Basic Notions Seminars

Fall Semester 2016

All talks are from 12:00-1:00 p.m. in the CH320, unless otherwise specified.

• Oct

  31
• Witchcraft: Spectral Graph Theory, The Minimum Rank Problem, and More

  Franklin Kenter

  Time: 12:00 PM

  View Abstract

  We will discuss basic notions of spectral graph theory and their applications to various graph-theoretic problems. This includes: Expanding-Mixing Lemma, Isoperimetric Inequalities, Spanning Tree Theorem, and Graph Coloring, among others. We will also discuss the Minimum Rank Problem on Graphs and discuss its applications.

• Oct

  03
• Mixing and Rank-One Transformations

  Darren Creutz

  Time: 12:00 PM

  View Abstract

  Ergodic theory (the classical theory) is the study of transformations on probability spaces. This talk will introduce the basic notions of the theory: ergodicity and various forms of mixing; then introduce a class of transformations constructed by an intuitive process of "cutting and stacking". These transformations (rank-one transformations) have been studied since the 1940s as a means to understand the mixing notions. The talk will present some of the main results beginning with Chacon's proof of weak mixing not implying strong mixing and Ornstein's proof of the existence of zero entropy transformations with no square root which are strong mixing and conclude with the presenter's work (partly joint with C. Silva) on constructing explicit examples of such transformations.

• Sep

  26
• Counting with Barvinok's Algorithm (With Pictures!)

  Daphne Skipper

  USNA

  Time: 12:00 PM

  View Abstract

  Barvinok's algorithm counts the number of integer points in a polytope. This is a very difficult problem in general, so Barvinok's algorithm (1994), which solves the problem in polynomial time if the dimension is fixed, was a celebrated result. I will present a variant of Barvinok's algorithm using (mostly 2-dimensional) pictures to give a sense of how the algorithm works from a geometric perspective.

• Sep

  19
• Fundamental questions in matroids

  Carolyn Chun

  Time: 12:00 PM

  View Abstract

  A matroid is a mathematical structure that generalizes the notion of linear independence in a matrix. In this talk, I will discuss "recent" progress on the most compelling "open" question in matroid theory, Rota’s conjecture.