
Date Time 
Location  Speaker 
Title – click for abstract 

08/26 3:00pm 
BLOC 628 
Guangbo Xu Texas A&M University 
Introduction to Floer homology
In this talk, after reviewing the classical finite dimensional
Morse theory, I will give a short introduction to various versions of
Floer homology theories, for example, Lagrangian intersection Floer
homology in symplectic geometry and instanton Floer homology in gauge
theory. I will also explain the conceptual picture of the celebrated
AtiyahFloer conjecture. Nonexperts, especially graduate students are
welcome. 

09/02 3:00pm 
BLOC 628 
Mounir Nisse Xiamen University Malaysia 
Phase tropical varieties are topological manifolds
After defining some tropical tools and giving an overview of the subject, we prove first that phase tropical curves, that are limits of algebraic smooth complete intersection curves, are topological manifolds. We generalize this fact to phase tropical kplanes, and then to phase tropical varieties that are limits of algebraic smooth complete intersection varieties (work is in progress). 

09/20 4:00pm 
BLOC 628 
A. Conner TAMU 
Border Apolarity of tensors and matrix multiplication
I will present a new method for border rank lower bounds of tensors
which exploits continuous symmetry. I will discuss new results from
this method's application to the matrix multiplication tensor, whose
border rank is fundamentally related to the complexity of matrix
multiplication. 

09/27 4:00pm 
BLOC 628 
Souvik Goswami Texas A&M University 
Height pairing on Bloch's higher cycles and mixed Hodge structures.
In a previous work with José Ignacio Burgos, we have studied the higher arithmetic Chow groups. As a by product, an Archimedean height pairing between higher cycles has been defined. Classically, Hain has shown that the Archimedean component of the height pairing between ordinary cycles can be interpreted as the class of a biextension in the category of mixed Hodge structures.
In the current work we study the mixed Hodge structure defined by a pair of higher cycles intersecting properly and show that, in a special case, the Archimedean height pairing is one of the periods attached to such mixed Hodge structure.
This is joint work in progress with Greg Pearlstein and José Ignacio Burgos. 

10/04 4:00pm 
BLOC 628 
Ursula Whitcher University of Michigan 
Zeta functions of alternate mirror CalabiYau families
Mirror symmetry predicts surprising geometric correspondences between
distinct families of algebraic varieties. In some cases, these
correspondences have arithmetic consequences. For example, one can use
mirror symmetry to explore the structure of the zeta function, which
encapsulates information about the number of points on a variety over a
finite field. We prove that if two CalabiYau invertible pencils in
projective space have the same dual weights, then they share a common
polynomial factor in their zeta functions related to a hypergeometric
PicardFuchs differential equation. The polynomial factor is defined
over the rational numbers and has degree greater than or equal to the
order of the PicardFuchs equation. This talk describes joint work with
Charles Doran, Tyler Kelly, Adriana Salerno, Steven Sperber, and John
Voight.


10/05 10:00am 
BLOC 628 

Fall TAGS program.
The Texas Algebraic Geometry Symposium is a joint seminar of Rice University, Texas A&M University, and the University of Texas at Austin. This conference aims to bring to a regional audience the latest developments in Algebraic Geometry.
This Fall there will be a weekend program to complement the main conference series. These events will be held at Texas A&M campus on October 5 and October 6. The speakers will be:
Jennifer Balakrishnan, Boston University.
Daniel Erman, University of WisconsinMadison
Sarah Frei, Rice University.
Jessica Sidman, Mt. Holyoke College
Emanuele Ventura, Texas A&M University.
Ursula Whitcher, University of Michigan Abstract 

10/07 3:00pm 
BLOC 628 
Matthew Ballard University of South Carolina 
Can the derived category detect rationality?
Rationality questions and the structure of derived categories of coherent sheaves have been shown to be intimately tied together over the past 30 years  both via evidence and tantalizing conjectures. Perhaps the most basic question one can ask is: are there natural conditions on D(X) which would imply the rationality of X? One of the simplest structural conditions on D(X) is that it can be broken into pieces that are derived categories of (smooth) points. In joint work with Duncan, Lamarche, and McFaddin, we show that this is insufficient to guarantee the existence of a kpoint in general much less rationality. However if one assumes all the points are just Spec k then we verify this guarantees rationality for toric varieties. 

