics course.)<br />
__NOTOC__<br />
<br />
== Spring 2017 ==<br />
<br />
<center><br />
{| style="color:black; font-size:120%" border="0" cellpadding="14" cellspacing="5"<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|'''Date'''<br />
| bgcolor="#A6B658" width="300" align="center"|'''Speaker'''<br />
| bgcolor="#BCD2EE" width="300" align="center"|'''Title (click to see abstract)'''<br />
|-<br />
| bgcolor="#E0E0E0"| February 14<br />
| bgcolor="#C6D46E"| Moisés Herradón Cueto<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#February 14| Fun with commutative groups]]<br />
|-<br />
| bgcolor="#E0E0E0"| February 21<br />
| bgcolor="#C6D46E"| Moisés Herradón Cueto<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#February 21| <math>\mathcal F</math>un with commutative groups]]<br />
|-<br />
| bgcolor="#E0E0E0"| February 28<br />
| bgcolor="#C6D46E"| Dima Arinkin<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#February 28| ODEs: algebraic vs analytic vs formal]]<br />
|-<br />
| bgcolor="#E0E0E0"| March 7<br />
| bgcolor="#C6D46E"| Vladimir Sotirov<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#March 7| TBD]]<br />
|-<br />
| bgcolor="#E0E0E0"| March 14<br />
| bgcolor="#C6D46E"| David Wagner<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#March 14| TBD]]<br />
|-<br />
| bgcolor="#E0E0E0"| March 21<br />
| bgcolor="#C6D46E"| TBD<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#March 21| TBD]]<br />
|-<br />
| bgcolor="#E0E0E0"| March 28<br />
| bgcolor="#C6D46E"| Spring break<br />
| bgcolor="#BCE2FE"| Whoo!<br />
|-<br />
| bgcolor="#E0E0E0"| April 4<br />
| bgcolor="#C6D46E"| Rachel Davis<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#April 4| TBD]]<br />
|-<br />
| bgcolor="#E0E0E0"| April 11<br />
| bgcolor="#C6D46E"| Brandon Boggess<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#April 11| TBD]]<br />
|-<br />
| bgcolor="#E0E0E0"| April 18<br />
| bgcolor="#C6D46E"| Soumya Sankar<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#April 18| TBD]]<br />
|-<br />
| bgcolor="#E0E0E0"| April 25<br />
| bgcolor="#C6D46E"| Solly Parenti<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#April 25| TBD]]<br />
|-<br />
| bgcolor="#E0E0E0"| May 2<br />
| bgcolor="#C6D46E"| TBD<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#May 2| TBD]]<br />
|}<br />
</center><br />
<br />
== February 14 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Moisés Herradón Cueto'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Fun with commutative groups<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: <br />
<br />
My goal is to next week talk about Gerard Laumon's preprint ''Transformation de Fourier généralisée'', which will encapsulate all the Fourier transforms I can name (which for me includes the Fourier transform for D-modules on affine space, the Mellin transform, the Fourier-Mukai transform for abelian varieties and the rare John Mahoney transform between modules on the punctured line and vector spaces with a Z-action) into one crazy package.<br />
<br />
In order to achieve this altered mental state, we will have to rethink all our preconceptions, and rediscover algebraic groups, make sense of Cartier duality for them, define formal groups along the way, and see how duality of Abelian varieties relates to Cartier duality. If you come to the talk in an already in this altered mental state, then hopefully I'll do some examples that you've been too lazy to work out for yourself.<br />
<br />
|} <br />
</center><br />
<br />
== February 21 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''<math>\mathcal F</math>un with commutative groups'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: <math>\mathcal F</math>un with commutative groups<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: <br />
<br />
