• Speaker: Nick Rekuski, MSU
• Title: Schubert Calculus and Cohomology of Grassmannains
• Date: 03/19/2018
• Time: 4:10 PM - 5:00 PM
• Place: C517 Wells Hall

In this second talk, we will present formulas for the multiplicative structure of the Grassmannian’s cohomology. Using these formulas, we shall answer the problems raised last time and more. These problems will include “Fix four lines in P^3. How many lines will intersect all four of these lines?” and “Fix four curves in P^3. How many lines will intersect all four of these curves?”

• Speaker: Guowei Wei; Vladimir Peller; Mark Iwen
• Title: Faculty Research Presentations
• Date: 03/20/2018
• Time: 4:10 PM - 5:10 PM
• Place: C304 Wells Hall

These talks are aimed at first and second year students. Faculty will give an overview of problems that a student could work on. At the 3/20 seminar, we will have 1) Guowei Wei, Is it time for a great chemistry between mathematics and biology?; 2) Vladimir Peller, Contemporary problems of operator theory; and 3) Mark Iwen, Computational Nonlinear Approximation in Signal Processing and Inverse Problems.

• Speaker: Tyler Bongers, MSU
• Title: Holder regularity of quasi-conformal maps
• Date: 03/21/2018
• Time: 4:10 PM - 5:00 PM
• Place: C517 Wells Hall

Quasiconformal maps in the complex plane are homeomorphisms that satisfy certain geometric distortion inequalities; infinitesimally, they map circles to ellipses with bounded eccentricity. The local distortion properties of these maps give rise to a certain degree of global regularity and Holder continuity. In this talk, we will discuss improved lower bounds for the Holder continuity of these maps; the analysis is based on combining the isoperimetric inequality with a study of the length of quasicircles. Furthermore, the extremizers for Holder continuity can be characterized, and we will also give some applications to solutions to elliptic partial differential equations.

• Speaker: Adam Lowrance, Vassar College
• Title: Almost alternating, Turaev genus one, and semi-adequate links
• Date: 03/22/2018
• Time: 2:00 PM - 3:00 PM
• Place: C304 Wells Hall

A link is almost alternating if it is non-alternating and has a diagram such that one crossing change transforms it into an alternating diagram. Turaev genus one links are a certain generalization of non-alternating Montesinos links. A link is semi-adequate if it has a diagram where at least one of the all-A or all-B Kauffman state graphs is loopless. In this talk, we discuss the Jones polynomial and Khovanov homology of links in these three classes, and we discuss open problems about the relationships between the three classes.

• Speaker: Rajesh Kulkarni; Matt Hirn; Di Liu
• Title: Faculty Research Presentations
• Date: 03/22/2018
• Time: 4:10 PM - 5:10 PM
• Place: C304 Wells Hall

These talks are aimed at first and second year students. Faculty will give an overview of problems that a student could work on. At the 3/22 seminar, we will have 1) Rajesh Kulkarni; 2) Matt Hirn, Understanding high dimensional data analysis and machine learning via harmonic analysis; 3) Di Liu

• Speaker: Shitao Liu, Clemson University
• Title: Observability of the visco-elastic wave equation
• Date: 03/23/2018
• Time: 4:10 PM - 5:00 PM
• Place: C100 Wells Hall

In this talk we give a proof of the Neumann boundary observability inequality for the visco-elastic wave equation in an arbitrary space dimension. To do this, we first give a new proof of the boundary observability for the classical wave equation that extends the harmonic analysis perspective of D.L.Russell to higher space dimensions. We then argue by perturbation to show the Riesz sequence property of the corresponding harmonic system for the visco-elastic wave equation.

• Speaker: Kristen Hendricks, Mathematics, MSU
• Title: Avoiding Collisions and Braiding String: Configuration Spaces and the Braid Group
• Date: 03/23/2018
• Time: 4:10 PM - 5:00 PM
• Place: C304 Wells Hall

There are many real-world problems that amount to studying the possible paths of n objects through a space X such that those objects never collide. (Examples include flight traffic patterns around an airport, or automated carts moving around a factory floor.) We think about such problems by studying paths in configuration spaces, spaces consisting of ordered sets of distinct points in X. In one of the simplest cases, these spaces turn out to be closely linked to a seemingly different mathematical object, the n-stranded braid group. We introduce configuration spaces and the braid group and learn about their relationship.