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The AMS Student Chapter Seminar is an informal, graduate student-run seminar on a wide range of mathematical topics. Pastries (usually donuts) will be provided.
The AMS Student Chapter Seminar (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, 3:00 PM – 3:30 PM
* '''When:''' Wednesdays, 3:30 PM – 4:00 PM
* '''Where:''' Van Vleck, 9th floor lounge
* '''Where:''' Van Vleck, 9th floor lounge (unless otherwise announced)
* '''Organizers:''' Daniel Hast, Ryan Julian, Laura Cladek, Cullen McDonald, Zachary Charles
* '''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.


== Fall 2015 ==
The schedule of talks from past semesters can be found [[AMS Student Chapter Seminar, previous semesters|here]].


=== October 7, Eric Ramos ===
== Fall 2023==


Title: Configuration Spaces of Graphs
===September 7, Alex Mine===
Title: My Favorite Fact about Continued Fractions


Abstract: A configuration of n points on a graph is just a choice of n distinct points. The set of all such configurations is a topological space, and so one can study its properties. Unsurprisingly, one can determine a lot of information about this configuration space from combinatorial data of the graph. In this talk, we consider some of the most basic properties of these spaces, and discuss how they can be applied to things like robotics. Note that most of the talk will amount to drawing pictures until everyone agrees a statement is true.
===September 14, Mei Rose Connor ===
Title: All Things Necessary and Possible: an introduction to the Kripke semantics of modal logic


=== October 14, Moisés Herradón ===
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.


Title: The natural numbers form a field
===September 21, Sun Woo Park ===
Title: What I did in my military service II (A functorial formulation of deep learning algorithms)


Abstract: But of course, you already knew that they form a field: you just have to biject them into Q and then use the sum and product from the rational numbers. However, out of the many field structures the natural numbers can have, the one I’ll talk about is for sure the cutest. I will discuss how this field shows up in "nature" (i.e. in the games of some fellows of infinite jest) and what cute properties it has.
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.


=== October 21, David Bruce ===
===September 28, Caroline Nunn===
Title: Phinary Numbers


Title: Coverings, Dynamics, and Kneading Sequences
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: Given a continuous map f:X—>X of topological spaces and a point x in X one can consider the set {x, f(x), f(f(x)), f(f(f(x))),…} i.e, the orbit of x under the map f. The study of such things even in simple cases, for example when X is the complex numbers and f is a (quadratic) polynomial, turns out to be quite complex (pun sort of intended). (It also gives rise to main source of pretty pictures mathematicians put on posters.) In this talk I want to show how the study of such orbits is related to the following question: How can one tell if a (ramified) covering of S^2 comes from a rational function? No background will be assumed and there will be pretty pictures to stare at.
===October 5, Gabriella Brown===
Title: Topological Entropy in Shift Spaces


=== October 28, Paul Tveite ===
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.


Title: Gödel Incompleteness, Goodstein's Theorem, and the Hydra Game
===October 12, Nakid Cordero===
Title: How to prove the Riemann Hypothesis: a logician's approach


Abstract: Gödel incompleteness states, roughly, that there are statements about the natural numbers that are true, but cannot be proved using just Peano Arithmetic. I will give a couple concrete examples of such statements, and prove them in higher mathematics.
Abstract: ''Hint:'' ''Prove that you cannot disprove it.''


=== November 4, Wanlin Li ===
===October 19, Ari Davidovsky===
Title: Using Ultrafilters in Additive Combinatorics


Title: Expander Families, Ramanujan graphs, and Property tau
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.


Abstract: Expander family is an interesting topic in graph theory. I will define it, give non-examples and talk about the ideal kind of it, i.e. Ramanujan graph. Also, I will talk about property tau of a group and how it is related to expander families. To make the talk not full of definitions, here are part of the things I'm not going to define: Graph, regular graph, Bipartite graph, Adjacency matrix of a graph and tea...
===October 26, Otto Baier===
Title: "Circulant Matrices and the Discrete Fourier Transform"


=== November 11, Daniel Hast ===
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!


