Summer School in GromovWitten
Theory 2014
Pingree Park, Colorado


GW2014
Schedule
Minicourses: Getting
There
Confirmed
Participants

Talks
HuaiLiang Chang Landau Ginzburg
type theories from algebraic geometry The
Landau Ginzburg model unifies differerent
moduli spaces and their counting in A side of
mirror symmetry. Algebro geometric approach
to define it via p field and cosection localization
unifies these different theories, as like Gromov
Witten theory, FJRW theory, and also others. We will brief on their
constructions, comparisons, and also relations which is work under
progress. Bohan Fang EynardOrantin
recursion and all genus mirror symmetry of a projective line The
mirror of a toric variety is a LandauGinzburg model. In case this mirror could be reduced to
an affine curve, one could run the EynardOrantin
recursion and obtain higher genus invariants, which should predict GW
invariants of the original toric variety. When the toric variety is a CY 3fold, this is the BKMP
conjecture. I will illustrate this phenomenon through a more basic example 
the equivariant projective line. Jeremy Guere Genuszero quantum
invariants of chain polynomials : how to overcome nonconcavity and matrix
factorizations Yunfeng Jiang On the crepant transformation conjecture for toric
birational transformations. Atsushi Kanazawa Trilinear
forms and Chern classes of CalabiYau threefolds I
will talk about the interplay of the intersection trilinear
forms and Chern classes of a CalabiYau
threefold. A natural question is, what kind of trilinear forms, 0th approximation of GW invariants,
occur on a CalabiYau threefold? This question is
also related to topology of CalabiYau threefolds due to Wall's structure theorem on real
6folds. I will provide new formulae that hold for an arbitrary compact CalabiYau threefold. This is a joint work with P.H.M.
Wilson. Byenongho Lee Frobenius manifolds and symmetries. Cristina Manolache Comparing GromovWitten and stable quasimap
invariants Howard Nuer CalabiYau 3folds containing Enriques
surfaces and degenerations to a strange family Andrea Petracci Quantum periods of
del Pezzo surfaces with 1/3(1,1) singularities Recent work of CoatesCortiGalkinKasprzyk uses quantum cohomology to reproduce the IskovskikhMoriMukai classification of smooth Fano
3folds. The central idea is that the quantum period of a smooth Fano 3fold corresponds to the classical period of
certain Laurent polynomials supported on 3dimensional reflexive polytopes. It is conjectured that a similar correspondence
holds between del Pezzo surfaces with isolated
quotient singularities and a certain class of Laurent polynomials supported
on Fano polygons. In this talk
I will show some examples of such a correspondence. This is joint work with
Alessandro Oneto. Yefeng Shen Mirror symmetry for
exceptional unimodular singularities I would like to talk about the mirror theorem between the
Saito Givental theory of exceptional unimodular singularities on LandauGinzburg
Bside and the FanJarvisRuanWitten theory of
their BHKmirror partners on LandauGinzburg
Aside. On the Bside, we develop a perturbative
method to compute the genuszero correlation functions associated to the
primitive forms. This is applied to the exceptional unimodular
singularities, and we show that the numerical invariants match the orbifoldGrothendieckRiemann Roch and WDVV calculations in FJRW theory on the Aside.
The coincidence of the full data at all genera is established by
reconstruction techniques. This is joint work with Changzheng
Li, Si Li and Kyoji Saito. Amit Solomon Morse theory illustrates the intimate relationship
between the critical points of a smooth function on a manifold and the topology
of the manifold: Given a generic function with nondegenerate critical
points, one can construct a chain complex, known as the Morse complex, whose homology
equals the singular homology of the manifold. complex construction fails miserably. In
recent work with J. Solomon, we make the first step towards extending the Morse
complex to a class of degenerate functions. Namely, we endow the stable set of a degenerate
critical point with a natural stratification generalizing
the concept of the stable manifold. Michel Van Garrel Integrality of relative
BPS state counts of toric Del Pezzo
surfaces Zhengyu Zong The orbifold topological vertex 