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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.
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
* '''When:''' Thursdays 4:00-4:30pm
* '''Where:''' Van Vleck, 9th floor lounge (unless otherwise announced)
* '''Where:''' Van Vleck, 9th floor lounge (unless otherwise announced)
* '''Organizers:''' Ivan Aidun, Kaiyi Huang, Ethan Schondorf  
* '''Organizers:''' Ivan Aidun, Kaiyi Huang, Ethan Schondorf  
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]].


== Spring 2023 ==
== Fall 2024 ==
<center>
{| cellspacing="5" cellpadding="14" border="0" style="color:black; font-size:120%"
! align="center" width="200" bgcolor="#D0D0D0" |'''Date'''
! align="center" width="200" bgcolor="#A6B658" |'''Speaker'''
! align="center" width="300" bgcolor="#BCD2EE" |'''Title'''
! align="center" width="400" bgcolor="#BCD2EE" |'''Abstract'''
|-
| bgcolor="#D0D0D0" |September 12
| bgcolor="#A6B658" |Ari Davidovsky
| bgcolor="#BCD2EE" |95% of people can't solve this!
| bgcolor="#BCD2EE" | [[File:Image.png|360px]]


=== January 25, Michael Jeserum ===
We will attempt to answer this question and along the way explore how algebra and geometry work together to solve problems in number theory.
|-
| bgcolor="#D0D0D0" |September 19
| bgcolor="#A6B658" |CANCELLED
| bgcolor="#BCD2EE" |NONE
| bgcolor="#BCD2EE" |NONE
|-
| bgcolor="#D0D0D0" |September 26
| bgcolor="#A6B658" |Mateo Morales
| bgcolor="#BCD2EE" |Officially petitioning the department to acquire a ping pong table.
| bgcolor="#BCD2EE" |Ever want to prove something is a free group of rank 2? Me too. One way to do this is to use a ping pong argument of how a group generated by two elements acts on a set.
I will illustrate the ping pong argument using an example of matrices, explain how it works, and explain why, kinda.


 
Very approachable if you know what a group is but does require tons of ping pong experience.
 
|-
Title: Totally Realistic Supply Chains
| bgcolor="#D0D0D0" |October 3
 
| bgcolor="#A6B658" |Karthik Ravishankar
Abstract: Inspired by a group of fifth and sixth graders, we'll embark on a journey to discover how supply chains definitely work in real life. Along the way, we'll eat donuts, learn about graphs and the magical world of chip-firing, and maybe even make new friends!
| bgcolor="#BCD2EE" |Incompleteness for the working mathematician
 
| bgcolor="#BCD2EE" |In this talk we'll take a look at Gödels famous incompleteness theorems and look at some of its immediate as well as interesting consequences. No background in logic is necessary!
=== February 1, Summer al Hamdani ===
|-
 
| bgcolor="#D0D0D0" |October 10
 
| bgcolor="#A6B658" |Elizabeth Hankins
 
| bgcolor="#BCD2EE" |Mathematical Origami and Flat-Foldability
Title: Monkeying Around: On the Infinite Monkey Theorem
| bgcolor="#BCD2EE" |If you've ever unfolded a piece of origami, you might have noticed complicated symmetries in the pattern of creases left behind. What patterns of lines can and cannot be folded into origami? And why is it sometimes hard to determine?
 
|-
Abstract: Will monkeys keyboard bashing eventually type all of Hamlet? Yes, almost surely. We will discuss the history and proof of the infinite monkey theorem.
| bgcolor="#D0D0D0" |October 17
 
| bgcolor="#A6B658" |CANCELLED
=== February 8, Dionel Jaime ===
| bgcolor="#BCD2EE" |NONE
 
| bgcolor="#BCD2EE" |NONE
 
|-
 
| bgcolor="#D0D0D0" |October 24
Title: The weird world of polynomial curve fitting.
| bgcolor="#A6B658" |CANCELLED
 
| bgcolor="#BCD2EE" |NONE
Abstract: You have some continuous function, and you decide you want to find a polynomial curve that looks a lot like your function. That is a very smart and easy thing to do. Nothing will go wrong.
| bgcolor="#BCD2EE" |NONE
 
