Geometry Seminar
The seminar meets Mondays at 3 o'clock in BLOC 220,
and Fridays at 4 o'clock in BLOC 117.
Talks are 5060 minutes.
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Give a Good Colloquium by John E. McCarthy.

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 

03/10 4:00pm 
BLOC 628 
Scott Aaronson UT Austin 
TBA 

03/24 4:00pm 
BLOC 628 
Robert Williams TAMU 
TBA
TBA 

03/31 4:00pm 
BLOC 628 
Ata Firat Pir 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 


04/28 4:00pm 
BLOC 628 
Elham Izadi UC San Diego 
TBA 
Archives
Please contact
Timo de Wolff
for more information.