I will talk about how last week's Cartier duality relates to duality for abelian varieties. Then we will see how this allows us to take certain complexes of groups which are self dual, going back to altered mental states which are now derived.<br />
<br />
If we're going to Fourier transform something, it should be a sheaf, but what is even a sheaf on a complex of groups? Once we see what it should be, I will handwave what the Fourier transform is and give a bunch of concrete examples.<br />
<br />
|} <br />
</center><br />
<br />
== February 28 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''TBD'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: TBD<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: <br />
<br />
TBD<br />
<br />
|} <br />
</center><br />
<br />
== March 7 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''TBD'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: TBD<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: <br />
<br />
TBD<br />
<br />
|} <br />
</center><br />
<br />
== March 14 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''TBD'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: TBD<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: <br />
<br />
TBD<br />
<br />
|} <br />
</center><br />
<br />
== March 21 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''TBD'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: TBD<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: <br />
<br />
TBD<br />
<br />
|} <br />
</center><br />
<br />
== April 4 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''TBD'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: TBD<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: <br />
<br />
TBD<br />
<br />
|} <br />
</center><br />
<br />
== April 11 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''TBD'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: TBD<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: <br />
<br />
TBD<br />
<br />
|} <br />
</center><br />
<br />
== April 18 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''TBD'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: TBD<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: <br />
<br />
TBD<br />
<br />
|} <br />
</center><br />
<br />
== April 25 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''TBD'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: TBD<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: <br />
<br />
TBD<br />
<br />
|} <br />
</center><br />
<br />
== May 2 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''TBD'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: TBD<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: <br />
<br />
TBD<br />
<br />
|} <br />
</center><br />
<br />
<br />
== Organizers' Contact Info ==<br />
[http://www.math.wisc.edu/~juliettebruce Juliette Bruce]<br />
<br />
[http://www.math.wisc.edu/~clement Nathan Clement]<br />
<br />
[https://www.math.wisc.edu/~moises Moisés Herradón Cueto]<br />
<br />
== Past Semesters ==<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2017 Fall 2017]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2017 Spring 2017]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2016 Fall 2016]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2016 Spring 2016]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_(Fall_2015) Fall 2015]</div>Arinkinhttps://www.math.wisc.edu/wiki/index.php?title=Algebra_and_Algebraic_Geometry_Seminar_Spring_2018&diff=15141Algebra and Algebraic Geometry Seminar Spring 20182018-02-16T20:24:14Z<p>Arinkin: </p>
<hr />
<div>The seminar meets on Fridays at 2:25 pm in room B113.<br />
<br />
Here is the schedule for [[Algebraic Geometry Seminar Spring 2017 | the previous semester]].<br />
<!--, [[Algebraic Geometry Seminar Spring 2018 | the next semester]], and for [[Algebraic Geometry Seminar | this semester]]. --><br />
<br />
==Algebra and Algebraic Geometry Mailing List==<br />
<br />
<br />
