# AMS Student Chapter Seminar: Difference between revisions

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The AMS Student Chapter Seminar is an informal, graduate student | 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: | * '''When:''' Wednesdays, 3:30 PM – 4:00 PM | ||

* '''Where:''' Van Vleck, 9th floor lounge | * '''Where:''' Van Vleck, 9th floor lounge (unless otherwise announced) | ||

* '''Organizers:''' | * '''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 | 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]]. | |||

== | == Spring 2023 == | ||

=== | === January 25, Michael Jeserum === | ||

Title: Totally Realistic Supply Chains | |||

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! | |||

=== | === February 1, Summer al Hamdani === | ||

Title: Monkeying Around: On the Infinite Monkey Theorem | |||

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. | |||

=== February 8, Dionel Jaime === | |||

Title: | Title: The weird world of polynomial curve fitting. | ||

Abstract: | 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. | ||

===February | === February 15, Sun Woo Park === | ||

Title: What I did in my military service (Universal covers and graph neural networks) | |||

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! | |||

=== February 22: NO SEMINAR === | |||

=== February 28, Owen Goff === | |||

Title: The RSK Correspondence | |||

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. | |||

=== March 8, Pubo Huang === | |||

Title: 2-dimensional Dynamical Billiards | |||

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. | |||

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. | |||

===March | === March 15: NO SEMINAR (SPRING BREAK) === | ||

=== March 22: Vicky Wen === | |||

Title: On Mostow's Rigidity Theorem | |||

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: | 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: | Title: Morse Theory in Algebraic Topology (According to ChatGPT) | ||

Speaker: Alex Hof | |||

Abstract: | |||

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! | |||

== Spring 2022 == | |||

=== February 9, Alex Mine === | |||

Title: Would you like to play a game? | |||

Abstract: We'll look at some fun things in combinatorial game theory. | |||

=== February 16, Michael Jeserum === | |||

Title: The Internet's Take on Number Bases | |||

Abstract: Inspired by a TikTok video, we'll embark on a journey to find the best number base to work in*. | |||

<nowiki>*</nowiki>Disclaimer: audience may not actually learn what the best number base is. | |||

=== February 23, Erika Pirnes === | |||

Title: Staying Balanced- studying the balanced algebra | |||

Abstract: The balanced algebra has two generators, R and L, and its defining relations are that any pair of balanced words commutes. For example, RL and LR are balanced (contain the same number of both generators), so in the balanced algebra, (RL)(LR)=(LR)(RL). The goal is to find out which pairs are required to commute in order to make any pair of balanced words commute. This talk includes beautiful mountain landscapes and requires very minimal background knowledge. | |||

=== March 2, Jason Torchinsky === | |||

Title: Holmes and Watson and the case of the tropical climate | |||

Abstract: With a case as complex as the tropical climate, who else could you call? In this talk, we will discuss a strategy for getting models to team up to create a faithful simulation through an analogy of the original sleuthing dynamic duo, Sherlock Holmes and Dr. James Watson. | |||

=== March 7, Devanshi Merchant === | |||

Title: Mathematics of soap films | |||

Abstract: Nature is a miser when it comes to energy. This tendency, in case of soap films motivates mathematicians to study minimal surfaces. This study leads to some beautiful geometry that we will explore. | |||

=== March 30, Jacob Denson === | |||

Title: Proofs in 3 bits or less | |||

Abstract: What can you prove with a string of bits? Is there a proof of Fermat's Last Theorem of the form: "101"? Let's eat donuts, and then talk about it. | |||

=== April 6, Aidan Howells === | |||

Title: Goodstein Sequences, Hercules, and the Hydra | |||

Abstract: We'll discuss Goodstein sequences, Goodstein's theorem, and the Kirby–Paris theorem. We'll relate this to the hydra game of Kirby and Paris. The next time you are supposed to be working, instead check out the hydra game here: <nowiki>http://www.madore.org/~david/math/hydra0.xhtml</nowiki> | |||

Can you beat the hydra? Can you devise a winning strategy, and prove that it always wins? If that's too easy, a harder Hydra game is here: <nowiki>http://www.madore.org/~david/math/hydra.xhtml</nowiki> | |||

