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 seminar on a wide range of mathematical topics. Pastries (usually donuts) will be provided.
  
 
* '''When:''' Wednesdays, 3:20 PM – 3:50 PM
 
* '''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/~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]
+
* '''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], Carrie Chen
  
 
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.
Line 9: Line 9:
 
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]].
  
== Fall 2018 ==
+
== Spring 2019 ==
  
 +
=== February 6, Xiao Shen (in VV B139)===
  
=== September 26, Vladimir Sotirov ===
+
Title: Limit Shape in last passage percolation
  
Title: Geometric Algebra
+
Abstract: Imagine the following situation, attached to each point on the integer lattice Z^2 there is an arbitrary amount of donuts.  Fix x and y in Z^2, if you get to eat all the donuts along an up-right path between these two points, what would be the maximum amount of donuts you can get? This model is often called last passage percolation, and I will discuss a classical result about its scaling limit: what happens if we zoom out and let the distance between x and y tend to infinity.
  
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.
+
=== February 13, Michel Alexis (in VV B139)===
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: An instructive yet useless theorem about random Fourier Series
  
Title: Kissing Conics
+
Abstract: Consider a Fourier series with random, symmetric, independent coefficients. With what probability is this the Fourier series of a continuous function? An <math>L^{p}</math> function? A surprising result is the Billard theorem, which says such a series results almost surely from an <math>L^{\infty}</math> function if and only if it results almost surely from a continuous function. Although the theorem in of itself is kind of useless in of itself, its proof is instructive in that we will see how, via the principle of reduction, one can usually just pretend all symmetric random variables are just coin flips (Bernoulli trials with outcomes <math>\pm 1</math>).
  
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 20, Geoff Bentsen ===
  
=== October 10, Kurt Ehlert ===
+
Title: An Analyst Wanders into a Topology Conference
  
Title: How to bet when gambling
+
Abstract: Fourier Restriction is a big open problem in Harmonic Analysis; given a "small" subset <math>E</math> of <math>R^d</math>, can we restrict the Fourier transform of an <math>L^p</math> function to <math>E</math> and retain any information about our original function? This problem has a nice (somewhat) complete solution for smooth manifolds of co-dimension one. I will explore how to start generalizing this result to smooth manifolds of higher co-dimension, and how a topology paper from the 60s about the hairy ball problem came in handy along the way.
  
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 27, James Hanson ===
  
=== October 17, Bryan Oakley ===
+
Title: What is...a Topometric Space?
  
Title: Mixing rates
+
Abstract: Continuous first-order logic is a generalization of first-order logic that is well suited for the study of structures with a natural metric, such as Banach spaces and probability algebras. Topometric spaces are a simple generalization of topological and metric spaces that arise in the study of continuous first-order logic. I will discuss certain topological issues that show up in topometric spaces coming from continuous logic, as well as some partial solutions and open problems. No knowledge of logic will be required for or gained from attending the talk.
  
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 6, Working Group to establish an Association of Mathematics Graduate Students ===
  
=== October 24, Micky Soule Steinberg ===
+
Title: Introducing GRAMS (Graduate Representative Association of Mathematics Students)
 +
 
 +
Abstract: Over the past couple months, a handful of us have been working to create the UW Graduate Representative Association of Mathematics Students (GRAMS).  This group, about 5-8 students, is intended to be a liaison between the graduate students and faculty, especially in relation to departmental policies and decisions that affect graduate students. We will discuss what we believe GRAMS ought to look like and the steps needed to implement such a vision, then open up the floor to a Q&A. Check out our [http://sites.google.com/wisc.edu/grams/home website] for more information.
 +
 
 +
=== March 13, Connor Simpson ===
 +
 
 +
Title: Counting faces of polytopes with algebra
 +
 
 +
Abstract: A natural question is: with a fixed dimension and number of vertices, what is the largest number of d-dimensional faces that a polytope can have? We will outline a proof of the answer to this question.
 +
 
 +
=== March 26 (Prospective Student Visit Day), Multiple Speakers ===
 +
 
 +
====Eva Elduque, 11-11:25====
 +
 
 +
Title: Will it fold flat?
 +
 
 +
Abstract: Picture the traditional origami paper crane. It is a 3D object, but if you don’t make the wings stick out, it is flat. This is the case for many origami designs, ranging from very simple (like a paper hat), to complicated tessellations. Given a crease pattern on a piece of paper, one might wonder if it is possible to fold along the lines of the pattern and end up with a flat object. We’ll discuss necessary and sufficient conditions for a crease pattern with only one vertex to fold flat, and talk about what can be said about crease patterns with multiple vertices.
 +
 
