Skip to content
Texas A&M University
Mathematics

Geometry Seminar

Fall 2016

 

Date:September 23, 2016
Time:4:00pm
Location:BLOC 628
Speaker:Patricio Gallardo, University of Georgia
Title:On geometric invariant theory for hypersurfaces and their hyperplane sections.
Abstract: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. Martinez-Garcia.

Date:September 26, 2016
Time:3:00pm
Location:BLOC 220
Speaker:Nida Obatake, Texas A&M University
Title:"Rat GPS" - Drawing Place Field Diagrams of Neural Codes Using Toric Ideals
Abstract: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.

Date:October 7, 2016
Time:4:00pm
Location:BLOC 628
Speaker:JM Landsberg, TAMU
Title:Optimality v. Symmetry
Abstract: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^{n-1} n-th 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 n-1 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.

Date:October 10, 2016
Time:3:00pm
Location:BLOC 220
Speaker:Kevin Kordek, TAMU
Title:Picard groups of moduli spaces of curves with symmetry
Abstract: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 Birman-Hilden, 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.

Date:October 14, 2016
Time:4:00pm
Location:BLOC 628
Speaker:Maurice Rojas, TAMU
Title:How Quickly Can we Find the Shapes of Algebraic Sets? Part 1: Feasibility over C
Abstract: 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 non-empty 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 number-theoretic method of Koiran. Along the way, we'll also see the connections between computing complex dimension and separations of complexity classes.

Date:October 28, 2016
Time:4:00pm
Location:BLOC 628
Speaker:Maurice Rojas, TAMU
Title:How Quickly Can we Find the Shapes of Algebraic Sets? Part 2: Computing Topology over R
Abstract: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 n-variate 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 NP-hardness for k on the order of n^epsilon.

Date:November 4, 2016
Time:4:00pm
Location:Blocker
Speaker:TGTC
Title:

Date:November 5, 2016
Time:09:00am
Location:Blocker
Speaker:TGTC all day
Title:

Date:November 6, 2016
Time:09:00am
Location:BLOC  
Speaker:TGTC
Title:

Date:November 11, 2016
Time:4:00pm
Location:BLOC 628
Speaker:Jerzy Weyman, U. Conn.
Title:Towards the geometric interpretation of tameness
Abstract:I will discuss some geometric problems related to characterization of finite representation type and tame algebras. In particular this will involve the multiplicity free property of rings of semi-invariants, and the dense orbit property. We will show how some of our conjectures can are related to the Ringel conjectures of the strong forms of Drozd Trichotomy Theorem. The talk is based on joint work with Andrew Carroll, Calin Chindris, Ryan Kinser and Amelie Schreiber.

Date:November 18, 2016
Time:4:00pm
Location:BLOC 628
Speaker:Tim Magee, UT Austin
Title:Log Calabi-Yau mirror symmetry and representation theory
Abstract:Mark Gross, Paul Hacking, Sean Keel, and Bernd Siebert have been developing a mirror symmetry program for log CYs-- varieties U that come with a unique volume form Ω having at worst a simple pole along any divisor in any compactification of U. My goal will be to convince you that this mirror symmetry program actually gives a nice back door into representation theory. I'll focus on a particular example-- finding the structure constants for decomposing a tensor product of GL_n irreps into a sum, the “Littlewood- Richardson coefficients”. We'll get the Knutson-Tao hive cone encoding these constants as part of a broader framework, one that in principal has nothing to do with representation theory at all and should only depend upon having a variety with the right type of volume form.

Date:December 5, 2016
Time:3:00pm
Location:BLOC 220
Speaker:Roberto Barrera, TAMU
Title:A finiteness result for local cohomology modules of Stanley-Reisner rings
Abstract:While local cohomology modules of a ring may not be finitely generated, they still may possess other finiteness properties. In 1990, Craig Huneke asked if the number of associated prime ideals of a local cohomology module is finite. Huneke's question has since been answered in the affirmative for various families of rings by using different methods in characteristic 0 and in positive characteristic. In 2010, Gennady Lyubeznik gave a characteristic free proof that the local cohomology modules of the polynomial ring have finitely many associated prime ideals. In this talk, I will give the necessary background from D-module theory and local cohomology and then answer Huneke's question for local cohomology modules of Stanley-Reisner rings using techniques inspired by Lyubeznik. This is joint work with Jeffrey Madsen and Ashley Wheeler.

Date:December 9, 2016
Time:4:00pm
Location:BLOC 628
Speaker:Tian Yang, Stanford University
Title:Volume conjectures for Reshetikhin-Turaev and Turaev-Viro invariants