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Herbstsemester 2023

Datum / Zeit Referent:in Titel Ort
22. August 2023
13:30-15:00 		Prof. Dr. Longting Wu
SUSTech (Shenzhen)
Details

Algebraic Geometry and Moduli Seminar

Titel Towards a mathematical description of 5D Wilson loop amplitudes
Referent:in, Affiliation Prof. Dr. Longting Wu, SUSTech (Shenzhen)
Datum, Zeit 22. August 2023, 13:30-15:00
Ort ITS
Abstract Wilson loop amplitudes are a central concept in gauge theories, offering a way to study the behavior of particles and their interactions with gauge fields as they move along closed paths in spacetime. In this talk, we give a mathematical description of Wilson loop amplitudes in 5D gauge theory. This description will lead to conjectures about structures of Gromov-Witten invariants of some compact semi-Fano threefolds. We will give some evidence for these conjectures. This is a work in progress with Shuai Guo and Xin Wang.
Towards a mathematical description of 5D Wilson loop amplitudesread_more
ITS
30. August 2023
13:30-15:00 		Prof. Dr. Yongbin Ruan
Zhejiang University
Details

Algebraic Geometry and Moduli Seminar

Titel Logarithmic R-map
Referent:in, Affiliation Prof. Dr. Yongbin Ruan, Zhejiang University
Datum, Zeit 30. August 2023, 13:30-15:00
Ort ITS
Abstract Over last decade, various variant of stable maps modular space has been studied in connection to gauged linear sigma model. In this talk, we first propose the notion R-map to conceptualize these new modular space. The bulk of talk is to compactify these (open) moduli space by logarithmic R-map which carry two virtual fundamental cycles. Applications will be discussed. This is joint work with Qile Chen and Felix Janda.
Logarithmic R-mapread_more
ITS
* 11. September 2023
17:30-19:00 		Prof. Dr. John Pardon
Simons center (Stony Brook)
Details

Algebraic Geometry and Moduli Seminar

Titel Universally counting curves in Calabi-Yau threefolds
Referent:in, Affiliation Prof. Dr. John Pardon, Simons center (Stony Brook)
Datum, Zeit 11. September 2023, 17:30-19:00
Ort Zoom
Abstract Enumerating curves in algebraic varieties traditionally involves choosing a compactification of the space of smooth embedded curves in the variety. There are many such compactifications, hence many different enumerative invariants. I will propose a "universal" (very tautological) enumerative invariant which takes values in a certain Grothendieck group of 1-cycles. It is often the case with such "universal" constructions that the resulting Grothendieck group is essentially uncomputable. But in this case, the cluster formalism of Ionel and Parker shows that, in the case of threefolds with nef anticanonical bundle, this Grothendieck group is freely generated by local curves. This reduces the MNOP conjecture (in the case of nef anticanonical bundle and primary insertions) to the case of local curves, where it is already known due to work of Bryan--Pandharipande and Okounkov--Pandharipande.
Universally counting curves in Calabi-Yau threefoldsread_more
Zoom
22. September 2023
16:00-17:30 		Dr. Michele Graffeo
Politecnico di Milano
Details

Algebraic Geometry and Moduli Seminar

Titel The geometry of double nested Hilbert shemes
Referent:in, Affiliation Dr. Michele Graffeo, Politecnico di Milano
Datum, Zeit 22. September 2023, 16:00-17:30
Ort HG G 43
Abstract The Hilbert scheme Hilb^nX of n points on a quasi-projective variety X is a geometrical object introduced by Grothendieck and it has a prominent rôle in many areas of algebraic geometry. Recently, many variants of Hilb^nX have been introduced. My talk will focus on the double nested Hilbert scheme of points on X defined by S. Monavari. Specifically, I will explain how, when X is a smooth irreducible curve, its geometry is influenced by the combinatorics of reverse plane partitions and exhibits several pathologies. This is a joint project with Lella, Monavari, Ricolfi, Sammartano and it is partially funded by: PRIN 2020 “Squarefree Gröbner degenerations, special varieties and related topics” (MUR, project number 2020355B8Y)
The geometry of double nested Hilbert shemesread_more
HG G 43
27. September 2023
14:00-15:00 		Prof. Dr. Motohico Mulase
UC Davis
Details

