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Spring Semester 2019

Date / Time Speaker Title Location
20 February 2019
15:30-16:45 		Dr. Pierrick Bousseau
ETHZ-ITS
Details

Algebraic Geometry and Moduli Seminar

Title Tropical geometry, log geometry, and applications to Gromov-Witten theory I
Speaker, Affiliation Dr. Pierrick Bousseau, ETHZ-ITS
Date, Time 20 February 2019, 15:30-16:45
Location HG G 19.2
Abstract In this series of talks I will start with a general introduction to tropical/log geometry as a tool to study degenerations in algebraic geometry. I will then focus on Gromov-Witten theory and describe the decomposition formula of Abramovich-Chen-Gross-Siebert, giving a combinatorial picture of the (virtual) degeneration of moduli spaces of stable maps in a normal crossing degeneration. I will end by applications to concrete questions in Gromov-Witten theory.
Tropical geometry, log geometry, and applications to Gromov-Witten theory Iread_more
HG G 19.2
22 February 2019
16:00-17:15 		Dr. Pierrick Bousseau
ETHZ-ITS
Details

Algebraic Geometry and Moduli Seminar

Title Tropical geometry, log geometry, and applications to Gromov-Witten theory II
Speaker, Affiliation Dr. Pierrick Bousseau, ETHZ-ITS
Date, Time 22 February 2019, 16:00-17:15
Location HG G 43
Abstract In this series of talks I will start with a general introduction to tropical/log geometry as a tool to study degenerations in algebraic geometry. I will then focus on Gromov-Witten theory and describe the decomposition formula of Abramovich-Chen-Gross-Siebert, giving a combinatorial picture of the (virtual) degeneration of moduli spaces of stable maps in a normal crossing degeneration. I will end by applications to concrete questions in Gromov-Witten theory.
Tropical geometry, log geometry, and applications to Gromov-Witten theory IIread_more
HG G 43
27 February 2019
15:30-16:45 		Dr. Pierrick Bousseau
ETHZ-ITS
Details

Algebraic Geometry and Moduli Seminar

Title Tropical geometry, log geometry, and applications to Gromov-Witten theory III
Speaker, Affiliation Dr. Pierrick Bousseau, ETHZ-ITS
Date, Time 27 February 2019, 15:30-16:45
Location HG G 19.2
Abstract In this series of talks I will start with a general introduction to tropical/log geometry as a tool to study degenerations in algebraic geometry. I will then focus on Gromov-Witten theory and describe the decomposition formula of Abramovich-Chen-Gross-Siebert, giving a combinatorial picture of the (virtual) degeneration of moduli spaces of stable maps in a normal crossing degeneration. I will end by applications to concrete questions in Gromov-Witten theory.
Tropical geometry, log geometry, and applications to Gromov-Witten theory IIIread_more
HG G 19.2
1 March 2019
16:00-17:15 		Dr. Pierrick Bousseau
ETHZ-ITS
Details

Algebraic Geometry and Moduli Seminar

Title Tropical geometry, log geometry, and applications to Gromov-Witten theory IV
Speaker, Affiliation Dr. Pierrick Bousseau, ETHZ-ITS
Date, Time 1 March 2019, 16:00-17:15
Location HG G 43
Abstract In this series of talks I will start with a general introduction to tropical/log geometry as a tool to study degenerations in algebraic geometry. I will then focus on Gromov-Witten theory and describe the decomposition formula of Abramovich-Chen-Gross-Siebert, giving a combinatorial picture of the (virtual) degeneration of moduli spaces of stable maps in a normal crossing degeneration. I will end by applications to concrete questions in Gromov-Witten theory.
Tropical geometry, log geometry, and applications to Gromov-Witten theory IVread_more
HG G 43
13 March 2019
15:30-16:45 		Prof. Dr. Hiroshi Iritani
University of Kyoto
Details

