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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. 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, B115
* '''Where:''' Van Vleck, 9th floor lounge (unless otherwise announced)
* '''Organizers:''' Daniel Hast, Ryan Julian, Cullen McDonald, Zachary Charles
* '''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.


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]].


== Fall 2016 ==
== Spring 2020 ==


=== October 12, Soumya Sankar ===
=== February 5, Alex Mine===


Title: Primes of certain forms and covering systems
Title: Khinchin's Constant


Abstract: A lot of classical questions revolve around primes of the form 2^n + k, where k is an odd integer. I will talk about such primes, or the lack thereof, and use this to convert coffee into covering systems. Time permitting, I'll talk about a few cool results and conjectures related to the notion of covering systems.
Abstract: I'll talk about a really weird fact about continued fractions.


=== October 19, Daniel Hast ===
=== February 12, Xiao Shen===


Title: A combinatorial lemma in linear algebra
Title: Coalescence estimates for the corner growth model with exponential weights


Abstract: I'll talk about a fun little lemma in linear algebra and its combinatorial interpretation. (It might be "well-known" to someone, but I'd never heard of it before.) If there's time, I'll discuss some possible generalizations.
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.


=== October 26, Brandon Alberts ===
=== February 19, Hyun Jong Kim===


Title: An Introduction to Matroids
Title: Orbifolds for Music


Abstract: What if you wanted to do linear algebra, but couldn't use addition or scalar multiplication? Can we still have a notion of independence and bases? The answer is yes, and these are called matroids. Not only will I introduce matroids, but I will give an example that shows not all matroids arise from vector spaces.
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.


=== November 2, Vlad Matei ===
=== February 26, Solly Parenti===


Title: Hadamard Matrices
Title: Mathematical Measuring


Abstract: A Hadamard matrix is a square matrix whose entries are either +1 or −1 and whose rows are mutually orthogonal. The most important open question in the theory of Hadamard matrices is that of existence. The Hadamard conjecture proposes that a Hadamard matrix of order 4k exists for every positive integer k. The Hadamard conjecture has also been attributed to Paley, although it was considered implicitly by others prior to Paley's work.
Abstract: What's the best way to measure things? Come find out!


=== November 9, David Bruce ===
=== March 4, Cancelled===


Title: Some Numbers Are Sometimes Bigger Than Others (Sometimes...)
=== March 11, Ivan Aidun===


Abstract: I will write down two numbers and show that one of them is larger than the other.
Title: The Notorious CRT


=== November 16, Solly Parenti ===
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?


Title: TBA
=== March 24 - Visit Day (talks cancelled)===


Abstract: TBA
==== Brandon Boggess, Time TBD ====


=== November 30, TBA ===
Title: TBD


=== December 7, Will Mitchell ===
Abstract: TBD


Title: An unsolved isomorphism problem from plane geometry
==== Yandi Wu, Time TBD====


Abstract: A geometric n-configuration is a collection of points and lines in the Euclidean plane such that each point lies on exactly n lines and each line passes through n points. While the study of 3-configurations dates to the nineteenth century, the first example of a 4-configuration appeared only in 1990.  I will say a few things about 4-configurations and state an unsolved problem, and I hope that someone in the audience will decide to work on it.  There will be nice pictures and a shout-out to the singular value decomposition.
Title: TBD


=== December 14, TBA ===
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!!!
 
[[File: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.
 
[[File: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.

Revision as of 16:49, 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]\displaystyle{ \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.