
Date Time 
Location  Speaker 
Title – click for abstract 

01/17 3:00pm 
506A 
Kevin Tucker Univ. of Illinois at Chicago 
Local Fundamental Groups of Strongly FRegular Varieties
One may study the nonmanifold points of a complex algebraic
variety by analyzing the link of the singularity, i.e. the
intersection of a small nearby sphere with the variety. For varieties
of (complex) dimension two, it was shown by Mumford that the link is
simply connected if and only if the variety is actually smooth. A
similar statement fails in higher dimensions, but Kollár has
conjectured that fundamental group of the link should be finite for
certain mild and wellstudied singularities called Kawamata Log
Terminal singularities. In this talk, I will give an overview of this
conjecture, and discuss ongoing recent work (with CarvajalSchwede and
BhattCarvajalGrafSchwede) on a positive characteristic weak variant
 the finiteness of local fundamental groups for strongly Fregular
varieties. 

01/30 3:00pm 
BLOC 220 
Taylor Brysiewicz TAMU 
The degree of SO(n)
The degree of a variety is one of the most natural invariants to try to
compute. We give a formula for the degree of the special orthogonal
group SO(n) for the first time. This formula has a combinatorial
interpretation via nonintersecting lattice paths and also has
applications to lowrank semidefinite programming. We explain how to
verify this formula explicitly using a monodromy algorithm in numerical
algebraic geometry (for n<=7) and how such computations aid in further
study of the variety. 

02/17 4:00pm 
BLOC 628 
Timo de Wolff TAMU 
Constrained Polynomial Optimization via SONCs and Relative Entropy Programming
Deciding nonnegativity of real polynomials is a fundamental problem in real algebraic geometry and polynomial optimization. Since this problem is NPhard, one is interested in finding sufficient conditions (certificates) for nonnegativity, which are easier to check. The standard certificates for nonnegativity are sums of squares (SOS). In practice, SOS based semidefinite programming (SDP) is the standard method to solve polynomial optimization problems.
In 2014, Iliman and I introduced an entirely new nonnegativity certificate based on sums of nonnegative circuit polynomials (SONC), which are independent of sums of squares. We successfully applied SONCs to global nonnegativity problems.
In Summer 2016, Dressler, Iliman, and I proved a Positivstellensatz for SONCs, which provides a converging hierarchy of lower bounds for constrained polynomial optimization problems. These bounds can be computed efficiently via relative entropy programming.
In this second of two talks on the topic I will give a brief overview about semidefinite, geometric, and relative entropy programming as well as Lasserre Relaxation. Afterwards, I will explain our converging hierarchy of lower bounds for constrained polynomial optimization and how they can be computed via relative entropy programming.
The first, corresponding talk will occur directly before in the algebra and combinatorics seminar. 

02/24 4:00pm 
BLOC 628 
JM Landsberg TAMU 
Symmetry v. Optimality
The talk will be a colloquium style talk  all are welcome.
I will discuss uses of algebraic geometry and representation theory in
complexity theory. I will explain how these geometric methods have been successful in proving lower complexity bounds: unblocking the problem of lower bounds for the complexity of matrix multiplication, which had been stalled for over thirty years, and providing the first exponential separation of the permanent from the determinant in any restricted model. (The permanent v. determinant problem is an algebraic cousin of the P v. NP problem.) I will also discuss exciting new work that indicates that these methods can also be used to provide complexity upper bounds, in fact construct explicit algorithms. This is joint work with numerous coauthors including G. Ballard, A. Conner, C. Ikenmeyer, M. Michalek, G. Ottaviani, and N. Ryder. 

03/10 4:00pm 
BLOC 220  NOTE 
Scott Aaronson UT Austin 
Boson Sampling and the Permanents of Gaussian Matrices
I'll discuss BosonSampling, a proposal by myself and Alex
Arkhipov to demonstrate "quantum supremacy" (that is, an exponential
computational speedup over classical computers), using a
linearoptical setup that falls far short of being a universal quantum
computer. The goal, in BosonSampling, is to sample from a certain
kind of probability distribution, in which the probabilities are given
by the absolute squares of permanents of complex matrices (nbyn
matrices, if there are n photons involved). Of particular interest to
mathematicians is that the BosonSampling program leads naturally to
rich mathematical questionssome of which we've answered, but many
of which remain openabout the permanent itself. (For example: are
permanents of i.i.d. Gaussian matrices close to lognormally
distributed? Is there an efficient algorithm to estimate them?) I'll
focus mainly on those questions. No quantum computation background is
needed for this talk. 

03/24 4:00pm 
BLOC 628 
Robert Williams TAMU 
An introduction to convex neural codes
The brain encodes spatial structure via special neurons called
place cells which are associated with convex regions of space. We seek
to answer the decoding problem that arises from this situation: knowing
only the firing pattern of neurons, how can we tell if it corresponds to
convex regions? We will introduce tools from algebra and geometry and
show how they can be used to determine if a given neural code can arise
from place cells.
This talk is a practice talk for a job talk. 

03/31 4:00pm 
BLOC 628 
Ata Firat Pir TAMU 
Irrational Toric Varieties
Classical toric varieties come in two flavors: Normal toric varieties are given by rational fans in R^n. A (not necessarily normal) affine toric variety is given by finite subset A of Z^n. Toric varieties are well understood and they can be approached in a combinatorial way, making it possible to compute examples of abstract concepts. Applications of mathematics have long studied the positive real part of a toric variety as the main object, where the points in A may be arbitrary points in R^n. In 1963, Birch showed the such an irrational toric variety is homeomorphic to the convex hull of the set A.
Recent work showing that all Hausdorff limits of translates of irrational toric varieties are toric degenerations suggested the need for a theory of irrational toric varieties associated to arbitrary fans in R^n. These are R^n_>equivariant cell complexes dual to the fan. Among the pleasing parallels with the classical theory is that the space of Hausdorff limits of the irrational projective toric variety of a finite set A in R^n is homeomorphic to the secondary polytope of A.
This talk will sketch this story of irrational toric varieties. It represents work in progress with Sottile. 

04/07 4:00pm 

Alperen Ergur NC State University 
TBA
TBA 

04/10 3:00pm 
BLOC 220 
Fulvio Gesmundo TAMU 
TBA
TBA 

04/14 4:00pm 
BLOC 628 
Kaitlyn Phillipson St. Edwards Univ. 
TBA 

04/17 4:00pm 
BLOC 628 
Frank Sottile TAMU 
TBA
TBA 

04/21 10:00pm 

TAGS Conference 


04/24 3:00pm 
BLOC 628 
Corey Harris Florida State 
TBA 

04/28 4:00pm 
BLOC 628 
Elham Izadi UC San Diego 
TBA 

05/01 3:00pm 
BLOC 220 
Jeff Sommars Univ. of Illinois at Chicago 
TBA
TBA 

05/12 4:00pm 
BLOC 628 
Luca DiCerbo ITCP 
TBA 

05/15 4:00pm 
BLOC 628 
G. Ballard Wake Forest 
TBA 