Departement Mathematik

Algebraic geometry and moduli seminar

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Herbstsemester 2017

Datum / Zeit Referent:in Titel Ort
21. August 2017
13:30-15:00 		Dr. Felix Janda
Univ. of Michigan
Details

Algebraic Geometry and Moduli Seminar

Titel Four ways of computing the locus of holomorphic differentials
Referent:in, Affiliation Dr. Felix Janda, Univ. of Michigan
Datum, Zeit 21. August 2017, 13:30-15:00
Ort HG G 43
Four ways of computing the locus of holomorphic differentials
HG G 43
15. September 2017
16:00-17:15 		Christoph Schiessl
ETH Zürich
Details

Algebraic Geometry and Moduli Seminar

Titel Cohomology of configuration spaces of the sphere
Referent:in, Affiliation Christoph Schiessl, ETH Zürich
Datum, Zeit 15. September 2017, 16:00-17:15
Ort HG G 43
Abstract I will discuss some classic computations of the cohomology of configuration spaces of the plane and show how they can be used to determine the cohomology of configuration spaces of the sphere.
Cohomology of configuration spaces of the sphereread_more
HG G 43
20. September 2017
13:30-15:00 		Prof. Dr. Claire Voisin
Collège de France and ETH-ITS
Details

Algebraic Geometry and Moduli Seminar

Titel Segre numbers of tautological bundles on Hilbert schemes
Referent:in, Affiliation Prof. Dr. Claire Voisin, Collège de France and ETH-ITS
Datum, Zeit 20. September 2017, 13:30-15:00
Ort HG G 43
Abstract We establish geometric vanishings in certain ranges for top Segre classes of tautological bundles of punctual Hilbert schemes of K3 surfaces and K3 surfaces blown-up at one point. We show how all these Segre numbers for any surface and any polarization are formally determined by these vanishings.
Segre numbers of tautological bundles on Hilbert schemesread_more
HG G 43
22. September 2017
16:00-17:15 		Dr. Helge Ruddat
Universität Mainz
Details

Algebraic Geometry and Moduli Seminar

Titel Local and relative Gromov-Witten invariants
Referent:in, Affiliation Dr. Helge Ruddat, Universität Mainz
Datum, Zeit 22. September 2017, 16:00-17:15
Ort HG G 43
Abstract Given a smooth projective X with a smooth nef divisor D, the Gromov-Witten invariants of the total space of O(-D) are called local invariants. On the other hand one may consider Gromov-Witten invariants of X relative to the divisor D. In a joint work with Michel van Garrel and Tom Graber, we show these two invariants are related by a simple formula. I will explain how the proof which uses the degeneration formula to achieve an identification of virtual fundamental classes. If time permits, I will also explain the generalization where D is simple normal crossings and the local invariants are to the sum of line bundles given by the components of D. Tropical geometry and log Gromov-Witten theory are the key new tools in achieving these results. Our result has applications to the computation of symplectic cohomology.
Local and relative Gromov-Witten invariantsread_more
HG G 43
27. September 2017
13:30-15:00 		Junliang Shen
ETH Zürich
Details

Algebraic Geometry and Moduli Seminar

Titel Gopakumar-Vafa invariants via vanishing cycles I
Referent:in, Affiliation Junliang Shen, ETH Zürich
Datum, Zeit 27. September 2017, 13:30-15:00
Ort HG G 43
Abstract In the lecture series, we focus on the definition and properties of Gopakumar-Vafa invariants for Calabi-Yau 3-folds. GV invariants were first introduced by Gupakumar and Vafa as integer valued curve counting invariants from considerations in physics. Although they should be viewed as ideal curve counting invariants, there are serious difficulties to find a rigorous geometric definition. We will discuss the ideas of Hosono-Saito-Takahashi, Kiem-Li, and in particular the recent work by Maulik-Toda for defining GV invariants using perverse sheaves of vanishing cycles. Examples will be illustrated.
Gopakumar-Vafa invariants via vanishing cycles Iread_more
HG G 43
29. September 2017
16:00-17:15 		Prof. Dr. David Holmes
University of Leiden
Details

Algebraic Geometry and Moduli Seminar

Titel A universal resolution of the Abel-Jacobi map
Referent:in, Affiliation Prof. Dr. David Holmes, University of Leiden
Datum, Zeit 29. September 2017, 16:00-17:15
Ort HG G 43
Abstract It is well-known that the Abel-Jacobi map does not extend over the boundary of the moduli space of stable marked curves. We consider the problem of resolving this map by making blowups of the moduli space, with a particular focus on extending the double ramification cycle. We construct a certain `universal resolution' of the Abel-Jacobi map, and show that the resulting extension of the double ramification cycle coincides with that constructed by Graber and Vakil via virtual fundamental classes (and recently computed by Janda, Pixton, Pandharipande and Zvonkine).
A universal resolution of the Abel-Jacobi mapread_more
HG G 43
4. Oktober 2017
13:00-14:30 		Junliang Shen
ETH Zürich
Details