Algebraic Geometry and Moduli Seminar

Title Quantum cohomology of toric blow-ups
Speaker, Affiliation Prof. Dr. Hiroshi Iritani, University of Kyoto
Date, Time 13 March 2019, 15:30-16:45
Location HG G 19.2
Abstract I will describe the change of the quantum cohomology D-modules of toric orbifolds under toric birational transformations. The analysis is based on mirror symmetry for toric orbifolds studied in joint work with Coates, Corti and Tseng. In the case of toric blow-ups, we will relate the change of quantum cohomology with that of K-groups (or derived categories) via the gamma-integral structure.
Quantum cohomology of toric blow-ups read_more
HG G 19.2
15 March 2019
16:00-17:15 		Prof. Dr. Hiroshi Iritani
University of Kyoto
Details

Algebraic Geometry and Moduli Seminar

Title Gamma conjecture via tropical geometry
Speaker, Affiliation Prof. Dr. Hiroshi Iritani, University of Kyoto
Date, Time 15 March 2019, 16:00-17:15
Location HG G 43
Abstract Many people have observed that asymptotics of periods near the large complex structure limit involves characteristic numbers of mirror manifolds and Riemann zeta values. This phenomenon can be formulated in terms of a certain characteristic class called the Gamma class. In this talk, I will explain how zeta values appear from tropical geometry and the SYZ picture. This is based on joint work with Mohammed Abouzaid, Sheel Ganatra and Nick Sheridan.
Gamma conjecture via tropical geometry read_more
HG G 43
20 March 2019
15:30-16:45 		Prof. Dr. Paul Norbury
University of Melbourne
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Algebraic Geometry and Moduli Seminar

Title A new cohomology class on the moduli space of stable curves
Speaker, Affiliation Prof. Dr. Paul Norbury, University of Melbourne
Date, Time 20 March 2019, 15:30-16:45
Location HG G 19.2
Abstract We define a collection of cohomology classes on the moduli space of curves. We prove that a generating function for the intersection numbers involving these new cohomology classes is a tau function of the KdV hierarchy. This is analogous to the theorem conjectured by Witten and proven by Kontsevich that a generating function for intersection numbers on the moduli space of curves is a tau function of the KdV hierarchy.
A new cohomology class on the moduli space of stable curvesread_more
HG G 19.2
22 March 2019
16:00-17:15 		Prof. Dr. Paul Norbury
University of Melbourne
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Algebraic Geometry and Moduli Seminar

Title Polynomial relations among kappa classes on the moduli space of curves
Speaker, Affiliation Prof. Dr. Paul Norbury, University of Melbourne
Date, Time 22 March 2019, 16:00-17:15
Location HG G 43
Abstract We construct an infinite collection of universal. i.e. independent of (g,n), polynomials in the Miller-Morita-Mumford kappa classes, defined over the moduli space of genus g stable curves with n labeled points. We conjecture vanishing of these polynomials in a range depending on g and n. This is joint work with Maxim Kazarian.
Polynomial relations among kappa classes on the moduli space of curvesread_more
HG G 43
27 March 2019
13:30-14:45 		Prof. Dr. Ben Bakker
University of Georgia
Details

Algebraic Geometry and Moduli Seminar

Title o-minimal GAGA
Speaker, Affiliation Prof. Dr. Ben Bakker, University of Georgia
Date, Time 27 March 2019, 13:30-14:45
Location HG G 43
Abstract For a complex projective variety, Serre's classical GAGA theorem asserts that the analytification functor from algebraic coherent sheaves to analytic coherent sheaves is an equivalence of categories. For non-proper varieties, however, this theorem easily fails. In joint work with Y. Brunebarbe and J. Tsimerman, we show that a GAGA theorem holds even in the non-proper case if one restricts to analytic structures that are "tame" in a sense made precise by the notion of o-minimality. We will also discuss some related algebraization theorems.
o-minimal GAGAread_more
HG G 43
29 March 2019
16:00-17:15 		Prof. Dr. Bjorn Poonen
MIT
Details