10/11 4:00pm 
BLOC 628 
Taylor Brysiewicz Texas A&M University 
The degree of Stiefel manifolds and spaces of Parseval frames.
The (k, n)th Stiefel manifold is the space of k×n matrices M with the property that M*M^T=Id. Equivalently, this is the space of Parseval nframes for kdimensional space. The polynomial equations characterizing the Stiefel manifold define an embedded affine algebraic variety. We will sketch our proof of a formula for its degree using aspects of representation theory, GelfandTsetlin polytopes, and the combinatorics of nonintersecting lattice paths. [joint work with Fulvio Gesmundo] 

10/18 4:00pm 
BLOC 628 
Paulo LimaFilho Texas A&M University 
Transforms of geometric currents under correspondences and regulators for Higher Chow groups.
In this talk we show how equidimensional algebraic correspondences between complex algebraic varieties can be used to construct pullbacks and transforms on a class of currents representable by integration. As a main application we exhibit explicit formulas at the level of complexes for a regulator map from the Higher Chow groups of smooth quasiprojective complex algebraic varieties to DeligneBeilinson cohomology, utilizing the original simplicial description of Higher Chow groups with integral coefficients. The main ingredients come from Suslin's equidimensionality results, which show that suitable complexes of equidimensional correspondences are quasiisomorphic to Bloch's original complex. We indicate how this can be applied to Voevodsky's motivic complexes and realizations of mixed motives. The GMT constructions may be extended to more general metric spaces, such as rigid analytic spaces. This is joint work with Pedro dos Santos and Robert Hardt. 

10/21 3:00pm 
BLOC 628 
Donghao Wang MIT 
Finite Energy Monopoles on $\C \times \Sigma$
The SeibergWitten (monopole) equations and the monopole invariants introduced by Witten have greatly influenced the study of smooth 4manifolds since 1994. By studying its dimensional reduction in dimension 3, KronheimerMrowka defined the monopole Floer homology for any closed 3manifolds. In this talk, we continue this reduction process and consider the moduli space of solutions on $X=\mathbb{C}\times\Sigma$, where $\Sigma$ is a compact Riemann surface. We will classify solutions to the SeibergWitten equations on $X$ with finite analytic energy and estimate their decay rates at infinity according to the algebraic input.
The motivation is to extend the construction of KronheimerMrowka for compact 3manifolds with boundary, and this work is the first step towards this goal. 

10/25 4:00pm 
BLOC 628 
Jordyn Harriger Indiana University 
Planar Algebras Related to the Symmetric Groups.
What makes the symmetric groups special ? Well, one interesting thing about
S_n is that it has a subgroup of index n and that the permutation representation
of S_n comes from inducing the trivial representation of that subgroup. How
could this generalize if n was not an integer? Using planar algebras we can
describe Rep(S_n) graphically. Then using this graphical description we can
construct a planar algebra for Rep(S_t), where t is not an integer, via inter
polation between the Rep(S_n)'s. Additionally, I will describe how this planar
algebra can from a special biadjunction between tensor categories, which gen
eralizes the induction and restriction relations between S_n and S_{n1}. I will
also discuss the relationship between these planar algebras and usual partition
algebra description of Rep(S_t). 

11/01 4:00pm 
BLOC 628 
Margaret Regan Notre Dame 
Applications of Parameterized Polynomial Systems.
Many problems in computer vision and engineering can be formulated
using a parameterized system of polynomials which must be solved for
given instances of the parameters. Due to the nature of these
applications, solutions and behaviour over the real numbers are those
that provide meaningful information for the system. This talk will describe
using homotopy continuation within numerical algebraic geometry to solve these
parameterized polynomial systems. It will also discuss applications
regarding 2D image reconstruction in computer vision and 3RPR
mechanisms in kinematics. 