Algebraic Geometry and Moduli Seminar

Titel Gopakumar-Vafa invariants via vanishing cycles II
Referent:in, Affiliation Junliang Shen, ETH Zürich
Datum, Zeit 4. Oktober 2017, 13:00-14:30
Ort HG G 43
Abstract In the lecture series, we focus on the definition and properties of Gopakumar-Vafa invariants for Calabi-Yau 3-folds. GV invariants were first introduced by Gupakumar and Vafa as integer valued curve counting invariants from considerations in physics. Although they should be viewed as ideal curve counting invariants, there are serious difficulties to find a rigorous geometric definition. We will discuss the ideas of Hosono-Saito-Takahashi, Kiem-Li, and in particular the recent work by Maulik-Toda for defining GV invariants using perverse sheaves of vanishing cycles. Examples will be illustrated.
Gopakumar-Vafa invariants via vanishing cycles IIread_more
HG G 43
6. Oktober 2017
16:00-17:15 		Dr. Longting Wu
ETH Zürich
Details

Algebraic Geometry and Moduli Seminar

Titel Gromov-Witten invariants of the quintic threefold
Referent:in, Affiliation Dr. Longting Wu, ETH Zürich
Datum, Zeit 6. Oktober 2017, 16:00-17:15
Ort HG G 43
Abstract The computation of Gromov-Witten invariants of quintic 3-fold plays an important role in the Gromov-Witten theory. In this talk, we will sketch the algorithm given by Maulik and Pandharipande, which can be used to determine Gromov-Witten invariants (in all genera) of quintic 3-fold. Inspired by Gathmann's proposal, Maulik and Pandharipande also gave a conjecture, which gives a new possible way to determine those invariants and may simplify their original algorithm. We will introduce their conjecture and show that their conjecture is true for genus 2 and 3.
Gromov-Witten invariants of the quintic threefold read_more
HG G 43
11. Oktober 2017
13:30-15:00 		Junliang Shen
ETH Zürich
Details

Algebraic Geometry and Moduli Seminar

Titel Gopakumar-Vafa invariants via vanishing cycles III
Referent:in, Affiliation Junliang Shen, ETH Zürich
Datum, Zeit 11. Oktober 2017, 13:30-15:00
Ort HG G 43
Abstract In the lecture series, we focus on the definition and properties of Gopakumar-Vafa invariants for Calabi-Yau 3-folds. GV invariants were first introduced by Gupakumar and Vafa as integer valued curve counting invariants from considerations in physics. Although they should be viewed as ideal curve counting invariants, there are serious difficulties to find a rigorous geometric definition. We will discuss the ideas of Hosono-Saito-Takahashi, Kiem-Li, and in particular the recent work by Maulik-Toda for defining GV invariants using perverse sheaves of vanishing cycles. Examples will be illustrated.
Gopakumar-Vafa invariants via vanishing cycles IIIread_more
HG G 43
25. Oktober 2017
13:30-15:00 		Dr. Ran Tessler
ETH Zürich
Details

Algebraic Geometry and Moduli Seminar

Titel Stationary open intersection theory on CP1 and an open GW/H correspondence I
Referent:in, Affiliation Dr. Ran Tessler, ETH Zürich
Datum, Zeit 25. Oktober 2017, 13:30-15:00
Ort HG G 43
Abstract We shall describe the open genus 0 (disks) intersection theory of maps to CP^1 with boundary on RP^1 in the stationary sector and derive a localization formula. We then formally extend the fornula to higher genus and prove a cool decomposition formula. We continue by describing the open Hurwitz theory and show that if our formal definition for the open GWs really comes from a geometric definition, then the all-genus open GW/H holds.
Stationary open intersection theory on CP1 and an open GW/H correspondence Iread_more
HG G 43
27. Oktober 2017
16:00-17:15 		Dr. Honglu Fan
ETH Zürich
Details