Algebraic Geometry and Moduli Seminar

Titel À la recherche de courbes cachées
Referent:in, Affiliation Prof. Dr. Motohico Mulase, UC Davis
Datum, Zeit 27. September 2023, 14:00-15:00
Ort HG G 43
Abstract In some problems, sometimes finding a hidden curve behind the scene becomes a key to solve the problem. I will explain a few results from the past with a new perspective: (1) Construction of a D-module on a Jacobian; and (2) Finding the right coordinate on the hidden curve to understand the relation between enumeration problems and the quantities on the Deligne-Mumford moduli stack of curves. Then I will try to explain (3) An attempt toward describing the character variety on a curve in a combinatorial manner. The last one is an ongoing project with Olivia Dumitrescu (UNC).
À la recherche de courbes cachéesread_more
HG G 43
* 2. Oktober 2023
17:30-19:00 		Prof. Dr. Georg Oberdieck
KTH Stockholm
Details

Algebraic Geometry and Moduli Seminar

Titel Curve counting on the Enriques surface and the Klemm-Marino formula
Referent:in, Affiliation Prof. Dr. Georg Oberdieck, KTH Stockholm
Datum, Zeit 2. Oktober 2023, 17:30-19:00
Ort Zoom
Abstract An Enriques surface is the quotient of a K3 surface by a fixed point-free involution. Klemm and Marino conjectured a formula expressing the Gromov-Witten invariants of the local Enriques surface in terms of automorphic forms. In particular, the generating series of elliptic curve counts on the Enriques should be the Fourier expansion of (a certain power of) Borcherds automorphic form on the moduli space of Enriques surfaces. In this talk I will explain a proof of this conjecture. The proof uses the geometry of the Enriques Calabi-Yau threefold in fiber classes. If time permits, I will also discuss various conjectures about non-fiber classes.
Curve counting on the Enriques surface and the Klemm-Marino formularead_more
Zoom
6. Oktober 2023
16:00-17:30 		Dr. Yalong Cao
RIKEN (Japan)
Details

Algebraic Geometry and Moduli Seminar

Titel Gopakumar-Vafa type invariants of holomorphic symplectic 4-folds
Referent:in, Affiliation Dr. Yalong Cao, RIKEN (Japan)
Datum, Zeit 6. Oktober 2023, 16:00-17:30
Ort HG G 43
Abstract BPS invariants were introduced by Gopakumar-Vafa on Calabi-Yau 3-folds, Klemm-Pandharipande on CY 4-folds and Pandharipande-Zinger on CY 5-folds. They are conjectured to be integers (proven in many cases) and have correspondence with Gromov-Witten invariants. On holomorphic symplectic 4-folds, (ordinary) GW and hence BPS invariants vanish, one can consider reduced GW invariants which are usually nontrivial rational numbers. In this talk, we will introduce BPS invariants for such a reduced theory. Joint works with Georg Oberdieck and Yukinobu Toda.
Gopakumar-Vafa type invariants of holomorphic symplectic 4-foldsread_more
HG G 43
9. Oktober 2023
15:00-16:30 		Dr. Yalong Cao
RIKEN (Japan)
Details

Algebraic Geometry and Moduli Seminar

Titel Quasimaps to quivers with potentials
Referent:in, Affiliation Dr. Yalong Cao, RIKEN (Japan)
Datum, Zeit 9. Oktober 2023, 15:00-16:30
Ort ITS
Abstract Quivers with potentials are fundamental objects in geometric representation theory and important also in Donaldson-Thomas theory of Calabi-Yau 3-categories. In this talk, we will introduce quantum corrections to such objects by counting quasimaps from curves to the critical locus of the potential. Our construction is based on the theory of gauged linear sigma model (GLSM) and uses recent development of DT theory of CY 4-folds. Joint work with Gufang Zhao.
Quasimaps to quivers with potentials read_more
ITS
11. Oktober 2023
13:30-15:00 		Dr. Johannes Schmitt
ETH Zürich
Details

