Difference between revisions of "AMS Student Chapter Seminar"

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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.
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The AMS Student Chapter Seminar (aka Donut Seminar) is an informal, graduate student seminar on a wide range of mathematical topics. Pastries (usually donuts) will be provided.
  
* '''When:''' Wednesdays, 3:30 PM – 4:00 PM
+
* '''When:''' Wednesdays, 3:20 PM – 3:50 PM
* '''Where:''' Van Vleck, 9th floor lounge
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* '''Where:''' Van Vleck, 9th floor lounge (unless otherwise announced)
* '''Organizers:''' Daniel Hast, Ryan Julian, Laura Cladek, Cullen McDonald, Zachary Charles
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* '''Organizers:''' [https://www.math.wisc.edu/~malexis/ Michel Alexis], [https://www.math.wisc.edu/~drwagner/ David Wagner], [http://www.math.wisc.edu/~nicodemus/ Patrick Nicodemus], [http://www.math.wisc.edu/~thaison/ Son Tu], Carrie Chen
  
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.
  
== Spring 2016 ==
+
The schedule of talks from past semesters can be found [[AMS Student Chapter Seminar, previous semesters|here]].
  
=== January 27, Wanlin Li ===
+
== Spring 2020 ==
  
Title: The Nottingham group
+
=== February 5, Alex Mine===
  
Abstract: It's the group of wild automorphisms of the local field F_q((t)). It's a finitely generated pro-p group. It's hereditarily just infinite. Every finite p-group can be embedded in it.  It's a favorite test case for conjectures concerning pro-p groups.  It's the Nottingham group! I will introduce you to this nice pro-p group which is loved by group theorists and number theorists.
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Title: Khinchin's Constant
  
=== February 3, Will Cocke ===
+
Abstract: I'll talk about a really weird fact about continued fractions.
  
Title: Who or What is the First Order & Why Should I Care?
+
=== February 12, Xiao Shen===
  
Abstract: As noted in recent films, the First Order is very powerful. We will discuss automated theorem proving software, including what exactly that means. We will then demonstrate some theorems, including previously unknown results, whose proofs can be mined from your computer.
+
Title: Coalescence estimates for the corner growth model with exponential weights
  
=== February 10, Jason Steinberg ===
+
Abstract: (Joint with Timo Seppalainen) I will talk about estimates for the coalescence time of semi-infinite directed geodesics in the planar corner growth model. Not much probability background is needed.
  
Title: Mazur's Swindle
+
=== February 19, Hyun Jong Kim===
  
Abstract: If we sum the series 1-1+1-1+1-1+... in two ways, we get the nonsensical result 0=1 as follows: 0=(1-1)+(1-1)+(1-1)+...=1+(-1+1)+(-1+1)+...=1. While the argument is invalid in the context of adding infinitely many numbers together, there are other contexts throughout mathematics when it makes sense to take arbitrary infinite "sums" of objects in a way that these sums satisfy an infinite form of associativity. In such contexts, the above argument is valid. Examples of such contexts are connected sums of manifolds, disjoint unions of sets, and direct sums of modules, and in each case we can use this kind of argument to achieve nontrivial results fairly easily. Almost too easily...
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Title: Orbifolds for Music
  
=== February 17, Zachary Charles ===
+
Abstract: In the first-ever music theory article published by the journal ''Science'', Dmitri Tymoczko uses orbifolds to describe a general framework for thinking about musical tonality. I am going to introduce the musical terms and ideas needed to describe how such orbifolds arise so that we can see an example of Tymoczko's geometric analysis of chord progressions.
  
Title: #P and Me: A tale of permanent complexity
+
=== February 26, Solly Parenti===
  
Abstract: The permanent is the neglected younger sibling of the determinant. We will discuss the permanent, its properties, and its applications in graph theory and commutative algebra. We will then talk about computational complexity classes and why the permanent lies at a very strange place in the complexity hierarchy. If time permits, we will discuss operations with even sillier names, such as the immanant.
+
Title: Mathematical Measuring
  
=== February 24, Brandon Alberts ===
+
Abstract: What's the best way to measure things? Come find out!
  