Algebraic Geometry and Moduli Seminar

Titel Gromov-Witten invariants of hypersurfaces
Referent:in, Affiliation Dr. Honglu Fan, ETH Zürich
Datum, Zeit 27. Oktober 2017, 16:00-17:15
Ort HG G 43
Abstract I will talk about an idea relating GWI (Gromov-Witten invariants) of hypersurfaces to GWI of the ambient space. It almost determines all the GWI of hypersurface except some low degree invariants. There is a subsequent attempt (joint with Y.P. Lee and Ernst Schulte-Geers) hoping to improve this algorithm in order to determine all GWI of quintic 3-folds. But unfortunately this attempt failed in the end. I will also talk about this story.
Gromov-Witten invariants of hypersurfacesread_more
HG G 43
1. November 2017
13:30-15:00 		Dr. Ran Tessler
ETH Zürich
Details

Algebraic Geometry and Moduli Seminar

Titel Stationary open intersection theory on CP1 and an open GW/H correspondence II
Referent:in, Affiliation Dr. Ran Tessler, ETH Zürich
Datum, Zeit 1. November 2017, 13:30-15:00
Ort HG G 43
Abstract We shall describe the open genus 0 (disks) intersection theory of maps to CP^1 with boundary on RP^1 in the stationary sector, and derive a localization formula. We then formally extend the fornula to higher genus, and prove a cool decomposition formula. We continue by describing the open Hurwitz theory, and show that if our formal definition for the open GWs really comes from a geometric definition, the all-genus open GW/H holds.
Stationary open intersection theory on CP1 and an open GW/H correspondence IIread_more
HG G 43
3. November 2017
16:00-17:15 		Prof. Dr. Carel Faber
University of Utrecht
Details

Algebraic Geometry and Moduli Seminar

Titel Concomitants of ternary quartics, Siegel and Teichmüller modular forms, and the cohomology of local systems in genus 3
Referent:in, Affiliation Prof. Dr. Carel Faber, University of Utrecht
Datum, Zeit 3. November 2017, 16:00-17:15
Ort HG G 43
Abstract I will report on recent joint work with F. Cléry and G. van der Geer, which has led to an improved understanding of the objects in the title and the relations between them.
Concomitants of ternary quartics, Siegel and Teichmüller modular forms, and the cohomology of local systems in genus 3read_more
HG G 43
10. November 2017
16:00-17:15 		Johannes Schmitt
ETH Zürich
Details

Algebraic Geometry and Moduli Seminar

Titel Extending the tautlogical ring by Hurwitz cycles
Referent:in, Affiliation Johannes Schmitt, ETH Zürich
Datum, Zeit 10. November 2017, 16:00-17:15
Ort HG G 43
Abstract The tautological ring is a natural subring of the cohomology of the moduli spaces of stable curves. Many of its features - like a generating set, intersection products and pullbacks/pushforwards under natural maps - are accessible in terms of combinatorics. Unfortunately, in many cases the tautological ring is a strict subring of the (algebraic) cohomology. We show how this ring can be extended by adding the classes of Hurwitz loci, i.e. loci of curves forming ramified covers of curves of lower genus (like the sets of hyperelliptic or bielliptic curves). We demonstrate how this extended ring still admits a combinatorial description and how this can be used to compute many classes of Hurwitz loci that already lie in the tautological ring.
Extending the tautlogical ring by Hurwitz cyclesread_more
HG G 43
17. November 2017
16:00-17:15 		Dr. Hyenho Lho
ETH Zürich
Details

Algebraic Geometry and Moduli Seminar

Titel Holomorphic anomaly equations and the crepant resolution conjecture for C3/Z3
Referent:in, Affiliation Dr. Hyenho Lho, ETH Zürich
Datum, Zeit 17. November 2017, 16:00-17:15
Ort HG G 43
Abstract I will prove holomorphic anomaly equation for orbifold Gromov-witten invariants of [C3/Z_3]. After reviewing Gromov-Witten theory of local P2, I will prove crepant resolution conjecture for C3/Z3. This talk is based on joint work in progress with Coates, Iritani and Pandharipande.
Holomorphic anomaly equations and the crepant resolution conjecture for C3/Z3read_more
HG G 43
1. Dezember 2017
16:00-17:15 		Prof. Dr. Anton Mellit
Universität Wien
Details

Algebraic Geometry and Moduli Seminar

Titel Poincare polynomials of character varieties
Referent:in, Affiliation Prof. Dr. Anton Mellit, Universität Wien
Datum, Zeit 1. Dezember 2017, 16:00-17:15
Ort HG G 43
Abstract The conjectures of Hausel-Letellier-Rodriguez-Villegas predict a formula for the mixed Hodge polynomials of character varieties of Riemann surfaces with generic semisimple local monodromies. I will talk about proof of the specialization of their conjecture which gives Poincare polynomials, i.e. the generating functions of the Betti numbers of these character varieties. Using an approach of Schiffmann and Mozgovoy the claim is reduced to counting parabolic bundles with nilpotent endomorphism over finite fields. The main new technical ingredient is an interpretation of Macdonald polynomials as certain weighted counts of nilpotent matrices over power series rings.
Poincare polynomials of character varietiesread_more
HG G 43
6. Dezember 2017
13:30-15:00 		Jakob Oesinghaus
Universität Zürich
Details

