Title: Symplectic displacement energy for exact
Lagrangian immersions
Abstract: In this talk, I will explain an inequality
of displacement energy for exact Lagrangian immersions. Our approach is based
on Floer homology for Lagrangian immersions and Chekanov's homotopy technique
of continuations.
Cheol-Hyun Cho
Title: Constructive
mirror functor for punctured Riemann surfaces.
Abstract: We propose a
non-commutative mirror symmetry formalism. Given a family of
Lagrangian submanifold in a symplectic manifold, we use Maurer-Cartan formalism
to define the mirror non-commutative quiver algebra, with a central
element, such that it comes with a canonical A-infinity functor from Fukaya
category of the symplectic manifold to the matrix factorization category of
this central element. We illustrate this in the case of
punctured Riemann surfaces,@recovering Bocklandt's result in a geometric way. This is
a joint work with Hansol Hong and Siu-Cheong Lau.
Title: Equivalences
of derived factorization categories of gauged Landau-Ginzburg models
Abstract: Derived
factorization categories of gauged Landau-Ginzburg (LG) models are
generalizations of bounded derived categories of coherent sheaves on
varieties, and are considered as the categories of D-brane of type B for gauged
LG models. In this talk, for a given Fourier-Mukai equivalence of bounded
derived categories of coherent sheaves on smooth quasi-projective varieties, we
obtain Fourier-Mukai equivalences of derived factorization categories of gauged
LG models. As an application, we show some equivalences of derived
factorization categories of K-equivalent gauged LG model.
Title: Stability
conditions on Calabi-Yau completions for formal parameters
Abstract: The aim of this talk is to define the space of stability conditions
on an s-Calabi-Yau category for a complex number s. For this purpose, we introduce a
Calabi-Yau completion for a formal parameter and a variation of a Bridgeland
stability condition on it. We also discuss the relationship between central
charges of these stability conditions on Calabi-Yau completions of ADE-quivers
and twisted periods of ADE-singularities.
Title: Topological
recursion, quantum curves and Painlevé equations
Abstract: In this talk, Ifll explain about a relationship between the
Eynard-Orantinfs topological recursion and Painlevé equations. More precisely,
generalizing some results of Eynard-Orantin and their collaborators, wefll show
that the free energy defined by the topological recursion gives a tau-function
the Painlevé equations (for the first and the second equations; work in
progress for other Painlevé equations). Moreover, wefll see that the
topological recursion also recover the isomonodromy linear system (as a quantum
curve) for these Painlevé equations form their spectral curve.
This talk is based
on the joint work with Olivier Marchal (Lyon) and Axel Saenz (UC Davis).
Title: A partial
compactification of the Hori-Vafa toric mirror symmetry
Abstract: In this
talk, I will introduce a partial compactification of mirror symmetry for a
class of toric Calabi-Yau manifolds, discussing a new connection between SYZ
mirror symmetry and modular forms. This also gives an insight into mirror
symmetry for varieties of general type (for example, Seidel's work on genus two
Riemann surfaces). If time permits, I will discuss a higher dimensional
analogue of the Yau-Zaslow formula for an elliptic K3 surface. This talk is
based on a joint work with Siu-Cheong Lau.
Title: Mirror
Theorem for Elliptic Quasimap Invariants
Abstract: This is
a joint work with Hyenho Lho. We present a mirror theorem for the elliptic
quasimap invariants of smooth Calabi-Yau complete intersections in projective
spaces. The theorem combined with the wall-crossing formula implies mirror
theorems of Zinger and Popa for the elliptic Gromov-Witten invariants of those
varieties. The theorem and the wall-crossing formula provide a unified
framework for the mirror theory of rational and elliptic Gromov-Witten
invariants.
Title: Complete
intersection Calabi--Yau threefolds in Grassmannians with respect to
homogeneous vector bundles
Abstract: I will
talk about recent joint works with Daisuke Inoue and Atsushi Ito, on complete
intersection Calabi--Yau threefolds in Grassmannians with respect to
homogeneous vector bundles. We focus on those Calabi--Yau threefolds with
Picard number one and describe their geometry. I will also explain the
computation of the I-functions of those Calabi--
Yau threefolds and
discuss the mirror construction via conifold transition.
