# Difference between revisions of "Algebra"

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+ | [[http://www.math.wisc.edu/algrtg/]]http://www.math.wisc.edu/algrtg/ is the RTG homepage. | ||

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== '''Research at UW-Madison in algebra''' == | == '''Research at UW-Madison in algebra''' == | ||

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'''Tenured and tenure-track faculty in algebra''' | '''Tenured and tenure-track faculty in algebra''' | ||

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+ | [http://www.math.wisc.edu/~arinkin/ Dima Arinkin]: (Harvard, 2002) Algebraic geometry, geometric representation theory, especially geometric Langlands conjecture. | ||

[http://pages.cs.wisc.edu/~bach/bach.html Eric Bach:] (Berkeley, 1984) Theoretical computer science, computational number theory, algebraic algorithms, complexity theory, cryptography, six-string automata. (Joint appointment with CS.) | [http://pages.cs.wisc.edu/~bach/bach.html Eric Bach:] (Berkeley, 1984) Theoretical computer science, computational number theory, algebraic algorithms, complexity theory, cryptography, six-string automata. (Joint appointment with CS.) | ||

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[http://www.math.wisc.edu/~andreic/ Andrei Caldararu:] (Cornell, 2000) Algebraic geometry, homological algebra, string theory. | [http://www.math.wisc.edu/~andreic/ Andrei Caldararu:] (Cornell, 2000) Algebraic geometry, homological algebra, string theory. | ||

− | [http://www.math.yale.edu/~td252/ Tullia Dymarz:] (Chicago, 2007 | + | [http://www.math.yale.edu/~td252/ Tullia Dymarz:] (Chicago, 2007) Geometric group theory, quasi-isometric rigidity, large scale geometry of finitely generated groups, solvable groups and quasiconformal analysis. (Also in the geometry/topology group) |

[http://www.math.wisc.edu/~ellenber/ Jordan Ellenberg:] (Harvard, 1998) Arithmetic geometry and algebraic number theory, especially rational points on varieties over global fields. | [http://www.math.wisc.edu/~ellenber/ Jordan Ellenberg:] (Harvard, 1998) Arithmetic geometry and algebraic number theory, especially rational points on varieties over global fields. | ||

− | [http://www.math. | + | [http://www.math.wisc.edu/~derman/ Daniel Erman:] (Berkeley, 2010) Algebraic geometry and commutative algebra |

− | + | [http://www.math.wisc.edu/~shamgar/ Shamgar Gurevich:] (Tel Aviv, 2006) Geometric representation theory, with applications to harmonic analysis, signal processing, mathematical physics, and three-dimensional structuring of molecules. | |

− | + | [http://www.math.wisc.edu/~marshall/ Simon Marshall:] (Princeton, 2010) Analytic number theory (also in the analysis group.) | |

− | [http://www.math.wisc.edu/~ | + | |

+ | [https://www.math.wisc.edu/~maxim/ Laurentiu Maxim:] (Penn, 2005) Topology of algebraic varieties, singularities (also in the geometry/topology group.) | ||

+ | |||

+ | [http://www.math.wisc.edu/~svs/ Steven Sam:] (MIT, 2012) Commutative algebra, invariant theory, algebraic combinatorics | ||

[http://www.math.wisc.edu/~terwilli/ Paul Terwilliger:] (Illinois, 1982) Combinatorics, representation theory and special functions. | [http://www.math.wisc.edu/~terwilli/ Paul Terwilliger:] (Illinois, 1982) Combinatorics, representation theory and special functions. | ||

− | [http://math. | + | [http://www.math.wisc.edu/~mmwood/ Melanie Matchett Wood:] (Princeton, 2009) Number theory and arithmetic geometry. |

[http://www.math.wisc.edu/~thyang/ Tonghai Yang:] (Maryland, 1995) number theory, representation theory, and arithmetic geometry: especially L-functions, Eisenstein series, theta series, Shimura varieties, intersection theory, and elliptic curves. | [http://www.math.wisc.edu/~thyang/ Tonghai Yang:] (Maryland, 1995) number theory, representation theory, and arithmetic geometry: especially L-functions, Eisenstein series, theta series, Shimura varieties, intersection theory, and elliptic curves. | ||

