## Book Launch for The Usefulness of Useless Knowledge

March 13, 2017

Book Launch for The Usefulness of Useless Knowledge

March 13, 2017

Book Launch for The Usefulness of Useless Knowledge

Nir Bitansky

Massachusetts Institute of Technology

March 13, 2017

Xin Jin

Northwestern Univ

March 13, 2017

Abstract: In this talk, I will present the following application of microlocal sheaf theory in

symplectic topology. For every closed exact Lagrangian L in the cotangent bundle of a manifold

M, we associate a locally constant sheaf of categories on L, which we call Brane_L, whose fiber is

the infinity-category of k-modules, for k any ring spectrum. I will discuss the relation of Brane_L

with the usual brane structures in Floer theory, and its connection to the J-homomorphism in

symplectic topology. For every closed exact Lagrangian L in the cotangent bundle of a manifold

M, we associate a locally constant sheaf of categories on L, which we call Brane_L, whose fiber is

the infinity-category of k-modules, for k any ring spectrum. I will discuss the relation of Brane_L

with the usual brane structures in Floer theory, and its connection to the J-homomorphism in

Jake Solomon

IAS

March 13, 2017

Abstract: I plan to discuss the definition of open descendent integrals. In genus g>0, this involves

the moduli space of Riemann surfaces with boundary with an additional structure called a

grading. *Joint work with R. Tessler.

the moduli space of Riemann surfaces with boundary with an additional structure called a

grading. *Joint work with R. Tessler.

Tobias Dyckerhoff

University of Bonn

March 13, 2017

Abstract: Within an emerging approach to Fukaya categories via cohomology with categorical

coefficients, I will outline a theory of a particularly nice class of nonconstant coefficient systems

defined on Riemann surfaces. These are categorical analogues of perverse sheaves, called

perverse schobers. We provide a definition of perverse schobers as categorical sheaves on a

relative two-colored version of the unital Ran space of the surface. We explain how to describe

coefficients, I will outline a theory of a particularly nice class of nonconstant coefficient systems

defined on Riemann surfaces. These are categorical analogues of perverse sheaves, called

perverse schobers. We provide a definition of perverse schobers as categorical sheaves on a

relative two-colored version of the unital Ran space of the surface. We explain how to describe

Denis Auroux

IAS

March 13, 2017

Abstract: In this talk we will report on joint work in progress with Mohammed Abouzaid

concerning homological mirror symmetry for hypersurfaces in (C*)^n, namely, comparing the

derived category of the hypersurface and the Fukaya category of the mirror Landau-Ginzburg

model. We will then discuss the extension of these results to (essentially arbitrary) complete

intersections in toric Fano varieties.

concerning homological mirror symmetry for hypersurfaces in (C*)^n, namely, comparing the

derived category of the hypersurface and the Fukaya category of the mirror Landau-Ginzburg

model. We will then discuss the extension of these results to (essentially arbitrary) complete

intersections in toric Fano varieties.

Edward Witten

IAS

March 15, 2017

Nicolas Templier

Cornell

March 15, 2017

Abstract: We prove cases of Rietsch mirror conjecture that the A-model of projective

homogeneous varieties is isomorphic to the B-model of its mirror, which is a partially

compactified Landau--Ginzburg model constructed from Lie theory and geometric crystals. The

conjecture relates to deep objects in algebraic combinatorics. Our method of proof comes from

Langlands reciprocity, and consists in identifying the quantum connection as Galois and the

crystal as automorphic. I will mention further potential interactions between symplectic

homogeneous varieties is isomorphic to the B-model of its mirror, which is a partially

compactified Landau--Ginzburg model constructed from Lie theory and geometric crystals. The

conjecture relates to deep objects in algebraic combinatorics. Our method of proof comes from

Langlands reciprocity, and consists in identifying the quantum connection as Galois and the

crystal as automorphic. I will mention further potential interactions between symplectic

Clelia Pech

Kent University

March 15, 2017

Abstract: In this talk reporting on joint work with K. Rietsch and L. Williams, I will explain a new

version of the construction by Rietsch of a mirror for some varieties with a homogeneous Lie

group action. The varieties we study include quadrics and Lagrangian Grassmannians (i.e.,

Grassmannians of Lagrangian vector subspaces of a symplectic vector space). The mirror takes

the shape of a rational function, the superpotential, defined on a Langlands dual homogeneous

version of the construction by Rietsch of a mirror for some varieties with a homogeneous Lie

group action. The varieties we study include quadrics and Lagrangian Grassmannians (i.e.,

Grassmannians of Lagrangian vector subspaces of a symplectic vector space). The mirror takes

the shape of a rational function, the superpotential, defined on a Langlands dual homogeneous

Si Li

Tsinghua University

March 15, 2017

Abstract: We study the effective BV quantization theory for chiral deformation of two

dimensional conformal field theories. We establish an exact correspondence between

renormalized quantum master equations for effective functionals and Maurer-Cartan equations

for chiral vertex operators. The generating functions are proven to be almost holomorphic

modular forms. As an application, we construct an exact solution of quantum B-model (BCOV

theory) in complex one dimension that solves the higher genus mirror symmetry conjecture on

dimensional conformal field theories. We establish an exact correspondence between

renormalized quantum master equations for effective functionals and Maurer-Cartan equations

for chiral vertex operators. The generating functions are proven to be almost holomorphic

modular forms. As an application, we construct an exact solution of quantum B-model (BCOV

theory) in complex one dimension that solves the higher genus mirror symmetry conjecture on