Title: A twistor
approach to Kontsevich complexes
Abstract: Kontsevich complexes are families of complexes associated to
algebraic functions on smooth complex algebraic varieties. The concept was
introduced by M. Kontsevich in his study on the B-side of mirror symmetry. In
this talk, we revisit some interesting results due to H. Esnault, M.
Kontsevich, C. Sabbah, M. Saito and J.-D. Yu on Kontsevich complexes from a
twistor viewpoint. After a brief review on the general theory of mixed twistor
D-modules, we explain how to apply it to obtain the results on Kontsevich
complexes. We hope that this viewpoint would be useful to understand the
generalized Hodge theoretic property of Kontsevich complexes.
Title:
Degeneration and curves on K3 surfaces
Abstract:
A folklore conjecture concerning rational curves on K3 surfaces states that all
K3 surfaces contain infinite number of irreducible rational curves. It is known
that all K3 surfaces, except those contained in the countable union of
hypersurfaces in the moduli space of K3 surfaces satisfy this property. In this
talk, we present a new approach to this problem and prove that there is a
Zariski open dense subset in the moduli space of quartic K3 surfaces whose
members satisfy the conjecture. We also mention the case of more general K3
surfaces.
Shinnosuke Okawa
TitleF Compact moduli of marked noncommutative
cubic surfaces via quivers
Abstract: I
will explain in some detail about the compactified moduli spaces of marked
noncommutative cubic surfaces constructed by using quivers. In particular I
will show how the moduli spaces of quiver representations are used to recover
the data of a noncommutative projective plane plus six points on it from the
given relations of the quiver. This is a joint work with Tarig Abdelgadir and
Kazushi Ueda.
TitleF
Lagrangian embeddings of cubic fourfolds containing a plane
Abstract: For a
cubic 4-fold X not containing a plane, Lehn et al constructed an irreducible
holomorphic symplectic 8-fold which contains X as a Lagrangian submanifold via
twisted cubic curves on X. In this talk, I will talk about Lagrangian
embeddings of cubic 4-folds containing a plane. The desired irreducible
holomorphic symplectic 8-fold can be constructed as a moduli space of
Bridgeland stable objects on the derived categories of twisted K3 surfaces.
Title: A
generalization of WDVV equation and its applications
Abstract: The WDVV
equation arose from 2D topoligical field theory. In this talk, I introduce a
generalization of WDVV equation and apply it to flat coordinate system for
irreducible well-generated complex reflection groups and Painlevé VI.
This is a joint work with M. Kato and T. Mano.
Title: Orbifold
Jacobian Algebras for Invertible Polynomials
Abstract: Let f be
a quasihomogeneous polynomial with an isolated singularity at the origin. The
Jacobian algebra of f is the local algebra of its partial derivatives. It is
finite dimensional and has the structure of a Frobenius algebra. We consider a
group action on f. Let G be a finite group of symmetries of f. The pair (f,G)
is often called a Landau-Ginzburg orbifold. We want to construct an orbifold
version of the Jacobian algebra for the pair (f,G). This is a joint work with
Alexey Basalaev and Atsushi Takahashi.
Title: BCOV
invariant for Borcea-Voisin threefold
Abstract:
BCOV invariant is a holomorphic torsion invariant of Calabi-Yau threefold,
giving the genus-one string amplitude in B-model. Mirror symmetry at
genus-one is formulated as an explicit infinite product expression of the
BCVO invariant near the large complex structure limit point in terms of
genus-one instant numbers. In this talk, I will explain an explicit
formula for the BCOV invariant for Borcea-Voisin threefolds. If time permits, I
will also explain the construction of BCOV invariant for Calabi-Yau orbifolds
and its twisted version, as well as some of their properties.