## Geometry Seminar

**Date: ** September 7, 2018

**Time: ** 4:00PM - 5:00PM

**Location: ** BLOC 628

**Speaker: **Rafael Oliveria, U. Toronto

**Title: ***Scaling algorithms, applications and the null-cone problem*

**Abstract: **Scaling problems have a rich and diverse history, and thereby have found
numerous applications in several fields of science and engineering. For
instance, the matrix scaling problem has had applications ranging from
theoretical computer science to telephone forecasting, economics,
statistics, optimization, among many other fields. Recently, a
generalization of matrix scaling known as operator scaling has found
applications in non-commutative algebra, invariant theory, combinatorics
and algebraic complexity; and a further generalization (tensor scaling) has
found more applications in quantum information theory, geometric complexity
theory and invariant theory.
In this talk, we will describe in detail the scaling problems mentioned
above, showing how alternate minimization algorithms naturally arise in
this setting, and we shall present a general (3-step) framework to
rigorously analyze such algorithms. We will also present a more general
perspective on scaling algorithms, connecting it
to the null-cone problem in invariant theory. This framework is based on
concepts from invariant theory, which we will define.
No prior background on Invariant Theory will be needed.
Talk based on joint works with Peter Buergisser, Ankit Garg, Leonid
Gurvits, Michael Walter and Avi Wigderson.