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Autumn Semester 2018

Date / Time Speaker Title Location
* 19 September 2018
15:30-17:00 		Dr. Longting Wu
ETH Zürich
Details

Algebraic Geometry and Moduli Seminar

Title Structures on genus 0 absolute and relative GW theory I
Speaker, Affiliation Dr. Longting Wu, ETH Zürich
Date, Time 19 September 2018, 15:30-17:00
Location HG G 19.2
Abstract In the series of talks, we first review the moduli of stable maps, WDVV equation, and the construction of quantum cohomology. Next, we change our focus to relative Gromov--Witten (GW) theory and present some recent calculations on surfaces using an analog of WDVV equation in relative theory. Finally, we generalize the definition of relative GW theory to include negative contact orders, and discuss some parallel structures (quantum cohomology, Virasoro operators, etc.) on relative GW theory.
Structures on genus 0 absolute and relative GW theory Iread_more
HG G 19.2
* 26 September 2018
15:30-17:00 		Dr. Longting Wu
ETH Zürich
Details

Algebraic Geometry and Moduli Seminar

Title Structures on genus 0 absolute and relative GW theory II
Speaker, Affiliation Dr. Longting Wu, ETH Zürich
Date, Time 26 September 2018, 15:30-17:00
Location HG G 19.2
Abstract In the series of talks, we first review the moduli of stable maps, WDVV equation, and the construction of quantum cohomology. Next, we change our focus to relative Gromov--Witten (GW) theory and present some recent calculations on surfaces using an analog of WDVV equation in relative theory. Finally, we generalize the definition of relative GW theory to include negative contact orders, and discuss some parallel structures (quantum cohomology, Virasoro operators, etc.) on relative GW theory.
Structures on genus 0 absolute and relative GW theory IIread_more
HG G 19.2
28 September 2018
16:00-17:15 		Prof. Dr. Martijn Kool
University of Utrecht
Details

Algebraic Geometry and Moduli Seminar

Title New calculations in Vafa-Witten theory
Speaker, Affiliation Prof. Dr. Martijn Kool, University of Utrecht
Date, Time 28 September 2018, 16:00-17:15
Location HG G 43
Abstract In the 1990's, Vafa-Witten tested S-duality of N=4 SUSY Yang-Millstheory on a complex algebraic surface by studying modularity of a certain partition function. Recently, a mathematical definition of Vafa-Witten's invariants was given by Tanaka-Thomas. I outline amethod for calculating the instanton contribution to these invariants using Mochizuki's theory of algebraic Donaldson invariants. For SU(2), this leads to verifications of Vafa-Witten's original formula. For SU(3), we find a new formula which corrects an error in the physics literature. I discuss refinements of our instanton calculations to virtual \chi_y genus, elliptic genus, and cobordism class, which involves Jacobi forms and Borcherds lifts thereof. Joint with Göttsche.
New calculations in Vafa-Witten theoryread_more
HG G 43
* 3 October 2018
15:30-17:00 		Dr. Honglu Fan
ETH Zürich
Details

Algebraic Geometry and Moduli Seminar

Title Structures on genus 0 absolute and relative GW theory III
Speaker, Affiliation Dr. Honglu Fan, ETH Zürich
Date, Time 3 October 2018, 15:30-17:00
Location HG G 19.2
Abstract In the series of talks, we first review the moduli of stable maps, WDVV equation, and the construction of quantum cohomology. Next, we change our focus to relative Gromov-Witten (GW) theory and present some recent calculations on surfaces using an analog of WDVV equation in relative theory. Finally, we generalize the definition of relative GW theory to include negative contact orders, and discuss some parallel structures (quantum cohomology, Virasoro operators, etc.) on relative GW theory.
Structures on genus 0 absolute and relative GW theory IIIread_more
HG G 19.2
5 October 2018
16:00-17:15 		Dr. Pierrick Bousseau
ETHZ-ITS
Details

Algebraic Geometry and Moduli Seminar

Title Quantum mirrors of log Calabi-Yau surfaces and higher genus curve counting
Speaker, Affiliation Dr. Pierrick Bousseau, ETHZ-ITS
Date, Time 5 October 2018, 16:00-17:15
Location HG G 43
Abstract Gross-Hacking-Keel have given a construction of mirror families of log Calabi-Yau surfaces in terms of counts of rational curves. I will explain how to deform this construction by counts of higher genus curves to get non-commutative deformations of these mirror families.
Quantum mirrors of log Calabi-Yau surfaces and higher genus curve countingread_more
HG G 43
* 8 October 2018
15:30-17:00 		Dr. Honglu Fan
ETH Zürich
Details

