
08/31 4:00pm 
BLOC 628 
Frank Sottile Texas A&M University 
Galois Groups for Systems of Sparse Polynomials
Camille Jordan observed that Galois groups arise in enumerative geometry, and we now also understand them as monodromy groups. A study of this question in the Schubert calculus has determined many such Galois groups, all known Schubert Galois groups are either the full symmetric group or are imprimitive. Recently, Esterov considered this question for systems of sparse polynomials and proved this dichotomy in that setting. While this classification identifies polynomial systems with imprimitive Galois groups, it does not identify the groups. I will sketch the background, before explaining Esterov's classification and ongoing work identifying some of the imprimitive Galois groups for polynomial systems. 

09/07 4:00pm 
BLOC 628 
Rafael Oliveria U. Toronto 
Scaling algorithms, applications and the nullcone problem
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 noncommutative 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 (3step) framework to
rigorously analyze such algorithms. We will also present a more general
perspective on scaling algorithms, connecting it
to the nullcone 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. 

09/10 3:00pm 
BLOC 628 
JM Landsberg TAMU 
Several astounding conjectures on the asymptotic geometry of tensors.
Many computer scientists believe the astounding conjecture that
asymptotically (as n goes to infinity), it becomes almost as easy
to multiply matrices as to add them. Since progress on this conjecture stalled around 1989, Strassen made an even more astounding conjecture that would imply the matrix multiplication conjecture. Later BurgisserClausenShokrollahi
made an even more astounding generalization to the effect that
all tensors "asymptotically look the same" in a way I'll explain precisely. In this talk (joint work with A. Conner, F. Gesmundo, Y. Wang and E. Ventura), I will discuss these conjectures and insight geometry can provide us. 