For several classical nonnegative integer functions we investigate if they are members of the
counting complexity class# P or not. We prove# P membership in surprising cases, and in …

The representation theory of finite groups has, at its core, a collection of open problems.
Taken together, they are called 'local-global conjectures', although 'localglobal rough …

The exponent of matrix multiplication is the smallest constant ω such that two n× n matrices
may be multiplied by performing O (n ω+ ε) arithmetic operations for every ε> 0. Determining …

This paper proves a combinatorial rule giving all maximal and minimal partitions λ such that
the Schur function s λ appears in a plethysm of two arbitrary Schur functions. Determining …

We study the variety membership testing problem in the case when the variety is given as an
orbit closure and the ambient space is the set of all 3-tensors. The first variety that we …

De-bordering is the task of proving that a border complexity measure is bounded from
below, by a non-border complexity measure. This task is at the heart of understanding the …

Geometric complexity theory is an approach towards the separation of fundamental
algebraic complexity classes. Two papers by Mulmuley and Sohoni [KD Mulmuley and M …

Based on the vertex operator realization of the Schur functions, a determinant-type plethystic
Murnaghan-Nakayama rule is obtained and used to derive a general formula of the …

Geometric complexity theory (GCT) is an approach towards separating algebraic complexity
classes through algebraic geometry and representation theory. Originally Mulmuley and …

Let E be the natural representation of the special linear group SL 2 (K) over an arbitrary field
K. We use the two dual constructions of the symmetric power when K has prime …