*Please join the [https://admin.lists.wisc.edu/index.php?p=11&l=ags AGS Mailing List] to hear about upcoming seminars, lunches, and other algebraic geometry events in the department (it is possible you must be on a math department computer to use this link).<br />
<br />
== Spring 2018 Schedule ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s) <br />
<br />
|-<br />
|January 26<br />
|[http://homepages.math.uic.edu/~tmoulinos/ Tasos Moulinos (UIC)] <br />
|[[#Tasos Moulinos|Derived Azumaya Algebras and Twisted K-theory]]<br />
|Michael<br />
|-<br />
|February 2<br />
|Daniel Erman (Wisconsin) <br />
|[[#Daniel Erman|TBA]]<br />
|Local<br />
|-<br />
|'''February 8''' 2:30-3:30 in VV B113<br />
|[http://www.mathematics.pitt.edu/person/roman-fedorov/ Roman Fedorov (University of Pittsburgh)]<br />
|[[#Roman Fedorov|A conjecture of Grothendieck and Serre on principal bundles in mixed characteristic]]<br />
|Dima<br />
|-<br />
|February 9<br />
|Juliette Bruce (Wisconsin) <br />
|[[#Juliette Bruce|Asymptotic Syzygies in the Semi-Ample Setting ]]<br />
|Local<br />
|-<br />
|February 16<br />
|[http://www.math.wisc.edu/~andreic/ Andrei Caldararu (Wisconsin)]<br />
|[[#Andrei Caldararu|Computing a categorical Gromov-Witten invariant]]<br />
|Local<br />
|-<br />
|February 23<br />
|Aron Heleodoro (Northwestern) <br />
|[[#Aron Heleodoro|Normally ordered tensor product of Tate objects and decomposition of higher adeles]]<br />
|Dima<br />
|-<br />
|March 2<br />
|Moisés Herradón Cueto (Wisconsin)<br />
|[[#Moisés Herradón Cueto|TBA]]<br />
|Local<br />
|-<br />
|March 9<br />
|Eva Elduque (Wisconsin)<br />
|[[#Eva Elduque|On the signed Euler characteristic property for subvarieties of Abelian varieties]]<br />
|Local<br />
|-<br />
|March 16<br />
|[https://math.berkeley.edu/~chenhi/ Harrison Chen (Berkeley)]<br />
|[[#Harrison Chen|Equivariant localization for periodic cyclic homology and derived loop spaces]]<br />
|Andrei<br />
|-<br />
|March 23<br />
|[http://www-personal.umich.edu/~ptoste/ Phil Tosteson (Michigan)]<br />
|[[#Phil Tosteson|TBA]]<br />
|Steven<br />
|-<br />
|-<br />
|April 6<br />
|Jay Yang<br />
|TBA<br />
|Local<br />
|-<br />
|-<br />
|April 13<br />
|Reserved<br />
|<br />
|Daniel<br />
|-<br />
|April 20<br />
|Alena Pirutka (NYU)<br />
|[[#Alena Pirutka|TBA]]<br />
|Jordan<br />
|-<br />
|April 27<br />
|Alexander Yom Din (Caltech) <br />
|[[#Alexander Yom Din|TBA]]<br />
|Dima<br />
|-<br />
|May 4<br />
|John Lesieutre (UIC) <br />
|[[#John Lesieutre|TBA]]<br />
|Daniel<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===Tasos Moulinos===<br />
<br />
'''Derived Azumaya Algebras and Twisted K-theory'''<br />
<br />
Topological K-theory of dg-categories is a localizing invariant of dg-categories over <math> \mathbb{C} </math><br />
taking values in the <math> \infty </math>-category of <math> KU </math>-modules. In this talk I describe a relative version<br />
of this construction; namely for <math>X</math> a quasi-compact, quasi-separated <math> \mathbb{C} </math>-scheme I construct a<br />
functor valued in the <math> \infty </math>-category of sheaves of spectra on <math> X(\mathbb{C}) </math>, the complex points of <math>X</math>. For inputs<br />
of the form <math>\operatorname{Perf}(X, A)</math> where <math>A</math> is an Azumaya algebra over <math>X</math>, I characterize the values<br />
of this functor in terms of the twisted topological K-theory of <math> X(\mathbb{C}) </math>. From this I deduce<br />
a certain decomposition, for <math> X </math> a finite CW-complex equipped with a bundle <math> P </math> of projective<br />
spaces over <math> X </math>, of <math> KU(P) </math> in terms of the twisted topological K-theory of <math> X </math> ; this is<br />
a topological analogue of a result of Quillen’s on the algebraic K-theory of Severi-Brauer<br />
schemes.<br />
<br />
===Roman Fedorov===<br />
<br />
'''A conjecture of Grothendieck and Serre on principal bundles in mixed<br />
