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The AMS Student Chapter Seminar is an informal, graduate student seminar on a wide range of mathematical topics. Pastries (usually donuts) will be provided.
The AMS Student Chapter Seminar (aka Donut Seminar) is an informal, graduate student seminar on a wide range of mathematical topics. The goal of the seminar is to promote community building and give graduate students an opportunity to communicate fun, accessible math to their peers in a stress-free (but not sugar-free) environment. Pastries (usually donuts) will be provided.


* '''When:''' Wednesdays, 3:20 PM – 3:50 PM
* '''When:''' Wednesdays, 3:30 PM – 4:00 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:''' Ivan Aidun, Kaiyi Huang, Ethan Schondorf


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 25 minutes long and should avoid assuming significant mathematical background beyond first-year graduate courses.


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 2019 ==
== Fall 2023==


=== February 6, Xiao Shen (in VV B139)===
===September 7, Alex Mine===
Title: My Favorite Fact about Continued Fractions


Title: Limit Shape in last passage percolation
===September 14, Mei Rose Connor ===
Title: All Things Necessary and Possible: an introduction to the Kripke semantics of modal logic


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: Modal logic is a branch of formal logic with far–reaching applications to fields such as philosophy, mathematics, computer science, and other parts of logic itself. It deals with which propositions, some of which are necessarily true (in the words of philosophy, a priori) and some of which are possibly true (analogously, a posteriori). But this will not be a philosophy talk. This talk will cover the notation, syntax, and one choice of semantics for modal logic known as the Kripke semantics. The Kripke semantics is a powerful tool that allows us to make connections between modal statements and first–order (or higher–order) logic ones. Along the way, the talk will explore how the simple symbols □ and ♢ can help to model ethics, represent the knowledge of individuals and even lead to an elegant gateway into the First Incompleteness result.


=== February 13, Michel Alexis (in VV B139)===
===September 21, Sun Woo Park ===
Title: What I did in my military service II (A functorial formulation of deep learning algorithms)


Title: An instructive yet useless theorem about random Fourier Series
Abstract: Even though deep learning algorithms (say convolutional neural networks, graph neural networks, and attention-transformers) show outstanding performances in executing certain tasks, there are also certain tasks that these algorithms do not perform well. We'll try to give a naive attempt to understand why such problems can occur. Similar to last semester, I will once again recall what I was interested in during the last few months of my 3-year military service in South Korea.


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>).
===September 28, Caroline Nunn===
Title: Phinary Numbers


=== February 20, Geoff Bentsen ===
Abstract: Everyone and their grandmother knows about binary numbers.  But do you know about phinary numbers?  In this talk, we will explore the fun consequences of using an irrational number base system.  We will define phinary representations of real numbers and explore which real numbers can be written using finite or recurring phinary representations. 


Title: An Analyst Wanders into a Topology Conference
===October 5, Gabriella Brown===
Title: Topological Entropy in Shift Spaces


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: Entropy is a concept that many STEM disciplines engage with, which results in many different perspectives on what exactly it is. This talk will introduce the perspective of symbolic dynamics by defining shifts of finite type and showing how to compute their topological entropy.


=== February 27, James Hanson ===
===October 12, Nakid Cordero===
Title: How to prove the Riemann Hypothesis: a logician's approach


Title: What is...a Topometric Space?
Abstract: ''Hint:'' ''Prove that you cannot disprove it.''


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.
===October 19, Ari Davidovsky===
Title: Using Ultrafilters in Additive Combinatorics


=== March 6, Working Group to establish an Association of Mathematics Graduate Students ===
Abstract: The goal of this talk is to introduce the idea of ultrafilters and show how they help us prove some cool results from additive combinatorics. The main result proved will be Hindman's Theorem which states if we partition the natural numbers into finitely many sets then one of these sets A contains an infinite subset B such that the sum of any finitely many distinct elements in B will always be in A.


Title: Introducing GRAMS (Graduate Representative Association of Mathematics Students)
===October 26, Otto Baier===
Title: "Circulant Matrices and the Discrete Fourier Transform"


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.
Abstract: "Have you ever tried to use a finite difference method on a differential equation with periodic boundary conditions and said, 'I wonder how I could find the eigenvalues of this matrix analytically'? No? Well either way, you're going to find out!