Algebraic Geometry and Moduli Seminar

Title Structures on genus 0 absolute and relative GW theory IV
Speaker, Affiliation Dr. Honglu Fan, ETH Zürich
Date, Time 8 October 2018, 15:30-17:00
Location ML H 43
Abstract In the series of talks, we first review the moduli of stable maps, WDVV equation, and the construction of quantum cohomology. Next, we change our focus to relative Gromov--Witten (GW) theory and present some recent calculations on surfaces using an analog of WDVV equation in relative theory. Finally, we generalize the definition of relative GW theory to include negative contact orders, and discuss some parallel structures (quantum cohomology, Virasoro operators, etc.) on relative GW theory.
Structures on genus 0 absolute and relative GW theory IVread_more
ML H 43
* 9 October 2018
14:00-15:30 		Prof. Dr. Yuan-Pin Lee
University of Utah
Details

Algebraic Geometry and Moduli Seminar

Title From quantum flips to functoriality of Gromov-Witten theory
Speaker, Affiliation Prof. Dr. Yuan-Pin Lee, University of Utah
Date, Time 9 October 2018, 14:00-15:30
Location HG G 26.1
Abstract Gromov-Witten theory has limited functoriality. A basic example is the analytic continuation under crepant transformation (K-equivalence). A generalization of this when variety goes through flips will be discussed. We will see that the system of PDEs with iiregular singularities naturally occurs under flips. If time permits, we will discuss the role quantum flips should play in the quest for general functoriality, i.e., quantum motives.
From quantum flips to functoriality of Gromov-Witten theoryread_more
HG G 26.1
* 10 October 2018
15:30-17:00 		Prof. Dr. Dan Edidin
University of Missouri
Details

Algebraic Geometry and Moduli Seminar

Title Intersecting cycles on good moduli spaces
Speaker, Affiliation Prof. Dr. Dan Edidin, University of Missouri
Date, Time 10 October 2018, 15:30-17:00
Location HG G 19.2
Abstract Varieties with finite quotient singularities are coarse moduli spaces of smooth Deligne-Mumford stacks. Using the now well-developed intersection theory on DM stacks, it is possible to obtain a very satisfactory (rational) intersection theory on varieties with finite quotient singularities. In this talk we consider the problem of intersection theory on varieties which are locally the quotients of a smooth variety by a positive dimensional linearly reductive group. A class of such varieties is the class of good moduli spaces (in the sense of Alper) of smooth Artin stacks and examples include non-simplicial toric varieties. We present some recent progress as well as some open problems.
Intersecting cycles on good moduli spacesread_more
HG G 19.2
12 October 2018
16:00-17:15 		Prof. Dr. Dimitri Zvonkine
Université de Versailles
Details

Algebraic Geometry and Moduli Seminar

Title Chern classes of the Laughlin bundles -- the first steps
Speaker, Affiliation Prof. Dr. Dimitri Zvonkine, Université de Versailles
Date, Time 12 October 2018, 16:00-17:15
Location HG G 43
Abstract Vector bundles of Laughlin states were introduced by physicists to study the fractional quantum Hall effect and their Chern classes are related to measurable physical quantities. We will explain how they are related to the vector bundle of theta-functions over the moduli space and perform the first steps in the computation of their Chern classes. Work in progress with Semyon Klevtsov.
Chern classes of the Laughlin bundles -- the first stepsread_more
HG G 43
26 October 2018
16:00-17:15 		Prof. Dr. Georg Oberdieck
Universität Bonn
Details

Algebraic Geometry and Moduli Seminar

Title CHL Calabi-Yau threefolds: Curve counting and Mathieu moonshine
Speaker, Affiliation Prof. Dr. Georg Oberdieck, Universität Bonn
Date, Time 26 October 2018, 16:00-17:15
Location HG G 43
Abstract A CHL Calabi-Yau threefold is the quotient of the product K3xE by an order N automorphism which acts symplectically on the K3 surface and by shifting by an N-torsion point on the elliptic curve E. In this talk I will present a conjecture which relates the Donaldson-Thomas theory of CHL models to the twined elliptic genera which appear in Mathieu moonshine. Part of the conjecture exactly matches earlier predictions by string theory. However, not all geometric cases are covered by the physics formula and new Siegel modular forms appear in the curve counting formulas. This is joint work with Jim Bryan.
CHL Calabi-Yau threefolds: Curve counting and Mathieu moonshineread_more
HG G 43
* 14 November 2018
15:30-17:00 		Dr. Quoc Ho
IST Austria
Details

