
Date Time 
Location  Speaker 
Title – click for abstract 

01/22 3:00pm 
BLOC 628 
Frank Sottile TAMU 
NewtonOkounkov Bodies for Applications
NewtonOkounkov bodies were introduced by KavehKhovanskii and LazarsfeldMustata to extend the theory of Newton polytopes to functions more general than Laurent polynomials. This theory has at least two implications for applications. First is that NewtonOkounkov bodies provide an approach to counting the number of solutions to systems of equations that arise in applications. Another is that when the NewtonOkounkov body is an integer polytope (there is a Khovanskii basis), there is a degeneration to a toric variety which in principal should give a numerical homotopy algorithm for computing the solutions. This talk will sketch both applications. 

02/09 4:00pm 
BLOC 628 
Tri Lai University of Nebraska  Lincoln 
Tilings and More
The field of enumeration of tilings dates back to the early 1900s when MacMahon proved his classical theorem on plane partitions. The enumeration of tilings has since taken on a life of its own as a subfield of combinatorics with connections and applications to diverse areas of mathematics, including representation theory, linear algebra, group theory, mathematical physics, graph theory, probability, and cluster algebra, just to name a few. In this talk, we focus on an interesting connection between tilings, linear algebra, and a mathematical model of electrical networks. In particular, we will go over the proof of a conjecture of Kenyon and Wilson on `tilingrepresentation' of semicontiguous minors. 

02/16 4:00pm 
BLOC 628 
Sara Maloni University of Virginia 
The geometry of quasiHitchin symplectic Anosov representations
In this talk we will focus on our joint work in progress with Daniele Alessandrini and Anna Wienhard about quasiHitchin representations in Sp(4,C), which are deformations of Fuchsian representations which remain Anosov. These representations acts on the space Lag(C^4) of complex lagrangian subspaces of C^4. We will show that the quotient of the domain of discontinuity for this action is a fiber bundle over the surface and we will describe the fiber. In particular, we will describe how the projection map comes from an interesting parametrization of Lag(C^4) as the space of regular ideal hyperbolic tetrahedra and their degenerations. 

02/19 3:00pm 
BLOC 628 
Francis Bonahon USC 
The relation (X+Y)^n = X^n + Y^n, and miraculous cancellations in quantum SL_2
The convenient formula (X+Y)^n = X^n + Y^n is (unfortunately) frequently used by our calculus students. Our more advanced students know that this relation does hold in some special cases, for instance in prime characteristic n or when YX=qXY with q a primitive nroot of unity. I will discuss similar ``miraculous cancellations`` for 2by2 matrices, in the context of the quantum group U_q(sl_2).


02/26 3:00pm 
BLOC 628 
Ron Rosenthal Technion 
Random Steiner complexes
We will discuss a new model for random ddimensional simplicial complexes, for d ≥ 2, whose (d − 1)cells have bounded degrees. The construction relies on Keevash's results on the existence of Steiner systems which are generalizations of regular graphs. We will show that with high probability, complexes sampled according to this model are highdimensional expanders. This gives a full solution to a question raised by Dotterrer and Kahle, which was solved in the twodimensional case by Lubotzky and Meshulam. In addition, we will discuss the limits of their spectral measures and their relation to the spectral measure of certain highdimensional regular trees. Based on a joint work with Alex Lubotzky and Zur Luria and a work in progress with Yuval Peled. 

03/02 4:00pm 
BLOC 628 
J. Weyman U. Conn. 
Resonance varieties
I will discuss the Koszul modules introduced by Papadima and Suciu and their relation to Resonance Varieties and Alexander type invariants of finitely generated groups. In special case related to representations S_g(C^2) of SL_2 we get nilpotent modules whose nilpotency degree is related to Green conjecture for canonical curves of genus g. The talk is based on forthcoming work joint with Aprodu, Farkas, Papadima and Raicu. 

03/05 3:00pm 
BLOC 628 
Frank Sottile Texas A&M University 
Intersection Theory in Numerical Algebraic Geometry
I will describe how some ideas from intersection theory are useful in numerical algebraic geometry. The fundamental data structure in numerical algebraic geometry is that of a witness set, which is considered to be an instantiation of Weil’s notion of a generic point. Reinterpreting a witness set in terms of duality of the intersection pairing in intersection theory leads to a generalization of the notion that makes sense on many spaces and leads to a general notion of a witness set. I will also describe how rational equivalence is linked to homotopy methods. These notions are most productive for homogenous spaces, such as projective spaces, Grassmannians, and their products. After explaining the general theory, I will sketch what this means for the Grassmannian. This is joint work with Bates, Hauenstein, and Leykin. 

03/26 3:00pm 
BLOC 628 
Cris Negron MIT 
TBA 

04/06 4:00pm 

Texas Algebraic Geometry Seminar 


04/07 09:00am 

Texas Algebraic Geometry Seminar 


04/08 09:00am 

Texas Algebraic Geometry Seminar 


04/09 3:00pm 
BLOC 628 
Zhiwei Zheng Stony Brook 
Moduli spaces of cubic fourfolds with specified prime order automorphism groups, and their compactifications.
Period map is a powerful technique to study moduli spaces of many kinds of objects related to K3 surfaces and cubic fourfolds, thanks to the global Torelli theorems (see works by Shafarevich, Rapoport, Burns, Looijenga, Peters, etc for K3 surfaces, by Voisin, Laza, Looijenga, etc for cubic fourfolds). From this point of view, AllcockCarlsonToledo (2003) realized the moduli of smooth cubic threefolds as an arrangement complement in a 10dimensional arithmetic ball quotient and studied its compactifications (both GIT and SatakeBailyBorel); recently, LazaPearlsteinZhang studied the moduli of pairs consisting of a cubic threefold and a hyperplane section.
I will talk about a joint work with Chenglong Yu about moduli of cubic fourfolds with specified prime order automorphism groups, and their compactifications. We uniformly deal with a list consisting of 14 examples, including two corresponding to the works by AllcockCarlsonToledo and LazaPearlsteinZhang mentioned above. 

04/13 4:00pm 
BLOC 628 
Renaud Detcherry Michigan State Universeity 
Quantum representations and monodromies of fibered links
According to a conjecture of Andersen, Masbaum and Ueno, the WittenReshetikhinTuraev quantum representations of mapping class groups send pseudoAnosov mapping classes to infinite order elements, when the level is big enough. We relate this conjecture to a properties about the growth rate of TuraevViro invariants, and derive infinite families of pseudoAnosov mapping classes that satisfy the conjecture, in all surfaces with n boundary components and genus g>n>=2. These families are obtained as monodromies of fibered links containing some specific sublinks.


04/27 4:00pm 
BLOC 628 
Jen Berg Rice 
TBA 

04/30 3:00pm 
BLOC 628 
Christopher O'Neill UC Davis 
TBA 