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<!--[http://www.math.wisc.edu/~brownda/ David Brown:] (Berkeley, 2010) Number theory and arithmetic geometry, especially: p-adic cohomology, arithmetic of varieties, stacks, moduli, Galois representations, non-abelian techniques. | <!--[http://www.math.wisc.edu/~brownda/ David Brown:] (Berkeley, 2010) Number theory and arithmetic geometry, especially: p-adic cohomology, arithmetic of varieties, stacks, moduli, Galois representations, non-abelian techniques. | ||

− | [http://www.math.wisc.edu/~cais/ Bryden Cais:] (Michigan, 2007) Algebraic and arithmetic geometry, with a strong number theory bias. | + | [http://www.math.wisc.edu/~cais/ Bryden Cais:] (Michigan, 2007) Algebraic and arithmetic geometry, with a strong number theory bias. |

− | [http://www.math. | + | [http://www.math.wisc.edu/~ballard/ Matthew Ballard:] (U Washington, 2008) Homological mirror symmetry. |

− | Robert Harron: (Princeton, 2009): Algebraic number theory, Iwasawa theory, p-adic Galois representations and automorphic forms. | + | [http://www.math.wisc.edu/~rharron/ Robert Harron:] (Princeton, 2009): Algebraic number theory, Iwasawa theory, p-adic Galois representations and automorphic forms. |

− | Zev Klagsbrun: (UC-Irvine, 2011): Algebraic number theory and arithmetic geometry. | + | [http://www.math.wisc.edu/~klagsbru/ Zev Klagsbrun:] (UC-Irvine, 2011): Algebraic number theory and arithmetic geometry. |

+ | |||

+ | Parker Lowrey: (University of Texas-Austin, 2010) Algebraic geometry and algebraic topology | ||

+ | |||

+ | [http://www.math.wisc.edu/~srostami/ Sean Rostami:] (University of Maryland, 2012): representation theory of algebraic groups, local models of Shimura varieties | ||

+ | |||

+ | [http://www.math.wisc.edu/~josizemore/ Owen Sizemore:] (UCLA, 2012) Operator Algebras, Orbit Equivalence Ergodic Theory, Measure Equivalence Rigidity of Groups | ||

+ | --> | ||

+ | [http://www.math.wisc.edu/~grizzard/ Robert Grizzard:] (U Texas, 2014) Algebraic number theory, diophantine geometry, heights | ||

+ | |||

+ | [https://sites.google.com/a/wisc.edu/alexandra-a-kjuchukova/home Alexandra Kjuchukova:] (Penn, 2015) Topology of algebraic varieties, branched covers | ||

+ | |||

+ | [http://www.math.wisc.edu/~pavlov/ Alexander Pavlov:] (U Toronto, 2015) Commutative algebra, algebraic geometry | ||

+ | |||

+ | [http://www.math.wisc.edu/~ntalebiz Naser T. Sardari:] (Princeton, 2016) Number theory, especially: quadratic forms, automorphic forms, locally symmetric spaces | ||

+ | |||

+ | [http://www.math.wisc.edu/~wang/ Botong Wang:] (Purdue, 2012) Topology of algebraic varieties, topological methods in statistics | ||

+ | |||

+ | John Wiltshire-Gordon: (Michigan, 2016) Algebra, topology and combinatorics, especially: representation theory of categories | ||

− | |||

− | |||

'''Seminars in algebra''' | '''Seminars in algebra''' | ||

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The weekly schedule at UW features many seminars in the algebraic research areas of the faculty. | The weekly schedule at UW features many seminars in the algebraic research areas of the faculty. | ||

− | [https://www.math.wisc.edu/ | + | [https://www.math.wisc.edu/wiki/index.php/Algebraic_Geometry_Seminar Algebraic Geometry Seminar] (Fridays at 2:30) |