Algebraic Geometry and Moduli Seminar

Titel Log intersection theory: from toric varieties to moduli of curves I
Referent:in, Affiliation Dr. Johannes Schmitt, ETH Zürich
Datum, Zeit 11. Oktober 2023, 13:30-15:00
Ort HG G 43
Abstract Given a smooth algebraic variety (or orbifold) X with a normal crossings divisor D, the space X decomposes into strata describing the loci where various components of D (self-)intersect. In this series of four lectures, we will study the intersection theory of X, as well as certain birational modifications of X obtained by iteratively blowing up some of the strata. In recent years, the logarithmic Chow ring of the pair (X,D) was defined to encode the intersection theory of all such iterated blow-ups simultaneously. This allows to perform calculations with strict transforms of cycles on X without specifying a concrete birational model of X in which they live, and has been applied successfully in studying certain geometric cycles on moduli spaces. In the first lecture, we give an overview of the relevant definitions, a sketch of some of their applications, and a roadmap for the following talks. The second lecture talks about the case where X is a toric variety (and D its toric boundary), and explains that here the entire intersection theory is described in terms of convex geometric data (the fan Sigma of X and piecewise polynomial functions on Sigma). Then we show how the language of cone stacks and Artin fans can be used to generalize from the toric situation to arbitrary pairs (X,D). Finally, we talk about ongoing work on the logarithmic Chow ring of the moduli space of curves.
Log intersection theory: from toric varieties to moduli of curves Iread_more
HG G 43
13. Oktober 2023
16:00-17:30 		Dr. Fatemeh Rezaee
Cambridge and ETHZ
Details

Algebraic Geometry and Moduli Seminar

Titel Constructing smoothings of stable maps
Referent:in, Affiliation Dr. Fatemeh Rezaee, Cambridge and ETHZ
Datum, Zeit 13. Oktober 2023, 16:00-17:30
Ort HG G 43
Abstract Let X be a smooth projective variety. Define a stable map f : C → X to be eventually smoothable if there is an embedding X → PN such that (C,f) occurs as the limit of a 1-parameter family of stable maps to PN with smooth domain curves. Via an explicit deformation-theoretic construction, we produce a large class of stable maps (called stable maps with model ghosts), and show that they are eventually smoothable. This is joint work with Mohan Swaminathan.
Constructing smoothings of stable mapsread_more
HG G 43
18. Oktober 2023
13:30-15:00 		Dr. Johannes Schmitt
ETH Zürich
Details

Algebraic Geometry and Moduli Seminar

Titel Log intersection theory: from toric varieties to moduli of curves II
Referent:in, Affiliation Dr. Johannes Schmitt, ETH Zürich
Datum, Zeit 18. Oktober 2023, 13:30-15:00
Ort HG G 43
Log intersection theory: from toric varieties to moduli of curves II
HG G 43
20. Oktober 2023
16:00-17:30 		Dr. Alessandro Giacchetto
ETH Zürich
Details

Algebraic Geometry and Moduli Seminar

Titel The geometry of combinatorial moduli spaces
Referent:in, Affiliation Dr. Alessandro Giacchetto, ETH Zürich
Datum, Zeit 20. Oktober 2023, 16:00-17:30
Ort HG G 43
Abstract The Teichmüller space of bordered surfaces can be described via metric ribbon graphs, leading to a natural symplectic structure introduced by Kontsevich in his proof of Witten's conjecture. I will show that many tools of hyperbolic geometry can be adapted to this combinatorial setting, and in particular the existence of Fenchel–Nielsen coordinates that are Darboux. As applications of this setup, I will present a combinatorial analogue of Mirzakhani's identity, resulting in a completely geometric proof of Virasoro constraints as well as Norbury's recursion for the counting of integral points. Time permitting, I will describe how to count simple closed geodesics in this setting, and how its asymptotics compute Masur–Veech volumes of the moduli space of quadratic differentials.
The geometry of combinatorial moduli spacesread_more
HG G 43
25. Oktober 2023
13:30-15:00 		Ce Ji
Beijing Univ. and ETH Zürich
Details