Algebraic Geometry and Moduli Seminar

Title Densities and stability via factorization homology
Speaker, Affiliation Dr. Quoc Ho, IST Austria
Date, Time 14 November 2018, 15:30-17:00
Location HG G 19.2
Abstract Using factorization homology, we develop a uniform and conceptual approach for treating homological stability, homological densities, and arithmetic densities for configuration spaces (and generalizations thereof) in algebraic geometry. This categorifies and generalizes the coincidences appearing in the work of Farb-Wolfson-Wood, and in fact, provides a conceptual understanding of these coincidences. Our approach hinges on the study of homological stability of cohomological Chevalley complexes, which is of independent interest.
Densities and stability via factorization homologyread_more
HG G 19.2
* 15 November 2018
14:00-15:15 		Prof. Dr. Alexei Oblomkov
UMass Amherst
Details

Algebraic Geometry and Moduli Seminar

Title Virasoro constraints for PT theory
Speaker, Affiliation Prof. Dr. Alexei Oblomkov, UMass Amherst
Date, Time 15 November 2018, 14:00-15:15
Location HG G 19.1
Abstract alk is based on the joint work with Okounkov and Pandharipande. In my talk I will state the conjectural Virasoro constraints for PT theory. For toric varieties the stationary version of the constraint is derived from the Gromov-Witten constraints. In particular, we obtain a new set of constraints for the tautological classes integrals for Hilb_n(S), S is a compact toric surface. I will provide the details of GW/PT correspondence that relates the constraints, if time allows.
Virasoro constraints for PT theory read_more
HG G 19.1
16 November 2018
16:00-17:15 		Prof. Dr. David Holmes
University of Leiden
Details

Algebraic Geometry and Moduli Seminar

Title A formula for the canonical double ramification cycle
Speaker, Affiliation Prof. Dr. David Holmes, University of Leiden
Date, Time 16 November 2018, 16:00-17:15
Location HG G 43
Abstract The (canonical) double ramification cycle (DR) is a cycle on the moduli space of curves which measures how often a `random’ divisor of degree 2g-2 is in fact a canonical divisor. I will begin by describing a geometric way to extend the definition of the DR to singular curves, i.e. to the boundary of the moduli space of curves. I will then discuss recent joint work with Johannes Schmitt where we show that the resulting DR coincides with a formula proposed by Farkas and Pandharipande.
A formula for the canonical double ramification cycleread_more
HG G 43
* 21 November 2018
15:30-17:00 		Prof. Dr. Alessio Corti
Imperial College
Details

Algebraic Geometry and Moduli Seminar

Title Hyperelliptic integrals and mirrors of del Pezzo hypersurfaces
Speaker, Affiliation Prof. Dr. Alessio Corti, Imperial College
Date, Time 21 November 2018, 15:30-17:00
Location HG G 19.2
Abstract I sketch some new mirror constructions for del Pezzo surfaces with empty anticanonical series. I will keep the talk self-contained apart from elementary one-variable complex analysis. This is work of my PhD student Giulia Gugiatti.
Hyperelliptic integrals and mirrors of del Pezzo hypersurfacesread_more
HG G 19.2
* 22 November 2018
16:00-17:00 		Prof. Dr. Alexei Oblomkov
UMass Amherst
Details

Algebraic Geometry and Moduli Seminar

Title GW/PT descendent correspondence
Speaker, Affiliation Prof. Dr. Alexei Oblomkov, UMass Amherst
Date, Time 22 November 2018, 16:00-17:00
Location HG G 19.2
Abstract The talk is based on the joint work with R. Pandharipande and A, Okounkov. In my talk I will present a conjectural formula for the correspondence between GW and PT invariants with descendents. The conjecture is proven in the case of stationary descendents on compact toric manifolds. I will outline our strategy for the proof and will discuss difficulties outside stationary case.
GW/PT descendent correspondenceread_more
HG G 19.2
23 November 2018
16:00-17:15 		Prof. Dr. Alessio Corti
Imperial College
Details