+ | |||

+ | [http://uw-aas.tumblr.com Applied Algebra Seminar] (Thursdays 11) | ||

[http://www.math.wisc.edu/~terwilli/combsemsched.html Combinatorics Seminar] (Mondays at 2:25) | [http://www.math.wisc.edu/~terwilli/combsemsched.html Combinatorics Seminar] (Mondays at 2:25) | ||

− | [ | + | Lie Theory Seminar (Mondays at 1:20 in VV901) |

+ | <!-- | ||

+ | [https://www.math.wisc.edu/wiki/index.php/Group_Theory_Seminar Group Theory Seminar (mostly local speakers)] (Tuesdays at 4:00)--> | ||

[http://www.math.wisc.edu/wiki/index.php/NTS Number Theory Seminar (outside speakers)](Thursdays at 2:30) | [http://www.math.wisc.edu/wiki/index.php/NTS Number Theory Seminar (outside speakers)](Thursdays at 2:30) | ||

[http://www.math.wisc.edu/wiki/index.php/NTSGrad Number Theory Seminar (grad student speakers)] (Tuesdays at 2:30) | [http://www.math.wisc.edu/wiki/index.php/NTSGrad Number Theory Seminar (grad student speakers)] (Tuesdays at 2:30) | ||

+ | |||

+ | [http://silo.ece.wisc.edu/web/content/seminars SILO (Systems, Information, Learning and Optimization)] (Wednesdays at 12:30) | ||

+ | |||

+ | |||

'''Upcoming conferences in algebra held at UW''' | '''Upcoming conferences in algebra held at UW''' | ||

− | + | Midwest Algebraic Geometry Conference for Graduate Students -- watch this space! | |

− | |||

'''Previous conferences in algebra held at UW''' | '''Previous conferences in algebra held at UW''' | ||

+ | |||

+ | [http://www.math.wisc.edu/~boston/applalg3.html Applied Algebra Days 3], May 2016 | ||

+ | |||

+ | [http://www.math.wisc.edu/~derman/UMW.html Upper midwest commutative algebra colloquium], November 2015 | ||

+ | |||

+ | [http://www.math.wisc.edu/~maxim/Sing15.html Stratified spaces in geometric and computational topology and physics (Shaneson 70)], March 2015 | ||

+ | |||

+ | [http://www.math.wisc.edu/~boston/applalg2.html Applied Algebra Days 2], May 2014 | ||

+ | |||

+ | [https://sites.google.com/site/gtntd2013/ Group Theory, Number Theory, and Topology Day], January 2013 | ||

+ | |||

+ | [https://sites.google.com/site/mirrorsymmetryinthemidwest/ Mirror Symmetry in the Midwest], November 2012 | ||

+ | |||

+ | [https://sites.google.com/site/uwmagc/ Midwest Algebraic Geometry Graduate Conference], November 2012 | ||

+ | |||

+ | [http://www.math.wisc.edu/~boston/applalg.html Applied Algebra Days], October 2011 | ||

+ | |||

+ | [https://sites.google.com/site/mntcg2011/ Midwest Number Theory Conference for Graduate Students], November 2011 | ||

[http://sites.google.com/site/uwmagc/ RTG Graduate Student Workshop in Algebraic Geometry], October 2010 | [http://sites.google.com/site/uwmagc/ RTG Graduate Student Workshop in Algebraic Geometry], October 2010 | ||

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[http://www.math.wisc.edu/~ellenber/ProPday.html Pro-p groups and pro-p algebras in number theory], April 2007 | [http://www.math.wisc.edu/~ellenber/ProPday.html Pro-p groups and pro-p algebras in number theory], April 2007 | ||

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'''Graduate study at UW-Madison in algebra''' | '''Graduate study at UW-Madison in algebra''' | ||

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The department holds an [http://www.nsf.gov/awardsearch/showAward.do?AwardNumber=0838210&version=noscript NSF-RTG grant in number theory and algebraic geometry], which funds several research assistantships for graduate students (U.S. citizens and permanent residents) working in those areas. | The department holds an [http://www.nsf.gov/awardsearch/showAward.do?AwardNumber=0838210&version=noscript NSF-RTG grant in number theory and algebraic geometry], which funds several research assistantships for graduate students (U.S. citizens and permanent residents) working in those areas. | ||