Algebraic Geometry and Moduli Seminar

Title Bertini irreducibility theorems over finite fields
Speaker, Affiliation Prof. Dr. Bjorn Poonen, MIT
Date, Time 29 March 2019, 16:00-17:15
Location HG G 43
Abstract The classical Bertini irreducibility theorem states that if X is a geometrically irreducible subvariety of P^n over an infinite field k, and dim X >= 2, then there exists a hyperplane H in P^n over k whose intersection with X is geometrically irreducible. This can fail if k is finite, but certain variants are true. For instance, we prove that if X is as above but k is finite, then the fraction of degree d hypersurfaces H whose intersection with X is geometrically irreducible tends to 1 as d tends to infinity. This result, which is more difficult than the Bertini smoothness theorem over finite fields proved in 2004, is joint work with François Charles.
Bertini irreducibility theorems over finite fieldsread_more
HG G 43
3 April 2019
13:30-14:45 		Prof. Dr. Ben Bakker
University of Georgia
Details

Algebraic Geometry and Moduli Seminar

Title Algebraicity of period maps
Speaker, Affiliation Prof. Dr. Ben Bakker, University of Georgia
Date, Time 3 April 2019, 13:30-14:45
Location HG G 43
Abstract The cohomology groups of complex algebraic varieties come equipped with a powerful invariant called a Hodge structure. Going back to foundational work of Griffiths, Hodge theory has found many important applications to algebraic and arithmetic geometry, but its intrinsically analytic nature often leads to complications. Recent joint work with Y. Brunebarbe, B. Klingler, and J. Tsimerman has shown that in fact many Hodge-theoretic constructions can be carried out in an intermediate geometric category in which analytic structures are "tame" in the sense of o-minimality. In this talk I will use this perspective to give an easy proof of an important theorem of Cattani--Deligne--Kaplan on the algebraicity of Hodge loci and explain how o-minimal GAGA can be used to prove a conjecture of Griffiths on the quasiprojectivity of the images of period maps. We will also discuss some applications to moduli theory.
Algebraicity of period mapsread_more
HG G 43
10 April 2019
13:00-14:15 		Prof. Dr. Ben Bakker
University of Georgia
Details

Algebraic Geometry and Moduli Seminar

Title Transcendence of period maps
Speaker, Affiliation Prof. Dr. Ben Bakker, University of Georgia
Date, Time 10 April 2019, 13:00-14:15
Location ITS
Abstract A period domain D parametrizes Hodge structures and can be described as a certain analytic open set of a flag variety. Due to the presence of monodromy, the period map of a family of algebraic varieties lands in a quotient D/\Gamma by an arithmetic group. In the very special case when D/\Gamma is itself algebraic, understanding the interaction between algebraic structures on the source and target of the uniformization D\rightarrow D/\Gamma is a crucial component of the modern approach to the Andr\'e-Oort conjecture. We prove a version of the Ax-Schanuel conjecture for general period maps X\rightarrow D/\Gamma which says that atypical algebraic relations between X and D are governed by Hodge loci. We will also discuss some recent arithmetic applications due to Lawrence and Venkatesh. This is joint work with J. Tsimerman.
Transcendence of period mapsread_more
ITS
12 April 2019
16:00-17:15 		Tim Buelles
ETH Zürich
Details

Algebraic Geometry and Moduli Seminar

Title Gromov-Witten theory of K3 surfaces and tautological classes
Speaker, Affiliation Tim Buelles, ETH Zürich
Date, Time 12 April 2019, 16:00-17:15
Location HG G 43
Gromov-Witten theory of K3 surfaces and tautological classes
HG G 43
17 April 2019
13:30-14:45 		Younghan Bae
ETH Zürich
Details

Algebraic Geometry and Moduli Seminar

Title Tautological relations on the moduli space of stable maps
Speaker, Affiliation Younghan Bae, ETH Zürich
Date, Time 17 April 2019, 13:30-14:45
Location HG G 43
Abstract We will discuss tautological relations for the moduli space of stable maps to arbitrary smooth projective variety. Using the double ramification cycle formula for target varieties of Janda-Pandharipande-Pixton-Zvonkine, we construct non-trivial tautological relations parallel to Pixton’s double ramification cycle relations for the moduli of curves.
Tautological relations on the moduli space of stable mapsread_more
HG G 43
3 May 2019
16:00-17:15 		Dr. Drew Johnson
ETH Zürich
Details