=== April 13, Yu Fu === | |||

Title: How do generic properties spread? | |||

Abstract: Given a family of algebraic varieties, a natural question to ask is what type of properties of the generic fiber, and how those properties extend to other fibers. Let's explore this topic from an arithmetic point of view by looking at an example: given a 1-dim family of pairs of elliptic curves with the generic fiber be a pair of isogenous elliptic curves, how the property of 'being isogenous' extend to other fibers? | |||

=== April 20, Ivan Aidun === | |||

Title: The are no Orthogonal Latin Squares of Order 6 | |||

Abstract: The title says it all. | |||

== 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? |

## Latest revision as of 01:03, 1 July 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.

## Spring 2023

### January 25, Michael Jeserum

Title: Totally Realistic Supply Chains

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!

### February 1, Summer al Hamdani

Title: Monkeying Around: On the Infinite Monkey Theorem

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.

### February 8, Dionel Jaime

Title: The weird world of polynomial curve fitting.

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.

### February 15, Sun Woo Park

Title: What I did in my military service (Universal covers and graph neural networks)

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!

### February 22: NO SEMINAR

### February 28, Owen Goff

Title: The RSK Correspondence

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.

### March 8, Pubo Huang

Title: 2-dimensional Dynamical Billiards

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.

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.

### March 15: NO SEMINAR (SPRING BREAK)

### March 22: Vicky Wen

Title: On Mostow's Rigidity Theorem

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^{st} and 2^{nd} 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 `trouver`

, a Python librarythat I have been developing that uses machine learning models to help this process. In particular, `trouver`

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!

## Spring 2022

### February 9, Alex Mine

Title: Would you like to play a game?

Abstract: We'll look at some fun things in combinatorial game theory.

### February 16, Michael Jeserum

Title: The Internet's Take on Number Bases

Abstract: Inspired by a TikTok video, we'll embark on a journey to find the best number base to work in*.

*Disclaimer: audience may not actually learn what the best number base is.

### February 23, Erika Pirnes

Title: Staying Balanced- studying the balanced algebra

Abstract: The balanced algebra has two generators, R and L, and its defining relations are that any pair of balanced words commutes. For example, RL and LR are balanced (contain the same number of both generators), so in the balanced algebra, (RL)(LR)=(LR)(RL). The goal is to find out which pairs are required to commute in order to make any pair of balanced words commute. This talk includes beautiful mountain landscapes and requires very minimal background knowledge.

### March 2, Jason Torchinsky

Title: Holmes and Watson and the case of the tropical climate

Abstract: With a case as complex as the tropical climate, who else could you call? In this talk, we will discuss a strategy for getting models to team up to create a faithful simulation through an analogy of the original sleuthing dynamic duo, Sherlock Holmes and Dr. James Watson.

### March 7, Devanshi Merchant

Title: Mathematics of soap films

Abstract: Nature is a miser when it comes to energy. This tendency, in case of soap films motivates mathematicians to study minimal surfaces. This study leads to some beautiful geometry that we will explore.

### March 30, Jacob Denson

Title: Proofs in 3 bits or less

Abstract: What can you prove with a string of bits? Is there a proof of Fermat's Last Theorem of the form: "101"? Let's eat donuts, and then talk about it.

### April 6, Aidan Howells

Title: Goodstein Sequences, Hercules, and the Hydra

Abstract: We'll discuss Goodstein sequences, Goodstein's theorem, and the Kirby–Paris theorem. We'll relate this to the hydra game of Kirby and Paris. The next time you are supposed to be working, instead check out the hydra game here: http://www.madore.org/~david/math/hydra0.xhtml

Can you beat the hydra? Can you devise a winning strategy, and prove that it always wins? If that's too easy, a harder Hydra game is here: http://www.madore.org/~david/math/hydra.xhtml

### April 13, Yu Fu

Title: How do generic properties spread?

Abstract: Given a family of algebraic varieties, a natural question to ask is what type of properties of the generic fiber, and how those properties extend to other fibers. Let's explore this topic from an arithmetic point of view by looking at an example: given a 1-dim family of pairs of elliptic curves with the generic fiber be a pair of isogenous elliptic curves, how the property of 'being isogenous' extend to other fibers?

### April 20, Ivan Aidun

Title: The are no Orthogonal Latin Squares of Order 6

Abstract: The title says it all.

## 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

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?