Program: Week 1
All talks will be in Cottonwood A, in the Snowbird Center, Level 2.
Lecture Series
 Emily Clader The Gauged Linear Sigma Model
 Todor Milanov The LandauGinzburg Bmodel
 Dimitri Zvonkine Semisimple Cohomological Field Theories
Speakers, Titles, and Abstracts


 Chen, Qile Compactifying moduli of sections using stable logarithmic maps
Stable logarithmic maps in the sense of AbramovichChenGrossSiebert were developed to compactify the space of stable maps tangent to boundary divisors along marked points with fixed multiplicities. In this talk I will first review the theory of stable logarithmic maps. Then I will introduce recent joint work with Felix Janda, Yongbin Ruan, and Adrien Sauvaget on its application to sections of rspin bundles, aiming at a study of the Gauged Linear Sigma Model of FanJarvisRuan via compact logarithmic moduli spaces.  Janda, Felix Compactifying the space of maps with a pfield
I will explain a compactification of the moduli space of stable maps with pfields (obtained in joint work with Q. Chen and Y. Ruan, and used to compute highergenus invariants of quintic threefolds), and give an example computation using it.  Lee, Y.P. GromovWitten theory under Birational Maps and Transitions
In this talk I will summarize some of joint work with H.W. Lin, CL. Wang and F. Qu on functoriality of GromovWitten (GW) theory under birational transformations and extremal transition. In particular, the wallcrossing behavior of Kahler cones under special smooth flops, flips and blowups will be discussed. For the CalabiYau threefolds under conifold transitions, I will describe a conjectural linking GW invariants and how their wallcrossing might be related to ChernSimons theory.  Liu, ChiuChu Melissa Holomorphic Anomaly Equations and Modular Anomaly Equations
I will survey conjectures and theorems on holomorphic anomaly equations and modular anomaly equations for both open and closed GromovWitten invariants.  Marcus, Steffen Logarithmic compactification of the AbelJacobi section
Given a smooth curve with weighted marked points, the AbelJacboi map produces a line bundle on the curve. This map fails to extend to the full boundary of the moduli space of stable pointed curves. Using logarithmic and tropical geometry, we describe a modular modification of the moduli space of curves over which the AbelJacobi map extends. This recovers the double ramification cycle, as well as variants associated to differentials.  Oh, Jeongseok Localized Chern characters for 2periodic complexes
For a twoperiodic complex of vector bundles, Polishchuk and Vaintrob have constructed its localized Chern character. We explore some basic properties of this localized Chern character. In particular, we show that the cosection localization defined by Kiem and Li is equivalent to a localized Chern character operation for the associated twoperiodic Koszul complex, strengthening a work of Chang, Li, and Li. We apply this equivalence to the comparison of virtual classes of moduli of εstable quasimaps and moduli of the corresponding LG εstable quasimaps, in full generality. The talk is based on joint work with Bumsig Kim.  Okounkov, Andrei Monodromy and derived equivalencesIn joint work with R. Bezrukavnikov, we prove that for many classes of equivariant symplectic resolutions, the BezrukavnikovKaledin derived autoequivalences act on Ktheory as the monodromy of the quantum differential equation. This talk will be an introduction to this topic and, time permitting, to a further development of these ideas in the context of the quantum difference equation in joint work with M. Aganagic.
 Webb, Rachel The AbelianNonabelian Correspondence for Ifunctions
When a complex reductive group G with maximal torus T acts on an affine variety W, one can form two (GIT) quotients: W// G and W// T. With the right hypotheses, W// G and W// T are both smooth projective varieties. The relationship between the cohomology rings of these two varieties is well understood. However, the relationship between their quantum cohomology rings is only known up to a conjectured correspondence of small Jfunctions (encoding GromovWitten invariants with one insertion). With a wallcrossing result of CiocanFontanine and Kim, this last piece becomes a correspondence of small Ifunctions. I will discuss a proof of the Ifunction correspondence when W is a vector space and G is connected.
Program: Week 2
All talks will be in Cottonwood A, in the Snowbird Center, Level 2.