Title: The Rado Graph
+
=== March 4, Cancelled===
  
Abstract: A graph so unique, that a countably infinite random graph is isomorphic to the Rado Graph with probability 1. This talk will define the Rado Graph and walk through a proof of this surprising property.
+
=== March 11, Ivan Aidun===
  
=== March 2, Vlad Matei ===
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Title: The Notorious CRT
  
Title: Pythagoras numbers of fields
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Abstract: You're walking up Bascomb hill when a troll suddenly appears and says he'll kill you unless you compute the determinant of
 +
:<math> \begin{bmatrix}0 & -7 & -17 & -5 & -13\\8 & -14 & 14 & 11 & 15\\-5 & -17 & 10 & 2 & 10\\17 & 3 & -16 & -13 & 7\\-1 & 2 & -13 & -11 & 10\end{bmatrix}</math>
 +
by hand.  wdyd?
  
Abstract: The Pythagoras number of a field describes the structure of the set of squares in the field. The Pythagoras number p(K) of a field K is the smallest positive integer p such that every sum of squares in K is a sum of p squares.
+
=== March 24 - Visit Day (talks cancelled)===
  
A pythagorean field is one with Pythagoras number 1: that is, every sum of squares is already a square.
+
==== Brandon Boggess, Time TBD ====
  
These fields have been studied for over a century and it all started with David Hilbert and his famous 17th problem and whether or not positive polynomial function on '''R'''^n can be written as a finite sum of squares of polynomial functions.
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Title: TBD
  
We explore the history and various results and some unanswered questions.
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Abstract: TBD
  
=== March 9, Micky Steinberg ===
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==== Yandi Wu, Time TBD====
  
Title: The Parallel Postulate and Non-Euclidean Geometry.
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Title: TBD
  
Abstract:
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Abstract: TBD
“Is Euclidean Geometry true? It has no meaning. We might as well ask if the metric system is true and if the old weights and measures are false; if Cartesian coordinates are true and polar coordinates false. One geometry cannot be more true than another: it can only be more convenient.” -Poincaré
 
  
Euclid’s Fifth Postulate is logically equivalent to the statement that there exists a unique line through a given point which is parallel to a given line. For 2000 years, mathematicians were sure that this was in fact a theorem which followed from his first four axioms. In attempts to prove the postulate by contradiction, three mathematicians accidentally invented a new geometry...
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==== Maya Banks, Time TBD====
  
=== March 16, Keith Rush ===
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Title: TBD
  
Title: TBA
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Abstract: TBD
  
Abstract: TBA
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==== Yuxi Han, Time TBD====
  
=== March 30, Iván Ongay Valverde ===
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Title: TBD
  
Title: Monstrosities out of measure
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Abstract: TBD
  
Abstract: It is a well known result that, using the Lebesgue measure, not all subsets of the real line are measurable. To get this result we use the property of invariance under translation and the axiom of choice. Is this still the case if we remove the invariance over translation? Depending how we answer this question the properties of the universe itself can change.
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==== Dionel Jaime, Time TBD====
  
=== April 6, Nathan Clement ===
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Title: TBD
  
Title: Algebraic Doughnuts
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Abstract: TBD
  
Abstract: A fun, elementary problem with a snappy solution from Algebraic Geometry. The only prerequisite for this talk is a basic knowledge of circles!
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==== Yun Li, Time TBD====
  
=== April 13, TBA ===
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Title: TBD
  
=== April 20, TBA ===
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Abstract: TBD
  
=== April 27, TBA ===
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==== Erika Pirnes, Time TBD====
  
=== May 4, TBA ===
+
Title: TBD
  
=== May 10, TBA ===
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Abstract: TBD
  
