Difference between revisions of "AMS Student Chapter Seminar"

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(February 6, Xiao Shen)
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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 ==
 
 
 
=== September 26, Vladimir Sotirov ===
 
 
Title: Geometric Algebra
 
 
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.
 
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: Kissing Conics
 
 
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.
 
 
=== October 10, Kurt Ehlert ===
 
 
Title: How to bet when gambling
 
 
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.
 
 
=== October 17, Bryan Oakley ===
 
 
Title: Mixing rates
 
 
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.
 
 
=== October 24, Micky Soule Steinberg ===
 
 
Title: What does a group look like?
 
 
Abstract: In geometric group theory, we often try to understand groups by understanding the metric spaces on which the groups act geometrically. For example, Z^2 acts on R^2 in a nice way, so we can think of the group Z^2 instead as the metric space R^2.
 
 
We will try to find (and draw) such a metric space for the solvable Baumslag-Solitar groups BS(1,n). Then we will briefly discuss what this geometric picture tells us about the groups.
 
 
=== October 31, Sun Woo Park ===
 
 
Title: Induction-Restriction Operators
 
 
Abstract: Given a "nice enough" finite descending sequence of groups <math> G_n \supsetneq G_{n-1} \supsetneq \cdots \supsetneq G_1 \supsetneq \{e\} </math>, we can play around with the relations between induced and restricted representations. We will construct a formal <math> \mathbb{Z} </math>-module of induction-restriction operators on a finite descending sequence of groups <math> \{G_i\} </math>, written as <math> IR_{\{G_i\}} </math>. The goal of the talk is to show that the formal ring <math> IR_{\{G_i\}} </math> is a commutative polynomial ring over <math> \mathbb{Z} </math>.  We will also compute the formal ring <math>IR_{\{S_n\}} </math> for a finite descending sequence of symmetric groups <math> S_n \supset S_{n-1} \supset \cdots \supset S_1 </math>. (Apart from the talk, I'll also prepare some treats in celebration of Halloween.)
 
 
=== November 7, Polly Yu ===
 
 
Title: Positive solutions to polynomial systems using a (mostly linear) algorithm
 
 
Abstract: "Wait, did I read the title correctly? Solving non-linear systems using linear methods?” Yes you did. I will present a linear feasibility problem for your favourite polynomial system; if the algorithm returns an answer, you’ve gotten yourself a positive solution to your system, and more than that, the solution set admits a monomial parametrization.
 
 
=== November 14, Soumya Sankar ===
 
 
Title: The worlds of math and dance
 
 
Abstract: Are math and dance related? Can we use one to motivate problems in the other? Should we all learn how to dance? I will answer these questions and then we will have some fun with counting problems motivated by dance.
 
 
=== November 28, Niudun Wang ===
 
 
Title: Continued fraction's bizarre adventure
 
 
Abstract: When using fractions to approximate a real number, continued fraction is known to be one of the fastest ways. For instance, 3 is close to pi (somehow), 22/7 was the best estimate for centuries, 333/106 is better than 3.1415 and so on. Beyond this, I am going to show how continued fraction can also help us with finding the unit group of some real quadratic fields. In particular, how to solve the notorious Pell's equation.
 
 
=== December 5, Patrick Nicodemus ===
 
 
Title: Applications of Algorithmic Randomness and Complexity
 
 
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, Wanlin Li ===
 
 
Title: Torsors
 
 
Abstract: I will talk about the notion of torsor based on John Baez's article 'Torsors made easy' and I will give a lot of examples. This will be a short and light talk to end the semester.
 
  
 
== Spring 2019 ==
 
== Spring 2019 ==
 
  
 
=== February 6, Xiao Shen ===
 
=== February 6, Xiao Shen ===

Revision as of 10:09, 28 January 2019

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.

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 2019

February 6, Xiao Shen

Title: Limit Shape in last passage percolation

Abstract: Imagine the following situation, attached to each point on the integer lattice Z^2 there is an arbitrary amount of donuts. Fix x and y in Z^2, if you get to eat all the donuts along an up-right path between these two points, what would be the maximum amount of donuts you can get? This model is often called last passage percolation, and I will discuss a classical result about its scaling limit: what happens if we zoom out and let the distance between x and y tend to infinity.

February 13, TBD

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February 20, TBD

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February 27, TBD

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March 6, TBD

Title: Math and Government

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March 13, TBD

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March 27 (Prospective Student Visit Day), Multiple Speakers

Eva Elduque

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April 3, TBD

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April 10, TBD

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April 17, TBD

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April 24, TBD

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