Lecture Series
 Li, WeiPing pfields and cosection localization
 Ross, Dusty Higher genus computations in FJRW theory
 Shoemaker, Mark Matrix Factorizations and the virtual class
Speakers, Titles, and Abstracts
 Bertram, Aaron Crossing Bridgeland Stability Walls
When we vary Bridgeland stability conditions on the moduli of vector bundles (or complexes of vector bundles) with a fixed Chern class, we may see birational transformations of moduli spaces, or even the creation (destruction) of entire components. I will illustrate this phenomenon with examples using the projective plane and projective threespace, in which the wallcrossing behavior is agrees with the variation of a geometric invariant theory quotient.  Blankers, Vance Descendent Potentials for Hassett Spaces with Diagonal Weights
Hassett spaces, or moduli spaces of weighted stable curves, are a family of compactifications of M_{g,n} associated to rational weight data (a_{1,}…, a_{n}). When all weights are 1, we recover the usual DeligneMumford compactification M_{g,n} We discuss the descendent potential for Hassett spaces with weights a_{n} = 1/q and relate it to the DeligneMumford descendent potential. As a corollary, we obtain a new proof of a result of Manin and Zograf connecting the Witten potential to the kappaclass potential on M_{g,n }via a change of variables.  Dumitrescu, Olivia Interplay between CohFT and Topological Recursion
We study a few examples of Cohomological field theories (CohFT) defined over a 1dimensional Frobenius algebra. We aim to develop a formalism to recover the spectral curve of topological recursion using the classification theorem of CohFT for semisimple Frobenius algebras. We present the relation between Hurwitz numbers and spectral curves, and we study intersection numbers of mixed kappa and psiclasses on the moduli spaces of curves. This is work in progress with Motohico Mulase.  Mi, Rongxiao Quantum Dmodules and Extremal Transitions
Extremal transitions are a contractdeform surgery, which play a significant role in classifying CalabiYau threefolds. In this talk, I will outline a framework that relates two quantum Dmodules under extremal transition. Then I will give several examples in the toric case (such as cubic and degreefour extremal transitions) and explain how it works.  Priddis, Nathan BorceaVoisin Mirror Symmetry for LG models
Borcea and Voisin described a particular version of mirror symmetry involving the quotient of the product of a K3 surface and an elliptic curve by a certain involution. This is often referred to as BorceaVoisin mirror symmetry. Using the ideas of wallcrossing, we obtain a corresponding LandauGinzburg model (FJRW theory). In this talk I will introduce the construction, the corresponding LG model and show how BorceaVoisin mirror symmetry translates into the LG theory.  Whitcher, Ursula Hypergeometric structure of K3 quartic pencils
We exploit intuition from the BHK mirror symmetry construction to study hypergeometric functions associated to five oneparameter deformations of Delsarte K3 quartic hypersurfaces in projective space. We write the point counts over finite fields in terms of explicit, hypergeometric global Lfunctions, each associated to a PicardFuchs differential equation. The computation gives a complete description of the motives for these pencils in terms of hypergeometric motives. This talk describes joint work with Charles Doran, Tyler Kelly, Adriana Salerno, Steven Sperber, and John Voight.  Zhang, Ming Verlinde algebra and quantum Ktheory with level structure
I will first introduce the level structure in quantum Ktheory. When the target is the Grassmannian, I will explain the wallcrossing approach to obtain the relation between quantum Kinvariants with level structure and Verlinde numbers. Based on joint work with Yongbin Ruan.  Zhou, Jie Mirror symmetry for elliptic curves and modular forms
Modular forms are interesting and useful tools in the studies of enumerative geometry of varieties related to elliptic curves. They also provide concrete formulae to test new ideas and techniques.In this mostly expository talk, I will try to discuss some interesting modular phenomena arising from the mirror symmetry of elliptic curves, part of which can hopefully be generalized to more general targets. I will first start with the GromovWitten theory for elliptic curves and explain why the generating series of GromovWitten invariants should be related to modular forms at all from the perspective of mirror symmetry. Then I will discuss the sheaftheoretic formulation of quasimodular forms and explain why the generating series should be quasimodular as opposed to being honestly modular. After that I will discuss some concrete examples in which modular transformations relate different enumerative theories. Finally, if time permits, I will try to say a few words about the nonholomorphicity in the modular completed generating series.  Zhou, Zijun GW/DT correspondence for local gerby curves with transversal A_{n} singularity
In this talk, I will discuss an ongoing joint project with Zhengyu Zong on the GromovWitten/DonaldsonThomas correspondence for local gerby curves, as an orbifold generalization of the corresponding work on the smooth case by BryanPandharipande and OkounkovPandharipande. By applying degeneration formulas, the correspondence can be reduced to the case of [ℂ^{2}/ℤ_{n+1}] × ℙ^{1}, where the 3point relative GW/DT invariants can be related to the quantum multiplication by divisors for Hilb([ℂ^{2}/ℤ_{n+1}] ) and Sym([ℂ^{2}/ℤ_{n+1}] ). This is a crepant resolution counterpart to the work of MaulikOblomkov and CheongGholampour.
 Chen, Qile Compactifying moduli of sections using stable logarithmic maps
