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2019-2020 Colloquia

Title: Cayley Hash functions and Open problems

Date: Wednesday, April 29, 2020

Time: 12:30pm—1:30pm

Room: S-213

Speaker: Dr. Bianca Sosnovski

Pizza and Soda will be served

Abstract

This talk is an introduction to Cayley hash functions. We review some of the latest Cayley hash algorithms and related open problems. 

Title: Algebraic aspects of magic matrices and semi-magic squares

Date: Wednesday, March 11, 2020

Time: 12:30pm—1:30pm

Room: S-213

Speaker: Dr. Robert Donley

Pizza and Soda will be served

Abstract

 A square matrix is called a magic matrix if each row and column have a common sum.  For the case of size three and nonnegative integer coefficients, counting such matrices is a problem of combinatorial number theory going back to MacMahon (1916), and these matrices play a central role in the theory of angular momentum coupling.  The goal of this talk is to explore the multiplicative properties of these matrices as complex algebras using the framework of elementary representation theory of finite groups.  Examples include permutation matrices, circulant matrices and dihedral groups.  This is joint work with M. S. Ravi.​

Title: Asymptotic Plateau Problem for two contours in hyperbolic 3-space

Date: Wednesday, November 13, 2019

Time: 12:30pm—1:30pm

Room: S-213

Speaker: Dr. Biao Wang

Refreshments will be served

Abstract

Consider the ball model of hyperbolic 3-space, that is, a unit 3-ball with hyperbolic metric. The boundary of the unit 3-ball is called the asymptotic boundary at infinity of hyperbolic space. Given a collection of finite disjoint  Jordan curves in the asymptotic boundary at infinity, the Asymptotic Plateau Problem asks the existence of (homotopically or homologically) area minimizing surface in hyperbolic 3-space which is asymptotic to these Jordan curves. Asymptotic Plateau Problem was solved by Michael Anderson in 1980’s in the case when there is only one Jordan curve in the asymptotic boundary. In this talk I will consider the case when there are two disjoint curves in the asymptotic boundary.

Title: Rmarkdown and Other Productivity Tools for Math Teachers

Date: Wednesday, October 23, 2019

Time: 12:10pm—1:00pm

Room: S-220

Speaker: Dr. Fei Ye

Refreshments will be served

Abstract

Markdown is a wonderful language for writing relatively simple documents which can be easily converted to word, LaTeX, pdf, html and many other document types via the universal document converter Pandoc. Rmarkdown greatly extends Markdown and provide more features such as executable code chunks. Using Rmarkdown, you may easily create simple documents (word, pdf or html), presentations (ppt, pdf or html5), blogs, ebooks (pdf or html) and scientific articles. For example, https://yfei.page/teaching/statistics/ma336-presentations-2019/ma-336-slides-topic-7-sampling-distributions#1, https://fy-blog.netlify.com/, and https://maple4calc.netlify.com/.
 
In this workshop, I will give a brief introduction to Rmarkdown and other productive tools, Typora, Git and Github, and Mathpix Snip,  for quickly creating exercises, slides and blogs. 

Title: From Classical Mechanics to Symplectic Geometry

Date: Wednesday, September 25th, 2019

Time: 12:30pm—1:30pm

Room: S-213

Speaker: Dr. David Pham

Refreshments will be served

Abstract

This talk is a basic introduction to some of the mathematical ideas coming from classical mechanics and how these ideas generalize in symplectic geometry.  The physics needed for this talk is minimal; the only physics one needs is Newton’s second law (F=ma), momentum, and potential energy.  In the first half of this talk, I will review the Lagrangian and Hamiltonian formulation of classical mechanics. In the second half of this talk, I show how the Hamiltonian formulation has a more geometric flavor to it and generalizes to differential geometry.  The result is symplectic geometry.  Hence, classical mechanics serves as early motivation or inspiration for symplectic geometry.  I will conclude the talk with a brief discussion of an open problem at the intersection of symplectic and complex geometry.

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