AMS Student Chapter Seminar: Difference between revisions
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Abstract: The Cahn-Hilliard equation is a classical PDE that models phase separation of two components. We add an advection term so that the two components are stirred by a velocity. We show that there exists a class of fluid that can prevent phase separation and enforce the solution converges to its average exponentially. | Abstract: The Cahn-Hilliard equation is a classical PDE that models phase separation of two components. We add an advection term so that the two components are stirred by a velocity. We show that there exists a class of fluid that can prevent phase separation and enforce the solution converges to its average exponentially. | ||
=== April 17, Hyun-Jong === | === April 17, Hyun-Jong Kim=== | ||
Title: TBD | Title: TBD | ||
Revision as of 14:20, 11 April 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.
- When: Wednesdays, 3:20 PM – 3:50 PM
- Where: Van Vleck, 9th floor lounge (unless otherwise announced)
- Organizers: Michel Alexis, David Wagner, Patrick Nicodemus, Son Tu
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 (in VV B139)
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, Michel Alexis (in VV B139)
Title: An instructive yet useless theorem about random Fourier Series
Abstract: Consider a Fourier series with random, symmetric, independent coefficients. With what probability is this the Fourier series of a continuous function? An [math]\displaystyle{ L^{p} }[/math] function? A surprising result is the Billard theorem, which says such a series results almost surely from an [math]\displaystyle{ L^{\infty} }[/math] function if and only if it results almost surely from a continuous function. Although the theorem in of itself is kind of useless in of itself, its proof is instructive in that we will see how, via the principle of reduction, one can usually just pretend all symmetric random variables are just coin flips (Bernoulli trials with outcomes [math]\displaystyle{ \pm 1 }[/math]).
February 20, Geoff Bentsen
Title: An Analyst Wanders into a Topology Conference
Abstract: Fourier Restriction is a big open problem in Harmonic Analysis; given a "small" subset [math]\displaystyle{ E }[/math] of [math]\displaystyle{ R^d }[/math], can we restrict the Fourier transform of an [math]\displaystyle{ L^p }[/math] function to [math]\displaystyle{ E }[/math] and retain any information about our original function? This problem has a nice (somewhat) complete solution for smooth manifolds of co-dimension one. I will explore how to start generalizing this result to smooth manifolds of higher co-dimension, and how a topology paper from the 60s about the hairy ball problem came in handy along the way.
February 27, James Hanson
Title: What is...a Topometric Space?
Abstract: Continuous first-order logic is a generalization of first-order logic that is well suited for the study of structures with a natural metric, such as Banach spaces and probability algebras. Topometric spaces are a simple generalization of topological and metric spaces that arise in the study of continuous first-order logic. I will discuss certain topological issues that show up in topometric spaces coming from continuous logic, as well as some partial solutions and open problems. No knowledge of logic will be required for or gained from attending the talk.
March 6, Working Group to establish an Association of Mathematics Graduate Students
Title: Introducing GRAMS (Graduate Representative Association of Mathematics Students)
Abstract: Over the past couple months, a handful of us have been working to create the UW Graduate Representative Association of Mathematics Students (GRAMS). This group, about 5-8 students, is intended to be a liaison between the graduate students and faculty, especially in relation to departmental policies and decisions that affect graduate students. We will discuss what we believe GRAMS ought to look like and the steps needed to implement such a vision, then open up the floor to a Q&A. Check out our website for more information.
March 13, Connor Simpson
Title: Counting faces of polytopes with algebra
Abstract: A natural question is: with a fixed dimension and number of vertices, what is the largest number of d-dimensional faces that a polytope can have? We will outline a proof of the answer to this question.
March 26 (Prospective Student Visit Day), Multiple Speakers
Eva Elduque, 11-11:25
Title: Will it fold flat?
