Geometry and Physics Seminar
4-6pm in 4088 East Hall

Note: Seminar is co-sponsored by MCTP
Oct 26: Igor Dolgachev (Michigan)
Dualities of quasi-homogeneous polynomials
Abstract: I will discuss different dualities between quasi-homogeneous polynomials in 3 variables. They are related to Arnold Strange duality for singularities, Mirror symmetry of K3 surfaces, Batyrev symmetry of reflexive polytoipes, Saito duality of monodromy zeta function of critical points, transpose duality of matrices defining the exponents of the monomials in the equations.
Nov 2: Tyler Jarvis (BYU)
Mirror symmetry and integrable hierarchies for the D_4 singularity
Abstract: Almost twenty years ago, Witten made a conjecture for the simple (ADE) singularities singularities, relating intersection theory on certain moduli spaces associated to each singularity and certain integrable hierarchies arising from the singularity. That conjecture was proved in the case of A_n singularities by Faber, Shadrin, and Zvonkine in 2006. Ruan, Fan, and I proved the conjecture for the D and E singularities last year, except for the case of D_4, which, surprisingly, was much harder to prove than the others. In this talk I will provide a survey the problem and its background, and then describe how we, together with my student Evan Merrell, completed the proof in the case of D_4.
Nov 9: Vincent Bouchard(Alberta)
Cut-and-join, mirror symmetry and topological recursion
Abstract: On the one hand, the topological recursion of Eynard and Orantin, which originated in Random Matrix Theory, has already found numerous applications in enumerative geometry. In particular, two years ago we conjectured that the recursion should govern Gromov-Witten theory of toric Calabi-Yau threefolds (and, in particular, Hurwitz theory). On the other hand, the cut-and-join equation is a well known recursive procedure to construct enumerative invariants, which has played an important role in Hurwitz theory and in the formulation of the mathematical theory of the topological vertex. The two recursions have very different flavors. But recently it has been shown that for simple geometries they are just two sides of the same coin; they seem to be "mirror" of each other. In this talk I will explore these exciting developments, and point towards further connections and generalizations which may shed new light on the nature of mirror symmetry for toric threefolds.
Nov 16: Dimitri Markouchevitch(Lille/Michigan)
Lagrangian fibrations from intermediate Jacobians
Abstract: The first example of a holomorphically symplectic variety admitting a Lagrangian fibration in intermediate Jacobians of algebraic varieties of dimension >1 was discovered by Donagi and Markman (1993). Since then, more examples were constructed by Iliev, Manivel and the author, where the fibers of the Lagrangian fibrations are the intermediate Jacobians of Fano varieties of dimension 3 or 5. I will survey these constructions and provide some new ones related to the intermediate Jacobians of 3-dimensional Calabi-Yau varieties and to (generalized) Prym varieties.
Nov 23: Alexei Oblomkov (UMass) (joint seminar with representation theory )
Note the different time and seminar room
Nov 30: Tian-Jun Li(Minnesota)
TBA
Dec 7: Ludmil Katzarkov(Miami)
TBA
Jan 25: Davesh Maulik (MIT)
TBA
Feb 1: Jeff Brown (Michigan)
TBA
Feb 6-7: Midwest Topology and Physics conference
Feb 8: Dan Freed (Texas-Austin)
TBA
April 17-18: RTG-Conference on Gromov-Witten theory and related topics