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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:''' [https://people.math.wisc.edu/~ywu495/ Yandi Wu], Maya Banks


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 2021 ==


Title: Configuration Spaces of Graphs
=== September 29, John Cobb ===


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.
Title: Rooms on a Sphere


=== October 14, Moisés Herradón ===
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.


Title: The natural numbers form a field
=== October 6, Karan Srivastava ===


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.
Title: An 'almost impossible' puzzle and group theory


=== October 21, David Bruce ===
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.


Title: Coverings, Dynamics, and Kneading Sequences
=== October 13, John Yin ===


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.
Title: TBA


=== October 28, Paul Tveite ===
Abstract: TBA


Title: Gödel Incompleteness, Goodstein's Theorem, and the Hydra Game
=== October 20, Varun Gudibanda ===


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.
Title: TBA


=== November 4, Wanlin Li ===
Abstract: TBA


Title: Expander Families, Ramanujan graphs, and Property tau
=== October 27, Andrew Krenz ===


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...
Title: The 3-sphere via the Hopf fibration


=== November 11, Daniel Hast ===
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.


Title: Scissor groups of polyhedra and Hilbert's third problem


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.
=== November 3, TBA ===


=== November 18, James Waddington ===
Title: TBA


Title: Euler Spoilers
Abstract: TBA


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.
=== November 10, TBA ===


=== December 2, TBA ===
Title: TBA


=== December 9, TBA ===
Abstract: TBA


==Spring 2015==
=== November 17, TBA ===


===January 28, Moisés Herradón===
Title: TBA


Title: Winning games and taking names
Abstract: TBA


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!
=== November 24, TBA ===


===February 11, Becky Eastham===
Title: TBA


Title: A generalization of van der Waerden numbers: (a, b) triples and (a_1, a_2, ..., a_n) (n + 1)-tuples
Abstract: TBA


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.
=== December 1, TBA ===


===February 18, Solly Parenti===
Title: TBA


Title: Chebyshev's Bias
Abstract: TBA


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.
=== December 8, TBA ===


===February 25, David Bruce===
Title: TBA


Title: Mean, Median, and Mode - Well Actually Just Median
Abstract: TBA
 
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?

Revision as of 20:39, 1 October 2021

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: Yandi Wu, Maya Banks

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 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, TBA

Title: TBA

Abstract: TBA

November 10, TBA

Title: TBA

Abstract: TBA

November 17, TBA

Title: TBA

Abstract: TBA

November 24, TBA

Title: TBA

Abstract: TBA

December 1, TBA

Title: TBA

Abstract: TBA

December 8, TBA

Title: TBA

Abstract: TBA