== Fall 2015 ==
+
==== Harry Liu, Time TBD====
  
=== October 7, Eric Ramos ===
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Title: TBD
  
Title: Configuration Spaces of Graphs
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Abstract: TBD
  
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.
+
==== Kit Newton, Time TBD====
  
=== October 14, Moisés Herradón ===
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Title: TBD
  
Title: The natural numbers form a field
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Abstract: TBD
  
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.
+
=== April 1, Ying Li (cancelled)===
  
=== October 21, David Bruce ===
+
Title: TBD
  
Title: Coverings, Dynamics, and Kneading Sequences
+
Abstract: TBD
  
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.
+
=== April 8, Ben Wright (cancelled)===
  
=== October 28, Paul Tveite ===
+
Title: TBD
  
Title: Gödel Incompleteness, Goodstein's Theorem, and the Hydra Game
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Abstract: TBD
  
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.
+
=== April 15, Owen Goff (cancelled)===
  
=== November 4, Wanlin Li ===
+
Title: TBD
  
Title: Expander Families, Ramanujan graphs, and Property tau
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Abstract: TBD
  
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...
+
== Fall 2019 ==
  
=== November 11, Daniel Hast ===
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=== October 9, Brandon Boggess===
  
Title: Scissor groups of polyhedra and Hilbert's third problem
+
Title: An Application of Elliptic Curves to the Theory of Internet Memes
  
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: Solve polynomial equations with this one weird trick! Math teachers hate him!!!
  
=== November 18, James Waddington ===
+
[[File:Thumbnail fruit meme.png]]
  
''Note: This week's talk will be from 3:15 to 3:45 instead of the usual time.''
+
=== October 16, Jiaxin Jin===
  
Title: Euler Spoilers
+
Title: Persistence and global stability for biochemical reaction-diffusion systems
  
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: The investigation of the dynamics of solutions of nonlinear reaction-diffusion PDE systems generated by biochemical networks is a great challenge; in general, even the existence of classical solutions is difficult to establish. On the other hand, these kinds of problems appear very often in biological applications, e.g., when trying to understand the role of spatial inhomogeneities in living cells. We discuss the persistence and global stability properties of special classes of such systems, under additional assumptions such as: low number of species, complex balance or weak reversibility.
  
=== December 9, Brandon Alberts ===
+
=== October 23, Erika Pirnes===
  
Title: The field with one element
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(special edition: carrot seminar)
  
=== December 16, Micky Soule Steinberg ===
+
Title: Why do ice hockey players fall in love with mathematicians? (Behavior of certain number string sequences)
  
Title: Intersective polynomials
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Abstract: Starting with some string of digits 0-9, add the adjacent numbers pairwise to obtain a new string. Whenever the sum is 10 or greater, separate its digits. For example, 26621 would become 81283 and then 931011. Repeating this process with different inputs gives varying behavior. In some cases the process terminates (becomes a single digit), or ends up in a loop, like 999, 1818, 999... The length of the strings can also start growing very fast. I'll discuss some data and conjectures about classifying the behavior.
  
==Spring 2015==
+
=== October 30, Yunbai Cao===
  
===January 28, Moisés Herradón===
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Title: Kinetic theory in bounded domains
  
Title: Winning games and taking names
+
Abstract: In 1900, David Hilbert outlined 23 important problems in the International Congress of Mathematics. One of them is the Hilbert's sixth problem which asks the mathematical linkage between the mechanics from microscopic view and the macroscopic view. A relative new mesoscopic point of view at that time which is "kinetic theory" was highlighted by Hilbert as the bridge to link the two. In this talk, I will talk about the history and basic elements of kinetic theory and Boltzmann equation, and the role boundary plays for such a system, as well as briefly mention some recent progress.
  