Algebraic Geometry and Moduli Seminar

Titel Chow group of expanded pairs and quasi-symmetric functions
Referent:in, Affiliation Jakob Oesinghaus, Universität Zürich
Datum, Zeit 6. Dezember 2017, 13:30-15:00
Ort HG G 43
Abstract We study the stack of expanded pairs originally defined by Jun Li, and in greater generality by Abramovich, Cadman, Fantechi, and Wise, which, roughly speaking, parametrises certain standard ways to expand a pair $(X,D)$ of a scheme $X$ and a Cartier divisor $D$. We use an alternative description of this stack as the moduli stack of aligned log structures to compute its Chow group, which turns out to be the ring of quasi-symmetric functions, a variant of the usual ring of symmetric functions. We discuss applications of this result to Chow groups of some moduli stacks of genus 0 semi-stable curves.
Chow group of expanded pairs and quasi-symmetric functionsread_more
HG G 43
8. Dezember 2017
16:00-17:15 		Prof. Dr. Albrecht Klemm
Universität Bonn
Details

Algebraic Geometry and Moduli Seminar

Titel D-brane masses and the motivic Hodge conjecture
Referent:in, Affiliation Prof. Dr. Albrecht Klemm, Universität Bonn
Datum, Zeit 8. Dezember 2017, 16:00-17:15
Ort HG G 43
Abstract We consider one the parameter mirror families W of the Calabi-Yau 3-folds with Picard-Fuchs equations of hypergeometric type. By mirror symmetry the even D-brane masses of orginial Calabi-Yau M can be identified with four periods w.r.t to an integral symplectic basis of H_3(W,Z) at the point of maximal unipotent monodromy. We establish that the masses of the D4 and D2 branes at the conifold are given by the two algebraically independent values of the L-function of the weight four holomorphic Hecke eigenform with eigenvalue one of \Gamma_0(N). For the quintic in CP4, this Hecke eigen form of \Gamma_0(25) was found by Chad Schoen. It was discovered by del la Ossa, Candelas and Villegas that its coefficients a_p count the number of solutions of the mirror quinitic at the conifold over the finite number field F_p. Using the theory of periods and quasi-periods of \Gamma_0(N) and the special geometry pairing on Calabi-Yau 3 folds we can fix further values in the connection matrix between the maximal unipotent monodromy point and the conifold point.
D-brane masses and the motivic Hodge conjectureread_more
HG G 43
13. Dezember 2017
13:30-15:00 		Prof. Dr. Alessandro Chiodo
Université Jussieu
Details

Algebraic Geometry and Moduli Seminar

Titel Mirror pairs and automorphisms
Referent:in, Affiliation Prof. Dr. Alessandro Chiodo, Université Jussieu
Datum, Zeit 13. Dezember 2017, 13:30-15:00
Ort HG G 43
Abstract We present a mirror construction where a Calabi-Yau X equipped with an order-N automorphism x mirrors another Calabi-Yau Y with an automorphism y of the same order N. For any l dividing N we consider the x^l-fixed locus X_l of X, its order-l autormorphism given by x. We find that this mirrors the y^m-fixed locus Y_m of Y for m=N/l. More precisely we consider on each side the Hodge diamond H_i(p,q) given by the eigenspace of the cohomology whose eigenvalue is a primitive root of unity or order i=l and m respectively. We get H_l(p,q)=H_m(d-p,q) where d is the dimension of the two fixed loci X_l and Y_m. This involves geometric loci which do not satisfy a Calabi-Yau condition. Furthermore, generalizations and variants of these relations allow us to revisit mirror symmetry for K3 surfaces and to generalize Borcea-Voisin duality in any dimension.
Mirror pairs and automorphismsread_more
HG G 43
15. Dezember 2017
16:00-17:15 		Ignacio Barros
Humboldt Universität Berlin
Details

Algebraic Geometry and Moduli Seminar

Titel Geometry of the moduli of n-pointed K3 surfaces of genus 11
Referent:in, Affiliation Ignacio Barros, Humboldt Universität Berlin
Datum, Zeit 15. Dezember 2017, 16:00-17:15
Ort HG G 43
Abstract We prove that the moduli space of polarized K3 surfaces of genus eleven with n marked points is unirational when n<=6 and uniruled when n<=7. As a consequence, we settle a long standing but not proved assertion about the unirationality of M_{11,n} for n<=6. We also prove that the moduli space of polarized K3 surfaces of genus eleven with 9 marked points has non-negative Kodaira dimension.
Geometry of the moduli of n-pointed K3 surfaces of genus 11read_more
HG G 43
* 8. Januar 2018
10:00-12:00 		Prof. Dr. Yongbin Ruan
University of Michigan
Details

