Colloquium Series

Spring 2022

Our Colloquium talks typically occur Wednesday afternoon at 3:45-4:45 PM, although there are occasionally special days and times. Talks will either by in person in room CH 110 or virtual on this Google Meet link.

• Apr

  21
• Existence theory and propagation of oscillations for the system of viscoelasticity of strain-rate type

  Athanasios Tzavaras

  King Abdullah University of Science and Technology

  Location: meet.google.com/jcy-zojt-xfw

  Time: 12:00 PM

  View Abstract

  I will review the existence and uniqueness theory for viscoelasticity of Kelvin-Voigt type with non-convex stored energies. The analysis is based on propagation of H1-regularity for the deformation gradient of weak solutions in two and three dimensions assuming that the stored energy satisfies the Andrews-Ball condition, in particular allowing for non-monotone stresses. It turns out that weak solutions with deformation gradient in H1 are in fact unique, providing a striking analogy to corresponding results in the theory of 2D Euler equations with bounded vorticity. On the opposite direction, while there is still existence of weak solution for initial data in L2, there can be propagation of oscillations of the deformation gradient. A counterexample indicates that for non-monotone stress-strain relations in 1-d initial oscillations of the strain lead to solutions with sustained oscillations. Similar phenomena appear in several space dimensions associated with lack of rank-one convexity of the stored energy. (joint work with K. Koumatos (U. of Sussex), C. Lattanzio and S. Spirito (U. of LAquila)).

• Apr

  20
• Pitfalls and Paradoxes in the History of Probability

  Mike Shlesinger

  Office of Naval Research

  Location: CH 110 (IN PERSON)

  Time: 03:45 PM

  View Abstract

  From the throwing of sticks, bones and dice, fascinating and sometimes puzzling questions have arisen in the initial application of probability. We discuss early books and personalities and their famous questions and paradoxes including Galileo and Newton’s dice game, de Mere’s Grand Scandal, the Pascal-Fermat letters, the St. Petersburg Paradox, Bernoulli’s Monster, Bayes’ inverse probability, and Bertrand’s Paradox. We discuss the discovery of limit theorems from DeMoivre who first arrived at the Gaussian to Poisson who studied the same process, but arrived at the Poisson distribution. Levy considered a similar random process, but with random variables with infinite moments to discover a new set of limit theorems that were a cornerstone of fractals.

• Mar

  02
• Inequalities/Geometry/Optimization

  Geraldo De Souza

  Auburn University

  Location: virtual

  Time: 03:45 PM

  View Abstract

  I view this presentation as simples or perhaps an elementary approach to the subject. On the other hand, this talk will show some interesting observations that are part of the folklore of mathematics. I will go over some very common and important inequalities that we see in the course of Analysis and even in Calculus. I will give some different views of different proofs, using Geometry, Graphing and some of them “a new analytic proof” by using optimization of functions of two variables. This talk will be beneficial to all, and especially for those teaching Calculus of one and two variables. I hope you will take time of your busy schedule to attend it.

• Feb

  23
• Energy Landscapes, Metastability, and Transition Paths

  Katie Newhall

  University of North Carolina, Chapel Hill

  Location: CH 110 (IN PERSON)

  Time: 03:45 PM

  View Abstract

  The classic example of metastability (infrequent jumps between deterministically-stable states) arises in noisy systems when the thermal energy is small relative to the energy barrier separating two energy-minimizing states. My work seeks to extend this idea to infinite dimensional systems and systems with non-gradient forces, extending the usefulness of the underlying energy landscape in the classic metastability analysis. Such example systems are a spatially-extended magnetic system with spatially-correlated noise designed to sample the Gibbs distribution relative to a defined energy functional, and a polymer bead-spring model of chromosome dynamics with additional stochastically-binding proteins that push the system out of equilibrium.

• Feb

  11
• Remodeling the mathematics core at the Air Force Academy

  Danny Kaplan

  United States Air Force Academy

  Location: CH 110 (IN PERSON)

  Time: 03:45 PM

  View Abstract

  USAFA has had a two-semester core calculus course for about 60 years. Based on a traditional Calc I/II sequence, it has changed incrementally over the years. Several years ago, USAFA determined that incremental change is insufficient and that a new core course should be developed from scratch. The new course is oriented around modeling and computation and includes topics not usually seen in Calc I/II such as dimensional analysis, linear algebra, and dynamics. USAFA does not have tracks in its core curriculum, so the new course has to be accessible to all cadets, regardless of math background, aptitude, or intended major. In this talk, I’ll briefly outline the course, focusing mainly on how the course can be accessible while being engaging and meaningful for students who have had previous calculus and who are heading toward STEM majors. A draft textbook for the course, “MOSAIC Calculus,” is available freely online at mosaic-web.org/MOSAIC-Calculus/