Seminars and Colloquia Schedule

No Seminar

Series
Geometry Topology Seminar
Time
Monday, October 12, 2015 - 14:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Christopher Columbus – Republic of Genoa

Minimisers of the Allen-Cahn equation on hyperbolic groups

Series
CDSNS Colloquium
Time
Wednesday, October 14, 2015 - 11:00 for 1 hour (actually 50 minutes)
Location
Skiles 05
Speaker
Blaz Mramor – Univ. Freiburg
The Allen-Cahn equation is a second order semilinear elliptic PDE that arises in mathematical models describing phase transitions between two constant states. The variational structure of this equation allows us to study energy-minimal phase transitions, which correspond to uniformly bounded non-constant globally minimal solutions. The set of such solutions depends heavily on the geometry of the underlying space. In this talk we shall focus on the case where the underlying space is a Cayley graph of a group with the word metric. More precisely, we assume that the group is hyperbolic and show that there exists a minimal solution with any “nice enough” asymptotic behaviour prescribed by the two constant states. The set in the Cayley graph where the phase transition for such a solution takes place corresponds to a solution of an asymptotic Plateau problem.

Walkers Induced Wobbling of Pedestrian Bridges

Series
Research Horizons Seminar
Time
Wednesday, October 14, 2015 - 12:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Prof. Guillermo Goldsztein – School of Mathematics, Georgia Institute of Technology –

Food and Drinks will be provided before the seminar.

We will discussing the wobbling of some pedestrian bridges induced by walkers when crowded and show how this discussion leads to several problems that can be studied with the help of mathematical modeling, analysis and simulations.

(unusual date and room) Numerical Analysis in Metric Spaces

Series
Applied and Computational Mathematics Seminar
Time
Wednesday, October 14, 2015 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 270
Speaker
Vira Babenko – The University of Utah –
A wide variety of questions which range from social and economic sciences to physical and biological sciences lead to functions with values that are sets in finite or infinite dimensional spaces, or that are fuzzy sets. Set-valued and fuzzy-valued functions attract attention of a lot of researchers and allow them to look at numerous problems from a new point of view and provide them with new tools, ideas and results. In this talk we consider a generalized concept of such functions, that of functions with values in so-called L-space, that encompasses set-valued and fuzzy functions as special cases and allow to investigate them from the common point of view. We will discus several problems of Approximation Theory and Numerical Analysis for functions with values in L-spaces. In particular numerical methods of solution of Fredholm and Volterra integral equations for such functions will be presented.

Best and random approximation of convex bodies by polytopes

Series
School of Mathematics Colloquium
Time
Thursday, October 15, 2015 - 11:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Prof. Dr. Elisabeth Werner – Case Western Reserve University –
How well can a convex body be approximated by a polytope? This is a fundamental question in convex geometry, also in view of applications in many other areas of mathematics and related fields. It often involves side conditions like a prescribed number of vertices, or, more generally, k-dimensional faces and a requirement that the body contains the polytope or vice versa. Accuracy of approximation is often measured in the symmetric difference metric, but other metrics can and have been considered. We will present several results about these issues, mostly related to approximation by “random polytopes”.

Self-Avoiding Modes of Motion in a Deterministic Lorentz Lattice Gas

Series
Math Physics Seminar
Time
Friday, October 16, 2015 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Ben Webb – Brigham Young University
We consider the motion of a particle on the two-dimensional hexagonal lattice whose sites are occupied by flipping rotators, which scatter the particle according to a deterministic rule. We find that the particle's trajectory is a self-avoiding walk between returns to its initial position. We show that this behavior is a consequence of the deterministic scattering rule and the particular class of initial scatterer configurations we consider. Since self-avoiding walks are one of the main tools used to model the growth of crystals and polymers, the particle's motion in this class of systems is potentially important for the study of these processes.