Algebraic Geometry and Moduli Seminar

Title Strange duality, Quot schemes, and multiple point formulas
Speaker, Affiliation Dr. Drew Johnson, ETH Zürich
Date, Time 3 May 2019, 16:00-17:15
Location HG G 43
Abstract Given a pair of moduli spaces of sheaves with orthogonal invariants, strange duality is a conjectural perfect pairing between spaces of sections of induced line bundles on the moduli spaces. We will review the formulation of strange duality and its statement and proof for curves which uses finite Quot schemes. We will then talk about work of Bertram, Johnson, and Goller which attempts to find an analog of these ideas for strange duality on del Pezzo surfaces when one of the moduli spaces is the Hilbert scheme of points. The expected cardinality of the finite Quot scheme is given by multiple point formulas.
Strange duality, Quot schemes, and multiple point formulasread_more
HG G 43
8 May 2019
13:30-14:45 		Prof. Dr. Claude Sabbah
École Polytechnique and CNRS
Details

Algebraic Geometry and Moduli Seminar

Title On a conjecture of Katzarkov-Kontsevich-Pantev
Speaker, Affiliation Prof. Dr. Claude Sabbah, École Polytechnique and CNRS
Date, Time 8 May 2019, 13:30-14:45
Location HG G 43
Abstract To a regular function on a smooth complex quasi-projective variety are associated "irregular Hodge numbers". The conjecture of KKP (2014) identifies them, under some assumptions on the regular function, with numbers deduced from the sizes of the Jordan blocks of the monodromy around infinity. I will explain a proof of this conjecture for Laurent polynomials.
On a conjecture of Katzarkov-Kontsevich-Pantevread_more
HG G 43
10 May 2019
16:00-17:15 		Dr. Drew Johnson
ETH Zürich
Details

Algebraic Geometry and Moduli Seminar

Title Strange duality and universal series
Speaker, Affiliation Dr. Drew Johnson, ETH Zürich
Date, Time 10 May 2019, 16:00-17:15
Location HG G 43
Abstract In the previous talk, we discussed the "finite Quot scheme method" for investigating strange duality when one of the moduli spaces is the Hilbert scheme of points. In this talk, we interpret the cardinality of the finite Quot scheme as a Chern number on the Hilbert scheme. The Euler characteristic of the line bundle involved in strange duality is also a Chern number on the Hilbert scheme of points. These numbers have a nice structure, given by "universal" series, and strange duality suggests a surprising relationship between these. Part of this relationship was recently proven by Marian, Opera, and Panharipande.
Strange duality and universal seriesread_more
HG G 43
15 May 2019
13:30-14:45 		Dr. Daniele Agostini
Humboldt-Universität Berlin
Details

Algebraic Geometry and Moduli Seminar

Title Syzygies, secants and tautological bundles
Speaker, Affiliation Dr. Daniele Agostini, Humboldt-Universität Berlin
Date, Time 15 May 2019, 13:30-14:45
Location HG G 43
Abstract The syzygies of an algebraic variety are the algebraic relations amongst its equations. They often encode surprising geometric informations: for example, it was recently shown by Ein and Lazarsfeld that syzygies of high degree can detect the gonality of a smooth curve. In my talk, I will present an extension of this result to higher dimensions, with applications to rationality questions. A key role in our proof is played by tautological bundles on Hilbert schemes of points.
Syzygies, secants and tautological bundlesread_more
HG G 43
17 May 2019
16:00-17:15 		Prof. Dr. Renzo Cavalieri
Colorado State University
Details