characteristic'''<br />
<br />
Let G be a reductive group scheme over a regular local ring R. An old<br />
conjecture of Grothendieck and Serre predicts that such a principal<br />
bundle is trivial, if it is trivial over the fraction field of R. The<br />
conjecture has recently been proved in the "geometric" case, that is,<br />
when R contains a field. In the remaining case, the difficulty comes<br />
from the fact, that the situation is more rigid, so that a certain<br />
general position argument does not go through. I will discuss this<br />
difficulty and a way to circumvent it to obtain some partial results.<br />
<br />
===Juliette Bruce===<br />
<br />
'''Asymptotic Syzygies in the Semi-Ample Setting'''<br />
<br />
In recent years numerous conjectures have been made describing the asymptotic Betti numbers of a projective variety as the embedding line bundle becomes more ample. I will discuss recent work attempting to generalize these conjectures to the case when the embedding line bundle becomes more semi-ample. (Recall a line bundle is semi-ample if a sufficiently large multiple is base point free.) In particular, I will discuss how the monomial methods of Ein, Erman, and Lazarsfeld used to prove non-vanishing results on projective space can be extended to prove non-vanishing results for products of projective space.<br />
<br />
===Andrei Caldararu===<br />
<br />
'''Computing a categorical Gromov-Witten invariant'''<br />
<br />
In his 2005 paper "The Gromov-Witten potential associated to a TCFT" Kevin Costello described a procedure for recovering an analogue of the Gromov-Witten potential directly out of a cyclic A-inifinity algebra or category. Applying his construction to the derived category of sheaves of a complex projective variety provides a definition of higher genus B-model Gromov-Witten invariants, independent of the BCOV formalism. This has several advantages. Due to the categorical invariance of these invariants, categorical mirror symmetry automatically implies classical mirror symmetry to all genera. Also, the construction can be applied to other categories like categories of matrix factorization, giving a direct definition of FJRW invariants, for example.<br />
<br />
In my talk I shall describe the details of the computation (joint with Junwu Tu) of the invariant, at g=1, n=1, for elliptic curves. The result agrees with the predictions of mirror symmetry, matching classical calculations of Dijkgraaf. It is the first non-trivial computation of a categorical Gromov-Witten invariant.<br />
<br />
===Aron Heleodoro===<br />
<br />
'''Normally ordered tensor product of Tate objects and decomposition of higher adeles'''<br />
<br />
In this talk I will introduce the different tensor products that exist on Tate objects over vector spaces (or more generally coherent sheaves on a given scheme). As an application, I will explain how these can be used to describe higher adeles on an n-dimensional smooth scheme. Both Tate objects and higher adeles would be introduced in the talk. (This is based on joint work with Braunling, Groechenig and Wolfson.)<br />
<br />
===Harrison Chen===<br />
<br />
'''Equivariant localization for periodic cyclic homology and derived loop spaces'''<br />
<br />
There is a close relationship between derived loop spaces, a geometric object, and (periodic) cyclic homology, a categorical invariant. In this talk we will discuss this relationship and how it leads to an equivariant localization result, which has an intuitive interpretation using the language of derived loop spaces. We discuss ongoing generalizations and potential applications in computing the periodic cyclic homology of categories of equivariant (coherent) sheaves on algebraic varieties.<br />
<br />
===Alexander Yom Din===<br />
<br />
'''TBA'''</div>Arinkinhttps://www.math.wisc.edu/wiki/index.php?title=Algebra_and_Algebraic_Geometry_Seminar_Spring_2018&diff=14916Algebra and Algebraic Geometry Seminar Spring 20182018-01-29T22:02:11Z<p>Arinkin: /* Spring 2018 Schedule */</p>
