Many problems from complexity theory can be phrased in terms of
tensors. I will begin by reviewing basic properties of tensors and
discussing several measures of the complexity of a tensor. I'll
then focus on the complexity of matrix...
This talk is intended for a general audience. The recent
discovery of an interpretation of constructive type theory into
abstract homotopy theory has led to a new approach to foundations
with both intrinsic geometric content and a computational...
Holant Problems are a broad framework to describe counting
problems. The framework generalizes counting Constraint
Satisfaction Problems and partition functions of Graph
Homomorphisms.
We prove a complexity dichotomy theorem for Holant problems
over...
Recently Nicolas and Serre have determined the structure of the
Hecke algebra acting on modular forms of level 1 modulo 2, and
Serre has conjectured the existence of a universal Galois
representation over this algebra. I'll explain the proof of...
I will give an introduction to symplectic geometry and
Hamiltonian systems and then introduce an invariant called
symplectic cohomology. This has many applications in symplectic
geometry and has been used a lot especially in the last 5-10
years...
We study the hole probability of Gaussian entire functions. More
specifically, we work with entire functions given by a Taylor
series with i.i.d complex Gaussian random variables and arbitrary
non-random coefficients. A 'hole' is the event where the...
A twenty-year old conjecture by Manickam, Mikl\'os, and Singhi
asked whether for any integers $n, k$ satisfying $n \ge 4k$, every
set of $n$ real numbers with nonnegative sum always has at least
$\binom{n-1}{k-1}$ $k$-element subsets whose sum is...