 +
====Soumya Sankar, 11:30-11:55====
 +
 
 +
Title: An algebro-geometric perspective on integration
 +
 
 +
Abstract: Integrals are among the most basic tools we learn in complex analysis and yet are extremely versatile. I will discuss one way in which integrals come up in algebraic geometry and the surprising amount of arithmetic and geometric information this gives us.
 +
 
 +
====Chun Gan, 12:00-12:25====
 +
 
 +
Title: Extension theorems in complex analysis
 +
 
 +
Abstract: Starting from Riemann's extension theorem in one complex variable, there have been many generalizations to different situations in several complex variables. I will talk about Fefferman's field's medal work on Fefferman extension and also the celebrated Ohsawa-Takegoshi L^2 extension theorem which is now a cornerstone for the application of pluripotential theory to complex analytic geometry.
 +
 
 +
====Jenny Yeon, 2:00-2:25====
 +
 
 +
Title: Application of Slope Field
 +
 
 +
Abstract: Overview of historical problems in Dynamical Systems and what CRN(chemical reaction network) group at UW Madison does. In particular, what exactly is the butterfly effect? Why is this simple-to-state problem so hard even if it is only 2D (Hilbert's 16th problem)? What are some modern techniques availble? What do the members of CRN group do? Is the theory of CRN applicable? 
 +
 
 +
====Rajula Srivastava, 2:30-2:55====
 +
 
 +
Title: The World of Wavelets
 +
 
 +
Abstract: Why the fourier series might not be the best way to represent functions in all cases, and why wavelets might be a good alternative in some of these.
 +
 
 +
====Shengyuan Huang, 3:00-3:25====
 +
 
 +
Title: Group objects in various categories
 +
 
 +
Abstract: I will introduce categories and talk about group objects in the category of sets and manifolds.  The latter leads to the theory of Lie group and Lie algebras.  We can then talk about group objects in some other category coming from algebraic geometry and obtain similar results as Lie groups and Lie algebras.
 +
 
 +
====Ivan Ongay Valverde, 3:30-3:55====
 +
 
 +
Title: Games and Topology
 +
 
 +
Abstract: Studying the topology of the real line leads to really interesting questions and facts. One of them is the relation between some kind of infinite games, called topological games, and specific properties of a subsets of reals. In this talk we will study the perfect set game.
 +
 
 +
====Sun Woo Park, 4:00-4:25====
 +
 
 +
Title: Reconstruction of character tables of Sn
 +
 
 +
Abstract: We will discuss how we can relate the columns of the character tables of Sn and the tensor product of irreducible representations over Sn. Using the relation, we will also indicate how we can recover some columns of character tables of Sn. 
 +
 
 +
====Max Bacharach, 4:30-4:55====
 +
 
 +
Title: Clothes, Lice, and Coalescence
 +
 
 +
Abstract: A gentle introduction to coalescent theory, motivated by an application which uses lice genetics to estimate when human ancestors first began wearing clothing.
 +
 
 +
=== April 3, Yu Feng ===
 +
 
 +
Title: Suppression of phase separation by mixing
 +
 
 +
Abstract: The Cahn-Hilliard equation is a classical PDE that models phase separation of two components. We add an advection term so that the two components are stirred by a velocity. We show that there exists a class of fluid that can prevent phase separation and enforce the solution converges to its average exponentially.
 +
 
 +
=== April 17, Hyun Jong Kim===
 +
 
 +
Title: Musical Harmony for the Mathematician
 +
 
 +
Abstract: Harmony can refer to the way in which multiple notes that are played simultaneously come together in music. I will talk about some aspects of harmony in musical analysis and composition and a few ways to interpret harmonic phenomena mathematically. The mathematical interpretations will mostly revolve around symmetry and integer arithmetic modulo 12.
 +
 
 +
=== April 24, Carrie Chen ===
 +
 
 +
Title: Pedestrian model
 +
 
 +
Abstract: When there are lots of people in a supermarket, and for some reason they have to get out as soon as possible, how do you expect the crowd to behave? Suppose each person is a rational individual and assume that each person has all knowledge to other people’s position at every time and further the number of people is huge, we can model it using mean field game model and get the macroscopic behaviour.
 +
 
