AMS Student Chapter Seminar: Difference between revisions

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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
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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]].


== 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: TBD
 
Abstract: TBD
 
=== March 6, Working Group to establish an Association of Mathematics Graduate Students ===
 
Title: Math and Government
 
Abstract: TBD
 
=== 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.


Title: Mixing rates
=== March 26 (Prospective Student Visit Day), Multiple Speakers ===


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.
====Eva Elduque====


=== October 24, Micky Soule Steinberg ===
Title: TBD


Title: What does a group look like?
Abstract: TBD


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.
====Rajula Srivastava====


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: TBD
 
Abstract: TBD


=== October 31, Sun Woo Park ===
====Soumya Sankar====


Title: Induction-Restriction Operators on a Finite Descending Sequence of Groups
Title: TBD


Abstract: We will state what induced and restricted representations are. We will then 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>.
Abstract: TBD


=== November 7, TBD ===
====Ivan Ongay Valverde, 3pm====


Title: TBD
Title: TBD
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Abstract: TBD
Abstract: TBD


=== November 14, Soumya Sankar ===
====[Insert Speaker]====


Title: TBD
Title: TBD
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Abstract: TBD
Abstract: TBD


=== November 21, Cancelled due to Thanksgiving===
====[Insert Speaker]====


Title: TBD
Title: TBD
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Abstract: TBD
Abstract: TBD


=== November 28, Niudun Wang ===
====[Insert Speaker]====


Title: TBD
Title: TBD
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Abstract: TBD
Abstract: TBD


=== December 5, Patrick Nicodemus ===
====[Insert Speaker]====


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
 
====[Insert Speaker]====
 
Title: TBD
 
Abstract: TBD
 
=== April 3, TBD ===
 
Title: TBD
 
Abstract: TBD
 
=== April 10, TBD ===
 
Title: TBD
 
Abstract: TBD
 
=== April 17, Hyun-Jong ===
 
Title: TBD
 
Abstract: TBD


=== December 12, TBD ===
=== April 24, TBD ===


Title: TBD
Title: TBD


Abstract: TBD
Abstract: TBD

Revision as of 20:43, 19 February 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]\displaystyle{ L^{p} }[/math] function? A surprising result is the Billard theorem, which says such a series results almost surely from an [math]\displaystyle{ 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]\displaystyle{ \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]\displaystyle{ E }[/math] of [math]\displaystyle{ R^d }[/math], can we restrict the Fourier transform of an [math]\displaystyle{ L^p }[/math] function to [math]\displaystyle{ 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: TBD

Abstract: TBD

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

Title: Math and Government

Abstract: TBD

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

Title: TBD

Abstract: TBD

Rajula Srivastava

Title: TBD

Abstract: TBD

Soumya Sankar

Title: TBD

Abstract: TBD

Ivan Ongay Valverde, 3pm

Title: TBD

Abstract: TBD

[Insert Speaker]

Title: TBD

Abstract: TBD

[Insert Speaker]

Title: TBD

Abstract: TBD

[Insert Speaker]

Title: TBD

Abstract: TBD

[Insert Speaker]

Title: TBD

Abstract: TBD

[Insert Speaker]

Title: TBD

Abstract: TBD

April 3, TBD

Title: TBD

Abstract: TBD

April 10, TBD

Title: TBD

Abstract: TBD

April 17, Hyun-Jong

Title: TBD

Abstract: TBD

April 24, TBD

Title: TBD

Abstract: TBD