Peter Bürgisser's Mathematical Colloquium at SISSA

[Antonio Lerario]

Dear everyone,

this is to announce next SISSA mathematical colloquium:

Speaker: Peter Bürgisser (TU Berlin)
Title: Efficient algorithms for moment polytopes and the null cone problem
from invariant theory
When: Monday, October 28 at 2pm
Where: SISSA main building, room A-005

Abstract: Suppose a reductive group G acts linearly on a finite dimensional
complex vector space V. The corresponding null cone, which may be thought
of the set of "singular objects'', consists of those vectors that cannot be
distinguished from the zero vector by means of polynomial invariants. The
null cone was introduced by Hilbert in his seminal work on invariant theory
around 1900.

Quite surprisingly, the computational problem of testing membership to the
null cone turned out to be of relevance for geometric complexity theory,
quantum information theory, and other areas. Notably, a thorough study of
the null cone for the simultaneous left/right action on tuples of matrices
was crucial for finding a deterministic polynomial time algorithm for
verifying algebraic identities.

Despite the algebraic nature of the problem, numerical optimization
algorithms seem to be the most efficient general methods for solving the
null cone problem. This also applies to the related problem of testing
membership to moment polytopes, which e.g., generalizes Horn's problem on
the eigenvalues of sums of matrices.
The long term goal is to find polynomial time algorithms for these problems.
In the special case of abelian groups, such algorithms are provided by
linear programming, e.g., by interior methods. Condition numbers are likely
to play an important role in this endeavour.


Everyone is welcome!
A.

-- 
*http://people.sissa.it/~lerario <http://people.sissa.it/~lerario>*