Algebraic Geometry and Moduli Seminar

Title Some conjectures on deformations of toric singularities and toric Fano varieties
Speaker, Affiliation Prof. Dr. Alessio Corti, Imperial College
Date, Time 23 November 2018, 16:00-17:15
Location HG G 43
Abstract I will speak about what is in the title and discuss implications for a program to classify Fano manifolds and their LG mirrors in dimension 4.
Some conjectures on deformations of toric singularities and toric Fano varietiesread_more
HG G 43
* 28 November 2018
15:30-17:00 		Prof. Dr. Thomas Willwacher
ETH Zürich
Details

Algebraic Geometry and Moduli Seminar

Title Configuration spaces of points and real Goodwillie-Weiss calculus I
Speaker, Affiliation Prof. Dr. Thomas Willwacher, ETH Zürich
Date, Time 28 November 2018, 15:30-17:00
Location HG G 19.2
Abstract The manifold calculus of Goodwillie and Weiss proposes to reduce questions about embedding spaces of manifolds to questions about mapping spaces of the (little-disks modules of) configuration spaces of points on those manifolds. We will discuss real models for these configuration spaces. Furthermore, we will see that a real version of the aforementioned mapping spaces is computable in terms of graph complexes. In particular, this yields a new tool to study diffeomorphism groups and moduli spaces. (The part about diffeomorphism groups and moduli spaces is work in progress and still somewhat speculative and incomplete.)
Configuration spaces of points and real Goodwillie-Weiss calculus Iread_more
HG G 19.2
* 29 November 2018
14:00-15:15 		Dr. Jeongseok Oh
Korea Institute for Advanced Study
Details

Algebraic Geometry and Moduli Seminar

Title Localized Chern characters for 2-periodic complexes
Speaker, Affiliation Dr. Jeongseok Oh, Korea Institute for Advanced Study
Date, Time 29 November 2018, 14:00-15:15
Location HG G 19.1
Abstract For a two-periodic 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 two-periodic Koszul complex, strengthening a work of Chang, Li, and Li. We apply this equivalence to the comparison of virtual classes of moduli of ε-stable quasimaps and moduli of the corresponding LG ε-stable quasimaps. This is based on joint work with Bumsig Kim. Furthermore, if the time is permitted, we discuss the comparison of virtual structure sheaves either. The latter is joint work with B. Sreedhar.
Localized Chern characters for 2-periodic complexesread_more
HG G 19.1
* 30 November 2018
14:00-15:15 		Prof. Dr. Thomas Willwacher
ETH Zürich
Details

Algebraic Geometry and Moduli Seminar

Title Configuration spaces of points and real Goodwillie-Weiss calculus II
Speaker, Affiliation Prof. Dr. Thomas Willwacher, ETH Zürich
Date, Time 30 November 2018, 14:00-15:15
Location HG G 19.2
Abstract The manifold calculus of Goodwillie and Weiss proposes to reduce questions about embedding spaces of manifolds to questions about mapping spaces of the (little-disks modules of) configuration spaces of points on those manifolds. We will discuss real models for these configuration spaces. Furthermore, we will see that a real version of the aforementioned mapping spaces is computable in terms of graph complexes. In particular, this yields a new tool to study diffeomorphism groups and moduli spaces. (The part about diffeomorphism groups and moduli spaces is work in progress and still somewhat speculative and incomplete.)
Configuration spaces of points and real Goodwillie-Weiss calculus IIread_more
HG G 19.2
* 5 December 2018
15:30-17:00 		Prof. Dr. Filippo Viviani
Universität Rom III
Details

Algebraic Geometry and Moduli Seminar

Title On the first steps of the minimal model program for the moduli space of stable pointed curves
Speaker, Affiliation Prof. Dr. Filippo Viviani, Universität Rom III
Date, Time 5 December 2018, 15:30-17:00
Location HG G 19.2
Abstract I will report on a joint work (partially in progress) with G. Codogni and L. Tasin, in which we study all the natural first steps of the minimal model program for the moduli space of stable pointed curves. We prove that they admit a modular interpretation and we study their geometry properties. As a particular case, we recover the first few Hassett-Keel log canonical models. As a by-product, we produce many birational morphisms from the moduli space of stable pointed curves to alternative modular projective compactifications of the moduli space of pointed curves.
On the first steps of the minimal model program for the moduli space of stable pointed curvesread_more
HG G 19.2
* 6 December 2018
14:00-15:15 		Dr. Kaloyan Slavov
ETH Zürich
Details

