Spring 2019 colloquia

Colloquium talks this spring will be held in MS 2.02.02 Fridays 4:00-5:00pm..

• Friday 15 February 2019
  Sasha Wang (Boise State University)
  Constructive Mathematics Learning Pathways: An Integrated STEM Approach
  Show abstract
  Currently, the development of mathematics content knowledge for prospective elementary teachers (PSETs) takes place in undergraduate courses (CBMS, 2012; AMTE, 2017). In many teacher education programs, PSETs are required to take one or more mathematics content courses from a mathematics department prior to admission into the program. Teacher education and research communities have been examining ways to help PSETs develop a deeper understanding of mathematical concepts, situate mathematics learning in meaningful contexts, and create learning communities in which teachers and students engage in rich mathematical discourses. Some researchers suggest that providing the opportunity of an early field experience to PSETs while they are learning the mathematics could enhance their content knowledge and beliefs. However, very little research has studied PSETs mathematics learning in a mathematics content course through the integration of STEM inquiries that extends their learning experiences beyond mathematics.
  There is a need to elevate the mathematics learning experiences for PSETs in acquiring mathematics knowledge through inquiries, exploring the role of mathematics in other STEM disciplines, and solidifying knowledge and skills in teaching contexts as sustainable practices. During the colloquium talk, I will introduce an ACE course design model and will discuss its potential for creating an active learning environment to engage PSETs’ mathematics learning. In addition, a framework of designing integrated STEM inquiry will be shared to demonstrate the learning opportunities that PSETs are engaged in.
  
• Friday 8 March 2019
  Marcelo Disconzi (Vanderbilt University)
  Recent developments in relativistic viscous fluids
  Show abstract
  Relativistic hydrodynamics, the study of fluids in regimes where relativity theory cannot be neglected, is one of the most widely used tools in the study of relativistic phenomena. It is fundamental in the construction of the standard model of cosmology and has a wide variety of applications in nuclear high energy physics and astrophysics. The last decade has witnessed a spark of interest in the study of relativistic fluids with viscosity, in part due to the rich dynamics of the quark-gluon plasma and the growing awareness of the importance if viscous dissipation in neutron star mergers. Despite its importance, the construction of consistent models of relativistic viscous fluids has proven to be quite challenging. The simplest and most natural models have been showed to be unstable and to violate causality, the latter being a fundamental property of relativity theory. More sophisticated models have been showed to be causal and stable near equilibrium and at the linearized level and in Minkowski background (i.e., without coupling to gravity). Besides these restrictions, in all such models it is not known if solutions to the equations of motion exist and are unique (except for highly symmetric situations). In this talk, after introducing the appropriate background, we will discuss some recent results that settle the question of causality, existence, and uniqueness of solutions for different models of relativistic viscous fluids.
• Friday 22 March 2019
  Michael Kiessling (Rutgers University)
  The Einstein-Infeld-Hoffmann legacy in Mathematical Relativity
  Show abstract
  Einstein’s General Relativity Theory is usually summarized, in a nutshell, as follows: “Matter tells spacetime how to curve, and spacetime curvature tells matter how to move.” In particular, one learns that uncharged point particles of rest mass m >0 move along (time-like) geodesics. This law of geodetic motion is based on the notion of “test particle” — a theoretical fiction which assumes that the contribution of the very point particle to the curvature of spacetime can be ignored. In their Annals of Mathematics paper of 1938, Albert Einstein, Leo Infeld, and Banesh Hoffmann tried to go beyond this test-particle fiction by arguing that Einstein’s gravitational field equations would also dictate the motion of point particles which “do tell spacetime how to curve.” Needless to say that their paper was not mathematically rigorous by modern standards; worse, their claim cannot be true in the generality in which the claims was made. In this talk I first explain the physical background, then formulate the problem mathematically sharply, then survey what’s rigorously known about it, and last not least I point out important open problems which have resisted the attempts of mathematical relativists so far.
• Friday 5 April 2019
  Louis Kauffman (University Illinois at Chicago)
  Introduction to the Mathematics of Rope Magic
  Show abstract
  In this talk we will demonstrate a number of topological tricks with rope, bands, belts and paper strips. In each case there is some surprising phenomenon that can actually be used for the performance of magic. Each phenomenon is, in fact a mathematical phenomenon and leads to interesting and sometimes deep aspects of the relationship of magic with topology, physics and natural science. The talk will be be self-contained.
• Friday 12 April 2019
  Mrinal Roychowdhury (UT Rio Grande Valley)
  Quantization for Probability Distributions
  Show abstract
  Quantization for probability distributions refers to the idea of estimating a given probability by a discrete probability supported by a set with no more than n points. It has broad application in signal processing and data compression. Quantization dimension gives the speed how fast the specified measure of the error goes to zero as n approaches to infinity. Quantization dimension is also connected with other dimensions of dynamical systems such as Hausdorff, packing and box counting dimensions. It is also connected with the temperature function that arises in the thermodynamic formalism in multrifractal analysis. In the discretization process it is much more difficult to find the optimal sets of n-means than to calculate the quantization dimension. I will talk about all of these.
• WEDNESDAY 17 April 2019 in FLN 4.01.20 at 3pm
  [NOTE nonstandard room, date and time!]
  Mehrdad Kalantar (University of Houston)
  Quasi-regular representations of discrete groups
  Show abstract
  We introduce several equivalence relations on the set of subgroups of a countable group G, defined in terms of the quasi-regular representations. We investigate the comparison of these equivalence relations, and prove some rigidity results for certain classes of subgroups in terms of these equivalence relations. Time permitting, we discuss some results concerning the ideal structure of the C*-algebras generated by the quasi-regular representations.

  This is joint work with Bachir Bekka.

• Friday 19 April 2019
  Yuanwei Qi (University of Central Florida)
  Traveling Waves of Gray-Scott System: Results and Perspective
  Show abstract
  In this talk, I shall report some recent progress on the existence and multiplicity of traveling waves to one of the most important models in Turing Pattern Formation. In addition, I shall pose some questions which are wide open which demand new ideas and fresh approaches.
• Friday 26 April 2019
  Carlos Vargas Obieta (CIMAT, Mexico)
  Non-commutative distributions for simplicial complexes
  Show abstract
  One of the main ideas behind Topological Data Analysis is to use Betti numbers as parameters in statistics, for classification purposes.

  In this talk, we show that Betti numbers appear quite naturally when we associate non-commutative distributions with graphs and simplicial complexes.