 +
== Fall 2019 ==
 +
 
 +
=== September 25, TBD===
 +
 
 +
Title: TBD
 +
 
 +
Abstract: TBD
 +
 
 +
=== October 2, TBD===
 +
 
 +
Title: TBD
 +
 
 +
Abstract: TBD
 +
 
 +
=== October 9, TBD===
  
 
Title: TBD
 
Title: TBD
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Abstract: TBD
 
Abstract: TBD
  
=== October 31, Sun Woo Park ===
+
=== October 16, TBD===
  
 
Title: TBD
 
Title: TBD
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Abstract: TBD
 
Abstract: TBD
  
=== November 7, TBD ===
+
=== October 23, TBD===
  
 
Title: TBD
 
Title: TBD
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Abstract: TBD
 
Abstract: TBD
  
=== November 14, Soumya Sankar ===
+
=== October 30, TBD===
  
 
Title: TBD
 
Title: TBD
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Abstract: TBD
 
Abstract: TBD
  
=== November 21, Cancelled due to Thanksgiving===
+
=== November 6, TBD===
  
 
Title: TBD
 
Title: TBD
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Abstract: TBD
 
Abstract: TBD
  
=== November 28, Niudun Wang ===
+
=== November 13, TBD===
  
 
Title: TBD
 
Title: TBD
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Abstract: TBD
 
Abstract: TBD
  
=== December 5, Patrick Nicodemus ===
+
=== November 20, TBD===
  
Title: Applications of Algorithmic Randomness and Complexity
+
Title: TBD
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.
+
 
 +
Abstract: TBD
 +
 
 +
=== December 4, TBD===
 +
 
 +
Title: TBD
 +
 
 +
Abstract: TBD
  
=== December 12, TBD ===
+
=== December 12, TBD===
  
 
Title: TBD
 
Title: TBD
  
 
Abstract: TBD
 
Abstract: TBD

Latest revision as of 12:08, 25 April 2019

The AMS Student Chapter Seminar is an informal, graduate student 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.

Spring 2019

February 6, Xiao Shen (in VV B139)

Title: Limit Shape in last passage percolation

Abstract: Imagine the following situation, attached to each point on the integer lattice Z^2 there is an arbitrary amount of donuts. Fix x and y in Z^2, if you get to eat all the donuts along an up-right path between these two points, what would be the maximum amount of donuts you can get? This model is often called last passage percolation, and I will discuss a classical result about its scaling limit: what happens if we zoom out and let the distance between x and y tend to infinity.

February 13, Michel Alexis (in VV B139)

Title: An instructive yet useless theorem about random Fourier Series

Abstract: Consider a Fourier series with random, symmetric, independent coefficients. With what probability is this the Fourier series of a continuous function? An [math]L^{p}[/math] function? A surprising result is the Billard theorem, which says such a series results almost surely from an [math]L^{\infty}[/math] function if and only if it results almost surely from a continuous function. Although the theorem in of itself is kind of useless in of itself, its proof is instructive in that we will see how, via the principle of reduction, one can usually just pretend all symmetric random variables are just coin flips (Bernoulli trials with outcomes [math]\pm 1[/math]).

February 20, Geoff Bentsen

Title: An Analyst Wanders into a Topology Conference

Abstract: Fourier Restriction is a big open problem in Harmonic Analysis; given a "small" subset [math]E[/math] of [math]R^d[/math], can we restrict the Fourier transform of an [math]L^p[/math] function to [math]E[/math] and retain any information about our original function? This problem has a nice (somewhat) complete solution for smooth manifolds of co-dimension one. I will explore how to start generalizing this result to smooth manifolds of higher co-dimension, and how a topology paper from the 60s about the hairy ball problem came in handy along the way.

February 27, James Hanson

Title: What is...a Topometric Space?

Abstract: Continuous first-order logic is a generalization of first-order logic that is well suited for the study of structures with a natural metric, such as Banach spaces and probability algebras. Topometric spaces are a simple generalization of topological and metric spaces that arise in the study of continuous first-order logic. I will discuss certain topological issues that show up in topometric spaces coming from continuous logic, as well as some partial solutions and open problems. No knowledge of logic will be required for or gained from attending the talk.

March 6, Working Group to establish an Association of Mathematics Graduate Students

Title: Introducing GRAMS (Graduate Representative Association of Mathematics Students)

Abstract: Over the past couple months, a handful of us have been working to create the UW Graduate Representative Association of Mathematics Students (GRAMS). This group, about 5-8 students, is intended to be a liaison between the graduate students and faculty, especially in relation to departmental policies and decisions that affect graduate students. We will discuss what we believe GRAMS ought to look like and the steps needed to implement such a vision, then open up the floor to a Q&A. Check out our website for more information.

March 13, Connor Simpson

Title: Counting faces of polytopes with algebra

Abstract: A natural question is: with a fixed dimension and number of vertices, what is the largest number of d-dimensional faces that a polytope can have? We will outline a proof of the answer to this question.

March 26 (Prospective Student Visit Day), Multiple Speakers

Eva Elduque, 11-11:25

Title: Will it fold flat?

