
Date Time 
Location  Speaker 
Title – click for abstract 

08/31 4:00pm 
BLOC 628 
Frank Sottile Texas A&M University 
Galois Groups for Systems of Sparse Polynomials
Camille Jordan observed that Galois groups arise in enumerative geometry, and we now also understand them as monodromy groups. A study of this question in the Schubert calculus has determined many such Galois groups, all known Schubert Galois groups are either the full symmetric group or are imprimitive. Recently, Esterov considered this question for systems of sparse polynomials and proved this dichotomy in that setting. While this classification identifies polynomial systems with imprimitive Galois groups, it does not identify the groups. I will sketch the background, before explaining Esterov's classification and ongoing work identifying some of the imprimitive Galois groups for polynomial systems. 

09/03 3:00pm 
BLOC 628 
A. Conner TAMU 
Tensors with large symmetry groups
I will describe two new paths using algebraic geometry and representation
theory to prove upper bounds on the exponent of matrix multiplication.
The first approach aims to apply the laser method of Strassen to
previously unstudied tensors which uniquely share certain geometric properties
with the CoppersmithWinograd tensor.
The second approach for upper bounds transforms the problem
into that of finding a certain sequence of finite groups and associated representations.
The first approach is joint work with Fulvio Gesmundo, JM Landsberg, and
Emanuele Ventura. 

09/07 4:00pm 
BLOC 628 
Rafael Oliveria U. Toronto 
Scaling algorithms, applications and the nullcone problem
Scaling problems have a rich and diverse history, and thereby have found
numerous applications in several fields of science and engineering. For
instance, the matrix scaling problem has had applications ranging from
theoretical computer science to telephone forecasting, economics,
statistics, optimization, among many other fields. Recently, a
generalization of matrix scaling known as operator scaling has found
applications in noncommutative algebra, invariant theory, combinatorics
and algebraic complexity; and a further generalization (tensor scaling) has
found more applications in quantum information theory, geometric complexity
theory and invariant theory.
In this talk, we will describe in detail the scaling problems mentioned
above, showing how alternate minimization algorithms naturally arise in
this setting, and we shall present a general (3step) framework to
rigorously analyze such algorithms. We will also present a more general
perspective on scaling algorithms, connecting it
to the nullcone problem in invariant theory. This framework is based on
concepts from invariant theory, which we will define.
No prior background on Invariant Theory will be needed.
Talk based on joint works with Peter Buergisser, Ankit Garg, Leonid
Gurvits, Michael Walter and Avi Wigderson. 

09/10 3:00pm 
BLOC 628 
JM Landsberg TAMU 
Several astounding conjectures on the asymptotic geometry of tensors.
Many computer scientists believe the astounding conjecture that
asymptotically (as n goes to infinity), it becomes almost as easy
to multiply matrices as to add them. Since progress on this conjecture stalled around 1989, Strassen made an even more astounding conjecture that would imply the matrix multiplication conjecture. Later BurgisserClausenShokrollahi
made an even more astounding generalization to the effect that
all tensors "asymptotically look the same" in a way I'll explain precisely. In this talk (joint work with A. Conner, F. Gesmundo, Y. Wang and E. Ventura), I will discuss these conjectures and insight geometry can provide us. 

10/01 3:00pm 
BLOC 628 
Guangbo Xu Simons Center of Geometry and Physics of Stony Brook 
BershadskyCecottiOoguriVafa torsion of LandauGinzburg Models
In their seminal work in 1994, BershadskyCecottiOoguriVafa introduced a particular RaySinger analytic torsion of CalabiYau manifolds which coincides with the genus one topological string partition function. They also proved a holomorphic anomaly formula for this torsion which is related to the variation of Hodge structure and the WeilPetersson geometry of deformation spaces. In this joint work with Shu Shen and Jianqing Yu, we consider the similar object in LandauGinzburg models. We prove an index theorem for the associated Dirac operator and rigorously define the BCOV torsion. We also obtain a partial result towards proving a holomorphic anomaly formula. 

10/12 4:00pm 
BLOC 628 
B. Ullery Harvard 
The gonality of complete intersection curves (Postponed)
The gonality of a smooth projective curve is the smallest degree of a map
from the curve to the projective line. If a curve is embedded in projective
space, it is natural to ask whether the gonality is related to the
embedding. In my talk, I will discuss recent work with James Hotchkiss. Our
main result is that, under mild degree hypotheses, the gonality of a
general complete intersection curve in projective space is computed by
projection from a codimension 2 linear space, and any minimal degree
branched covering of P^1 arises in this way. 

10/15 3:00pm 
BLOC 628 
Sam Raskin UT Austin 
An overview of local geometric Langlands
Abstract: The (arithmetic) Langlands program is a cornerstone of modern representation theory and number theory. It has two incarnations: local and global. The former conjectures the existence of certain "local terms," and the latter predicts remarkable interactions between these local terms. By necessity, the global story is predicated on the local.
Geometric Langlands attempts to find similar patterns in the geometry of curves. However, the scope of the subject has been limited by a meager local theory, which has not been adequately developed.
The subject of this talk is a part of a larger investigation into local geometric Langlands. We will give an elementary overview of the expectations of this theory, discuss a certain concrete conjecture in the area (on "temperedness"), and provide evidence for this conjecture. One application of our results is a proof of BeilinsonBernstein localization for the affine Grassmannian for GL_2, which was previously conjectured by FrenkelGaitsgory.
(Note: the talk will have slides. I will post the slides online before the talk, so feel free to bring a laptop if you prefer to follow along on your own computer.) 

