AMS Student Chapter Seminar: Difference between revisions

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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]].


== Spring 2023 ==
== Fall 2023==


=== January 25, Michael Jeserum ===
===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.


Title: Totally Realistic Supply Chains
===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. 


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!
===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.


=== February 1, Summer al Hamdani ===
===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:
Abstract:


Title: Monkeying Around: On the Infinite Monkey Theorem
===November 2, Speaker TBA===
Title:
Abstract:


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


=== February 8, Dionel Jaime ===
===November 16, Speaker TBA===
Title:
Abstract:


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


===November 30, Speaker TBA===
Title:
Abstract:


Title: The weird world of polynomial curve fitting.
===December 7, Speaker TBA===
Title:
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.
===December 14, Maybe Cancelled?===
 
=== 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<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?

Revision as of 16:32, 13 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: Abstract:

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?

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