11/04 3:00pm 
BLOC 628 
Nida Obatake Texas A&M University 
Polyhedral methods for chemical reaction networks
Chemical Reaction Network theory is an area of mathematics that analyzes the behaviors of chemical processes. A major problem asks about the stability of steady states of these networks. Rubinstein et al. (2016) showed that the ERK network exhibits multiple steady states, bistability, and undergoes periodic oscillations for some choice of rate constants and total species concentrations. The ERK network reduces to the processive dualsite phosphorylation network when certain reactions are omitted, and this network is known to have a unique, stable steady state (Conradi and Shiu, 2015). To investigate how the dynamics change as reactions are removed from the ERK network, we analyze subnetworks of the ERK network. In particular, we prove that oscillations persist even after we greatly simplify the model by making all reactions irreversible and removing intermediates. To prove this, we introduce the Newtonpolytope Method: an algorithmic procedure that uses techniques from polyhedral geometry to construct a positive point where a pair of polynomials achieve certain desired sign conditions. We then use our algorithm to apply an algebraic criterion for Hopf bifurcations that relies on analyzing polynomials (Yang, 2002). Additionally, we investigate the maximum number of steady states of a system by defining a notion of a mixed volume of a chemical reaction network. In general, the mixed volume is an upper bound on the number of complexnumber steady states, but we show that this bound is tight for ERK networks. Joint work with Anne Shiu, Xiaoxian Tang and Angelica Torres. 

11/11 3:00pm 
BLOC 628 
M. Michalek MPI Leipzig 
Singularities of secant and tangential varieties of SegreVeronese varieties
We will show applications of ideas from statistics to study classical objects in algebraic geometry. A change of coordinates, inspired by computation of cumulants, reveals a toric structure on secant variety of any SegreVeronese variety. We will show how to exploit this structure to study the singularities. 

11/14 4:00pm 
BLOC 628 
M. Michalek MPI Leipzig 
C^*actions, MLdegree and various Grassmannians
Central questions in many branches of mathematics are related to understanding the cohomology class of a graph of a Cremona transformation. One case is statistics, where the Maximum Likelihood degree of Gaussian models can be expressed exactly in this terms. I will report on work in progress with Wisniewski, where we upgrade the relevant Cremona transformation to a C^* action on a blow up of a homogeneous variety. This leads to a new computational approach towards the ML degree. 

11/18 3:00pm 
BLOC 628 
Elise Walker Texas A&M University 
Toric degenerations and optimal homotopies from finite Khovanskii bases
Homotopies are useful numerical methods for solving systems of polynomial equations. I will present such a homotopy
method using Khovanskii bases. Finite Khovanskii bases provide a flat degeneration to a toric variety, which consequentially gives a homotopy. The polyhedral homotopy, which is implemented in PHCPack, can be used to solve for points on a general linear section of this toric variety. These points can then be traced via the Khovanskii homotopy to points on a general linear slice of the original variety. This is joint work with Michael Burr and Frank Sottile. 

11/22 4:00pm 
BLOC 628 
Guillem Cazassus Indiana University 
Equivariant Lagrangian Floer homology and extended Field theory
Given a Hamiltonian Gmanifold endowed with a pair of GLagrangians, we provide a construction for their equivariant Floer homology. Such groups have been defined previously by Hendricks, Lipshitz and Sarkar, and also by Daemi and Fukaya. A similar construction appeared independently in the work of Kim, Lau and Zheng.
We will discuss an attempt to use such groups to construct topological Field theories: these should be seen as 3morphism spaces in the Hamiltonian 3category, which should serve as a target for a Field theory corresponding to Donaldson polynomials. 

12/02 3:00pm 
BLOC 628 
Charles Doran University of Alberta, Canada 
CalabiYau Geometry of the Multiloop Sunset Feynman Integrals
We will explore the "geometric gems" that emerge naturally when computing the simplest infinite family of Feynman integrals. These include Hessians of cubic surfaces, complete intersections in permutohedral varieties, and LandauGinzburg mirrors of weak Fano varieties. An iterative fibration structure on CalabiYau varieties, and a consequent iterative description of their periods, is ultimately crucial to understanding these Feynman integrals. We derive from this a conjectural "motivic mirror" principle that recasts Feynman integrals in terms of LandauGinzburg models fibered by motivic CalabiYau varieties. 

12/13 4:00pm 
BLOC 628 
Tim Seynnaeve MPI Leipzig 
Uniform Matrix Product States from an Algebraic Geometer’s point of view
Uniform matrix product states are certain tensors that describe physically meaningful states in quantum information theory. We apply methods from algebraic geometry to study the set of uniform matrix product states. In particular, we provide many instances in which the set of uniform matrix product states is not closed, answering a question posed by Hackbusch. We also confirm a conjecture of Critch and Morton asserting that, under some assumptions, matrix product states are ``identifiable''. Roughly speaking, this means that the parametrizing map is as injective as it could possibly be. Finally, we managed to compute defining equations for the variety of uniform matrix product states for small parameter values.
This talk is based on joint work with Adam Czaplinski and Mateusz Michalek. 