<hr />
<div>The seminar meets on Fridays at 2:25 pm in room B113.<br />
<br />
Here is the schedule for [[Algebraic Geometry Seminar Spring 2017 | the previous semester]].<br />
<!--, [[Algebraic Geometry Seminar Spring 2018 | the next semester]], and for [[Algebraic Geometry Seminar | this semester]]. --><br />
<br />
==Algebra and Algebraic Geometry Mailing List==<br />
<br />
<br />
*Please join the [https://admin.lists.wisc.edu/index.php?p=11&l=ags AGS Mailing List] to hear about upcoming seminars, lunches, and other algebraic geometry events in the department (it is possible you must be on a math department computer to use this link).<br />
<br />
== Spring 2018 Schedule ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s) <br />
<br />
|-<br />
|January 26<br />
|[http://homepages.math.uic.edu/~tmoulinos/ Tasos Moulinos (UIC)] <br />
|[[#Tasos Moulinos|Derived Azumaya Algebras and Twisted K-theory]]<br />
|Michael<br />
|-<br />
|February 2<br />
|Daniel Erman (Wisconsin) <br />
|[[#Daniel Erman|TBA]]<br />
|Local<br />
|-<br />
|'''February 8''' 2:30-3:30 in VV B113<br />
|[http://www.mathematics.pitt.edu/person/roman-fedorov/ Roman Fedorov (University of Pittsburgh)]<br />
|[[#Roman Fedorov|A conjecture of Grothendieck and Serre on principal bundles in mixed characteristic]]<br />
|Dima<br />
|-<br />
|February 9<br />
|Juliette Bruce (Wisconsin) <br />
|[[#Juliette Bruce|TBA]]<br />
|Local<br />
|-<br />
|February 16<br />
|[http://www.math.wisc.edu/~andreic/ Andrei Caldararu (Wisconsin)]<br />
|[[#Andrei Caldararu|Computing a categorical Gromov-Witten invariant]]<br />
|Local<br />
|-<br />
|February 23<br />
|Aron Heleodoro (Northwestern) <br />
|[[#Aron Heleodoro|TBA]]<br />
|Dima<br />
|-<br />
|March 2<br />
|Moisés Herradón Cueto (Wisconsin)<br />
|[[#Moisés Herradón Cueto|TBA]]<br />
|Local<br />
|-<br />
|April 6<br />
|[http://www-personal.umich.edu/~ptoste/ Phil Tosteson (Michigan)]<br />
|[[#Phil Tosteson|TBA]]<br />
|Steven<br />
|-<br />
|-<br />
|April 13<br />
|Reserved<br />
|<br />
|Daniel<br />
|-<br />
|April 20<br />
|Alena Pirutka (NYU)<br />
|[[#Alena Pirutka|TBA]]<br />
|Jordan<br />
|-<br />
|April 27<br />
|Alexander Yom Din (Caltech) <br />
|[[#Alexander Yom Din|TBA]]<br />
|Dima<br />
|-<br />
|May 4<br />
|John Lesieutre (UIC) <br />
|[[#John Lesieutre|TBA]]<br />
|Daniel<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===Tasos Moulinos===<br />
<br />
'''Derived Azumaya Algebras and Twisted K-theory'''<br />
<br />
Topological K-theory of dg-categories is a localizing invariant of dg-categories over <math> \mathbb{C} </math><br />
taking values in the <math> \infty </math>-category of <math> KU </math>-modules. In this talk I describe a relative version<br />
of this construction; namely for <math>X</math> a quasi-compact, quasi-separated <math> \mathbb{C} </math>-scheme I construct a<br />
functor valued in the <math> \infty </math>-category of sheaves of spectra on <math> X(\mathbb{C}) </math>, the complex points of <math>X</math>. For inputs<br />
of the form <math>\operatorname{Perf}(X, A)</math> where <math>A</math> is an Azumaya algebra over <math>X</math>, I characterize the values<br />
of this functor in terms of the twisted topological K-theory of <math> X(\mathbb{C}) </math>. From this I deduce<br />
a certain decomposition, for <math> X </math> a finite CW-complex equipped with a bundle <math> P </math> of projective<br />
spaces over <math> X </math>, of <math> KU(P) </math> in terms of the twisted topological K-theory of <math> X </math> ; this is<br />
a topological analogue of a result of Quillen’s on the algebraic K-theory of Severi-Brauer<br />
schemes.<br />
<br />
===Roman Fedorov===<br />
<br />
'''A conjecture of Grothendieck and Serre on principal bundles in mixed<br />
characteristic'''<br />
<br />