Algebraic Geometry and Moduli Seminar

Titel Toward a generalization of the Witten conjecture from spectral curve
Referent:in, Affiliation Ce Ji, Beijing Univ. and ETH Zürich
Datum, Zeit 25. Oktober 2023, 13:30-15:00
Ort HG G 43
Abstract Over decades of development of the Witten conjecture, Many enumerative geometries are related to integrable hierarchies. Simultaneously, such theories can also be reconstructed from topological recursion, an algorithm producing multi-differential forms from the underlying spectral curve. In this talk, we propose a generalization of the Witten conjecture from spectral curve, which produce descendent potential functions for corresponding enumerative geometry related to certain reductions of (multi-component) KP hierarchy. Proof for genus zero spectral curve with one boundary will be sketched, which can be applied to deduce the rKdV integrability of deformed negative r-spin theory, conjectured by Chidambaram--Garcia-Falide--Giacchetto.
Toward a generalization of the Witten conjecture from spectral curveread_more
HG G 43
30. Oktober 2023
15:00-16:30 		Dr. Alessandro Giacchetto
ETH Zürich
Details

Algebraic Geometry and Moduli Seminar

Titel Resurgent large genus asymptotics of intersection numbers
Referent:in, Affiliation Dr. Alessandro Giacchetto, ETH Zürich
Datum, Zeit 30. Oktober 2023, 15:00-16:30
Ort ITS
Abstract Factorials can be recursively computed through their definition, but the computation gets difficult quite quickly when the number of interest gets larger and larger. A workaround is given by Stirling’s approximation: a closed, asymptotic formula for factorials. A similar (but much more complicated) situation occurs when trying to compute Witten’s intersection numbers. Virasoro constraints recursively compute these numbers, but the computation gets difficult when the genus gets larger and larger. An approximation has been recently proved by Aggarwal by studying the structure of the associated Virasoro constraints. I will present an alternative proof of Aggarwal’s result based on quantum curves and resurgence. The advantage of this strategy is that it easily generalises to several problems (like r-spin intersection numbers, Norbury’s intersection numbers, etc) and gives higher-order corrections.
Resurgent large genus asymptotics of intersection numbersread_more
ITS
1. November 2023
13:30-15:00 		Dr. Johannes Schmitt
ETH Zürich
Details

Algebraic Geometry and Moduli Seminar

Titel Log intersection theory: from toric varieties to moduli of curves III
Referent:in, Affiliation Dr. Johannes Schmitt, ETH Zürich
Datum, Zeit 1. November 2023, 13:30-15:00
Ort HG G 43
Log intersection theory: from toric varieties to moduli of curves III
HG G 43
3. November 2023
16:00-17:30 		Prof. Dr. Radu Laza
SUNY Stony Brook
Details

Algebraic Geometry and Moduli Seminar

Titel Birational geometry of the moduli space of low degree K3 surfaces
Referent:in, Affiliation Prof. Dr. Radu Laza, SUNY Stony Brook
Datum, Zeit 3. November 2023, 16:00-17:30
Ort HG G 43
Abstract It is a question of major interest to construct meaningful compactifications for moduli spaces of algebraic varieties. A case that proved challenging is that of polarized K3 surfaces. I will survey the problem and the proposed solutions to it. Then, I will discus an alternative, variational approach to it, proposed by O’Grady and I, which is particularly relevant in the case of low degree K3 surfaces. Namely, in the case of low degree K3 surfaces there are at least two natural compactifications — the Baily-Borel compactifciation and the GIT compactification. They are related by a series of simple birational transformations “wall crossings”, that can be described explicitly. The degree 2 case is classical, going back to the 80s, the degree 4 was completed a few years ago by myself and O’Grady. Here, I report on the degree 6 case, which is work in progress with Francois Greer, Zhiyuan Li, and Fei Si.
Birational geometry of the moduli space of low degree K3 surfacesread_more
HG G 43
13. November 2023
15:00-16:30 		Dr. Denis Nesterov
IST Austria
Details

