Difference between revisions of "AMS Student Chapter Seminar"

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The AMS Student Chapter Seminar is an informal, graduate student-run seminar on a wide range of mathematical topics. Pastries (usually donuts) will be provided.
 
The AMS Student Chapter Seminar is an informal, graduate student-run seminar on a wide range of mathematical topics. Pastries (usually donuts) will be provided.
  
* '''When:''' Wednesdays, 3:00 PM – 3:30 PM
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* '''When:''' Wednesdays, 3:20 PM – 3:50 PM
 
* '''Where:''' Van Vleck, 9th floor lounge (unless otherwise announced)
 
* '''Where:''' Van Vleck, 9th floor lounge (unless otherwise announced)
* '''Organizers:''' [https://www.math.wisc.edu/~hast/ Daniel Hast], [https://www.math.wisc.edu/~mrjulian/ Ryan Julian], Cullen McDonald, [https://www.math.wisc.edu/~zcharles/ Zachary Charles]
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* '''Organizers:''' [https://www.math.wisc.edu/~malexis/ Michel Alexis], [https://www.math.wisc.edu/~drwagner/ David Wagner], [http://www.math.wisc.edu/~nicodemus/ Patrick Nicodemus], [http://www.math.wisc.edu/~thaison/ Son Tu]
  
 
Everyone is welcome to give a talk. To sign up, please contact one of the organizers with a title and abstract. Talks are 30 minutes long and should avoid assuming significant mathematical background beyond first-year graduate courses.
 
Everyone is welcome to give a talk. To sign up, please contact one of the organizers with a title and abstract. Talks are 30 minutes long and should avoid assuming significant mathematical background beyond first-year graduate courses.
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The schedule of talks from past semesters can be found [[AMS Student Chapter Seminar, previous semesters|here]].
 
The schedule of talks from past semesters can be found [[AMS Student Chapter Seminar, previous semesters|here]].
  
== Spring 2017 ==
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== Fall 2018 ==
  
=== January 25, Brandon Alberts ===
 
  
Title: Ultraproducts - they aren't just for logicians
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=== September 26, Vladimir Sotirov ===
  
Abstract: If any of you have attended a logic talk (or one of Ivan's donut seminar talks) you may have learned about ultraproducts as a weird way to mash sets together to get bigger sets in a nice way. Something particularly useful to set theorists, but maybe not so obviously useful to the rest of us. I will give an accessible introduction to ultraproducts and motivate their use in other areas of mathematics.
+
Title: Geometric Algebra
  
=== February 1, Megan Maguire ===
+
Abstract: Geometric algebra, developed at the end of the 19th century by Grassman, Clifford, and Lipschitz, is the forgotten progenitor of the linear algebra we use to this day developed by Gibbs and Heaviside.
 +
In this short introduction, I will use geometric algebra to do two things. First, I will construct the field of complex numbers and the division algebra of the quaternions in a coordinate-free way. Second, I will derive the geometric interpretation of complex numbers and quaternions as representations of rotations in 2- and 3-dimensional space.
  
Title: Hyperbolic crochet workshop
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=== October 3, Juliette Bruce ===
  
Abstract: TBA
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Title: Kissing Conics
  
=== February 8, Cullen McDonald ===
+
Abstract: Have you every wondered how you can easily tell when two plane conics kiss (i.e. are tangent to each other at a point)? If so this talk is for you, if not, well there will be donuts.
  
=== February 15, Paul Tveite ===
+
=== October 10, Kurt Ehlert ===
  
Title: Fun with Hamel Bases!
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Title: How to bet when gambling
  
Abstract: If we view the real numbers as a vector field over the rationals, then of course they have a basis (assuming the AOC). This is called a Hamel basis and allows us to do some cool things. Among other things, we will define two periodic functions that sum to the identity function.
+
Abstract: When gambling, typically casinos have the edge. But sometimes we can gain an edge by counting cards or other means. And sometimes we have an edge in the biggest casino of all: the financial markets. When we do have an advantage, then we still need to decide how much to bet. Bet too little, and we leave money on the table. Bet too much, and we risk financial ruin. We will discuss the "Kelly criterion", which is a betting strategy that is optimal in many senses.
  
=== February 22, Wil Cocke ===
+
=== October 17, Bryan Oakley ===
  
Title: Practical Graph Isomorphism
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Title: Mixing rates
  
Abstract: Some graphs are different and some graphs are the same. Sometimes graphs differ only in name. When you give me a graph, you've picked an order. But, is it the same graph across every border?
+
Abstract: Mixing is a necessary step in many areas from biology and atmospheric sciences to smoothies. Because we are impatient, the goal is usually to improve the rate at which a substance homogenizes. In this talk we define and quantify mixing and rates of mixing. We present some history of the field as well as current research and open questions.
  