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 6, Tung Nguyen===
  
===February 11, Becky Eastham===
+
Title: Introduction to Chemical Reaction Network
  
Title: A generalization of van der Waerden numbers: (a, b) triples and (a_1, a_2, ..., a_n) (n + 1)-tuples
+
Abstract: Reaction network models are often used to investigate the dynamics of different species from various branches of chemistry, biology and ecology. The study of reaction network has grown significantly and involves a wide range of mathematics and applications. In this talk, I aim to show a big picture of what is happening in reaction network theory. I will first introduce the basic dynamical models for reaction network: the deterministic and stochastic models. Then, I will mention some big questions of interest, and the mathematical tools that are used by people in the field. Finally, I will make connection between reaction network and other branches of mathematics such as PDE, control theory, and random graph theory.
  
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.
+
=== November 13, Jane Davis===
  
===February 18, Solly Parenti===
+
Title: Brownian Minions
  
Title: Chebyshev's Bias
+
Abstract: Having lots of small minions help you perform a task is often very effective. For example, if you need to grade a large stack of calculus problems, it is effective to have several TAs grade parts of the pile for you. We'll talk about how we can use random motions as minions to help us perform mathematical tasks. Typically, this mathematical task would be optimization, but we'll reframe a little bit and focus on art and beauty instead. We'll also try to talk about the so-called "storytelling metric," which is relevant here. There will be pictures and animations! 🎉
  
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.
+
Sneak preview: some modern art generated with MATLAB.
  
===February 25, David Bruce===
+
[[File:Picpic.jpg]]
  
Title: Mean, Median, and Mode - Well Actually Just Median
+
=== November 20, Colin Crowley===
  
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.
+
Title: Matroid Bingo
  
===March 4, Jing Hao===
+
Abstract: Matroids are combinatorial objects that generalize graphs and matrices. The famous combinatorialist Gian Carlo Rota once said that "anyone who has worked with matroids has come away with the conviction that matroids are one of the richest and most useful ideas of our day." Although his day was in the 60s and 70s, matroids remain an active area of current research with connections to areas such as algebraic geometry, tropical geometry, and parts of computer science. Since this is a doughnut talk, I will introduce matroids in a cute way that involves playing bingo, and then I'll show you some cool examples.
  
Title: Error Correction Codes
+
=== December 4, Xiaocheng Li===
  
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!
+
Title: The method of stationary phase and Duistermaat-Heckman formula
  
===March 10 (Tuesday), Nathan Clement===
+
Abstract: The oscillatory integral $\int_X e^{itf(x)}\mu=:I(t), t\in \mathbb{R}$ is a fundamental object in analysis. In general, $I(t)$ seldom has an explicit expression as Fourier transform is usually inexplicit. In practice, we are interested in the asymptotic behavior of $I(t)$, that is, for $|t|$ very large. A classical tool of getting an approximation is the method of stationary phase which gives the leading term of $I(t)$. Furthermore, there are rare instances for which the approximation coincides with the exact value of $I(t)$. One example is the Duistermaat-Heckman formula in which the Hamiltonian action and the momentum map are addressed. In the talk, I will start with basic facts in Fourier analysis, then discuss the method of stationary phase and the Duistermaat-Heckman formula.
  
''Note: This week's seminar will be on Tuesday at 3:30 instead of the usual time.''
+
=== December 11, Chaojie Yuan===
  
Title: Two Solutions, not too Technical, to a Problem to which the Answer is Two
+
Title: Coupling and its application in stochastic chemical reaction network
  
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.
+
Abstract: Stochastic models for chemical reaction networks have become increasingly popular in the past few decades. When the molecules are present in low numbers, the chemical system always displays randomness in their dynamics, and the randomness cannot be ignored as it can have a significant effect on the overall properties of the dynamics. In this talk, I will introduce the stochastic models utilized in the context of biological interaction network. Then I will discuss coupling in this context, and illustrate through examples how coupling methods can be utilized for numerical simulations. Specifically, I will introduce two biological models, which attempts to address the behavior of interesting real-world phenomenon.
 
