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Autumn Semester 2023

Date / Time Speaker Title Location
22 August 2023
13:30-15:00		 Prof. Dr. Longting Wu
SUSTech (Shenzhen)
Event Details

Algebraic Geometry and Moduli Seminar

Title Towards a mathematical description of 5D Wilson loop amplitudes
Speaker, Affiliation Prof. Dr. Longting Wu,SUSTech (Shenzhen)
Date, Time 22 August 2023, 13:30-15:00
Location 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
Event Details

Algebraic Geometry and Moduli Seminar

Title Logarithmic R-map
Speaker, Affiliation Prof. Dr. Yongbin Ruan,Zhejiang University
Date, Time 30 August 2023, 13:30-15:00
Location 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)
Event Details

Algebraic Geometry and Moduli Seminar

Title Universally counting curves in Calabi-Yau threefolds
Speaker, Affiliation Prof. Dr. John Pardon,Simons center (Stony Brook)
Date, Time 11 September 2023, 17:30-19:00
Location 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
Event Details

Algebraic Geometry and Moduli Seminar

Title The geometry of double nested Hilbert shemes
Speaker, Affiliation Dr. Michele Graffeo,Politecnico di Milano
Date, Time 22 September 2023, 16:00-17:30
Location HG G 43
Abstract 希尔伯特计划Hilb ^ nX n个点的准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
Event Details

Algebraic Geometry and Moduli Seminar

Title À la recherche de courbes cachées
Speaker, Affiliation Prof. Dr. Motohico Mulase,UC Davis
Date, Time 27 September 2023, 14:00-15:00
Location 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 October 2023
17:30-19:00		 Prof. Dr. Georg Oberdieck
KTH Stockholm
Event Details

Algebraic Geometry and Moduli Seminar

Title Curve counting on the Enriques surface and the Klemm-Marino formula
Speaker, Affiliation Prof. Dr. Georg Oberdieck,KTH Stockholm
Date, Time 2 October 2023, 17:30-19:00
Location Zoom
Abstract 商的讹凯斯表面K3面e 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 October 2023
16:00-17:30		 Dr. Yalong Cao
RIKEN (Japan)
Event Details

Algebraic Geometry and Moduli Seminar

Title Gopakumar-Vafa type invariants of holomorphic symplectic 4-folds
Speaker, Affiliation Dr. Yalong Cao,RIKEN (Japan)
Date, Time 6 October 2023, 16:00-17:30
Location 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 October 2023
15:00-16:30		 Dr. Yalong Cao
RIKEN (Japan)
Event Details

Algebraic Geometry and Moduli Seminar

Title Quasimaps to quivers with potentials
Speaker, Affiliation Dr. Yalong Cao,RIKEN (Japan)
Date, Time 9 October 2023, 15:00-16:30
Location 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 potentialsread_more
ITS
11 October 2023
13:30-15:00		 Dr. Johannes Schmitt
ETH Zürich
Event Details

Algebraic Geometry and Moduli Seminar

Title Log intersection theory: from toric varieties to moduli of curves I
Speaker, Affiliation Dr. Johannes Schmitt,ETH Zürich
Date, Time 11 October 2023, 13:30-15:00
Location HG G 43
Abstract 给定一个光滑的代数品种(或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 October 2023
16:00-17:30		 Dr. Fatemeh Rezaee
Cambridge and ETHZ
Event Details

Algebraic Geometry and Moduli Seminar

Title Constructing smoothings of stable maps
Speaker, Affiliation Dr. Fatemeh Rezaee,Cambridge and ETHZ
Date, Time 13 October 2023, 16:00-17:30
Location 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 October 2023
13:30-15:00		 Dr. Johannes Schmitt
ETH Zürich
Event Details

Algebraic Geometry and Moduli Seminar

Title Log intersection theory: from toric varieties to moduli of curves II
Speaker, Affiliation Dr. Johannes Schmitt,ETH Zürich
Date, Time 18 October 2023, 13:30-15:00
Location HG G 43
Log intersection theory: from toric varieties to moduli of curves II
HG G 43
20 October 2023
16:00-17:30		 Dr. Alessandro Giacchetto
ETH Zürich
Event Details