Algebraic Geometry and Moduli Seminar

Titel Unramified Gromov-Witten and Gopakumar-Vafa invariants I
Referent:in, Affiliation Dr. Denis Nesterov, IST Austria
Datum, Zeit 13. November 2023, 15:00-16:30
Ort ITS
Abstract Kim, Kresch and Oh constructed compactified moduli spaces of unramified maps from nodal curves to an arbitrary smooth projective target. The associated invariants were called unramified Gromov-Witten invariants. In dimension 1, these spaces are familiar moduli spaces of admissible covers introduced by Harris and Mumford. In dimension 3,Pandharipande conjectured that unramified Gromov-Witten invariants are equal to Gopakumar-Vafa invariants (BPS invariants) for Fano and primitive Calabi-Yau classes. After an introduction to unramified Gromov-Witten theory, I will present a work in progress which aims to prove this conjecture. The approach is based on a certain wall-crossing technique, whose wall-crossing invariants are given by Hodge integrals on moduli spaces of stable marked curves.
Unramified Gromov-Witten and Gopakumar-Vafa invariants I read_more
ITS
15. November 2023
13:30-15:00 		Dr. Denis Nesterov
IST Austria
Details

Algebraic Geometry and Moduli Seminar

Titel Unramified Gromov-Witten and Gopakumar-Vafa invariants II
Referent:in, Affiliation Dr. Denis Nesterov, IST Austria
Datum, Zeit 15. November 2023, 13:30-15:00
Ort HG G 43
Abstract Kim, Kresch and Oh constructed compactified moduli spaces of unramified maps from nodal curves to an arbitrary smooth projective target. The associated invariants were called unramified Gromov-Witten invariants. In dimension 1, these spaces are familiar moduli spaces of admissible covers introduced by Harris and Mumford. In dimension 3, Pandharipande conjectured that unramified Gromov Witten invariants are equal to Gopakumar-Vafa invariants (BPS invariants) for Fano and primitive Calabi-Yau classes. After an introduction to unramified Gromov-Witten theory, I will present a work in progress which aims to prove this conjecture. The approach is based on a certain wall-crossing technique, whose wall-crossing invariants are given by Hodge integrals on moduli spaces of stable marked curves.
Unramified Gromov-Witten and Gopakumar-Vafa invariants II read_more
HG G 43
* 18. November 2023
11:30-13:00 		Prof. Dr. Angela Gibney
University of Pennsylvania
Details

Algebraic Geometry and Moduli Seminar

Titel The F-Conjecture
Referent:in, Affiliation Prof. Dr. Angela Gibney, University of Pennsylvania
Datum, Zeit 18. November 2023, 11:30-13:00
Ort ITS
Abstract The F-Conjecture is an old problem about the Mori Cone of the moduli space of curves. In this talk I will describe the conjecture, its origins, what is known, and what we would know if it were to be true. I’ll also describe some evidence that vertex operator algebras may play a role in refining our understanding of the problem.
The F-Conjectureread_more
ITS
22. November 2023
13:30-15:00 		Dr. Johannes Schmitt
ETH Zürich
Details

Algebraic Geometry and Moduli Seminar

Titel Log intersection theory: from toric varieties to moduli of curves IV
Referent:in, Affiliation Dr. Johannes Schmitt, ETH Zürich
Datum, Zeit 22. November 2023, 13:30-15:00
Ort HG G 43
Log intersection theory: from toric varieties to moduli of curves IV
HG G 43
6. Dezember 2023
13:30-15:00 		Ajith Urundolil-Kumaran
University of Cambridge
Details

