Thu, September 19, 2019
Public Access Category: All |
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- Time:
- 3:00pm-4:00pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
- Partial Differential Equations seminar.
Speaker: Rishabh Gvalani.
Affiliation: Imperial College London, United Kingdom.
Date and Time: Thursday 19 September, 3:00 pm - 4:00 pm.
Venue: Ramanujan Hall, Department of Mathematics.
Title: A mountain pass theorem in the space of probability measures and
applications.
Abstract: We prove a version of the mountain pass theorem for lower
semicontinuous and lambda-geodesically convex functionals on the space of
probability measures P(M) equipped with the W_2 Wasserstein metric,
where M is a compact Riemannian manifold or R^d. As an application of this
result, we show that the empirical process associated to a system of
weakly interacting diffusion processes exhibits a form of noise-induced
metastability. The result is based on an analysis of the associated
McKean–Vlasov free energy, which for suitable attractive interaction
potentials has at least two distinct global minima at the critical
parameter value b = b_c. Joint work with Andre Schlichting.
- Time:
- 4:00pm-5:00pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
- CACAAG seminar.
Speaker: Rekha Biswal.
Affiliation: Max Planck Institute for Mathematics, Bonn, Germany.
Date and Time: Thursday 19 September, 4:00 pm - 5:00 pm.
Venue: Ramanujan Hall, Department of Mathematics.
Title: Macdonald polynomials and level two Demazure modules for affine
sl_{n+1}.
Abstract:- Macdonald polynomials are a remarkable family of orthogonal
symmetric polynomials in several variables. An enormous amount of
combinatorics, group theory, algebraic geometry and representation theory
is encoded in these polynomials. It is known that the characters of level
one Demazure modules are non-symmetric Macdonald polynomials specialized
at t=0. In this talk, I will define a class of polynomials in terms of
symmetric Macdonald polynomials and using representation theory we will
see that these polynomials are Schur-positive and are equal to the graded
character of level two Demazure modules for affine sl_{n+1}. As an
application we will see how this gives rise to an explicit formula for the
graded multiplicities of level two Demazure modules in the excellent
filtration of Weyl modules. This is based on joint work with Vyjayanthi
Chari, Peri Shereen and Jeffrey Wand.