=== March 13, Connor Simpson ===
===November 2, Speaker TBA===
Title:


Title: Counting faces of polytopes with algebra
Abstract:


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.
===November 9, Owen Goff===
Title:


=== March 26 (Prospective Student Visit Day), Multiple Speakers ===
Abstract:


====Eva Elduque, 11-11:25====
===November 16, Speaker TBA===
Title:


Title: Will it fold flat?
Abstract:


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.
===November 23, CANCELLED FOR THANKSGIVING===


====Soumya Sankar, 11:30-11:55====
===November 30, Speaker TBA===
Title:


Title: An algebro-geometric perspective on integration
Abstract:


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.
===December 7, Speaker TBA===
Title:


====Chun Gan, 12:00-12:25====
Abstract:


Title: Extension theorems in complex analysis
===December 14, Maybe Cancelled?===
 
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: TBD
 
=== April 24, Carrie Chen ===
 
Title: TBD
 
Abstract: TBD
 
== 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

Latest revision as of 22:24, 25 October 2023

The AMS Student Chapter Seminar (aka Donut Seminar) is an informal, graduate student seminar on a wide range of mathematical topics. The goal of the seminar is to promote community building and give graduate students an opportunity to communicate fun, accessible math to their peers in a stress-free (but not sugar-free) environment. Pastries (usually donuts) will be provided.

  • When: Wednesdays, 3:30 PM – 4:00 PM
  • Where: Van Vleck, 9th floor lounge (unless otherwise announced)
  • Organizers: Ivan Aidun, Kaiyi Huang, Ethan Schondorf

Everyone is welcome to give a talk. To sign up, please contact one of the organizers with a title and abstract. Talks are 25 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 2023

September 7, Alex Mine

Title: My Favorite Fact about Continued Fractions

September 14, Mei Rose Connor

Title: All Things Necessary and Possible: an introduction to the Kripke semantics of modal logic

Abstract: Modal logic is a branch of formal logic with far–reaching applications to fields such as philosophy, mathematics, computer science, and other parts of logic itself. It deals with which propositions, some of which are necessarily true (in the words of philosophy, a priori) and some of which are possibly true (analogously, a posteriori). But this will not be a philosophy talk. This talk will cover the notation, syntax, and one choice of semantics for modal logic known as the Kripke semantics. The Kripke semantics is a powerful tool that allows us to make connections between modal statements and first–order (or higher–order) logic ones. Along the way, the talk will explore how the simple symbols □ and ♢ can help to model ethics, represent the knowledge of individuals and even lead to an elegant gateway into the First Incompleteness result.

September 21, Sun Woo Park

Title: What I did in my military service II (A functorial formulation of deep learning algorithms)

Abstract: Even though deep learning algorithms (say convolutional neural networks, graph neural networks, and attention-transformers) show outstanding performances in executing certain tasks, there are also certain tasks that these algorithms do not perform well. We'll try to give a naive attempt to understand why such problems can occur. Similar to last semester, I will once again recall what I was interested in during the last few months of my 3-year military service in South Korea.

September 28, Caroline Nunn

Title: Phinary Numbers

Abstract: Everyone and their grandmother knows about binary numbers. But do you know about phinary numbers? In this talk, we will explore the fun consequences of using an irrational number base system. We will define phinary representations of real numbers and explore which real numbers can be written using finite or recurring phinary representations.

October 5, Gabriella Brown

Title: Topological Entropy in Shift Spaces

Abstract: Entropy is a concept that many STEM disciplines engage with, which results in many different perspectives on what exactly it is. This talk will introduce the perspective of symbolic dynamics by defining shifts of finite type and showing how to compute their topological entropy.

October 12, Nakid Cordero

Title: How to prove the Riemann Hypothesis: a logician's approach

Abstract: Hint: Prove that you cannot disprove it.

October 19, Ari Davidovsky

Title: Using Ultrafilters in Additive Combinatorics

Abstract: The goal of this talk is to introduce the idea of ultrafilters and show how they help us prove some cool results from additive combinatorics. The main result proved will be Hindman's Theorem which states if we partition the natural numbers into finitely many sets then one of these sets A contains an infinite subset B such that the sum of any finitely many distinct elements in B will always be in A.

October 26, Otto Baier

Title: "Circulant Matrices and the Discrete Fourier Transform"

Abstract: "Have you ever tried to use a finite difference method on a differential equation with periodic boundary conditions and said, 'I wonder how I could find the eigenvalues of this matrix analytically'? No? Well either way, you're going to find out!

November 2, Speaker TBA

Title:

Abstract:

November 9, Owen Goff

Title:

Abstract:

November 16, Speaker TBA

Title:

Abstract:

November 23, CANCELLED FOR THANKSGIVING

November 30, Speaker TBA

Title:

Abstract:

December 7, Speaker TBA

Title:

Abstract:

December 14, Maybe Cancelled?