Colloquium Series
Spring 2022
Our Colloquium talks typically occur Wednesday afternoon at 3:454:45 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.

Apr21

Existence theory and propagation of oscillations for the system of viscoelasticity of strainrate typeAthanasios TzavarasKing Abdullah University of Science and TechnologyLocation: meet.google.com/jcyzojtxfwTime: 12:00 PM
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I will review the existence and uniqueness theory for viscoelasticity of KelvinVoigt type with nonconvex stored energies. The analysis is based on propagation of H1regularity for the deformation gradient of weak solutions in two and three dimensions assuming that the stored energy satisfies the AndrewsBall condition, in particular allowing for nonmonotone 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 nonmonotone stressstrain relations in 1d initial oscillations of the strain lead to solutions with sustained oscillations. Similar phenomena appear in several space dimensions associated with lack of rankone convexity of the stored energy. (joint work with K. Koumatos (U. of Sussex), C. Lattanzio and S. Spirito (U. of LAquila)).

Apr20

Pitfalls and Paradoxes in the History of ProbabilityMike ShlesingerOffice of Naval ResearchLocation: CH 110 (IN PERSON)Time: 03:45 PM
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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 PascalFermat 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.

Mar02

Inequalities/Geometry/OptimizationGeraldo De SouzaAuburn UniversityLocation: virtualTime: 03:45 PM
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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.

Feb23

Energy Landscapes, Metastability, and Transition PathsKatie NewhallUniversity of North Carolina, Chapel HillLocation: CH 110 (IN PERSON)Time: 03:45 PM
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The classic example of metastability (infrequent jumps between deterministicallystable states) arises in noisy systems when the thermal energy is small relative to the energy barrier separating two energyminimizing states. My work seeks to extend this idea to infinite dimensional systems and systems with nongradient forces, extending the usefulness of the underlying energy landscape in the classic metastability analysis. Such example systems are a spatiallyextended magnetic system with spatiallycorrelated noise designed to sample the Gibbs distribution relative to a defined energy functional, and a polymer beadspring model of chromosome dynamics with additional stochasticallybinding proteins that push the system out of equilibrium.

Feb11

Remodeling the mathematics core at the Air Force AcademyDanny KaplanUnited States Air Force AcademyLocation: CH 110 (IN PERSON)Time: 03:45 PM
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USAFA has had a twosemester 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 mosaicweb.org/MOSAICCalculus/