Abstract: Picture the traditional origami paper crane. It is a 3D object, but if you don’t make the wings stick out, it is flat. This is the case for many origami designs, ranging from very simple (like a paper hat), to complicated tessellations. Given a crease pattern on a piece of paper, one might wonder if it is possible to fold along the lines of the pattern and end up with a flat object. We’ll discuss necessary and sufficient conditions for a crease pattern with only one vertex to fold flat, and talk about what can be said about crease patterns with multiple vertices.
Soumya Sankar, 11:30-11:55
Title: An algebro-geometric perspective on integration
Abstract: Integrals are among the most basic tools we learn in complex analysis and yet are extremely versatile. I will discuss one way in which integrals come up in algebraic geometry and the surprising amount of arithmetic and geometric information this gives us.
Chun Gan, 12:00-12:25
Title: Extension theorems in complex analysis
Abstract: Starting from Riemann's extension theorem in one complex variable, there have been many generalizations to different situations in several complex variables. I will talk about Fefferman's field's medal work on Fefferman extension and also the celebrated Ohsawa-Takegoshi L^2 extension theorem which is now a cornerstone for the application of pluripotential theory to complex analytic geometry.
Jenny Yeon, 2:00-2:25
Title: Application of Slope Field
Abstract: Overview of historical problems in Dynamical Systems and what CRN(chemical reaction network) group at UW Madison does. In particular, what exactly is the butterfly effect? Why is this simple-to-state problem so hard even if it is only 2D (Hilbert's 16th problem)? What are some modern techniques availble? What do the members of CRN group do? Is the theory of CRN applicable?
Rajula Srivastava, 2:30-2:55
Title: The World of Wavelets
Abstract: Why the fourier series might not be the best way to represent functions in all cases, and why wavelets might be a good alternative in some of these.
Shengyuan Huang, 3:00-3:25
Title: Group objects in various categories
Abstract: I will introduce categories and talk about group objects in the category of sets and manifolds. The latter leads to the theory of Lie group and Lie algebras. We can then talk about group objects in some other category coming from algebraic geometry and obtain similar results as Lie groups and Lie algebras.
Ivan Ongay Valverde, 3:30-3:55
Title: Games and Topology
Abstract: Studying the topology of the real line leads to really interesting questions and facts. One of them is the relation between some kind of infinite games, called topological games, and specific properties of a subsets of reals. In this talk we will study the perfect set game.
Sun Woo Park, 4:00-4:25
Title: Reconstruction of character tables of Sn
Abstract: We will discuss how we can relate the columns of the character tables of Sn and the tensor product of irreducible representations over Sn. Using the relation, we will also indicate how we can recover some columns of character tables of Sn.
Max Bacharach, 4:30-4:55
Title: Clothes, Lice, and Coalescence
Abstract: A gentle introduction to coalescent theory, motivated by an application which uses lice genetics to estimate when human ancestors first began wearing clothing.
April 3, Yu Feng
Title: Suppression of phase separation by mixing
Abstract: The Cahn-Hilliard equation is a classical PDE that models phase separation of two components. We add an advection term so that the two components are stirred by a velocity. We show that there exists a class of fluid that can prevent phase separation and enforce the solution converges to its average exponentially.
April 17, Hyun-Jong Kim
Title: TBD
Abstract: TBD
April 24, Carrie Chen
Title: TBD
Abstract: TBD
Fall 2019
September 25, TBD
Title: TBD
Abstract: TBD
October 2, TBD
Title: TBD
Abstract: TBD
October 9, TBD
Title: TBD
Abstract: TBD
October 16, TBD
Title: TBD
Abstract: TBD
October 23, TBD
Title: TBD
Abstract: TBD
October 30, TBD
Title: TBD
Abstract: TBD
November 6, TBD
Title: TBD
Abstract: TBD
November 13, TBD
Title: TBD
Abstract: TBD
November 20, TBD
Title: TBD
Abstract: TBD
December 4, TBD
Title: TBD
Abstract: TBD
December 12, TBD
Title: TBD
Abstract: TBD