Shortlisted Pure Candidates: Cirstea, Sikora, Parkinson, Yan -- Research Talks

Here is the program for the research talks by the remaining
shortlisted candidates for the positions in pure mathematics.

All of the talks will be held in the Faculty of Science Seminar Room
(Room 535a/b, opposite Nalini’s office).

The unusual time for the third talk is to give us time to move
to Carslaw LT 375 for a teaching seminar by Shusen Yan starting
at 2.30.

Titles and abstracts are below

Wedesday, March 12:

11.00-12.00: Florica Cirstea
12.00- 1.00: Adam Sikora
 1.20- 2.20: James Parkinson

Thursday, March 13:

12.00-1.00: Shusen Yan

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Florica Cirstea:

Title: Singularities in nonlinear partial differential equations

Abstract: Nonlinear elliptic equations with singularities arise in
several areas of mathematics including geometry, mathematical
physics, biology and applied probability.
During the last decade an active investigation of singularities for
semilinear elliptic equations has led to new and exciting discoveries
by both analysts and probabilists. In this talk we discuss some
recent progress concerning the study of singularities and the precise
description of blow-up problems in nonlinear elliptic equations.

......................

Adam Sikora:

Title: Boundary conditions for Degenerate elliptic operators"

Abstract: Let S_t  be a submarkovian semigroup on L^2(R^n) generated by a divergence
form second order differential operator. We assume that the coefficients
matrix C is positive almost everywhere but allow for the possibility that
C is singular. Next, let  \Omega  be an open subset of R^n. We discuss
when S leaves L^2(\Omega) invariant and  the Dirichlet and Neumann boundary
conditions for \Omega in this situation. The presentation is based on
joint projects with Derek Robinson, Andrew Hassell, Thierry Coulhon, Tom
ter Elst, and Yueping Zhu.

......................

James Parkinson:

Title: Alcove walks in Lie theory

Abstract: The combinatorial language of alcove walks is a common
thread which ties together parts of building theory, symmetric
function theory, geometry, and representation theory. We illustrate
this point by writing down a combinatorial statement, along with
theorems from each of these subjects that is equivalent to it. We then
outline a simple proof of the combinatorial statement.

......................

Shusen Yan:

Elliptic Problems of Ambrosetti-Prodi Type

Abstract.  In this talk,  I will present some results on a conjecture
raised by Lazer and McKenna in the early 1980s on the multiplicity of
solutions for elliptic equations of Ambrosetti-Prodi type.