 
===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 11:49, 23 March 2020

The AMS Student Chapter Seminar (aka Donut Seminar) is an informal, graduate student seminar on a wide range of mathematical topics. Pastries (usually donuts) will be provided.

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 2020

February 5, Alex Mine

Title: Khinchin's Constant

Abstract: I'll talk about a really weird fact about continued fractions.

February 12, Xiao Shen

Title: Coalescence estimates for the corner growth model with exponential weights

Abstract: (Joint with Timo Seppalainen) I will talk about estimates for the coalescence time of semi-infinite directed geodesics in the planar corner growth model. Not much probability background is needed.

February 19, Hyun Jong Kim

Title: Orbifolds for Music

Abstract: In the first-ever music theory article published by the journal Science, Dmitri Tymoczko uses orbifolds to describe a general framework for thinking about musical tonality. I am going to introduce the musical terms and ideas needed to describe how such orbifolds arise so that we can see an example of Tymoczko's geometric analysis of chord progressions.

February 26, Solly Parenti

Title: Mathematical Measuring

Abstract: What's the best way to measure things? Come find out!

March 4, Cancelled

March 11, Ivan Aidun

Title: The Notorious CRT

Abstract: You're walking up Bascomb hill when a troll suddenly appears and says he'll kill you unless you compute the determinant of

[math] \begin{bmatrix}0 & -7 & -17 & -5 & -13\\8 & -14 & 14 & 11 & 15\\-5 & -17 & 10 & 2 & 10\\17 & 3 & -16 & -13 & 7\\-1 & 2 & -13 & -11 & 10\end{bmatrix}[/math]

by hand. wdyd?

March 24 - Visit Day (talks cancelled)

Brandon Boggess, Time TBD

Title: TBD

Abstract: TBD

Yandi Wu, Time TBD

Title: TBD

Abstract: TBD

Maya Banks, Time TBD

Title: TBD

Abstract: TBD

Yuxi Han, Time TBD

Title: TBD

Abstract: TBD

Dionel Jaime, Time TBD

Title: TBD

Abstract: TBD

Yun Li, Time TBD

Title: TBD

Abstract: TBD

Erika Pirnes, Time TBD

Title: TBD

Abstract: TBD

Harry Liu, Time TBD

Title: TBD

Abstract: TBD

Kit Newton, Time TBD

Title: TBD

Abstract: TBD

April 1, Ying Li (cancelled)

Title: TBD

Abstract: TBD

April 8, Ben Wright (cancelled)

Title: TBD

Abstract: TBD

April 15, Owen Goff (cancelled)

Title: TBD

Abstract: TBD

Fall 2019

October 9, Brandon Boggess

Title: An Application of Elliptic Curves to the Theory of Internet Memes

Abstract: Solve polynomial equations with this one weird trick! Math teachers hate him!!!

Thumbnail fruit meme.png

October 16, Jiaxin Jin

Title: Persistence and global stability for biochemical reaction-diffusion systems

Abstract: The investigation of the dynamics of solutions of nonlinear reaction-diffusion PDE systems generated by biochemical networks is a great challenge; in general, even the existence of classical solutions is difficult to establish. On the other hand, these kinds of problems appear very often in biological applications, e.g., when trying to understand the role of spatial inhomogeneities in living cells. We discuss the persistence and global stability properties of special classes of such systems, under additional assumptions such as: low number of species, complex balance or weak reversibility.

October 23, Erika Pirnes

(special edition: carrot seminar)

Title: Why do ice hockey players fall in love with mathematicians? (Behavior of certain number string sequences)

Abstract: Starting with some string of digits 0-9, add the adjacent numbers pairwise to obtain a new string. Whenever the sum is 10 or greater, separate its digits. For example, 26621 would become 81283 and then 931011. Repeating this process with different inputs gives varying behavior. In some cases the process terminates (becomes a single digit), or ends up in a loop, like 999, 1818, 999... The length of the strings can also start growing very fast. I'll discuss some data and conjectures about classifying the behavior.