Abstract: Picture the traditional origami paper crane. It is a 3D object, but if you don’t make the wings stick out, it is flat. This is the case for many origami designs, ranging from very simple (like a paper hat), to complicated tessellations. Given a crease pattern on a piece of paper, one might wonder if it is possible to fold along the lines of the pattern and end up with a flat object. We’ll discuss necessary and sufficient conditions for a crease pattern with only one vertex to fold flat, and talk about what can be said about crease patterns with multiple vertices.

Soumya Sankar, 11:30-11:55

Title: An algebro-geometric perspective on integration

Abstract: Integrals are among the most basic tools we learn in complex analysis and yet are extremely versatile. I will discuss one way in which integrals come up in algebraic geometry and the surprising amount of arithmetic and geometric information this gives us.

Chun Gan, 12:00-12:25

Title: Extension theorems in complex analysis

Abstract: Starting from Riemann's extension theorem in one complex variable, there have been many generalizations to different situations in several complex variables. I will talk about Fefferman's field's medal work on Fefferman extension and also the celebrated Ohsawa-Takegoshi L^2 extension theorem which is now a cornerstone for the application of pluripotential theory to complex analytic geometry.

Jenny Yeon, 2:00-2:25

Title: Application of Slope Field

Abstract: Overview of historical problems in Dynamical Systems and what CRN(chemical reaction network) group at UW Madison does. In particular, what exactly is the butterfly effect? Why is this simple-to-state problem so hard even if it is only 2D (Hilbert's 16th problem)? What are some modern techniques availble? What do the members of CRN group do? Is the theory of CRN applicable?

Rajula Srivastava, 2:30-2:55

Title: The World of Wavelets

Abstract: Why the fourier series might not be the best way to represent functions in all cases, and why wavelets might be a good alternative in some of these.

Shengyuan Huang, 3:00-3:25

Title: Group objects in various categories

Abstract: I will introduce categories and talk about group objects in the category of sets and manifolds. The latter leads to the theory of Lie group and Lie algebras. We can then talk about group objects in some other category coming from algebraic geometry and obtain similar results as Lie groups and Lie algebras.

Ivan Ongay Valverde, 3:30-3:55

Title: Games and Topology

Abstract: Studying the topology of the real line leads to really interesting questions and facts. One of them is the relation between some kind of infinite games, called topological games, and specific properties of a subsets of reals. In this talk we will study the perfect set game.

Sun Woo Park, 4:00-4:25

Title: Reconstruction of character tables of Sn

Abstract: We will discuss how we can relate the columns of the character tables of Sn and the tensor product of irreducible representations over Sn. Using the relation, we will also indicate how we can recover some columns of character tables of Sn.

Max Bacharach, 4:30-4:55

Title: Clothes, Lice, and Coalescence

Abstract: A gentle introduction to coalescent theory, motivated by an application which uses lice genetics to estimate when human ancestors first began wearing clothing.

April 3, Yu Feng

Title: Suppression of phase separation by mixing

Abstract: The Cahn-Hilliard equation is a classical PDE that models phase separation of two components. We add an advection term so that the two components are stirred by a velocity. We show that there exists a class of fluid that can prevent phase separation and enforce the solution converges to its average exponentially.

April 17, Hyun Jong Kim

Title: Musical Harmony for the Mathematician

Abstract: Harmony can refer to the way in which multiple notes that are played simultaneously come together in music. I will talk about some aspects of harmony in musical analysis and composition and a few ways to interpret harmonic phenomena mathematically. The mathematical interpretations will mostly revolve around symmetry and integer arithmetic modulo 12.

April 24, Carrie Chen

Title: Pedestrian model

Abstract: When there are lots of people in a supermarket, and for some reason they have to get out as soon as possible, how do you expect the crowd to behave? Suppose each person is a rational individual and assume that each person has all knowledge to other people’s position at every time and further the number of people is huge, we can model it using mean field game model and get the macroscopic behaviour.

Fall 2019

September 25, TBD

Title: TBD

Abstract: TBD

October 2, TBD

Title: TBD

Abstract: TBD

October 9, TBD

Title: TBD

Abstract: TBD

October 16, TBD

Title: TBD

Abstract: TBD

October 23, TBD

Title: TBD

Abstract: TBD

October 30, TBD

Title: TBD

Abstract: TBD

November 6, TBD

Title: TBD

Abstract: TBD

November 13, TBD

Title: TBD

Abstract: TBD

November 20, TBD

Title: TBD

Abstract: TBD

December 4, TBD

Title: TBD

Abstract: TBD

December 12, TBD

Title: TBD

Abstract: TBD