Wed, October 23, 2019
Public Access

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October 2019
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2:00pm [2:15pm] Vishal Vasan: ICTS Bengaluru.: Mathematics Colloquium
Mathematics Colloquium I. Speaker: Vishal Vasan. Affiliation: ICTS Bengaluru. Date and Time: Wednesday 23 October, 2:15 pm - 3:15 pm. Venue: Ramanujan Hall, Department of Mathematics. Title: Two unexpected applications of boundary value problems. Abstract: Partial differential equations (PDE) and their boundary value problems (BVP) arise naturally in a number of applications. Typically the system of interest is modelled by a PDE/BVP. In this talk, I will present two unexpected applications of BVPs where the original system does not immediately indicate their importance. The first application comes from the study of a particle moving in a fluid whose motion is modelled by a finite dimensional system. The analysis will imply a natural interpretation to the half derivative in terms of boundary-value problems. The second application comes from the classical study of dispersive shock waves (DSWs). DSWs are specific solutions to nonlinear dispersive equations. However, I will present a BVP for a linear equation which reproduces a number of DSW features. This raises an important question on how to match experimental DSWs with particular nonlinear models: qualitative comparisons do not suffice.

[2:30pm] Vinayak Vats:UBC, Vancouver
Number theory seminar I. Speaker: Vinayak Vatsal. Affiliation: UBC, Vancouver. Date and Time: Wednesday 23 October, 2:30 pm - 3:30 pm. Venue: Room 113, Department of Mathematics. Title: Iwasawa theory for Artin representations. Abstract: An Artin representation is simply a finite dimensional complex representation of the Galois group of a finite extension of the rational number field. Despite their apparent simplicity, Artin representations are very complicated and much harder to study than apaprently more complicated representations such as those attached to elliptic curves, and much of the theory remains conjectural. In this talk I will survey an aspect of the theory where Artin representations are actually simpler and more concrete than other kinds of representations.