=== March 1, Megan Maguire ===
+
=== October 24, Micky Soule Steinberg ===
  
Title: I stole this talk from Jordan.
+
Title: What does a group look like?
  
Abstract: Stability is cool! And sometimes things we think don't have stability secretly do. This is an abridged version of a very cool talk I've seen Jordan give a couple times. All credit goes to him. Man, I should have stolen his abstract too.
+
Abstract: In geometric group theory, we often try to understand groups by understanding the metric spaces on which the groups act geometrically. For example, Z^2 acts on R^2 in a nice way, so we can think of the group Z^2 instead as the metric space R^2.
  
=== March 7, Liban Mohamed ===
+
We will try to find (and draw) such a metric space for the solvable Baumslag-Solitar groups BS(1,n). Then we will briefly discuss what this geometric picture tells us about the groups.
  
Title: Strichartz Estimates from Qualitative to Quantitative
+
=== October 31, Sun Woo Park ===
  
Abstract: Strichartz estimates are inequalities that give one way understand the decay of solutions to dispersive PDEs. This talk is an attempt to reconcile the formal statements with physical intuition.
+
Title: Induction-Restriction Operators
  
=== March 15, Zachary Charles ===
+
Abstract: Given a "nice enough" finite descending sequence of groups <math> G_n \supsetneq G_{n-1} \supsetneq \cdots \supsetneq G_1 \supsetneq \{e\} </math>, we can play around with the relations between induced and restricted representations. We will construct a formal <math> \mathbb{Z} </math>-module of induction-restriction operators on a finite descending sequence of groups <math> \{G_i\} </math>, written as <math> IR_{\{G_i\}} </math>. The goal of the talk is to show that the formal ring <math> IR_{\{G_i\}} </math> is a commutative polynomial ring over <math> \mathbb{Z} </math>.  We will also compute the formal ring <math>IR_{\{S_n\}} </math> for a finite descending sequence of symmetric groups <math> S_n \supset S_{n-1} \supset \cdots \supset S_1 </math>. (Apart from the talk, I'll also prepare some treats in celebration of Halloween.)
  
Title: Netflix Problem and Chill
+
=== November 7, Polly Yu ===
  
Abstract: How are machine learning, matrix analysis, and Napoleon Dynamite related? Come find out!
+
Title: Positive solutions to polynomial systems using a (mostly linear) algorithm
  
=== April 5, Vlad Matei ===
+
Abstract: "Wait, did I read the title correctly? Solving non-linear systems using linear methods?” Yes you did. I will present a linear feasibility problem for your favourite polynomial system; if the algorithm returns an answer, you’ve gotten yourself a positive solution to your system, and more than that, the solution set admits a monomial parametrization.
  
=== April 12, Micky Steinberg ===
+
=== November 14, Soumya Sankar ===
  
=== April 19, Solly Parenti ===
+
Title: The worlds of math and dance
  
=== April 26, Ben Bruce ===
+
Abstract: Are math and dance related? Can we use one to motivate problems in the other? Should we all learn how to dance? I will answer these questions and then we will have some fun with counting problems motivated by dance.
  
=== May 3, TBA ===
+
=== November 21, Cancelled due to Thanksgiving===
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Title: TBD
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Abstract: TBD
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=== November 28, Niudun Wang ===
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Title: TBD
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Abstract: TBD
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=== December 5, Patrick Nicodemus ===
 +
 
 +
Title: Applications of Algorithmic Randomness and Complexity
 +
 
 +
Abstract: I will introduce the fascinating field of Kolmogorov Complexity and point out its applications in such varied areas as combinatorics, statistical inference and mathematical logic. In fact the Prime Number theorem, machine learning and Godel's Incompleteness theorem can all be investigated fruitfully through a wonderful common lens.
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=== December 12, TBD ===
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Title: TBD
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Abstract: TBD
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== Spring 2019 ==
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=== February 6, TBD ===
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Title: TBD
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Abstract: TBD
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=== February 13, TBD ===
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Title: TBD
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Abstract: TBD
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=== February 20, TBD ===
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Title: TBD
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Abstract: TBD
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=== February 27, TBD ===
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Title: TBD
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Abstract: TBD
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=== March 6, TBD ===
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Title: TBD
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Abstract: TBD
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=== March 13, TBD ===
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Title: TBD
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Abstract: TBD
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=== March 27, TBD ===
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Title: TBD
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Abstract: TBD
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=== April 3, TBD ===
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Title: TBD
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Abstract: TBD
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=== April 10, TBD ===
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Title: TBD
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Abstract: TBD
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=== April 17, TBD ===
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Title: TBD
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Abstract: TBD

Latest revision as of 16:15, 13 November 2018

The AMS Student Chapter Seminar is an informal, graduate student-run seminar on a wide range of mathematical topics. Pastries (usually donuts) will be provided.