|-
=== February 15, Sun Woo Park ===
| bgcolor="#D0D0D0" |October 31
 
| bgcolor="#A6B658" |Jacob Wood
 
| bgcolor="#BCD2EE" |What is the length of a <s>potato</s> pumpkin?
Title: What I did in my military service (Universal covers and graph neural networks)
| bgcolor="#BCD2EE" |How many is a jack-o-lantern? What is the length of a pumpkin? These questions sound like nonsense, but they have perfectly reasonable interpretations with perfectly reasonable answers. On our journey through the haunted house with two rooms, we will encounter some scary characters like differential topology and measure theory. Do not fear; little to no experience in either subject is required.
 
|-
Abstract: I'll try to motivate the relations between universal covers of graphs and graph isomorphism classification tasks implemented from graph neural networks. This is a summary of what I did during my 3 years of leave of absence due to compulsory military service in South Korea. Don't worry, everything I'll present here is already made public and not confidential, so you don't need to worry about the South Korean government officials suddenly appearing during the seminar and accusing me of misconduct!
| bgcolor="#D0D0D0" |November 7
 
| bgcolor="#A6B658" |CANCELLED: DISTINGUISHED LECTURE
=== February 22: NO SEMINAR ===
| bgcolor="#BCD2EE" |NONE
 
| bgcolor="#BCD2EE" |NONE
=== February 28, Owen Goff ===
|-
| bgcolor="#D0D0D0" |November 14
Title: The RSK Correspondence
| bgcolor="#A6B658" |Sapir Ben-Shahar
 
| bgcolor="#BCD2EE" |Hexaflexagons
Abstract:  In this talk I will show a brilliant 1-to-1 mapping between permutations on n elements and pairs of Standard Young Tableau of size n. This bijection, known as the Robinson-Schensted-Knuth correspondence, has many beautiful properties. It also tells you the best way for people to escape a series of rooms.
| bgcolor="#BCD2EE" |Come along for some hexaflexafun and discover the mysterious properties of hexaflexagons, the bestagons! Learn how to make and navigate through the folds of your very own paper hexaflexagon. No prior knowledge of hexagons (or hexaflexagons) is assumed.
 
|-
=== March 8, Pubo Huang  ===
| bgcolor="#D0D0D0" |November 21
 
| bgcolor="#A6B658" |Andrew Krenz
 
| bgcolor="#BCD2EE" |All concepts are database queries
 
| bgcolor="#BCD2EE" |A celebrated result of applied category theory states that the category of small categories is equivalent to the category of database schemas. Therefore, every theorem about small categories can be interpreted as a theorem about databases.  Maybe you've heard someone repeat Mac Lane's famous slogan "all concepts are Kan extensions."  In this talk, I'll give a high-level overview of/introduction to categorical database theory (developed by David Spivak) wherein Kan extensions play the role of regular every day database queries.  No familiarity with categories or databases will be assumed.
Title: 2-dimensional Dynamical Billiards
|-
 
| bgcolor="#D0D0D0" |November 28
Abstract: We have all played, or watched, a game of pool, and you probably noticed that when a ball hits the cushion on the table, its angle of rebound is equal to its angle of incidence.
| bgcolor="#A6B658" |THANKSGIVING
 
| bgcolor="#BCD2EE" |NONE
Dynamical Billiards is an idealization and generalization of the popular game called pool (or billiards, or snooker), and it aims to understand the trajectory (as time goes to infinity) of a ball on a frictionless table that rebounds perfectly. During the talk, I will provide a lot of examples of dynamical billiards on an actual table and compare it with its mathematical counterpart. We will also see how we can relate billiards on a rectangular table to the classical example of circle rotation in dynamics.
| bgcolor="#BCD2EE" |NONE
 
|-
=== March 15: NO SEMINAR (SPRING BREAK) ===
| bgcolor="#D0D0D0" |December 5
 
| bgcolor="#A6B658" |Caroline Nunn
=== March 22: Vicky Wen ===
| bgcolor="#BCD2EE" |Watch Caroline eat a donut: an introduction to Morse theory
 
| bgcolor="#BCD2EE" |Morse theory has been described as "one of the deepest applications of differential geometry to topology." However, the concepts involved in Morse theory are so simple that you can learn them just by watching me eat a donut (and subsequently watching me give a 20 minute talk explaining Morse theory.) No background is needed beyond calc 3 and a passing familiarity with donuts.
 
