The Prékopa-Leindler inequality (PL) and its strengthening, the
Borell-Brascamp-Lieb inequality, are functional extensions of the
Brunn-Minkowski inequality from convex geometry, which itself
refines the classical isoperimetric inequality. These...
Q1: A fundamental result in coding theory, known as the Plotkin
bound, suggests that a binary code can tolerate up to ¼ fraction of
adversarial corruptions. Can we design codes that handle more
errors if we allow interaction between the sender and...
A Richardson variety R in a cominuscule Grassmannian is defined
by a skew diagram of boxes. If this diagram has several connected
components, then R is a product of smaller Richardson varieties
given by the components. I will show that the Picard...
There are two major research trends in the theory of symmetric
functions arising from Dyck paths. One is the theory of Catalan
symmetric functions and its geometric realization conceived by
Chen-Haiman, following the works of Broer and Shimozono...
Observations of fluctuations in the CMB provide information
about primordial inhomogeneities in the universe. However, the
B-mode polarization of the inflationary gravitational wave is
contaminated by the Galactic dust and synchrotron foreground...
Suppose X is the affine cone of a projective variety. The
Hilbert series of the coordinate ring C[X] is the character of an
algebraic torus. More generally, one considers a reductive
algebraic group G
While mirror symmetry for flag varieties and Grassmannians has
been extensively studied, Schubert varieties in the Grassmannian
are singular, and hence standard mirror symmetry statements are not
well-defined. Nevertheless, in joint work with...
Springer fibers are subvarieties of the flag variety
parameterized by partitions. They are central objects of study in
geometric representation theory. Given a partition λ, one of the
key conclusions of Springer theory is that the top
dimensional...
Chow quotients of projective varieties by affine torus actions
provide alternative constructions of interesting geometric objects.
For example, the moduli space of stable genus 0 curves with n
marked points arises as the Chow quotient of the...
We will discuss invariants of lattice polytopes and their
subdivisions arising from Ehrhart and Hodge theory and introduce
their matroid theoretic analogues which are enriched versions of
the characteristic and Tutte polynomials.
