
Date Time 
Location  Speaker 
Title – click for abstract 

09/01 4:00pm 
BLOC 628 
E. Ventura TAMU 
Catalecticants, antipolars, and ranks of forms
The complex (or real) rank of a homogeneous polynomial is the smallest number of powers of complex (or real) linear forms such that the polynomial may be expressed as a linear combination of those. Such an expression is called a minimal Waring or symmetric decomposition. We will talk about real and complex ranks in the setting of bihomogeneous polynomials by the means of maps associated to them: catalecticants and antipolars. We will also explain how the latter ones are related to loci encoding information about minimal decompositions of these bihomogeneous polynomials. 

09/09 4:00pm 
Denton 

AMS mtg 

09/10 4:00pm 
Denton 

AMS mtg 

09/11 3:00pm 
BLOC 628 
A. Conner TAMU 
Geometry of symmetrized matrix multiplication 

09/15 4:00pm 
BLOC 628 
Souvik Goswami TAMU 
Higher arithmetic Chow groups
For a regular scheme, which is flat and quasiprojective over an arithmetic ring (typically the ring of integers of a number field), Gillet and Soul ́e defined an arithmetic version of the usual Chow groups, taking into account the complex embeddings of the scheme. Typically the complex embeddings add more complex analytic/ Hodgetheoretic informations to the usual Chow groups.
On the other hand, higher Chow groups were defined by Spencer Bloch as a simple example of a motivic cohomology. In this talk, we will explore the possibility to obtain a good definition for higher arithmetic Chow groups. This is a joint work with Jos ́e Ignacio Burgos from ICMAT, Madrid. 

09/18 3:00pm 
BLOC 628 
Gregory Pearlstein TAMU 
Mixed Hodge Metrics
I will give an overview of recent work with P. Brosnan on the asymptotic behavior of archimedean heights, and with C. Peters on the differential geometry of mixed period domains. 

09/22 4:00pm 
BLOC 628 
V. Makam U. Michicgan 
Degree bounds for invariant rings of quivers
The ring of polynomial invariants for a rational representation of a reductive group is finitely generated. Nevertheless, it remains a difficult task to find a minimal set of generators, or even a bound on their degrees. Combining ideas originating from Hochster, Roberts and Kempf with the study of various ranks associated to linear matrices, we prove "polynomial" bounds for various invariant rings associated to quivers.
The polynomiality of our bounds have strong consequences in algebraic complexity. If time permits, we will discuss these as well as applications to lower bounds for border rank of tensors. This is joint work with Derksen. 

09/25 3:00pm 
BLOC 628 
F. Gesmundo Copenhagen 
On multiplicativity of various notions of rank
Matrix rank has several different generalizations to the
setting of tensors. Whereas for matrices it is easy to show that rank
is multiplicative over tensor product (the matrix Kronecker product),
multiplicativity is not straightforward (and in most cases false) in
the setting of tensors. We discuss this problem for various notions of
rank: tensor rank, partially symmetric tensor rank and tensor border
rank in particular. The geometric framework allows for further
generalizations, that we briefly present. 

09/29 4:00pm 
BLOC 628 
JM Landsberg TAMU 
Quantum max flow v. quantum min cut and the geometry of matrix product states 

10/02 3:00pm 
BLOC 628 
Boris Hanin TAMU 
Pointwise Estimates in the Weyl Law on a Compact Manifold
Let (M,g) be a compact smooth Riemannian manifold. This talk focuses on connecting the structure of geodesics on (M,g) to the behavior of eigenfunctions of the Laplacian at high frequencies. I will explain a physical heuristic for why such a connection should exist. I will then present some new estimates for the second term in the pointwise Weyl Law. These estimates imply that if the geodesics passing through a given point on M are dispersive (in a suitable sense), then the spectral projector of the Laplacian onto the frequency interval (lambda,lambda+1] has a universal scaling limit as lambda goes to infinity (depending only on the dimension of M). This is joint work with Y. Canzani. 

10/13 4:00pm 
BLOC 628 
Emre Sen Northeastern 
Singularities of dual varieties associated to exterior representations
For a given irreducible projective variety $X$, the closure of the set of
all hyperplanes containing tangents to $X$ is the projectively dual variety
$X^{\vee}$. We study the singular locus of projectively dual varieties of
certain SegrePl\"{u}cker embeddings. We give a complete classification of
the irreducible components of the singular locus of several representation
classes. Basically, they admit two types of singularities: cusp type and
node type which are degeneracies of a certain Hessian matrix, and the
closure of the set of tangent planes having more than one critical point
respectively. In particular, our results include a description of
singularities of dual Grassmannian varieties. 

10/16 3:00pm 
BLOC 628 
Tian Yang TAMU 
Rigidity of hyperbolic cone metrics on triangulated 3manifolds
In this joint work with Feng Luo, we prove that a hyperbolic cone metric on an ideally triangulated compact 3manifold with boundary consisting of surfaces of negative Euler characteristic is determined by its combinatorial curvature. The proof uses a convex extension of the Legendre transformation of the volume function. 

10/20 4:00pm 
BLOC 628 
Michael Di Pasquale Oklahoma State University 
Homological Obstructions to Freeness of Multiarrangements
If the module of vector fields tangent to a multiarrangement is free over the underlying polynomial ring, we say that the multiarrangement is free. It is of particular interest in the theory of hyperplane arrangements to investigate the relation of freeness to the combinatorics of the intersection lattice  the holy grail here is Terao's conjecture that freeness of arrangements is detectable from the intersection lattice. It is known that corresponding statements for multiarrangements fail. Given a multiarrangement, we present a cochain complex derived from work of Brandt and Terao on kformality whose exactness encodes freeness of the multiarrangement. The cohomology groups of this cochain complex thus present obstructions to freeness of multiarrangements. Using this criterion we give an example showing that the property of being totally nonfree is not detectable from the intersection lattice. This builds on previous work with Francisco, Schweig, Mermin, and Wakefield.


10/23 3:00pm 
BLOC 628 
Shilin Yu TAMU 
Families of representations of Lie groups
Beilinson and Bernstein generalized the BorelWeilBott theorem and showed that representations of a (noncompact) reductive Lie group G can be realized as Dmodules on flag variety. In this talk, I will show that such Dmodules live naturally in families, which explains a mysterious analogy between representation theory of the group G and a related semidirect product group due to Mackey, Higson and Afgoustidis. Connection with Kirillov's coadjoint orbit method will be discussed. The talk is based partially on joint projects with Qijun Tan, Yijun Yao and Conan Leung. 

10/27 4:00pm 
BLOC 628 
Xiaoxian Tang TAMU 
TBA 

11/03 4:00pm 
BLOC 628 
John Calabrese Rice University 
TBA 

11/06 3:00pm 
BLOC 628 
Bo Lin UT Austin 
TBA 

11/10 4:00pm 
BLOC 628 
Alicia Harper Brown University 
Factorization of maps of DeligneMumford stacks 

11/13 3:00pm 
BLOC 628 
Abraham Martín del Campo CIMAT 
TBA 

11/17 4:00pm 
BLOC 628 
Taylor Brysiewicz TAMU 
TBA 

11/20 3:00pm 
BLOC 628 
Zheng Zhang TAMU 
TBA 

11/27 3:00pm 
BLOC 628 
Souvik Goswami TAMU 
TBA 

12/01 4:00pm 
BLOC 628 
Jose Rodriguez University of Chicago 
TBA 