− | Recent Ph.D. graduates from the group have been very successful on the job market; in the last few years, we have sent alumni to postdoctoral fellowships at Berkeley, Harvard, Imperial (UK), MIT, Princeton, Stanford, University of Cologne(Germany), | + | Recent Ph.D. graduates from the group have been very successful on the job market; in the last few years, we have sent alumni to postdoctoral fellowships at Berkeley, Harvard, Chicago, Michigan, Penn, Imperial (UK), MIT, Princeton, Stanford, University of Cologne(Germany), Max Planck Institut, and UT-Austin, to tenure-track jobs at Oregon, Wake Forest, SUNY-Geneseo, Bogacizi (Turkey), Chennai Mathematical Institute (India), CUNY, the University of Sheffield (UK), the University of Missouri, and the University of South Carolina, and to non-academic positions at places such as Google, Robart GMBH, Microsoft, Credit Suisse and the Center for Communications Research, La Jolla. |

+ | |||

+ | |||

+ | '''Emeritus faculty in algebra''' | ||

+ | |||

+ | Richard Askey | ||

+ | John Bascom Professor, Ph.D Princeton (1961) | ||

+ | Research: Special Functions | ||

+ | |||

+ | Steven Bauman | ||

+ | Professor, University of Illinois at Urbana-Champaign (1962) | ||

+ | Research: Finite group theory | ||

+ | |||

+ | Georgia Benkart | ||

+ | E. B. Van Vleck Professor of Mathematics, Ph.D. Yale University (1974) | ||

+ | Research: Lie Theory, Quantum Groups and Representation Theory. | ||

+ | |||

+ | Michael Bleicher | ||

+ | Professor, Ph.D. Tulane University and University of Warsaw (1961) | ||

+ | Research: Number theory and convex geometry | ||

+ | |||

+ | Richard A. Brualdi | ||

+ | Beckwith Bascom Professor of Mathematics, Ph.D. Syracuse University (1964) | ||

+ | Research: Combinatorics, Graph Theory, Matrix Theory, Coding Theory | ||

+ | |||

+ | Donald Crowe | ||

+ | Professor, Ph.D. University of Michigan (1959) | ||

+ | Research: Classical geometry and African patterns | ||

+ | |||

+ | Hiroshi Gunji | ||

+ | Professor, Ph.D. Johns Hopkins University (1962) | ||

+ | Research: Algebraic geometry | ||

+ | |||

+ | I. Martin Isaacs | ||

+ | Professor, Ph.D. Harvard University (1964) | ||

+ | Research: Group Theory, Algebra | ||

+ | |||

+ | Arnold Johnson | ||

+ | Professor, Ph.D. University of Notre Dame (1965) | ||

+ | Research: Classical Groups | ||

+ | |||

+ | Lawrence Levy | ||

+ | Professor, Ph.D. University of Illinois at Urbana-Champaign (1961) | ||

+ | Research: Commutative and noncommutative ring theory | ||

+ | |||

+ | J. Marshall Osborn | ||

+ | Professor, Ph.D. University of Chicago (1957) | ||

+ | Research: Non-associative rings and Lie algebras | ||

+ | |||

+ | Donald Passman | ||

+ | Richard Brauer Professor of Mathematics, Ph.D. Harvard University (1964) | ||

+ | Research: Associative Rings and Algebras, Group Theory | ||

+ | |||

+ | Hans Schneider | ||

+ | J. J. Sylvester Professor of Mathematics, Ph.D. University of Edinburgh (1952) | ||

+ | Research: Linear algebra and matrix theory | ||

+ | |||

+ | Louis Solomon | ||

+ | Professor, Ph.D. Harvard University (1958) | ||

+ | Research: Finite group theory and hyperplane arrangements | ||

+ | |||

+ | Robert Wilson | ||

+ | Professor, Ph.D. University of Wisconsin-Madison (1969) | ||

+ | Research: Algebra, Math. Education. |

## Revision as of 12:29, 15 September 2016

[[1]]http://www.math.wisc.edu/algrtg/ is the RTG homepage.