Algebraic Geometry and Moduli Seminar

Titel An overview of the program
Referent:in, Affiliation Prof. Dr. Yongbin Ruan, University of Michigan
Datum, Zeit 8. Januar 2018, 10:00-12:00
Ort HG G 19.1
An overview of the program
HG G 19.1
* 8. Januar 2018
14:00-16:00 		Prof. Dr. Ionut Ciocan-Fontanine
University of Minnesota
Details

Algebraic Geometry and Moduli Seminar

Titel Degeneration of virtual classes and wall-crossing for quasimaps to hypersurfaces
Referent:in, Affiliation Prof. Dr. Ionut Ciocan-Fontanine, University of Minnesota
Datum, Zeit 8. Januar 2018, 14:00-16:00
Ort HG G 19.1
Degeneration of virtual classes and wall-crossing for quasimaps to hypersurfaces
HG G 19.1
* 9. Januar 2018
10:00-12:00 		Prof. Dr. Qile Chen
Boston College
Details

Algebraic Geometry and Moduli Seminar

Titel Log compacfication of the GLSM moduli space and its virtual cycle
Referent:in, Affiliation Prof. Dr. Qile Chen, Boston College
Datum, Zeit 9. Januar 2018, 10:00-12:00
Ort HG G 19.1
Log compacfication of the GLSM moduli space and its virtual cycle
HG G 19.1
* 9. Januar 2018
14:30-16:30 		Dr. Hyenho Lho
ETH Zürich
Details

Algebraic Geometry and Moduli Seminar

Titel Holomorphic anomaly equation for local P2
Referent:in, Affiliation Dr. Hyenho Lho, ETH Zürich
Datum, Zeit 9. Januar 2018, 14:30-16:30
Ort HG G 19.1
Holomorphic anomaly equation for local P2
HG G 19.1
* 10. Januar 2018
10:00-12:00 		Dr. Felix Janda
Uniersity of Michigan
Details

Algebraic Geometry and Moduli Seminar

Titel Yamaguchi-Yau's conjecture and finite generation
Referent:in, Affiliation Dr. Felix Janda, Uniersity of Michigan
Datum, Zeit 10. Januar 2018, 10:00-12:00
Ort HG G 19.1
Yamaguchi-Yau's conjecture and finite generation
HG G 19.1
* 11. Januar 2018
10:00-12:00 		Prof. Dr. Shuai Guo
Peking University
Details

Algebraic Geometry and Moduli Seminar

Titel Holomorphic anomaly equation for the quintic 3-fold I
Referent:in, Affiliation Prof. Dr. Shuai Guo, Peking University
Datum, Zeit 11. Januar 2018, 10:00-12:00
Ort HG G 19.1
Holomorphic anomaly equation for the quintic 3-fold I
HG G 19.1
* 11. Januar 2018
14:30-16:30 		Prof. Dr. Albrecht Klemm
University of Bonn
Details

Algebraic Geometry and Moduli Seminar

Titel Higher genus invariants of elliptic CYs and Weyl invariant Jacobi forms
Referent:in, Affiliation Prof. Dr. Albrecht Klemm, University of Bonn
Datum, Zeit 11. Januar 2018, 14:30-16:30
Ort HG G 19.1
Higher genus invariants of elliptic CYs and Weyl invariant Jacobi forms
HG G 19.1
* 12. Januar 2018
10:00-12:00 		Dr. Felix Janda
Univ. of Michigan
Details

Algebraic Geometry and Moduli Seminar

Titel Moduli spaces and virtual classes related to the quintic
Referent:in, Affiliation Dr. Felix Janda, Univ. of Michigan
Datum, Zeit 12. Januar 2018, 10:00-12:00
Ort HG G 19.1
Moduli spaces and virtual classes related to the quintic
HG G 19.1
* 12. Januar 2018
14:30-16:30 		Prof. Dr. Shuai Guo
Peking University
Details

Algebraic Geometry and Moduli Seminar

Titel Holomorphic anomaly equation for the quintic 3-fold II
Referent:in, Affiliation Prof. Dr. Shuai Guo, Peking University
Datum, Zeit 12. Januar 2018, 14:30-16:30
Ort HG G 19.1
Holomorphic anomaly equation for the quintic 3-fold II
HG G 19.1

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