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.
+
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, 3:00 PM – 3:30 PM
+
* '''When:''' Wednesdays, 3:20 PM – 3:50 PM
 
* '''Where:''' Van Vleck, 9th floor lounge (unless otherwise announced)
 
* '''Where:''' Van Vleck, 9th floor lounge (unless otherwise announced)
* '''Organizers:''' [https://www.math.wisc.edu/~hast/ Daniel Hast], [https://www.math.wisc.edu/~mrjulian/ Ryan Julian], Cullen McDonald, [https://www.math.wisc.edu/~zcharles/ 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]].
  
== Spring 2017 ==
+
== Spring 2020 ==
  
=== January 25, Brandon Alberts ===
+
=== February 5, Alex Mine===
  
Title: Ultraproducts - they aren't just for logicians
+
Title: Khinchin's Constant
  
Abstract: If any of you have attended a logic talk (or one of Ivan's donut seminar talks) you may have learned about ultraproducts as a weird way to mash sets together to get bigger sets in a nice way. Something particularly useful to set theorists, but maybe not so obviously useful to the rest of us. I will give an accessible introduction to ultraproducts and motivate their use in other areas of mathematics.
+
Abstract: I'll talk about a really weird fact about continued fractions.
  
=== February 1, Megan Maguire ===
+
=== February 12, Xiao Shen===
  
Title: Hyperbolic crochet workshop
+
Title: Coalescence estimates for the corner growth model with exponential weights
  
Abstract: TBA
+
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 8, Cullen McDonald ===
+
=== February 19, Hyun Jong Kim===
  
=== February 15, Paul Tveite ===
+
Title: Orbifolds for Music
  
Title: Fun with Hamel Bases!
+
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.
  
Abstract: If we view the real numbers as a vector field over the rationals, then of course they have a basis (assuming the AOC). This is called a Hamel basis and allows us to do some cool things. Among other things, we will define two periodic functions that sum to the identity function.
+
=== February 26, Solly Parenti===
  
=== February 22, Wil Cocke ===
+
Title: Mathematical Measuring
  
Title: Practical Graph Isomorphism
+
Abstract: What's the best way to measure things? Come find out!
  
Abstract: Some graphs are different and some graphs are the same. Sometimes graphs differ only in name. When you give me a graph, you've picked an order. But, is it the same graph across every border?
+
=== March 4, Cancelled===
  
=== March 1, Megan Maguire ===
+
=== March 11, Ivan Aidun===
  
Title: I stole this talk from Jordan.
+
Title: The Notorious CRT
  
Abstract: Stability is cool! And sometimes things we think don't have stability secretly do. This is an abridged version of a very cool talk I've seen Jordan give a couple times. All credit goes to him. Man, I should have stolen his abstract too.
+
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 7, Liban Mohamed ===
+
=== March 24 - Visit Day (talks cancelled)===
  
Title: Strichartz Estimates from Qualitative to Quantitative
+
==== Brandon Boggess, Time TBD ====
  
Abstract: Strichartz estimates are inequalities that give one way understand the decay of solutions to dispersive PDEs. This talk is an attempt to reconcile the formal statements with physical intuition.
+
Title: TBD
  
=== March 15, Zachary Charles ===
+
Abstract: TBD
  
Title: Netflix Problem and Chill
+
==== Yandi Wu, Time TBD====
  
Abstract: How are machine learning, matrix analysis, and Napoleon Dynamite related? Come find out!
+
Title: TBD
  
=== April 5, Vlad Matei ===
+
Abstract: TBD
  
=== April 12, Micky Steinberg ===
+
==== Maya Banks, Time TBD====
  
Title: Groups as metric spaces
+
Title: TBD
  
Abstract: Given a group as a set of generators and relations, we can define the “word metric” on the group as the length of the shortest word “between” two elements. This isn’t well-defined, since different generating sets give different metrics, but it is well-defined up to “quasi-isometry”.  Come find out what we can do with this! There will lots of pictures and hand-waving!
+
Abstract: TBD
  
=== April 19, Solly Parenti ===
+
==== Yuxi Han, Time TBD====
  
Title: Elementary Integration
+
Title: TBD
  
Abstract: Are you like me? Have you also told your calculus students that finding the antiderivative of e^(-x^2) is impossible? Do you also only have a slight idea about how to prove it? Come find out more about the proof and free yourself of that guilt.
+
Abstract: TBD
  
=== April 26, Ben Bruce ===
+
==== Dionel Jaime, Time TBD====
  
=== May 3, Iván Ongay-Valverde ===
+
Title: TBD
Different Reals
+
 
 +
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.

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.