Let G be a reductive group scheme over a regular local ring R. An old<br />
conjecture of Grothendieck and Serre predicts that such a principal<br />
bundle is trivial, if it is trivial over the fraction field of R. The<br />
conjecture has recently been proved in the "geometric" case, that is,<br />
when R contains a field. In the remaining case, the difficulty comes<br />
from the fact, that the situation is more rigid, so that a certain<br />
general position argument does not go through. I will discuss this<br />
difficulty and a way to circumvent it to obtain some partial results.<br />
<br />
===Andrei Caldararu===<br />
<br />
'''Computing a categorical Gromov-Witten invariant'''<br />
<br />
In his 2005 paper "The Gromov-Witten potential associated to a TCFT" Kevin Costello described a procedure for recovering an analogue of the Gromov-Witten potential directly out of a cyclic A-inifinity algebra or category. Applying his construction to the derived category of sheaves of a complex projective variety provides a definition of higher genus B-model Gromov-Witten invariants, independent of the BCOV formalism. This has several advantages. Due to the categorical invariance of these invariants, categorical mirror symmetry automatically implies classical mirror symmetry to all genera. Also, the construction can be applied to other categories like categories of matrix factorization, giving a direct definition of FJRW invariants, for example.<br />
<br />
In my talk I shall describe the details of the computation (joint with Junwu Tu) of the invariant, at g=1, n=1, for elliptic curves. The result agrees with the predictions of mirror symmetry, matching classical calculations of Dijkgraaf. It is the first non-trivial computation of a categorical Gromov-Witten invariant.<br />
<br />
===Aron Heleodoro===<br />
<br />
'''TBA'''<br />
<br />
===Alexander Yom Din===<br />
<br />
'''TBA'''</div>Arinkinhttps://www.math.wisc.edu/wiki/index.php?title=Algebra_and_Algebraic_Geometry_Seminar_Spring_2018&diff=14915Algebra and Algebraic Geometry Seminar Spring 20182018-01-29T21:59:37Z<p>Arinkin: </p>
<hr />
<div>The seminar meets on Fridays at 2:25 pm in room B113.<br />
<br />
Here is the schedule for [[Algebraic Geometry Seminar Spring 2017 | the previous semester]].<br />
<!--, [[Algebraic Geometry Seminar Spring 2018 | the next semester]], and for [[Algebraic Geometry Seminar | this semester]]. --><br />
<br />
==Algebra and Algebraic Geometry Mailing List==<br />
<br />
<br />
*Please join the [https://admin.lists.wisc.edu/index.php?p=11&l=ags AGS Mailing List] to hear about upcoming seminars, lunches, and other algebraic geometry events in the department (it is possible you must be on a math department computer to use this link).<br />
<br />
== Spring 2018 Schedule ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s) <br />
<br />
|-<br />
|January 26<br />
|[http://homepages.math.uic.edu/~tmoulinos/ Tasos Moulinos (UIC)] <br />
|[[#Tasos Moulinos|Derived Azumaya Algebras and Twisted K-theory]]<br />
|Michael<br />
|-<br />
|February 2<br />
|Daniel Erman (Wisconsin) <br />
|[[#Daniel Erman|TBA]]<br />
|Local<br />
|-<br />
|February 8 ('''unusual date!''' 2:30-3:30 in VV B113)<br />
|[http://www.mathematics.pitt.edu/person/roman-fedorov/ Roman Fedorov (University of Pittsburgh)]<br />
|[[#Roman Fedorov|A conjecture of Grothendieck and Serre on principal bundles in mixed<br />
characteristic]]<br />
|Dima<br />
|-<br />
|February 9<br />
|Juliette Bruce (Wisconsin) <br />
|[[#Juliette Bruce|TBA]]<br />
|Local<br />
|-<br />
|February 16<br />
|[http://www.math.wisc.edu/~andreic/ Andrei Caldararu (Wisconsin)]<br />
|[[#Andrei Caldararu|Computing a categorical Gromov-Witten invariant]]<br />
|Local<br />
|-<br />
|February 23<br />
|Aron Heleodoro (Northwestern) <br />
|[[#Aron Heleodoro|TBA]]<br />
|Dima<br />
|-<br />
|March 2<br />
|Moisés Herradón Cueto (Wisconsin)<br />
|[[#Moisés Herradón Cueto|TBA]]<br />
