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[2:15pm] Vishal Vasan: ICTS Bengaluru.: Mathematics Colloquium
 Description:
 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 boundaryvalue 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
 Description:
 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.


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