10/19 4:00pm 
BLOC 628 
Yue Ren MPI MiS Leipzig 
TBA 

10/26 4:00pm 
BLOC 628 
Dylan Allegretti University of Sheffield 
The monodromy of meromorphic projective structures
A projective structure on an oriented surface S is an atlas of charts mapping open subsets of S into the Riemann sphere. There is a natural map from the space of projective structures to the PGL(2,C) character variety of S which sends a projective structure to its monodromy representation. In this talk, I will describe a meromorphic analog of this construction. I will introduce a moduli space parametrizing projective structures with poles at a discrete set of points. I will explain how, in this setting, the object parametrizing monodromy data is a type of cluster variety. This is joint work with Tom Bridgeland.


10/29 3:00pm 
BLOC 628 
C. Ikenmeyer Simons Inst. and Saarbruchen 
On Algebraic Branching Programs of Small Width
In 1979, Valiant showed that the complexity class VF of families with
polynomially bounded formula size is contained in the class VBP of
families that have algebraic branching programs (ABPs) of polynomially
bounded size. Motivated by the problem of separating these classes, we
study the topological closure of VF, i.e., the class of polynomials that
can be approximated arbitrarily closely by polynomials in VF. We
describe this closure using the wellknown continuant polynomial (in
characteristic different from 2). Further understanding this polynomial
seems to be a promising route to new formula size lower bounds. Our
methods are rooted in the study of ABPs of small constant width. In
1992, BenOr and Cleve showed that formula size is polynomially
equivalent to width3 ABP size. We extend their result (in
characteristic different from 2) by showing that approximate formula
size is polynomially equivalent to approximate width2 ABP size. This is
surprising because in 2011 Allender and Wang gave explicit polynomials
that cannot be computed by width2 ABPs at all! The details of our
construction lead to the aforementioned characterization of VF.
This is joint work with Bringmann and Zuiddam. 

11/02 4:00pm 
BLOC 628 
Sebastian CasalainaMartin University of Colorado at Boulder. 
Distinguished models of intermediate Jacobians
In this talk I will discuss joint work with J. Achter and C. Vial
showing that the image of the AbelJacobi map on algebraically trivial
cycles descends to the field of definition for smooth projective
varieties defined over subfields of the complex numbers. The main
focus will be on applications to topics such as: descending cohomology
geometrically, a conjecture of Orlov regarding the derived category
and Hodge theory, and motivated admissible normal functions.


11/03 10:30am 
BLOC 149 

Texas Algebraic Geometry Symposium, Fall Workshop
10:3011: Registration 1112: Alicia Harper, Weak Factorization for DeligneMumford Stacks. 121:30: Lunch 1:302:30: Sebastian CasalainaMartin, Geometry and topology of moduli space. 2:303: Tea. 34: Emily Witt, Frobenius powers of ideals. 44:20: Break. 4:205:20: Benjamin Schmidt, The Halphen Problem. Abstracts of the talks are available from the link below Abstract 

11/04 10:00am 
BLOC 149 

Texas Algebraic Geometry Symposium, Fall Workshop
1011: Souvik Goswami, Height Pairings 1111:20: Break. 11:2012:20: Daniel Hast, Rational Points and Unipotent Fundamental Groups.


11/16 4:00pm 
BLOC 628 
Giulio Belletti Scuola Normale Superiore, Pisa 
Asymptotics of TuraevViro invariants and volume
The basic building block of many quantum invariants of 3manifolds and
links is the quantum 6jsymbol. In this talk, I will introduce this
object and show how it can produce the TuraevViro invariants of
3manifolds. Furthermore, I will talk about a recent joint work with
Detcherry, Kalfagianni and Yang giving an asymptotically sharp upper
bound on the 6jsymbol, implying the TuraevViro volume conjecture for
an interesting infinite family of hyperbolic 3manifolds. If time
permits, I will also briefly discuss some applications of these
results to the study of quantum invariants. 

11/19 3:00pm 
BLOC 628 
Shuang Ming UC Davis 
On TQFT representations of mapping class groups with boundary
(2+1)dimensional topological quantum field theories provide many interesting finitedimensional representations of mapping class groups of surfaces. In this talk, I will discuss the irreducibility and denseness of those representations. This is joint work with Greg Kuperberg. 

11/26 3:00pm 
BLOC 628 
F. Gesmundo U. Copenhagen 
Rank of forms and partial derivatives
The polynomial Waring problem consists in determining a
decomposition of a (homogeneous) polynomial as sum of powers of linear
forms; the length of a minimal decomposition of this type is called
Waring rank. A classical generalization considers a number of
homogeneous polynomial and attempts to determine a simultaneous
decomposition of all of them. In recent work with A. Oneto and E.
Ventura, we established connections between the simultaneous Waring
rank of the partial derivatives of a polynomial and its (partially
symmetric) tensor rank. In this seminar, I will introduce Sylvester's
classical apolarity theory, which is the most used tool in this study,
and I present some of the results. 

11/30 4:00pm 
BLOC 628 
S. Gong 
TBA 