|Local<br />
|-<br />
|April 6<br />
|[http://www-personal.umich.edu/~ptoste/ Phil Tosteson (Michigan)]<br />
|[[#Phil Tosteson|TBA]]<br />
|Steven<br />
|-<br />
|-<br />
|April 13<br />
|Reserved<br />
|<br />
|Daniel<br />
|-<br />
|April 20<br />
|Alena Pirutka (NYU)<br />
|[[#Alena Pirutka|TBA]]<br />
|Jordan<br />
|-<br />
|April 27<br />
|Alexander Yom Din (Caltech) <br />
|[[#Alexander Yom Din|TBA]]<br />
|Dima<br />
|-<br />
|May 4<br />
|John Lesieutre (UIC) <br />
|[[#John Lesieutre|TBA]]<br />
|Daniel<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===Tasos Moulinos===<br />
<br />
'''Derived Azumaya Algebras and Twisted K-theory'''<br />
<br />
Topological K-theory of dg-categories is a localizing invariant of dg-categories over <math> \mathbb{C} </math><br />
taking values in the <math> \infty </math>-category of <math> KU </math>-modules. In this talk I describe a relative version<br />
of this construction; namely for <math>X</math> a quasi-compact, quasi-separated <math> \mathbb{C} </math>-scheme I construct a<br />
functor valued in the <math> \infty </math>-category of sheaves of spectra on <math> X(\mathbb{C}) </math>, the complex points of <math>X</math>. For inputs<br />
of the form <math>\operatorname{Perf}(X, A)</math> where <math>A</math> is an Azumaya algebra over <math>X</math>, I characterize the values<br />
of this functor in terms of the twisted topological K-theory of <math> X(\mathbb{C}) </math>. From this I deduce<br />
a certain decomposition, for <math> X </math> a finite CW-complex equipped with a bundle <math> P </math> of projective<br />
spaces over <math> X </math>, of <math> KU(P) </math> in terms of the twisted topological K-theory of <math> X </math> ; this is<br />
a topological analogue of a result of Quillen’s on the algebraic K-theory of Severi-Brauer<br />
schemes.<br />
<br />
===Roman Fedorov===<br />
<br />
'''A conjecture of Grothendieck and Serre on principal bundles in mixed<br />
characteristic'''<br />
<br />
Let G be a reductive group scheme over a regular local ring R. An old<br />
conjecture of Grothendieck and Serre predicts that such a principal<br />
bundle is trivial, if it is trivial over the fraction field of R. The<br />
conjecture has recently been proved in the "geometric" case, that is,<br />
when R contains a field. In the remaining case, the difficulty comes<br />
from the fact, that the situation is more rigid, so that a certain<br />
general position argument does not go through. I will discuss this<br />
difficulty and a way to circumvent it to obtain some partial results.<br />
<br />
===Andrei Caldararu===<br />
<br />
'''Computing a categorical Gromov-Witten invariant'''<br />
<br />
In his 2005 paper "The Gromov-Witten potential associated to a TCFT" Kevin Costello described a procedure for recovering an analogue of the Gromov-Witten potential directly out of a cyclic A-inifinity algebra or category. Applying his construction to the derived category of sheaves of a complex projective variety provides a definition of higher genus B-model Gromov-Witten invariants, independent of the BCOV formalism. This has several advantages. Due to the categorical invariance of these invariants, categorical mirror symmetry automatically implies classical mirror symmetry to all genera. Also, the construction can be applied to other categories like categories of matrix factorization, giving a direct definition of FJRW invariants, for example.<br />
<br />
In my talk I shall describe the details of the computation (joint with Junwu Tu) of the invariant, at g=1, n=1, for elliptic curves. The result agrees with the predictions of mirror symmetry, matching classical calculations of Dijkgraaf. It is the first non-trivial computation of a categorical Gromov-Witten invariant.<br />
<br />
===Aron Heleodoro===<br />
<br />
'''TBA'''<br />
<br />
===Alexander Yom Din===<br />
<br />
'''TBA'''</div>Arinkin