Algebraic Geometry and Moduli Seminar

Title The moduli space of hypersurfaces whose singular locus has high dimension
Speaker, Affiliation Dr. Kaloyan Slavov, ETH Zürich
Date, Time 6 December 2018, 14:00-15:15
Location ML H 34.3
Abstract Consider the moduli space of hypersurfaces of degree l in P^n whose singular locus has dimension at least b (for a fixed b>= 1). We prove that when l is large, this moduli space has a unique irreducible component of maximal dimension, consisting of the hypersurfaces singular along a linear b-dimensional space. The proof will involve a reduction to positive characteristic and a probabilistic counting argument over finite fields.
The moduli space of hypersurfaces whose singular locus has high dimensionread_more
ML H 34.3
* 7 December 2018
14:00-15:00 		Prof. Dr. Thomas Willwacher
ETH Zürich
Details

Algebraic Geometry and Moduli Seminar

Title Configuration spaces of points and real Goodwillie-Weiss calculus III
Speaker, Affiliation Prof. Dr. Thomas Willwacher, ETH Zürich
Date, Time 7 December 2018, 14:00-15:00
Location HG G 19.2
Abstract The manifold calculus of Goodwillie and Weiss proposes to reduce questions about embedding spaces of manifolds to questions about mapping spaces of the (little-disks modules of) configuration spaces of points on those manifolds. We will discuss real models for these configuration spaces. Furthermore, we will see that a real version of the aforementioned mapping spaces is computable in terms of graph complexes. In particular, this yields a new tool to study diffeomorphism groups and moduli spaces. (The part about diffeomorphism groups and moduli spaces is work in progress and still somewhat speculative and incomplete.)
Configuration spaces of points and real Goodwillie-Weiss calculus IIIread_more
HG G 19.2
* 7 December 2018
15:30-16:45 		Dr. Ulrike Riess
ETHZ-ITS
Details

Algebraic Geometry and Moduli Seminar

Title Base loci of big and nef line bundles on irreducible symplectic varieties
Speaker, Affiliation Dr. Ulrike Riess, ETHZ-ITS
Date, Time 7 December 2018, 15:30-16:45
Location HG G 43
Abstract The talk will start with a small introduction to irreducible symplectic varieties. Afterwards, I will give an overview on the current knowledge about base loci of big and nef line bundles on them: Under certain conditions, I will give a complete description of base divisors and then I will report what is known about base loci in higher codimension.
Base loci of big and nef line bundles on irreducible symplectic varietiesread_more
HG G 43
* 19 December 2018
15:30-17:00 		Shengxuan Liu
ETH Zürich
Details

Algebraic Geometry and Moduli Seminar

Title Introduction to the Grothendieck-Teichmüller group
Speaker, Affiliation Shengxuan Liu, ETH Zürich
Date, Time 19 December 2018, 15:30-17:00
Location HG G 19.2
Abstract In this talk, I will start with the definition of the Drinfel’d associator and show the sufficiency of the Pentagon equation. Then I will discuss the relationship of the Grothendieck-Teichmüller group with several other relations, including double shuffle relation, confluence relation, and Kashiwara-Vergne groups. If time permits, I will also discuss its relation with operads and differential geometry.
Introduction to the Grothendieck-Teichmüller groupread_more
HG G 19.2
4 January 2019
14:30-15:45 		Dr. Michel van Garrel
Univ. of Warwick
Details

Algebraic Geometry and Moduli Seminar

Title Mirror Symmetry in light of relative invariants
Speaker, Affiliation Dr. Michel van Garrel, Univ. of Warwick
Date, Time 4 January 2019, 14:30-15:45
Location HG G 43
Abstract Let X be a Fano manifold with smooth anticanonical divisor D. The invariants of interest to this talk are the genus 0 relative Gromov-Witten invariants of maximal tangency of (X,D) in the 'anticanonical direction'. I will describe a proposal on how to calculate these by passing to the mirror Landau-Ginzburg model. This is ongoing joint work with Honglu Fan and Fenglong You.
Mirror Symmetry in light of relative invariantsread_more
HG G 43
4 January 2019
16:00-17:15 		Dr. Fenglong You
Univ. of Alberta
Details