|}
Title: On Mostow's Rigidity Theorem
</center>
 
Abstract: Mostow rigidity is one of those famous theorems in hyperbolic geometry that links the topology and geometry of a hyperbolic space (aka a Riemannian manifold with constant curvature -1). It states that in higher dimension (n>2), the geometry of the space is completely determined by its fundamental group, which is a quiet strong and amazing result. In this talk I will try to explain the idea behind the proof and give some counterexamples in dimension 2.
 
=== March 24: VISIT DAY SPECIAL SESSIONS  ===
 
 
 
Title: Log concavity properties and combinatorial Hodge theory
 
Speaker: Colin Crowley
 
Abstract: Combinatorial Hodge theory is a newly created field (past decade) at the intersection of combinatorics and algebraic geometry. It has lead to proofs of long standing conjectures about matroids, which are objects that generalize finite graphs. I'll introduce some of the main objects, and tell a rough story of how this field came to be.
 
Title: Commutative algebra and geometry of systems of polynomials
 
Speaker: Maya Banks
 
Abstract: When your favorite computer algebra system solves systems of polynomials, it does so by computing something called a Groebner Basis. Groebner bases are collections of polynomials that have many algebraic and geometric properties that make them especially well suited for solving both computational and theoretical problems in commutative algebra and algebraic geometry. I’ll talk about how we (and our computers) make use of these tools and what behind-the-scenes algebra and geometry makes them special.
 
 
 
Title: Markov chains and upper bounds on ranks of quadratic twists of an elliptic curve.
 
Speaker: Sun Woo Park
 
Abstract: I will try to give a heuristic argument on how one can use Markov chains to understand the dimensions of some families of finite dimensional vector spaces over F2 (the finite field with 2 elements), which can be used to compute an upper bound on the rank of families of quadratic twists of an elliptic curve. The talk I will deliver will assume background in vector spaces / linear algebra over finite fields, and no prior knowledge about elliptic curves will be required.
 
 
 
Title: Coherent Structures in Convection.
 
Speaker: Varun Gudibanda
 
Abstract: Have you ever boiled water? If so, then that's really great I hope you made some tea. It also means that you are familiar with the concept of convection. In convective systems, there are fundamental structures which play an important role in dictating the heat transport and other properties of the system. Let's explore these structures and also learn about how a single number has divided a community of researchers for decades.
 
 
 
Title: Morse Theory in Algebraic Topology (According to ChatGPT)
 
Speaker: Alex Hof
 
 
 
Title: Life in a Hyperbolic City
 
Speaker: Daniel Levitin
 
Abstract: I will discuss the most important reason prospective students should come to UW Madison: the (almost) locally Euclidean geometry, and how much of a mess it would be to live in a hyperbolic city. I will then talk about some related concepts in geometric group theory. This should provide a soft introduction to the colloquium talk as well.
 
 
 
Title: Logic: What is it good for?
 
Speaker: John Spoerl
 
Abstract: What are the logicians doing in the math department? Are they philosophers or computer scientists in disguise? (No.) How can I be as cool and mysterious as the logicians? We’ll see how the methods of logic are the most “effective” ways to do mathematics.
 
 
 
Title: Fourier restriction and Kakeya problems
 
Speaker: Mingfeng Chen
 
Abstract: Fourier restriction problem was introduced by Elias Stein in the 1970s. It is a central problem in Harmonic analysis. Moreover, restriction problems have close connections with other important questions in Geometric Measure theory(Kakeya problem), Harmonic analysis, combinatorics, number theory and PDE. In this talk, I'm going to give a simple introduction to what it is and what we are going to do.
 