October 30, Yunbai Cao

Title: Kinetic theory in bounded domains

Abstract: In 1900, David Hilbert outlined 23 important problems in the International Congress of Mathematics. One of them is the Hilbert's sixth problem which asks the mathematical linkage between the mechanics from microscopic view and the macroscopic view. A relative new mesoscopic point of view at that time which is "kinetic theory" was highlighted by Hilbert as the bridge to link the two. In this talk, I will talk about the history and basic elements of kinetic theory and Boltzmann equation, and the role boundary plays for such a system, as well as briefly mention some recent progress.

November 6, Tung Nguyen

Title: Introduction to Chemical Reaction Network

Abstract: Reaction network models are often used to investigate the dynamics of different species from various branches of chemistry, biology and ecology. The study of reaction network has grown significantly and involves a wide range of mathematics and applications. In this talk, I aim to show a big picture of what is happening in reaction network theory. I will first introduce the basic dynamical models for reaction network: the deterministic and stochastic models. Then, I will mention some big questions of interest, and the mathematical tools that are used by people in the field. Finally, I will make connection between reaction network and other branches of mathematics such as PDE, control theory, and random graph theory.

November 13, Jane Davis

Title: Brownian Minions

Abstract: Having lots of small minions help you perform a task is often very effective. For example, if you need to grade a large stack of calculus problems, it is effective to have several TAs grade parts of the pile for you. We'll talk about how we can use random motions as minions to help us perform mathematical tasks. Typically, this mathematical task would be optimization, but we'll reframe a little bit and focus on art and beauty instead. We'll also try to talk about the so-called "storytelling metric," which is relevant here. There will be pictures and animations! 🎉

Sneak preview: some modern art generated with MATLAB.

Picpic.jpg

November 20, Colin Crowley

Title: Matroid Bingo

Abstract: Matroids are combinatorial objects that generalize graphs and matrices. The famous combinatorialist Gian Carlo Rota once said that "anyone who has worked with matroids has come away with the conviction that matroids are one of the richest and most useful ideas of our day." Although his day was in the 60s and 70s, matroids remain an active area of current research with connections to areas such as algebraic geometry, tropical geometry, and parts of computer science. Since this is a doughnut talk, I will introduce matroids in a cute way that involves playing bingo, and then I'll show you some cool examples.

December 4, Xiaocheng Li

Title: The method of stationary phase and Duistermaat-Heckman formula

Abstract: The oscillatory integral $\int_X e^{itf(x)}\mu=:I(t), t\in \mathbb{R}$ is a fundamental object in analysis. In general, $I(t)$ seldom has an explicit expression as Fourier transform is usually inexplicit. In practice, we are interested in the asymptotic behavior of $I(t)$, that is, for $|t|$ very large. A classical tool of getting an approximation is the method of stationary phase which gives the leading term of $I(t)$. Furthermore, there are rare instances for which the approximation coincides with the exact value of $I(t)$. One example is the Duistermaat-Heckman formula in which the Hamiltonian action and the momentum map are addressed. In the talk, I will start with basic facts in Fourier analysis, then discuss the method of stationary phase and the Duistermaat-Heckman formula.

December 11, Chaojie Yuan

Title: Coupling and its application in stochastic chemical reaction network

Abstract: Stochastic models for chemical reaction networks have become increasingly popular in the past few decades. When the molecules are present in low numbers, the chemical system always displays randomness in their dynamics, and the randomness cannot be ignored as it can have a significant effect on the overall properties of the dynamics. In this talk, I will introduce the stochastic models utilized in the context of biological interaction network. Then I will discuss coupling in this context, and illustrate through examples how coupling methods can be utilized for numerical simulations. Specifically, I will introduce two biological models, which attempts to address the behavior of interesting real-world phenomenon.