Algebraic Geometry and Moduli Seminar

Title Relative and orbifold Gromov-Witten theory
Speaker, Affiliation Dr. Fenglong You, Univ. of Alberta
Date, Time 4 January 2019, 16:00-17:15
Location HG G 43
Abstract Given a smooth projective variety X and a smooth divisor D \subset X, one can study the enumerative geometry of counting curves in X with tangency conditions along D. There are two theories associated to it: relative Gromov-Witten invariants of (X,D) and orbifold Gromov-Witten invariants of the r-th root stack X_{D,r}. For sufficiently large r, Abramovich-Cadman-Wise proved that genus zero relative invariants are equal to orbifold invariants of root stacks (with a counterexample in genus 1). We show that higher genus orbifold Gromov-Witten invariants of X_{D,r} are polynomials in r and the constant terms are exactly relative Gromov-Witten invariants of (X,D). If time permits, I will also talk about further results on structures of genus zero relative Gromov-Witten theory and mirror symmetry. This is based on joint work with Hsian-Hua Tseng, Honglu Fan and Longting Wu.
Relative and orbifold Gromov-Witten theoryread_more
HG G 43
* 7 January 2019
13:30-14:30 		Prof. Dr. Andrei Caldararu
Univ. of Wisconsin
Details

Algebraic Geometry and Moduli Seminar

Title Introduction to Costello's invariants
Speaker, Affiliation Prof. Dr. Andrei Caldararu, Univ. of Wisconsin
Date, Time 7 January 2019, 13:30-14:30
Location HG G 43
Abstract I will give an overview of the main moving parts involved in the definition of Costello's invariants, under one simplifying assumption. Main topics:
(1) the Weyl algebra, Fock module, and BV algebra associated to a representation of the category of annuli;
(2) solutions of the Maurer-Cartan equation in BV algebras;
(3) the BV algebra structure on singular chains on moduli spaces of curves and the distinguished solution of the MC equation (string vertices);
(4) the abstract categorical Gromov-Witten potential as an element of a Fock space;
(5) using a splitting of the Hodge-de Rham spectral sequence to convert the abstract GW potential to a concrete one.
Introduction to Costello's invariants read_more
HG G 43
* 7 January 2019
14:45-15:45 		Prof. Dr. Junwu Tu
Shanghai Tech Univ.
Details

Algebraic Geometry and Moduli Seminar

Title Categorical Saito Theory I
Speaker, Affiliation Prof. Dr. Junwu Tu, Shanghai Tech Univ.
Date, Time 7 January 2019, 14:45-15:45
Location HG G 43
Abstract We present the construction of an explicit cyclic minimal model for the category of matrix factorizations associated with a potential function W on C^N with an isolated singularity at origin. The key observation is to use Kontsevich's deformation quantization technique. As an application of this new technology, we prove the analogue of Caldararu's conjecture for matrix factorizations.
Categorical Saito Theory Iread_more
HG G 43
* 7 January 2019
16:30-17:30 		Prof. Dr. Nick Sheridan
Univ. of Edinburgh
Details

Algebraic Geometry and Moduli Seminar

Title Hodge-theoretic mirror symmetry
Speaker, Affiliation Prof. Dr. Nick Sheridan, Univ. of Edinburgh
Date, Time 7 January 2019, 16:30-17:30
Location HG G 43
Abstract I will explain in detail how to compute genus-zero Gromov-Witten invariants of a Calabi-Yau manifold from its Fukaya category. The main steps are to show that the periodic cyclic homology of the Fukaya category carries a natural structure of a Variation of Hodge Structures (VHS); and to identify this structure with the quantum VHS, from which the rational Gromov-Witten invariants can be extracted. This is based on joint work with Ganatra and Perutz.
Hodge-theoretic mirror symmetryread_more
HG G 43
* 8 January 2019
10:30-11:30 		Prof. Dr. Sergey Shadrin
Univ. of Amsterdam
Details

Algebraic Geometry and Moduli Seminar

Title Cohomological field theories and BV algebras
Speaker, Affiliation Prof. Dr. Sergey Shadrin, Univ. of Amsterdam
Date, Time 8 January 2019, 10:30-11:30
Location HG G 43
Abstract I'll discuss how a version of the Givental group action on cohomological field theories emerges from the structure of a differential graded BV algebra with a homotopically trivial BV operator. There are several different approaches to this general statement, but they all work so far only in genus 0, and I'll try to indicate the principle difficulties of their generalisations to higher genera. It also has a surprising and a very deep generalisation, where all the involved structures become non-commutative. If I'll have sufficient time, I'll talk about it as well. The talk is based on my joint papers with Anton Khoroshkin and Nikita Markarian and Vladimir Dotsenko and Bruno Vallette.
Cohomological field theories and BV algebrasread_more
HG G 43
* 8 January 2019
13:30-14:30 		Prof. Dr. Nick Sheridan
Univ. of Edinburgh
Details

