## Continuous covers on symplectic manifolds

François Lalonde

University of Montreal

March 24, 2017

Yve-Alain Bois

Pablo Picasso did not speak often about abstraction, but when he did, it was either to dismiss it as complacent decoration or to declare its very notion an oxymoron. The root of this hostility is to be found in the impasse that the artist reached in the summer 1910, when abstraction suddenly appeared as the logical development of his previous work, a possibility at which he recoiled in horror. But though he swore to never go again near abstraction, he could not prevent himself from testing his... Read more

François Lalonde

University of Montreal

March 24, 2017

Daniel Alvarez-Gavela

Stanford University

March 23, 2017

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.

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

Daniel Halpern-Leistner

Columbia University

March 16, 2017

Abstract: Mirror symmetry has led to deep conjectures regarding the geometry of Calabi-Yau

manifolds. One of the most intriguing of these conjectures states that various geometric

invariants, some classical and some more homological in nature, agree for any two Calabi-Yau

manifolds which are birationally equivalent to one another. I will discuss how new methods in

equivariant geometry have shed light on this conjecture over the past few years, ultimately

manifolds. One of the most intriguing of these conjectures states that various geometric

invariants, some classical and some more homological in nature, agree for any two Calabi-Yau

manifolds which are birationally equivalent to one another. I will discuss how new methods in

equivariant geometry have shed light on this conjecture over the past few years, ultimately

Ludmil Katzarkov

IAS

March 17, 2017

Abstract: In this talk we will combine classical mathematical structures and we will look at them

from a new prospective. Applications to geometry will be considered.

from a new prospective. Applications to geometry will be considered.

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

Tony Pantev

University of Pennsylvania

March 16, 2017

Abstract: I will describe descent formalism in categorical non-commutative geometry which is

geared towards constructions of Fourier–Mukai functors. The formalism allows one to carry out

descent constructions in general algebraic and analytic frameworks without resorting to

generators. I will discuss various applications, such as the connection to the classical Zariski and

flat descents, constructions of Fukaya categories, and homological mirror symmetry. This is a

joint work with Katzarkov and Kontsevich.

geared towards constructions of Fourier–Mukai functors. The formalism allows one to carry out

descent constructions in general algebraic and analytic frameworks without resorting to

generators. I will discuss various applications, such as the connection to the classical Zariski and

flat descents, constructions of Fukaya categories, and homological mirror symmetry. This is a

joint work with Katzarkov and Kontsevich.

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

Mauricio Romo

IAS

March 16, 2017

Abstract: I'll give an overview of basic concepts about B-branes and their central charges and

how they arise in physics and mathematics. In particular I'll present the gauge linear model

approach which allows for defining quantities in the full stringy Kahler moduli M of certain

Calabi-Yaus (CY). Then, I'll show some examples and motivate an intrinsic definition of the central

charges on phases (some sub-regions of M), based on field theory data. I'll put particular

how they arise in physics and mathematics. In particular I'll present the gauge linear model

approach which allows for defining quantities in the full stringy Kahler moduli M of certain

Calabi-Yaus (CY). Then, I'll show some examples and motivate an intrinsic definition of the central

charges on phases (some sub-regions of M), based on field theory data. I'll put particular