Algebraic Geometry and Moduli Seminar

Title Witten conjecture for Mumford's kappa classes
Speaker, Affiliation Prof. Dr. Renzo Cavalieri, Colorado State University
Date, Time 17 May 2019, 16:00-17:15
Location HG G 43
Abstract Kappa classes were introduced by Mumford, as a tool to explore the intersection theory of the moduli space of curves. Iterated use of the projection formula shows there is a close connection between the intersection theory of kappa classes on the moduli space of unpointed curves, and the intersection theory of psi classes on all moduli spaces. In terms of generating functions, we show that the potential for kappa classes is related to the Gromov-Witten potential of a point via a change of variables essentially given by complete symmetric polynomials, rediscovering a theorem of Manin and Zokgraf from '99. Surprisingly, the starting point of our story is a combinatorial formula that relates intersections of kappa classes and psi classes via a graph theoretic algorithm (the relevant graphs being dual graphs to stable curves). Further, this story is part of a large wall-crossing picture for the intersection theory of Hassett spaces, a family of birational models of the moduli space of curves. This is joint work with Vance Blanker (arXiv:1810.11443).
Witten conjecture for Mumford's kappa classesread_more
HG G 43
24 May 2019
16:00-17:15 		Dr. Drew Johnson
ETH Zürich
Details

Algebraic Geometry and Moduli Seminar

Title Generating series for Quot schemes and rationality
Speaker, Affiliation Dr. Drew Johnson, ETH Zürich
Date, Time 24 May 2019, 16:00-17:15
Location HG G 43
Abstract Let X be a smooth projective curve or suface. The schemes parameterizing quotients of a trivial bundle on X with support of positive codimension carry a natural virtual fundamental class. We review some recent results of Oprea and Pandharipande about tautological integrals against the virutal class, as well as virtual Euler characteristics. In some of these situations, the generating series is expected to be the expansion of a rational function.
Generating series for Quot schemes and rationalityread_more
HG G 43
29 May 2019
13:30-14:45 		Dr. Pierrick Bousseau
ETHZ-ITS
Details

Algebraic Geometry and Moduli Seminar

Title Structures in higher genus relative Gromov-Witten theory of CP2/E
Speaker, Affiliation Dr. Pierrick Bousseau, ETHZ-ITS
Date, Time 29 May 2019, 13:30-14:45
Location HG G 43
Abstract I will present some conjectural statements (explicit formulas in low genus, finite generation, holomorphic anomaly equation) for the higher genus Gromov-Witten theory of P^2 relative to a smooth cubic, and then some proof in genus one, relying on a comparison with local P^2. This is a report on work in progress joint with Honglu Fan and Longting Wu.
Structures in higher genus relative Gromov-Witten theory of CP2/Eread_more
HG G 43
* 31 May 2019
14:15-15:30 		Prof. Dr. Alexei Oblomkov
UMass Amherst
Details

Algebraic Geometry and Moduli Seminar

Title Matrix factorizations and sheaves on singular varieties
Speaker, Affiliation Prof. Dr. Alexei Oblomkov, UMass Amherst
Date, Time 31 May 2019, 14:15-15:30
Location HG E 33.3
Abstract In my talk, I will introduce matrix factorizations and will explain why matrix factorizations provide a good model for the category of sheaves on singular varieties. Our main example of the singular variety is the nested Hilbert scheme of points on C^2. In this setting, I give a rough idea of an interpretation (from our joint paper with Lev Rozansky) of the HOMFLYPT homology of links as space of global section of sheaf on the nested Hilbert scheme.
Matrix factorizations and sheaves on singular varietiesread_more
HG E 33.3
14 June 2019
14:15-15:30 		Prof. Dr. Tom Graber
California Institute of Technology
Details

Algebraic Geometry and Moduli Seminar

Title Localization for log stable maps
Speaker, Affiliation Prof. Dr. Tom Graber, California Institute of Technology
Date, Time 14 June 2019, 14:15-15:30
Location HG G 43
Abstract I will discuss a virtual localization formula for spaces with a torus equivariant logarithmic perfect obstruction theory and how it applies to the space of log stable maps to a toric variety.
Localization for log stable mapsread_more
HG G 43
26 June 2019
15:30-16:45 		Dr. Gleb Smirnov
ETH Zürich
Details

Algebraic Geometry and Moduli Seminar

Title Diffeomorphism groups of complex surfaces
Speaker, Affiliation Dr. Gleb Smirnov, ETH Zürich
Date, Time 26 June 2019, 15:30-16:45
Location HG G 43
Abstract We will prove that many algebraic surfaces have non-simply-connected diffeomorphism group; the examples to be discussed include rational surfaces and surfaces of general type.
Diffeomorphism groups of complex surfacesread_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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