Algebraic Geometry and Moduli Seminar

Title VHS from categories
Speaker, Affiliation Prof. Dr. Nick Sheridan, Univ. of Edinburgh
Date, Time 8 January 2019, 13:30-14:30
Location HG G 43
Abstract I will explain in detail how to compute genus-zero Gromov-Witten invariants of a Calabi-Yau manifold from its Fukaya category. The main steps are to show that the periodic cyclic homology of the Fukaya category carries a natural structure of a Variation of Hodge Structures (VHS); and to identify this structure with the quantum VHS, from which the rational Gromov-Witten invariants can be extracted. This is based on joint work with Ganatra and Perutz.
VHS from categoriesread_more
HG G 43
* 8 January 2019
15:00-16:00 		Prof. Dr. Andrei Caldararu
Univ. of Wisconsin
Details

Algebraic Geometry and Moduli Seminar

Title Costello's invariants (the real deal)
Speaker, Affiliation Prof. Dr. Andrei Caldararu, Univ. of Wisconsin
Date, Time 8 January 2019, 15:00-16:00
Location HG G 43
Abstract In the previous lecture I used a fundamental, unrealistic simplification of Costello's theory, namely I pretended that the TCFT associated to a cyclic A_infty algebra could be defined on chains with no inputs, only outputs. In the second lecture I will remove this simplifying assumption, using a certain Koszul resolution also suggested by Costello (unpublished). Along the way I will give a completely precise definition of string vertices (down to signs!) which is amenable to computer calculations.
Costello's invariants (the real deal)read_more
HG G 43
* 8 January 2019
16:30-17:30 		Prof. Dr. Junwu Tu
Shanghai Tech Univ.
Details

Algebraic Geometry and Moduli Seminar

Title Categorical Saito Theory II
Speaker, Affiliation Prof. Dr. Junwu Tu, Shanghai Tech Univ.
Date, Time 8 January 2019, 16:30-17:30
Location HG G 43
Abstract The proof of the analogue of Caldararu's conjecture for matrix factorizations follows from a comparison result between Variation of Semi-infinite Hodge Structures. In this talk, we describe a proof of this comparison using Tsygan formality map which looks like a B-model open-closed map. If time permits, we shall also present some recent progress on categorical Saito theory of equivariant matrix factorizations (specifically orbifold LG-models).
Categorical Saito Theory IIread_more
HG G 43
* 9 January 2019
10:30-11:30 		Prof. Dr. Sheel Ganatra
Univ. of Southern California
Details

Algebraic Geometry and Moduli Seminar

Title Open-closed maps and Calabi-Yau structures I
Speaker, Affiliation Prof. Dr. Sheel Ganatra, Univ. of Southern California
Date, Time 9 January 2019, 10:30-11:30
Location HG G 43
Abstract Open-closed TFTs are classified (according to Costello, Kontsevich-Vlassopoulous, Lurie) by A-infinity categories equipped with Calabi-Yau (CY) structures. There are two types of CY structures of relevance, "smooth CY" structures classify TFTs with at least one output and "proper CY" structures classify TFTs with at least one input. We will review this formalism, show how a version of the open-closed map allows one to equip Fukaya categories with a geometrically meaningful CY structure of either type (under suitable hypotheses), and describe some initial applications.
Open-closed maps and Calabi-Yau structures Iread_more
HG G 43
* 9 January 2019
13:30-14:30 		Prof. Dr. Nick Sheridan
Univ. of Edinburgh
Details

Algebraic Geometry and Moduli Seminar

Title Open-closed maps
Speaker, Affiliation Prof. Dr. Nick Sheridan, Univ. of Edinburgh
Date, Time 9 January 2019, 13:30-14:30
Location HG G 43
Abstract I will explain in detail how to compute genus-zero Gromov-Witten invariants of a Calabi-Yau manifold from its Fukaya category. The main steps are to show that the periodic cyclic homology of the Fukaya category carries a natural structure of a Variation of Hodge Structures (VHS); and to identify this structure with the quantum VHS, from which the rational Gromov-Witten invariants can be extracted. This is based on joint work with Ganatra and Perutz.
Open-closed mapsread_more
HG G 43
* 9 January 2019
15:00-16:00 		Prof. Dr. Andrei Caldararu
Univ. of Wisconsin
Details