Everyone is welcome to give a talk. To sign up, please contact one of the organizers with a title and abstract. Talks are 30 minutes long and should avoid assuming significant mathematical background beyond first-year graduate courses.

The schedule of talks from past semesters can be found here.

Fall 2018

September 26, Vladimir Sotirov

Title: Geometric Algebra

Abstract: Geometric algebra, developed at the end of the 19th century by Grassman, Clifford, and Lipschitz, is the forgotten progenitor of the linear algebra we use to this day developed by Gibbs and Heaviside. In this short introduction, I will use geometric algebra to do two things. First, I will construct the field of complex numbers and the division algebra of the quaternions in a coordinate-free way. Second, I will derive the geometric interpretation of complex numbers and quaternions as representations of rotations in 2- and 3-dimensional space.

October 3, Juliette Bruce

Title: Kissing Conics

Abstract: Have you every wondered how you can easily tell when two plane conics kiss (i.e. are tangent to each other at a point)? If so this talk is for you, if not, well there will be donuts.

October 10, Kurt Ehlert

Title: How to bet when gambling

Abstract: When gambling, typically casinos have the edge. But sometimes we can gain an edge by counting cards or other means. And sometimes we have an edge in the biggest casino of all: the financial markets. When we do have an advantage, then we still need to decide how much to bet. Bet too little, and we leave money on the table. Bet too much, and we risk financial ruin. We will discuss the "Kelly criterion", which is a betting strategy that is optimal in many senses.

October 17, Bryan Oakley

Title: Mixing rates

Abstract: Mixing is a necessary step in many areas from biology and atmospheric sciences to smoothies. Because we are impatient, the goal is usually to improve the rate at which a substance homogenizes. In this talk we define and quantify mixing and rates of mixing. We present some history of the field as well as current research and open questions.

October 24, Micky Soule Steinberg

Title: What does a group look like?

Abstract: In geometric group theory, we often try to understand groups by understanding the metric spaces on which the groups act geometrically. For example, Z^2 acts on R^2 in a nice way, so we can think of the group Z^2 instead as the metric space R^2.

We will try to find (and draw) such a metric space for the solvable Baumslag-Solitar groups BS(1,n). Then we will briefly discuss what this geometric picture tells us about the groups.

October 31, Sun Woo Park

Title: Induction-Restriction Operators

Abstract: Given a "nice enough" finite descending sequence of groups  G_n \supsetneq G_{n-1} \supsetneq \cdots \supsetneq G_1 \supsetneq \{e\} , we can play around with the relations between induced and restricted representations. We will construct a formal  \mathbb{Z} -module of induction-restriction operators on a finite descending sequence of groups  \{G_i\} , written as  IR_{\{G_i\}} . The goal of the talk is to show that the formal ring  IR_{\{G_i\}} is a commutative polynomial ring over  \mathbb{Z} . We will also compute the formal ring IR_{\{S_n\}} for a finite descending sequence of symmetric groups  S_n \supset S_{n-1} \supset \cdots \supset S_1 . (Apart from the talk, I'll also prepare some treats in celebration of Halloween.)

November 7, Polly Yu

Title: Positive solutions to polynomial systems using a (mostly linear) algorithm

Abstract: "Wait, did I read the title correctly? Solving non-linear systems using linear methods?” Yes you did. I will present a linear feasibility problem for your favourite polynomial system; if the algorithm returns an answer, you’ve gotten yourself a positive solution to your system, and more than that, the solution set admits a monomial parametrization.

November 14, Soumya Sankar

Title: The worlds of math and dance

Abstract: Are math and dance related? Can we use one to motivate problems in the other? Should we all learn how to dance? I will answer these questions and then we will have some fun with counting problems motivated by dance.

November 21, Cancelled due to Thanksgiving

Title: TBD

Abstract: TBD

November 28, Niudun Wang

Title: TBD

Abstract: TBD

December 5, Patrick Nicodemus

Title: Applications of Algorithmic Randomness and Complexity

Abstract: I will introduce the fascinating field of Kolmogorov Complexity and point out its applications in such varied areas as combinatorics, statistical inference and mathematical logic. In fact the Prime Number theorem, machine learning and Godel's Incompleteness theorem can all be investigated fruitfully through a wonderful common lens.

December 12, TBD

Title: TBD

Abstract: TBD


Spring 2019

February 6, TBD

Title: TBD

Abstract: TBD

February 13, TBD

Title: TBD

Abstract: TBD

February 20, TBD

Title: TBD

Abstract: TBD

February 27, TBD

Title: TBD

Abstract: TBD

March 6, TBD

Title: TBD

Abstract: TBD

March 13, TBD

Title: TBD

Abstract: TBD

March 27, TBD

Title: TBD

Abstract: TBD

April 3, TBD

Title: TBD

Abstract: TBD

April 10, TBD

Title: TBD

Abstract: TBD

April 17, TBD

Title: TBD

Abstract: TBD