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.
Visitor Information.
How to
Give a Good Colloquium by John E. McCarthy.

Date Time 
Location  Speaker 
Title – click for abstract 

09/23 4:00pm 
BLOC 628 
Patricio Gallardo University of Georgia 
On geometric invariant theory for hypersurfaces and their hyperplane sections.
Abstract: Geometric Invariant Theory (or GIT) is a method for
constructing moduli spaces of varieties in algebraic geometry. In
particular, for a hypersurface and a hyperplane in projective space,
there is a combinatorial algorithm that allows us to describe the varieties
parametrized by the GIT quotient. We will discuss the implementation of
this algorithm and the geometric analysis of its output. This is joint
work with J. MartinezGarcia. 

09/26 3:00pm 
BLOC 220 
Nida Obatake Texas A&M University 
"Rat GPS"  Drawing Place Field Diagrams of Neural Codes Using Toric Ideals
A rat has special neurons that encode its geographic location. These neurons are called place cells and each place cell points to a region in the space, called a place field. Neural codes are collections of the firing patterns of place cells. In this talk, we investigate how to algorithmically draw a place field diagram of a neural code, building on existing work studying neural codes, ideas developed in the field of information visualization, and the toric ideal of a neural code. This talk is based on joint work with Dr. Elizabeth Gross (San Jose State University) and Dr. Nora Youngs (Colby College) [see: arXiv:1607.00697].
Students of all backgrounds (esp. undergrads interested in math research) are welcome and encouraged to attend; no prior knowledge will be assumed for this talk. 

10/07 4:00pm 
BLOC 628 
JM Landsberg TAMU 
Optimality v. Symmetry
Given a polynomial or tensor with symmetry, does an optimal expression for it also have symmetry? A classical example is Fischer's expression for the monomial x_1x_2...x_n as a sum of 2^{n1} nth powers of linear forms.(Ranestad and Schreyer showed his expression is optimal.) The monomial is invariant under permutations of the basis vectors, the permutation group on n elements. Fischer's expression also has symmetry, but under the permutation group on n1 elements! I will discuss how to exploit such symmetry in two central problems in theoretical computer science: Valiant's algebraic analog of P v. NP and the problem of determining the number of arithmetic operations needed to multiply two nxn matrices. The first is a comparison of the permanent and determinant polynomials. The second became a question in 1969 when Strassen discovered the standard algorithm for multiplying matrices is not the optimal one, which, after much work, has led computer scientists to conjecture that as n grows, it becomes almost as easy to multiply nxn matrices as it is to add them!
The first project is joint work with N. Ressayre, the second is joint work with G. Ballard, L. Chiantini, C. Ikenmeyer, G. Ottaviani and N. Ryder. 

10/10 3:00pm 
BLOC 220 
Kevin Kordek TAMU 
Picard groups of moduli spaces of curves with symmetry
In 1960s, Mumford showed that the (orbifold) Picard group of the moduli space of genus g Riemann surfaces is isomorphic to the second integral cohomology of the genus g mapping class group. Technology developed since that time now allows one to productively study various generalizations of Mumford's original calculation. In this talk, I will explain how the theory of symmetric mapping class groups, developed by BirmanHilden, Harvey, and others, can be used to understand  and sometimes exactly compute  the Picard groups of various moduli spaces of curves with symmetry, for example the moduli spaces of hyperelliptic curves. 

10/14 4:00pm 
BLOC 628 
Maurice Rojas TAMU 
How Quickly Can we Find the Shapes of Algebraic Sets? Part 1: Feasibility over C
In this series of lectures, we review some old and new
results on computing the topology of algebraic sets. We work mainly
over the fields C, R, and F_p. These lectures are meant to be accessible
to first year graduate students.
We begin with the problem of deciding when an input collection of
multivariate polynomials has a nonempty complex zero set. To understand
the underlying algorithms, we compare how quick (or slow) it is to work with
Grobner bases, resultants, and a more recent numbertheoretic method of Koiran.
Along the way, we'll also see the connections between computing complex
dimension and separations of complexity classes. 

10/28 4:00pm 
BLOC 628 
Maurice Rojas TAMU 
How Quickly Can we Find the Shapes of Algebraic Sets? Part 2: Computing Topology over R
In this series of lectures, we review some old and new
results on computing the topology of algebraic sets. We work mainly
over the fields C, R, and F_p. These lectures are meant to be accessible
to first year graduate students.
We consider the complexity of computing the number of connected
components of the real zero set of a single sparse polynomial. Whereas the
first part of Hilbert's 16th Problem asks for the disposition of the ovals of
a plane curve of degree d, we instead consider the analogous problem for
nvariate polynomials (of arbitrary degree) having n+k monomial terms. We'll
see an efficient classification valid for k<=2. We then see why we get
NPhardness for k on the order of n^epsilon. 

11/04 4:00pm 
Blocker 
TGTC 


11/05 09:00am 
Blocker 
TGTC all day 


11/06 09:00am 
BLOC 
TGTC 


11/11 4:00pm 
BLOC 628 
Jerzy Weyman U. Conn. 
TBA 

11/18 4:00pm 
BLOC 628 
Tim Magee UT Austin 
TBA 
Archives
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Timo de Wolff
for more information.