Algebraic Geometry and Moduli Seminar

Titel Refined tropical curve counting with descendants
Referent:in, Affiliation Ajith Urundolil-Kumaran, University of Cambridge
Datum, Zeit 6. Dezember 2023, 13:30-15:00
Ort HG G 43
Abstract We introduce the enumerative geometry of curves in the algebraic torus (C*)^2. We show that a certain class of invariants associated with moduli spaces of curves in (C*)^2 can be calculated explicitly using a refined tropical correspondence theorem. If time permits we will explain how the proof relies on higher double ramification cycles and work of Buryak-Rossi on integrable systems on the moduli space of curves. This is joint work with Patrick Kennedy-Hunt and Qaasim Shafi.
Refined tropical curve counting with descendantsread_more
HG G 43
8. Dezember 2023
16:00-17:30 		Yannick Schuler
University of Sheffield
Details

Algebraic Geometry and Moduli Seminar

Titel Gromov-Witten theory and the refined topological string
Referent:in, Affiliation Yannick Schuler, University of Sheffield
Datum, Zeit 8. Dezember 2023, 16:00-17:30
Ort HG G 43
Abstract : I will make a proposal for a rigorous formulation of the so called refined topological string on a Calabi-Yau threefold X (admitting a torus action) in the framework of equivariant Gromov-Witten theory of X x C^2. After explaining how these GW invariants conjecturally relate to K-theoretic stable pair invariants, we will concentrate on the case when X is a local del Pezzo surface K_S. In this case the so called Nekrasov-Shatashvili limit can be identified with the GW theory of S relative a smooth anti-canonical curve which can be used to prove BPS integrality for S=P^2 in this limit. This is ongoing work with Andrea Brini.
Gromov-Witten theory and the refined topological stringread_more
HG G 43
13. Dezember 2023
13:30-15:00 		Pim Spelier
Leiden University
Details

Algebraic Geometry and Moduli Seminar

Titel Log gluing log curves and log cohomological field theories
Referent:in, Affiliation Pim Spelier, Leiden University
Datum, Zeit 13. Dezember 2023, 13:30-15:00
Ort HG G 43
Abstract The gluing maps on the moduli spaces Mbar_{g,n} have played a crucial role in the intersection theory of Mbar_{g,n}, for example playing a key part in the definition of its tautological ring and of cohomological field theories. In the last few years, interpreting Mbar_{g,n} as a logarithmic space has also been an incredibly useful tool for understanding classical invariants, such as the double ramification (DR) cycle. However, joining these two concepts has been proven difficult, as the gluing maps are not logarithmic and hence the log structure and the gluing do not interact. In this talk I will explain the DR cycle, explain the difficulty in log gluing, and present a definition of log gluing. This also allows for the definition of log cohomological field theories, and in particular we find that the log DR cycle is a log cohomological field theory. This talk is based on joint work with David Holmes (arxiv:2308.01099). No previous knowledge of DR cycles or log geometry is assumed.
Log gluing log curves and log cohomological field theoriesread_more
HG G 43
15. Dezember 2023
16:00-17:30 		Prof. Dr. Dan Petersen
University of Stockholm
Details

Algebraic Geometry and Moduli Seminar

Titel Top weight cohomology of M_g and the handlebody group
Referent:in, Affiliation Prof. Dr. Dan Petersen, University of Stockholm
Datum, Zeit 15. Dezember 2023, 16:00-17:30
Ort HG G 43
Abstract Chan-Galatius-Payne have recently identified an enormous amount of nontrivial unstable cohomology classes on the moduli spaces of curves, via an identification of the "top weight" cohomology of the mapping class group with the cohomology of Kontsevich's graph complex. I will explain that all these classes restrict nontrivially to the handlebody subgroup of the mapping class group, i.e. those mapping classes which extend to a handlebody filling. In the process we obtain a geometrically meaningful classifying space for the handlebody group. (Joint with Louis Hainaut.)
Top weight cohomology of M_g and the handlebody groupread_more
HG G 43

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