
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. 

11/01 4:00pm 
BLOC 628 
Margret Regan Notre Dame 
TBA 

11/04 3:00pm 
BLOC 628 
Nida Obatake Texas A&M University 
TBA
TBA 

11/18 3:00pm 
BLOC 628 
Elise Walker Texas A&M University 
TBA
TBA 

11/22 4:00pm 
BLOC 628 
Guillem Cazassus Indiana University 
TBA
TBA 

12/02 3:00pm 
BLOC 628 
Charles Doran University of Alberta, Canada 
TBA
TBA 