Algebraic Geometry and Moduli Seminar

Title The geometry of combinatorial moduli spaces
Speaker, Affiliation Dr. Alessandro Giacchetto,ETH Zürich
Date, Time 20 October 2023, 16:00-17:30
Location 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 October 2023
13:30-15:00		 Ce Ji
Beijing Univ. and ETH Zürich
Event Details

Algebraic Geometry and Moduli Seminar

Title Toward a generalization of the Witten conjecture from spectral curve
Speaker, Affiliation Ce Ji,Beijing Univ. and ETH Zürich
Date, Time 25 October 2023, 13:30-15:00
Location 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
2023年10月30日
15:00-16:30		 Dr. Alessandro Giacchetto
ETH Zürich
Event Details

Algebraic Geometry and Moduli Seminar

Title Resurgent large genus asymptotics of intersection numbers
Speaker, Affiliation Dr. Alessandro Giacchetto,ETH Zürich
Date, Time 2023年10月30日, 15:00-16:30
Location HG G 43
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
HG G 43
1 November 2023
13:30-15:00		 Dr. Johannes Schmitt
ETH Zürich
Event Details

Algebraic Geometry and Moduli Seminar

Title Log intersection theory: from toric varieties to moduli of curves III
Speaker, Affiliation Dr. Johannes Schmitt,ETH Zürich
Date, Time 1 November 2023, 13:30-15:00
Location 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
Event Details

Algebraic Geometry and Moduli Seminar

Title Title T.B.A.
Speaker, Affiliation Prof. Dr. Radu Laza,SUNY Stony Brook
Date, Time 3 November 2023, 16:00-17:30
Location HG G 43
Title T.B.A.
HG G 43
13 November 2023
15:00-16:30		 Dr. Denis Nesterov
IST Austria
Event Details

Algebraic Geometry and Moduli Seminar

Title Title T.B.A.
Speaker, Affiliation Dr. Denis Nesterov,IST Austria
Date, Time 13 November 2023, 15:00-16:30
Location HG G 43
Title T.B.A.
HG G 43
15 November 2023
13:30-15:00		 Dr. Denis Nesterov
IST Austria
Event Details

Algebraic Geometry and Moduli Seminar

Title Title T.B.A.
Speaker, Affiliation Dr. Denis Nesterov,IST Austria
Date, Time 15 November 2023, 13:30-15:00
Location HG G 43
Title T.B.A.
HG G 43
22 November 2023
13:30-15:00		 Dr. Johannes Schmitt
ETH Zürich
Event Details

Algebraic Geometry and Moduli Seminar

Title Log intersection theory: from toric varieties to moduli of curves IV
Speaker, Affiliation Dr. Johannes Schmitt,ETH Zürich
Date, Time 22 November 2023, 13:30-15:00
Location HG G 43
Log intersection theory: from toric varieties to moduli of curves IV
HG G 43
6 December 2023
13:30-15:00		 Ajith Urundolil-Kumaran
University of Cambridge
Event Details

Algebraic Geometry and Moduli Seminar

Title Title T.B.A.
Speaker, Affiliation Ajith Urundolil-Kumaran,University of Cambridge
Date, Time 6 December 2023, 13:30-15:00
Location HG G 43
Title T.B.A.
HG G 43
8 December 2023
16:00-17:30		 Yannick Schuler
University of Sheffield
Event Details

Algebraic Geometry and Moduli Seminar

Title Title T.B.A.
Speaker, Affiliation Yannick Schuler,University of Sheffield
Date, Time 8 December 2023, 16:00-17:30
Location HG G 43
Title T.B.A.
HG G 43
13 December 2023
13:30-15:00		 Pim Spelier
Leiden University
Event Details

Algebraic Geometry and Moduli Seminar

Title Title T.B.A.
Speaker, Affiliation Pim Spelier,Leiden University
Date, Time 13 December 2023, 13:30-15:00
Location HG G 43
Title T.B.A.
HG G 43
15 December 2023
16:00-17:30		 Prof. Dr. Dan Petersen
University of Stockholm
Event Details

Algebraic Geometry and Moduli Seminar

Title Title T.B.A.
Speaker, Affiliation Prof. Dr. Dan Petersen,University of Stockholm
Date, Time 15 December 2023, 16:00-17:30
Location HG G 43
Title T.B.A.
HG G 43

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