Algebraic Geometry and Moduli Seminar

Title The elliptic curve example
Speaker, Affiliation Prof. Dr. Andrei Caldararu, Univ. of Wisconsin
Date, Time 9 January 2019, 15:00-16:00
Location HG G 43
Abstract We put together all the moving parts we have developed in the previous lectures in order to calculate the g=1, n=1 B-model GW invariant of the family of elliptic curves, using the Hodge-de Rham splitting obtained from monodromy around the cusp point. If time allows we will also discuss similar calculations for the category of A_n singularities arising from the category of matrix factorizations.
The elliptic curve exampleread_more
HG G 43
* 9 January 2019
16:30-17:30 		Prof. Dr. Yongbin Ruan
Univ. of Michigan
Details

Algebraic Geometry and Moduli Seminar

Title The structure of higher genus Gromov-Witten theory of quintic 3-folds
Speaker, Affiliation Prof. Dr. Yongbin Ruan, Univ. of Michigan
Date, Time 9 January 2019, 16:30-17:30
Location HG G 43
Abstract One of biggest and most difficult problems in the subject of Gromov-Witten theory is to compute higher genus Gromov-Witten theory of compact Calabi-Yau 3-fold. There have been a collection of remarkable conjectures from physics for the so-called 14 one-parameter models, the simplest compact Calabi-Yau 3-folds similar to the quintic 3-folds. The backbone of this collection of conjectures are four structural conjectures: (1) Yamaguchi-Yau finite generation; (2) Holomorphic anomaly equation; (3) Orbifold regularity and (4) Conifold gap condition. In the talk, I will present a proof of first three conjectures for quintic 3-folds. This is a joint work with F. Janda and S. Guo. Our proof is based on certain localization formula from log GLSM theory developed by Q. Chen, F. Janda and myself.
The structure of higher genus Gromov-Witten theory of quintic 3-foldsread_more
HG G 43
* 10 January 2019
15:00-16:00 		Prof. Dr. Sheel Ganatra
Univ. of Southern California
Details

Algebraic Geometry and Moduli Seminar

Title Open-closed maps and Calabi-Yau structures II
Speaker, Affiliation Prof. Dr. Sheel Ganatra, Univ. of Southern California
Date, Time 10 January 2019, 15:00-16:00
Location HG G 43
Abstract Open-closed TFTs are classified (according to Costello,Kontsevich-Vlassopoulous, Lurie) by A-infinity categories equipped with Calabi-Yau (CY) structures. There are two types of CY structures of relevance, "smooth CY" structures classify TFTs with at least one output and "proper CY" structures classify TFTs with at least one input. We will review this formalism, show how a version of the open-closed map allows one to equip Fukaya categories with ageometrically meaningful CY structure of either type (under suitable hypotheses), and describe some initial applications.
Open-closed maps and Calabi-Yau structures IIread_more
HG G 43
* 10 January 2019
16:30-17:30 		Prof. Dr. Junwu Tu
Shanghai Tech Univ.
Details

Algebraic Geometry and Moduli Seminar

Title Givental's formula and Costello's higher genus categorical invariants
Speaker, Affiliation Prof. Dr. Junwu Tu, Shanghai Tech Univ.
Date, Time 10 January 2019, 16:30-17:30
Location HG G 43
Abstract We describe some work in progress to use Givental's formula to explicitly describe Costello's higher genus categorical Gromov-Witten invariants. Almost no axioms of GW theory are known to hold for Costello's categorical invariants, except the dimension axiom. Nevertheless, we argue that, in the categorical context, the holomorphic anomaly equation is a formal consequence of the Givental's formula.
Givental's formula and Costello's higher genus categorical invariantsread_more
HG G 43
16 January 2019
15:30-16:45 		Dr. Junliang Shen
MIT
Details

Algebraic Geometry and Moduli Seminar

Title Perverse filtrations, curve counting invariants, and hyper-Kähler geometry
Speaker, Affiliation Dr. Junliang Shen, MIT
Date, Time 16 January 2019, 15:30-16:45
Location HG G 43
Abstract For a hyper-kähler variety equipped with a Lagrangian fibration, an increasing filtration is defined on its rational cohomology using the perverse t-structure. We will discuss the role played by this filtration in the study of the topology and geometry of hyper-kähler varieties, as well as the connection to curve counting invariants of Calabi-Yau 3-folds. In particular, we will present recent progress on the P=W conjecture for Hitchin systems, and its compact analog for Lagrangian fibrations. Based on joint work with Qizheng Yin and Zili Zhang.
Perverse filtrations, curve counting invariants, and hyper-Kähler geometryread_more
HG G 43

Notes: events marked with an asterisk (*) indicate that the time and/or location are different from the usual time and/or location.

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