Current Colloquium Series

Date/Time/Location: Thursday Sep 8, 2022 from 3:00-3:50pm in BAC 219

Speaker/Affiliation: Andrew NewmanCarnegie Mellon University

Title: Complexes of nearly maximum diameter

Abstract: The combinatorial diameter of a simplicial complex, or uniform hypergraph, is the diameter of its dual graph. Here we overview results and open problems about the maximum possible diameter for different classes of simplicial complexes. In particular we show a probabilistic construction that gives a lower bound on the maximum diameter for an arbitrary simplicial complex of dimension d on n vertices that nearly matches a simple upper bound. This is based on joint work with Tom Bohman.


Date/Time/Location: Thursday Sep 15, 2022 from 3:00-3:50pm in BAC 219

Speaker/Affiliation:  Michał Wojciechowski, Polish Academy of Science

Title: Microlocal approach to the Hausdorff dimension of measures

Abstract: We present the study of the dependence of geometric properties of Radon measures, such as Hausdorff dimension and rectifiability of singular sets, on the wavefront set. We prove our results by adapting the method of Brummelhuis to the non-analytic case. As an application we obtain a general form of the Uncertainty Principle for measures on the complex sphere. This instance of the UP generalizes the celebrated theorem of Aleksandrov and Forelli concerning regularity of pluriharmonic measures.


Date/Time/Location: Thursday Sep 22, 2022 from 3:00-3:50pm in BAC 219

Speaker/Affiliation:  Dave Richeson, Dickinson College

Title: A Romance of Many (and Fractional) Dimensions

Abstract: Dimension seems like an intuitive idea. We are all familiar with zero dimensional points, one-dimensional curves, two-dimensional surfaces, and three-dimensional solids. Yet dimension is a slippery idea that took mathematicians many years to understand. We will discuss the history of dimension, which includes Cantor's troubling discovery, the surprise of space-filling curves, the public's infatuation with the fourth dimension, time as an extra dimension, the meaning of non-integer dimensions, and the unexpected properties of high-dimensional spaces.


Date/Time/Location: Thursday Nov 3, 2022 from 3:00-3:50pm in BAC 219

Speaker/Affiliation:  Emily Buhnerkempe, University of Illinois Laboratory High School

Title: My Experiences Teaching Math through Interdisciplinary Projects and My Experiences Teaching Math with Standards-Based Grading

Abstract: Interdisciplinary is a buzz word that many educators use to describe one type of higher-level learning. In this talk we will discuss some of the benefits to teaching math through interdisciplinary projects. I plan to share student work and project examples with attendees. You will leave this session with a variety of resources that you could modify for your own courses, including project descriptions and rubrics.

Many K-12 schools have seen a migration toward Standards-Based Grading. In this talk I plan to share my experiences implementing standards-based grading in my classes, including its benefits for students, parents, and teachers, as well as challenges I have encountered. For those that have not yet worked with standards-based grading, we will discuss some ways to get started using standards-based grading in your own classes. You will leave this talk with resources you could implement the next time you teach a course.


Date/Time/Location: Thursday Dec 1, 2022 from 3:00-3:50pm in BAC 219

Speaker/Affiliation:  Stephane Lafortune, College of Charleston

Title: Stability Analysis of Solutions to shallow water wave equations with Peakon solutions

Abstract: The Camassa-Holm equation with linear dispersion was originally derived as an asymptotic equation in shallow water wave theory. Among its many interesting mathematical properties, perhaps the most striking is the fact that it admits weak multi-soliton solutions - `peakons' - with a peaked shape corresponding to a discontinuous first derivative. There exists a one-parameter family of generalized Camassa-Holm equations, most of which are not integrable, but which all admit peakon solutions. In this talk, we establish information about the spectral stability/instability of those solutions. By spectral stability analysis, we mean the analysis of the spectrum of the operator arising from the linearised equation. The computation of the spectrum differs from similar problems due to the following two facts: the solutions to the equations are not analytical, and the linear operator is nonlocal as it contains integral terms. These results were obtained in collaboration with E.G. Charalampidis, A. Hone, P.G. Kevrekidis, R. Parker, and D.E. Pelinovsky.