Title: Scissor groups of polyhedra and Hilbert's third problem
===November 2, Speaker TBA===
Title:


Abstract: Given two polytopes of equal measure (area, volume, etc.), can the first be cut into finitely many polytopic pieces and reassembled into the second? To investigate this question, we will introduce the notion of a "scissor group" and compute the scissor group of polygons. We will also discuss the polyhedral case and how it relates to Dehn's solution to Hilbert's third problem. If there is time, we may mention some fancier examples of scissor groups.
Abstract:


=== November 18, James Waddington ===
===November 9, Owen Goff===
Title:


''Note: This week's talk will be from 3:15 to 3:45 instead of the usual time.''
Abstract:


Title: Euler Spoilers
===November 16, Speaker TBA===
Title:


Abstract: Leonhard Euler is often cited as one of the greatest mathematicians of the 18. Century. His solution to the Königsburg Bridge problem is an important result of early topology. Euler also did work in combinatorics and in number theory. Often his methods tended to be computational in nature (he was a computer in the traditional sense) and from these he proposed many conjectures, a few of which turned out to be wrong. Two failed conjectures of Euler will be presented.
Abstract:


=== December 9, Brandon Alberts ===
===November 23, CANCELLED FOR THANKSGIVING===


Title: The field with one element
===November 30, Speaker TBA===
Title:


=== December 16, Micky Soule Steinberg ===
Abstract:


Title: Intersective polynomials
===December 7, Speaker TBA===
Title:


==Spring 2015==
Abstract:


===January 28, Moisés Herradón===
===December 14, Maybe Cancelled?===
 
Title: Winning games and taking names
 
Abstract:  So let’s say we’re already amazing at playing one game (any game!) at a time and we now we need to play several games at once, to keep it challenging. We will see that doing this results in us being able to define an addition on the collection of all games, and that it actually turns this collection into a Group. I will talk about some of the wonders that lie within the group. Maybe lions? Maybe a field containing both the real numbers and the ordinals? For sure it has to be one of these two!
 
===February 11, Becky Eastham===
 
Title: A generalization of van der Waerden numbers: (a, b) triples and (a_1, a_2, ..., a_n) (n + 1)-tuples
 
Abstract: Van der Waerden defined w(k; r) to be the least positive integer such that for every r-coloring of the integers from 1 to w(k; r), there is a monochromatic arithmetic progression of length k.  He proved that w(k; r) exists for all positive k, r.  I will discuss the case where r = 2.  These numbers are notoriously hard to calculate: the first 6 of these are 1, 3, 9, 35, 178, and 1132, but no others are known.  I will discuss properties of a generalization of these numbers, (a_1, a_2, ..., a_n) (n + 1)-tuples, which are sets of the form {d, a_1x + d, a_2x + 2d, ..., a_nx + nd}, for d, x positive natural numbers.
 
===February 18, Solly Parenti===
 
Title: Chebyshev's Bias
 
Abstract: Euclid told us that there are infinitely many primes.  Dirichlet answered the question of how primes are distributed among residue classes.  This talk addresses the question of "Ya, but really, how are the primes distributed among residue classes?"  Chebyshev noted in 1853 that there seems to be more primes congruent to 3 mod 4 than their are primes congruent to 1 mod 4.  It turns out, he was right, wrong, and everything in between.  No analytic number theory is presumed for this talk, as none is known by the speaker.
 
===February 25, David Bruce===
 
Title: Mean, Median, and Mode - Well Actually Just Median
 
Abstract: Given a finite set of numbers there are many different ways to measure the center of the set. Three of the more common measures, familiar to any middle school students, are: mean, median, mode. This talk will focus on the concept of the median, and why in many ways it's sweet. In particular, we will explore how we can extend the notion of a median to higher dimensions, and apply it to create more robust statistics. It will be awesome, and there will be donuts.
 
===March 4, Jing Hao===
 
Title: Error Correction Codes
 
Abstract: In the modern world, many communication channels are subject to noise, and thus errors happen. To help the codes auto-correct themselves, more bits are added to the codes to make them more different from each other and therefore easier to tell apart. The major object we study is linear codes. They have nice algebraic structure embedded, and we can apply well-known algebraic results to construct 'nice' codes. This talk will touch on the basics of coding theory, and introduce some famous codes in the coding world, including several prize problems yet to be solved!
 
===March 10 (Tuesday), Nathan Clement===
 
''Note: This week's seminar will be on Tuesday at 3:30 instead of the usual time.''
 
Title: Two Solutions, not too Technical, to a Problem to which the Answer is Two
 
Abstract: A classical problem in Algebraic Geometry is this: Given four pairwise skew lines, how many other lines intersect all of them. I will present some (two) solutions to this problem. One is more classical and ad hoc and the other introduces the Grassmannian variety/manifold and a little intersection theory.
 
