Difference between revisions of "AMS Student Chapter Seminar"

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(Spring 2020)
 
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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 is an informal, graduate student seminar on a wide range of mathematical topics. Pastries (usually donuts) will be provided.
  
 
* '''When:''' Wednesdays, 3:20 PM – 3:50 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/~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]
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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 30 minutes long and should avoid assuming significant mathematical background beyond first-year graduate courses.
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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 2018 ==
+
== Spring 2020 ==
  
 +
=== February 5, TBD===
  
=== September 26, Vladimir Sotirov ===
+
Title: TBD
  
Title: Geometric Algebra
+
Abstract: TBD
  
Abstract: Geometric algebra, developed at the end of the 19th century by Grassman, Clifford, and Lipschitz, is the forgotten progenitor of the linear algebra we use to this day developed by Gibbs and Heaviside.
+
=== February 12, TBD===
In this short introduction, I will use geometric algebra to do two things. First, I will construct the field of complex numbers and the division algebra of the quaternions in a coordinate-free way. Second, I will derive the geometric interpretation of complex numbers and quaternions as representations of rotations in 2- and 3-dimensional space.
 
  
=== October 3, Juliette Bruce ===
+
Title: TBD
  
Title: Kissing Conics
+
Abstract: TBD
  
Abstract: Have you every wondered how you can easily tell when two plane conics kiss (i.e. are tangent to each other at a point)? If so this talk is for you, if not, well there will be donuts.
+
=== February 19, TBD===
  
=== October 10, Kurt Ehlert ===
+
Title: TBD
  
Title: How to bet when gambling
+
Abstract: TBD
  
Abstract: When gambling, typically casinos have the edge. But sometimes we can gain an edge by counting cards or other means. And sometimes we have an edge in the biggest casino of all: the financial markets. When we do have an advantage, then we still need to decide how much to bet. Bet too little, and we leave money on the table. Bet too much, and we risk financial ruin. We will discuss the "Kelly criterion", which is a betting strategy that is optimal in many senses.
+
=== February 26, TBD===
  
=== October 17, Bryan Oakley ===
+
Title: TBD
  
Title: Mixing rates
+
Abstract: TBD
  
Abstract: Mixing is a necessary step in many areas from biology and atmospheric sciences to smoothies. Because we are impatient, the goal is usually to improve the rate at which a substance homogenizes. In this talk we define and quantify mixing and rates of mixing. We present some history of the field as well as current research and open questions.
+
=== March 4, TBD===
 
 
=== October 24, Micky Soule Steinberg ===
 
  
 
Title: TBD
 
Title: TBD
Line 43: Line 41:
 
Abstract: TBD
 
Abstract: TBD
  
=== October 31, Sun Woo Park ===
+
== Fall 2019 ==
 +
 
 +
=== October 9, Brandon Boggess===
 +
 
 +
Title: An Application of Elliptic Curves to the Theory of Internet Memes
  
Title: Induced and Restricted Representations of a Sequence of Groups
+
Abstract: Solve polynomial equations with this one weird trick! Math teachers hate him!!!
  
Abstract: Given a sequence of groups <math> G_n \supset G_{n-1} \supset \cdots \supset G_2 \supset G_1 = \{1\} </math>, we can construct a formal ring of induction-restriction operators on <math> S_n </math>, which we denote by <math> \mathbb{Z} \langle Ind(Res), Ind^2(Res^2), \cdots, Ind^n(Res^n) \rangle </math>. Using Frobenius reciprocity, we will show that the formal ring for any group <math> G_n </math> is in fact a commutative polynomial ring of 1 variable. If time allows, we will also show that for a sequence of symmetric groups <math> S_n \supset S_{n-1} \supset \cdots \supset S_2 \supset S_1 = \{1\} </math>, the formal ring of <math> S_n </math>  isomorphic to a polynomial ring <math> \mathbb{Z}[x]/(f(x)) </math>, where <math>f(x)</math> is a polynomial of degree <math> n </math>.
+
[[File:Thumbnail fruit meme.png]]
  
=== November 7, TBD ===
+
=== October 16, Jiaxin Jin===
  
Title: TBD
+
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: TBD
+
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 14, Soumya Sankar ===
+
=== November 13, Stephen Davis===
  
Title: TBD
+
Title: Brownian Minions
  
Abstract: TBD
+
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! 🎉
  
=== November 21, Cancelled due to Thanksgiving===
+
Sneak preview: some modern art generated with MATLAB.
  
Title: TBD
+
[[File:Picpic.jpg]]
  
Abstract: TBD
+
=== November 20, Colin Crowley===
  
=== November 28, Niudun Wang ===
+
Title: Matroid Bingo
  
Title: TBD
+
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.
  
Abstract: TBD
+
=== December 4, Xiaocheng Li===
  
=== December 5, Patrick Nicodemus ===
+
Title: The method of stationary phase and Duistermaat-Heckman formula
  
Title: Applications of Algorithmic Randomness and Complexity
+
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.
Abstract: I will introduce the fascinating field of Kolmogorov Complexity and point out its applications in such varied areas as combinatorics, statistical inference and mathematical logic. In fact the Prime Number theorem, machine learning and Godel's Incompleteness theorem can all be investigated fruitfully through a wonderful common lens.
 
  
=== December 12, TBD ===
+
=== December 11, Chaojie Yuan===
  
 
Title: TBD
 
Title: TBD
  
 
Abstract: TBD
 
Abstract: TBD

Latest revision as of 17:49, 4 December 2019

The AMS Student Chapter 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 30 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, TBD

Title: TBD

Abstract: TBD

February 12, TBD

Title: TBD

Abstract: TBD

February 19, TBD

Title: TBD

Abstract: TBD

February 26, TBD

Title: TBD

Abstract: TBD

March 4, TBD

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, Stephen 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: TBD

Abstract: TBD