" Meromorphic open-string vertex algebras, nonlinear sigma models and Witten's Dirac operators on loop spaces "
Time: 1:30 PM
Location: Hill 525
Abstract: Mathematicians have been searching for a construction of nonlinear sigma models for many years. Such a construction would allow us to turn the insights of physicists on the geometry and topology of Riemannian manifolds into a rigorous mathematical theory. There exist constructions of vertex operator (super)algebras from suitable manifolds in the literature. But unfortunately even the resulting algebras for flat manifolds in these constructions do not agree with the known sigma models for flat manifolds. In this talk, I will discuss a construction of modules of meromorphic open-string vertex algebras (suitable noncommutative generalizations of vertex algebras) generated from functions on Riemmannian manifolds. I believe that these modules are the basic ingredients needed in the future full construction of nonlinear sigma models. I will also discuss a recent construction of a Dirac-like operator on the loop space of a Riemmannian manifold proposed first by Witten. I will present some conjectures on the connections of the representation theory of these meromorphic open-string vertex algebras with elliptic genera, Calabi-Yau manifolds and the chiral de Rham complexes of Malikov, Schechtman and Vantrob.
Monday, April 8th
Aleksey Zinger , Stonybrook/IAS
"Mirror Symmetry for Stable Quotients Invariants"
Time: 1:30 PM
Location: Hill 425
Abstract: We describe a mirror formula for the direct analogue of
Givental's J-function in the SQ theory. The mirror formula in
the SQ theory is remarkably similar to that in the Gromov-Witten
theory, but the former does not involve a change of variables. This suggests that the mirror map relating the GW-invariants to the B-model
of the mirror is more reflective of the choice of curve counting theory
on the A side than of mirror symmetry. The proof of the mirror formula
in the Fano case is as in the GW-theory. On the other hand, the proof in the Calabi-Yau case consists of showing that it is a consequence of the Fano case. This is joint work with Y. Cooper.
Monday, April 1st
Alberto Garcia-Raboso, Univ. of Penn.
"A nonabelian Hodge theorem for twisted vector bundles "
Time: 1:30 PM
Location: Hill 525
Monday, March 25th
Penka Georgieva, Princeton Univ.
"Orientability in real Gromov-Witten theory"
Time: 1:30 PM
Location: Hill 525
Abstract: For a symplectic manifold M, equipped with an anti-symplectic involution,
one can consider the moduli space of J-holomorphic maps from a symmetric Riemann
surface to M commuting with the involutions on the domain and the target. These
moduli spaces play an important role in real enumerative geometry and string
theory, as seen in the works of J.-Y. Welschinger and J. Walcher. The goal of this
talk is to describe what the orientability of the moduli spaces depends on, which
is an essential ingredient in defining real Gromov-Witten type invariants. This is
a joint work A. Zinger.
Monday, March 11th
Howard Nuer, Rutgers
"Families of Calabi-Yau 3-folds containing Enriques surfaces and their birational geometry"
Time: 1:30 PM
Location: Hill 525
Abstract: We discuss the construction of families of Calabi-Yau 3-folds
containing Enriques surfaces and their birational geometry. By
considering certain 1-parameter families in the boundary of our moduli
space, we find an example of a family of Calabi-Yau 3-folds exhibiting
very surprising properties with regard to mirror symmetry. The first
part of the talk is joint work with Lev Borisov, while the second is
work-in-progress with Pat Devlin.
Monday, February 25th
Michael McBreen, Columbia
"Quantum cohomology and mirror symmetry for hypertoric varieties "
Time: 1:30 PM
Location: Hill 525
Abstract: Hypertoric varieties are holomorphic symplectic analogues of
toric varieties. I will describe joint work with Daniel Shenfeld
computing their quantum cohomology and producing a mirror formula for
their quantum connection, and describe potential applications to the
representation theory of the Yangian.
Monday, February 18th
Chris Woodward, Rutgers
"Quantum Witten localization and abelianization of qde solutions"
Time: 1:30 PM
Location: Hill 525
Abstract: I will describe a quantum version of Witten's localization principle for Gromov-Witten invariants of git
quotients, joint with E. Gonzalez.
Monday, February 11th
Benoit Charbonneau, St. Jerome\'s University in the University of Waterloo
"Fake G_2 instantons, singular monopoles and pairs"
Time: 1:30 PM
Location: Serin E372
Abstract: In joint work with Jacques Hurtubise (McGill), we introduced some time ago a relation between singular monopoles on the product of a circle and a Riemann surface with stable pairs on the Riemann surface. In current joint work with Spiro Karigiannis and Aaron Smith (both uWaterloo), we exploit a similar approach to link G_2 instantons (and more) on the product of a circle and a Calabi--Yau 3-fold and stable pairs on the Calabi--Yau. This talk is an account of how these stories intertwine and how we failed to answer big questions about G_2-instantons and yet provide an interesting sandbox to test certain ideas in higher dimensional gauge theory.
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