=== March 29, Ivan Aidun ===
 
 
 
'''Title:''' Fractional Calculus
 
'''Abstract:''' We teach our calculus students about 1<sup>st</sup> and 2<sup>nd</sup> derivatives, but what about 1/2th derivatives?  What about πth derivatives?  Can we make sense of these derivatives?  Can we use them for anything?
 
=== April 5, Diego Rojas La Luz ===
 
 
 
Title: Eating a poisoned chocolate bar
 
Abstract: Today we are going to talk about Chomp, a game where you take turns eating chocolate and you try not to die from poisoning. This is one of those very easy-to-state combinatoric games which happens to be very hard to fully analyze. We'll see that we can say some surprising things regarding winning strategies, so stay tuned for that. Who wants to play?
 
=== April 12, Taylor Tan ===
 
 
 
Title: A Proof From The Hall of Fame -- Topological Methods in Combinatorics
 
Abstract: Consider the collection of all n-sets from a 2n+k element ground set. This collection can be partitioned into k+2 partite classes such that there are no intersections between n-sets in the same partite class. In 1955, Kneser conjectured that this bound was sharp, but the problem remained open for two decades until László Lovász gave a proof through topological methods in 1978, thereby inventing the field of topological combinatorics. Another few decades later, a greatly simplified proof (it fits in one paragraph!) was discovered by Joshua Greene and his beautiful proof will be presented in all its glory.  
 
=== April 19, NO SEMINAR  ===
 
=== April 26, Hyun Jong Kim  ===
 
 
Title: Machine Learning Tools for the Working Mathematician
 
Abstract: Mathematicians often have to learn new concepts. I will briefly present <code>trouver</code>​, a Python librarythat I have been developing that uses machine learning models to help this process. In particular, <code>trouver</code>​ can categorize types of mathematical text, identify where notations are introduced in such mathematical text, and attempt to summarize what these notations denote. I will also talk about some high-level ideas go into training such machine learning models in the modern day without huge amounts of data and computational resources.
 
=== May 3, Asvin G ===
Title: On the random graph on countably many vertices 
 
Abstract: I will tell you about "the" graph on countably many vertices. It has many remarkable properties - for instance, any "property" true of it is true for almost all finite graphs!
 
 
== Fall 2021 ==
 
=== September 29, John Cobb ===
 
Title: Rooms on a Sphere
 
Abstract: A classic combinatorial lemma becomes very simple to state and prove when on the surface of a sphere, leading to easy constructive proofs of some other well known theorems.
 
=== October 6, Karan Srivastava ===
 
Title: An 'almost impossible' puzzle and group theory
 
Abstract: You're given a chessboard with a randomly oriented coin on every square and a key hidden under one of them; player one knows where the key is and flips a single coin; player 2, using only the information of the new coin arrangement must determine where the key is. Is there a winning strategy? In this talk, we will explore this classic puzzle in a more generalized context, with n squares and d sided dice on every square. We'll see when the game is solvable and in doing so, see how the answer relies on group theory and the existence of certain groups.
 
=== October 13, John Yin ===
 
Title: TBA
 
Abstract: TBA
 
=== October 20, Varun Gudibanda ===
 
Title: TBA
 
Abstract: TBA
 
=== October 27, Andrew Krenz ===
 
Title: The 3-sphere via the Hopf fibration
 
Abstract: The Hopf fibration is a map from $S^3$ to $S^2$.  The preimage (or fiber) of every point under this map is a copy of $S^1$. In this talk I will explain exactly how these circles “fit together” inside the 3-sphere. Along the way we’ll discover some other interesting facts in some hands-on demonstrations using paper and scissors.  If there is time I hope to also relate our new understanding of $S^3$ to some other familiar models.
=== November 3, Asvin G  ===
 
Title: Probabilistic methods in math
 
Abstract: I'll explain how you can provr that something has to be true because it's probably true in a couple of examples. One of the proofs is by Erdos on the "sum set problem" and it is a proof that "only an alien could have come up with" according to a friend.
 
