Date and Time: Tuesday 17 September, 4:00 pm - 5:00 pm.
Venue: Ramanujan Hall, Department of Mathematics.
Title: PLFit estimation procedure and its consistency.
Abstract: In Clauset et. al. (2009), PLFit estimation procedure has been
proposed for the power-law index and became popular immediately for its
versatile applicability. This has been used in many areas including
scale-free networks, energy networks, preferential attachment model,
teletrafic data etc. But the theoretical support for this estimation
procedure is still lacking. In this talk, consistency of PLFit procedure
will be addressed under semiparametric assumption. This is an ongoing
joint work with Bohan Chen, Remco van der Hofstad and Bert Zwart.
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
McKeanâ€“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.