===March 25, Eric Ramos===
 
Title: Braids, Knots and Representations
 
Abstract: In the 1920's Artin defined the braid group, B_n, in an attempt to understand knots in a more algebraic setting. A braid is a certain arrangement of strings in three-dimensional space. It is a celebrated theorem of Alexander that every knot is obtainable from a braid by identifying the endpoints of each string. Because of this correspondence, the Jones and Alexander polynomials, two of the most important knot invariants, can be described completely using the braid group. In fact, Jones was able to show that knot invariants can often be realized as characters of special representations of the braid group.
 
The purpose of this talk is to give a very light introduction to braid and knot theory. The majority of the talk will be comprised of drawing pictures, and nothing will be treated rigorously.
 
===April 8, James Waddington===
 
Title: Goodstein's Theorem
 
Abstract: One of the most important results in the development of mathematics are
Gödel's Incompleteness theorems. The first incompleteness theorem shows that no
list of axioms one could provide could extend number theory to a complete and
consistent theory. The second showed that one such statement was no
axiomatization of number theory could be used to prove its own consistency.
Needless to say this was not viewed as a very natural independent statement
from arithmetic.
 
Examples of non-metamathematical results that were independent of PA, but true
of second order number theory, were not discovered until much later. Within a
short time of each three such statements that were more "natural" were
discovered. The Paris–Harrington Theorem, which was about a statement in Ramsey
theory, the Kirby–Paris theorem, which showed the independence of Goodstein's
theorem from Peano Arithmetic and the Kruskal's tree theorem, a statement about
finite trees.
 
In this talk I shall discuss Goodstein's theorem which discusses the end
behavior of a certain "Zero player" game about k-nary expansions of numbers.
I will also give some elements of the proof of the Kirby–Paris theorem.
 
===April 22, William Cocke===
 
Title: Finite Groups aren't too Square
 
Abstract: We investigate how many non-p-th powers a group can have for a given prime p.
We will show using some elementary group theory, that if np(G) is the number of non-p-th powers
in a group G, then G has order bounded by np(G)(np(G)+1). Time permitting we will show this bound
is strict and that mentioned results involving more than finite groups.
 
==Fall 2014==
 
===September 25, Vladimir Sotirov===
 
Title: [[Media:Compact-openTalk.pdf|The compact open topology: what is it really?]]
 
Abstract:  The compact-open topology on the space C(X,Y) of continuous functions from X to Y is mysteriously generated by declaring that for each compact subset K of X and each open subset V of Y, the continous functions f: X->Y conducting K inside V constitute an open set. In this talk, I will explain the universal property that uniquely determines the compact-open topology, and sketch a pretty constellation of little-known but elementary facts from domain theory that dispell the mystery of the compact-open topology's definition.
 
===October 8, David Bruce===
 
Title: Hex on the Beach
 
Abstract: The game of Hex is a two player game played on a hexagonal grid attributed in part to John Nash. (This is the game he is playing in /A Beautiful Mind./) Despite being relatively easy to pick up, and pretty hard to master, this game has surprising connections to some interesting mathematics. This talk will introduce the game of Hex, and then explore some of these connections. *As it is a lot more fun once you've actually played Hex feel free to join me at 3:00pm on the 9th floor to actually play a few games of Hex!*
 
===October 22, Eva Elduque===
 
Title: The fold and one cut problem
 
Abstract: What shapes can we get by folding flat a piece of paper and making (only) one complete straight cut? The answer is surprising: We can cut out any shape drawn with straight line segments. In the talk, we will discuss the two methods of approaching this problem, focusing on the straight skeleton method, the most intuitive of the two.
 
===November 5, Megan Maguire===
 
Title: Train tracks on surfaces
 
Abstract: What is a train track, mathematically speaking? Are they interesting? Why are they interesting? Come find out!
 
===November 19, Adrian Tovar-Lopez===
 
Title:  Hodgkin and Huxley equations of a single neuron
 
===December 3, Zachary Charles===
 
Title:  Addition chains: To exponentiation and beyond
 
Abstract: An addition chain is a sequence of numbers starting at one, such that every number is the sum of two previous numbers. What is the shortest chain ending at a number n? While this is already difficult, we will talk about how addition chains answer life's difficult questions, including: How do we compute 2^4? What can the Ancient Egyptians teach us about elliptic curve cryptography? What about subtraction?

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?