**Research at UW-Madison in algebra**

UW-Madison offers a large, active, and varied research group in algebra, including researchers in number theory, combinatorics, group theory, algebraic geometry, representation theory, and algebra with applications to science and engineering.

**Tenured and tenure-track faculty in algebra**

Dima Arinkin: (Harvard, 2002) Algebraic geometry, geometric representation theory, especially geometric Langlands conjecture.

Eric Bach: (Berkeley, 1984) Theoretical computer science, computational number theory, algebraic algorithms, complexity theory, cryptography, six-string automata. (Joint appointment with CS.)

Nigel Boston: (Harvard, 1987) Algebraic number theory, group theory, arithmetic geometry, computational algebra, coding theory, cryptography, and other applications of algebra to electrical engineering. (Joint appointments with ECE and CS.)

Andrei Caldararu: (Cornell, 2000) Algebraic geometry, homological algebra, string theory.

Tullia Dymarz: (Chicago, 2007) Geometric group theory, quasi-isometric rigidity, large scale geometry of finitely generated groups, solvable groups and quasiconformal analysis. (Also in the geometry/topology group)

Jordan Ellenberg: (Harvard, 1998) Arithmetic geometry and algebraic number theory, especially rational points on varieties over global fields.

Daniel Erman: (Berkeley, 2010) Algebraic geometry and commutative algebra

Shamgar Gurevich: (Tel Aviv, 2006) Geometric representation theory, with applications to harmonic analysis, signal processing, mathematical physics, and three-dimensional structuring of molecules.

Simon Marshall: (Princeton, 2010) Analytic number theory (also in the analysis group.)

Laurentiu Maxim: (Penn, 2005) Topology of algebraic varieties, singularities (also in the geometry/topology group.)

Steven Sam: (MIT, 2012) Commutative algebra, invariant theory, algebraic combinatorics

Paul Terwilliger: (Illinois, 1982) Combinatorics, representation theory and special functions.

Melanie Matchett Wood: (Princeton, 2009) Number theory and arithmetic geometry.

Tonghai Yang: (Maryland, 1995) number theory, representation theory, and arithmetic geometry: especially L-functions, Eisenstein series, theta series, Shimura varieties, intersection theory, and elliptic curves.

**Postdoctoral fellows in algebra**

Robert Grizzard: (U Texas, 2014) Algebraic number theory, diophantine geometry, heights

Alexandra Kjuchukova: (Penn, 2015) Topology of algebraic varieties, branched covers

Alexander Pavlov: (U Toronto, 2015) Commutative algebra, algebraic geometry

Naser T. Sardari: (Princeton, 2016) Number theory, especially: quadratic forms, automorphic forms, locally symmetric spaces

Botong Wang: (Purdue, 2012) Topology of algebraic varieties, topological methods in statistics

John Wiltshire-Gordon: (Michigan, 2016) Algebra, topology and combinatorics, especially: representation theory of categories

**Seminars in algebra**

The weekly schedule at UW features many seminars in the algebraic research areas of the faculty.

Algebraic Geometry Seminar (Fridays at 2:30)

Applied Algebra Seminar (Thursdays 11)

Combinatorics Seminar (Mondays at 2:25)

Lie Theory Seminar (Mondays at 1:20 in VV901)

Number Theory Seminar (outside speakers)(Thursdays at 2:30)

Number Theory Seminar (grad student speakers) (Tuesdays at 2:30)

SILO (Systems, Information, Learning and Optimization) (Wednesdays at 12:30)

**Upcoming conferences in algebra held at UW**

Midwest Algebraic Geometry Conference for Graduate Students -- watch this space!

