Schedule-at-a-Glance

44 PRIMA 2013 AbstractsLet G denote a Lie group. In this talk we will discussa classifying space constructed from the commuting elementsin G. We compute its cohomology and describe itsgeometry and homotopy type.Virtual neighborhood techniques in Gromov-Witten theoryBohui ChenSichuan University, Chinabohui@cs.wisc.edu>Abstract: In this talk, I will explain the construction ofvirtual orbifolds for the moduli spaces of stable curves.In particular, I will explain how to deal with the nonsmoothnessissues arised from the infinite dimensionalset-ups.Algebra of Legendrian surgeryYakov EliashbergStanford University, USAeliash math.stanford.eduI will discuss algebraic structures arising in connectionwith Legendrian surgery, which enter the computation ofholomorphic curve invariants of Weinstein domains andtheir boundaries. This is a joint work with F. Bourgeoisand T. Ekholm.Fock sheaf of Givental quantizationHiroshi IritaniKyoto University, Japaniritani@math.kyoto-u.ac.jpI will talk about joint work with Tom Coates (ImperialCollege London) on a global version of Givental quantization.Based on a generalized variation of Hodge structure(the so-called semi-infinite variation of Hodge structure),we construct a sheaf of Fock spaces which can be identifiedwith Givental’s Fock space infinitesimally. An oppositesubspace which yields a Frobenius structure on thebase plays a role of polarization in the context of geometricquantization. As applications, we discuss modularityof Gromov-Witten potential of local projective plane, andalso holomorphic anomaly equation.Categories and dynamical systemsLudmil KatzarkovUniversity of Miami, USA and University of Vienna, Austrial.katzarkov@math.miami.eduIn this talk we will discuss recent developments in thetheory of stability conditions of categories. We will outlinesome parallels with classical results from dynamicalsystems.Quasimap invariants and mirror mapsBumsig KimKorea Institute for Advanced Study, Koreabumsig@kias.re.krThe moduli spaces of stable quasimaps unify various moduliappearing in the study of Gromov-Witten Theory.We introduce big I-functions as the quasimap version ofJ-functions, generalizing Givental’s small I-functions ofsmooth toric complete intersections. The J-functions arethe GW counterparts of periods of mirror families. Wediscuss some advantages of I-functions, in particular anexplanation of mirror maps. This is joint work with I.Ciocan-Fontanine.The Eynard-Orantin recursion in singularitytheoryTodor MilanovKavli Institute for the Physics and Mathematics of theUniverse, Japantodor.milanov@ipmu.jpIt was proved recently that the correlation functions ofa semi-simple cohomological field theory satisfy the socalled local Eynard–Orantin topological recursion. In mytalk, I would like to explain this result in the settings ofsingularity theory. In my earlier work with B. Bakalov,we have constructed a certain twisted representation ofthe Heisenberg vertex operator algebra associated withthe vanishing cohomology of the singularity. The kernel ofthe Eynard-Orantin recursion is essentially obtained fromthe so called operator product expansion of the fields thatdefine the representation. Finally, I would like to reportmy progress on finding the global recursion, which seemsto be related to the theory of W -algebras.Orbifold Hurwitz numbers and Eynard-Orantin invariantsPaul NorburyUniversity of Melbourne, Australianorbury@unimelb.edu.auI will describe a generalisation of simple Hurwitz numbersdue to Johnson, Pandharipande and Tseng and provethat they satisfy the topological recursion of Eynard andOrantin. This generalises the Bouchard-Marino conjectureand places Hurwitz-Hodge integrals, which arise inthe Gromov-Witten theory of target curves with orbifoldstructure, in the context of the Eynard-Orantin topologicalrecursion.Translated points and contact rigiditySheila SandonUniversité de Nantes, Francesheila.sandon@univ-nantes.frI will discuss the role played by translated points ofcontactomorphisms in contact rigidity phenomena suchas non-squeezing, orderability and the existence of biinvariantmetrics on the contactomorphism group. I willthen either concentrate on presenting the construction ofthe discriminant metric on the contactomorphism group(which is joint work with Vincent Colin) or discuss ananalogue for translated points of the Arnold conjectureon fixed points of Hamiltonian symplectomorphisms, anda joint work in progress with Yasha Savelyev and EgorShelukhin to prove this conjecture by constructing a Floerhomology theory for translated points.On a certain generalization of Virasoro constraintsfor Frobenius manifoldsYoujin ZhangTsinghua University, Chinayoujin@mail.tsinghua.edu.cnWe show that the Virasoro operators associated to anarbitray Frobenius manifold admit certain deformationswhich give additional constraints for the genus zero freeenergy of the Frobenius manifold. We discuss applicationsof such additional constraints and their analoguesfor higher genus free energies.Gopakumar-Vafa invariants of local Calabi-Yau 3-Folds