=== November 10, Ivan Aidun ===
[[File:Screen Shot 2021-11-15 at 3.25.38 PM.png|thumb]]
Title: Intersection Permutations
 
Abstract: During a boring meeting, your buddy slips you a Paris metro ticket with this cryptic diagram (see left).
 
What could it mean?  The only way to find out is to come to this Donut Talk!
 
=== December 1, Yuxi Han  ===
 
Title: Homocidal Chaffeur Problem
 
Abstract: I will briefly introduce the canonical example of differential games, called the homicidal chauffeur problem and how to use PDE to run down pedestrians optimally.
 
=== December 8, Owen Goff  ===
 
Title: The Mathematics of Cribbage
 
Abstract: Cribbage is a card game that I have played many times over the years, that involves, among other things, finding subsets of set of numbers that equal a specific value (in the game that value is 15). In this donut talk I will attempt to use the power of combinatorics to find the optimal strategy for this game, particularly to solve one problem -- is there a way you can guarantee yourself at least one extra point by adding an additional card to your set?
 
== Spring 2022 ==
 
=== February 9, Alex Mine ===

Latest revision as of 19:14, 2 December 2024

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: Thursdays 4:00-4:30pm
  • 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 2024

Date Speaker Title Abstract
September 12 Ari Davidovsky 95% of people can't solve this! Image.png

We will attempt to answer this question and along the way explore how algebra and geometry work together to solve problems in number theory.

September 19 CANCELLED NONE NONE
September 26 Mateo Morales Officially petitioning the department to acquire a ping pong table. Ever want to prove something is a free group of rank 2? Me too. One way to do this is to use a ping pong argument of how a group generated by two elements acts on a set.

I will illustrate the ping pong argument using an example of matrices, explain how it works, and explain why, kinda.

Very approachable if you know what a group is but does require tons of ping pong experience.

October 3 Karthik Ravishankar Incompleteness for the working mathematician In this talk we'll take a look at Gödels famous incompleteness theorems and look at some of its immediate as well as interesting consequences. No background in logic is necessary!
October 10 Elizabeth Hankins Mathematical Origami and Flat-Foldability If you've ever unfolded a piece of origami, you might have noticed complicated symmetries in the pattern of creases left behind. What patterns of lines can and cannot be folded into origami? And why is it sometimes hard to determine?
October 17 CANCELLED NONE NONE
October 24 CANCELLED NONE NONE
October 31 Jacob Wood What is the length of a potato pumpkin? How many is a jack-o-lantern? What is the length of a pumpkin? These questions sound like nonsense, but they have perfectly reasonable interpretations with perfectly reasonable answers. On our journey through the haunted house with two rooms, we will encounter some scary characters like differential topology and measure theory. Do not fear; little to no experience in either subject is required.
November 7 CANCELLED: DISTINGUISHED LECTURE NONE NONE
November 14 Sapir Ben-Shahar Hexaflexagons Come along for some hexaflexafun and discover the mysterious properties of hexaflexagons, the bestagons! Learn how to make and navigate through the folds of your very own paper hexaflexagon. No prior knowledge of hexagons (or hexaflexagons) is assumed.
November 21 Andrew Krenz All concepts are database queries A celebrated result of applied category theory states that the category of small categories is equivalent to the category of database schemas. Therefore, every theorem about small categories can be interpreted as a theorem about databases.  Maybe you've heard someone repeat Mac Lane's famous slogan "all concepts are Kan extensions."  In this talk, I'll give a high-level overview of/introduction to categorical database theory (developed by David Spivak) wherein Kan extensions play the role of regular every day database queries.  No familiarity with categories or databases will be assumed.
November 28 THANKSGIVING NONE NONE
December 5 Caroline Nunn Watch Caroline eat a donut: an introduction to Morse theory Morse theory has been described as "one of the deepest applications of differential geometry to topology." However, the concepts involved in Morse theory are so simple that you can learn them just by watching me eat a donut (and subsequently watching me give a 20 minute talk explaining Morse theory.) No background is needed beyond calc 3 and a passing familiarity with donuts.
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