**Previous conferences in algebra held at UW**

Applied Algebra Days 3, May 2016

Upper midwest commutative algebra colloquium, November 2015

Stratified spaces in geometric and computational topology and physics (Shaneson 70), March 2015

Applied Algebra Days 2, May 2014

Group Theory, Number Theory, and Topology Day, January 2013

Mirror Symmetry in the Midwest, November 2012

Midwest Algebraic Geometry Graduate Conference, November 2012

Applied Algebra Days, October 2011

Midwest Number Theory Conference for Graduate Students, November 2011

RTG Graduate Student Workshop in Algebraic Geometry, October 2010

Workshop on Pseudo-Anosovs with Small Dilatation, April 2010

Singularities in the Midwest, March 2010

RTG Midwest Graduate Student Conference in Number Theory, November 2009

Midwest Number Theory Day, November 2009

Miniconference on pro-p groups in number theory, April 2008

Pro-p groups and pro-p algebras in number theory, April 2007

**Graduate study at UW-Madison in algebra**

Algebra is among the most popular specializations for UW Ph.D. students. Regularly offered courses include a four-semester sequence in number theory; a two-semester sequence in algebraic geometry; homological algebra; representation theory; advanced topics in group theory. We also regularly offer more advanced topics courses, which in recent years have included the Gross-Zagier formula, classification of algebraic surfaces, and p-adic Hodge theory. Here is a list of this fall's graduate courses.

The department holds an NSF-RTG grant in number theory and algebraic geometry, which funds several research assistantships for graduate students (U.S. citizens and permanent residents) working in those areas.

Recent Ph.D. graduates from the group have been very successful on the job market; in the last few years, we have sent alumni to postdoctoral fellowships at Berkeley, Harvard, Chicago, Michigan, Penn, Imperial (UK), MIT, Princeton, Stanford, University of Cologne(Germany), Max Planck Institut, and UT-Austin, to tenure-track jobs at Oregon, Wake Forest, SUNY-Geneseo, Bogacizi (Turkey), Chennai Mathematical Institute (India), CUNY, the University of Sheffield (UK), the University of Missouri, and the University of South Carolina, and to non-academic positions at places such as Google, Robart GMBH, Microsoft, Credit Suisse and the Center for Communications Research, La Jolla.

**Emeritus faculty in algebra**

Richard Askey John Bascom Professor, Ph.D Princeton (1961) Research: Special Functions

Steven Bauman Professor, University of Illinois at Urbana-Champaign (1962) Research: Finite group theory

Georgia Benkart E. B. Van Vleck Professor of Mathematics, Ph.D. Yale University (1974) Research: Lie Theory, Quantum Groups and Representation Theory.

Michael Bleicher Professor, Ph.D. Tulane University and University of Warsaw (1961) Research: Number theory and convex geometry

Richard A. Brualdi Beckwith Bascom Professor of Mathematics, Ph.D. Syracuse University (1964) Research: Combinatorics, Graph Theory, Matrix Theory, Coding Theory

Donald Crowe Professor, Ph.D. University of Michigan (1959) Research: Classical geometry and African patterns

Hiroshi Gunji Professor, Ph.D. Johns Hopkins University (1962) Research: Algebraic geometry

I. Martin Isaacs Professor, Ph.D. Harvard University (1964) Research: Group Theory, Algebra

Arnold Johnson Professor, Ph.D. University of Notre Dame (1965) Research: Classical Groups

Lawrence Levy Professor, Ph.D. University of Illinois at Urbana-Champaign (1961) Research: Commutative and noncommutative ring theory

J. Marshall Osborn Professor, Ph.D. University of Chicago (1957) Research: Non-associative rings and Lie algebras

Donald Passman Richard Brauer Professor of Mathematics, Ph.D. Harvard University (1964) Research: Associative Rings and Algebras, Group Theory

Hans Schneider J. J. Sylvester Professor of Mathematics, Ph.D. University of Edinburgh (1952) Research: Linear algebra and matrix theory

Louis Solomon Professor, Ph.D. Harvard University (1958) Research: Finite group theory and hyperplane arrangements

Robert Wilson Professor, Ph.D. University of Wisconsin-Madison (1969) Research: Algebra, Math. Education.