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Autumn Semester 2024

Date / Time Speaker Title Location
* 16 September 2024
15:30-17:00 		Dr. Sam Canning
ETH Zürich
Details

Algebraic Geometry and Moduli Seminar

Title The tautological ring of the moduli space of stable curves is rarely Gorenstein
Speaker, Affiliation Dr. Sam Canning, ETH Zürich
Date, Time 16 September 2024, 15:30-17:00
Location ITS
Abstract A central difficulty in the study of the intersection theory of the moduli space of curves is that there may exist tautological classes that are nonzero but intersect trivially with all tautological classes of complementary codimension. I will explain some recent progress on studying such classes by intersecting with classes outside of the tautological ring.
The tautological ring of the moduli space of stable curves is rarely Gorensteinread_more
ITS
* 18 September 2024
13:30-15:00 		Aitor Iribar López
ETH Zürich
Details

Algebraic Geometry and Moduli Seminar

Title Complex abelian varieties and their moduli I
Speaker, Affiliation Aitor Iribar López, ETH Zürich
Date, Time 18 September 2024, 13:30-15:00
Location HG F 26.1
Abstract Seminar lecture I Seminar goals: review the moduli of abelian varieties and how they degenerate, understand the construction of its toroidal compactifications, using inputs from tropical and logarithmic geometry, study different topics that arise naturally:intersection theory on these moduli spaces, the compactification interesting loci from, logarithmic abelian varieties and some arithmetic side of the whole story. See https://people.math.ethz.ch/~airibar/reading_seminar
Complex abelian varieties and their moduli Iread_more
HG F 26.1
* 20 September 2024
16:00-17:30 		Dr. Johannes Schmitt
ETH Zürich
Details

Algebraic Geometry and Moduli Seminar

Title Enumerative invariants from log intersection numbers
Speaker, Affiliation Dr. Johannes Schmitt, ETH Zürich
Date, Time 20 September 2024, 16:00-17:30
Location HG G 19.2
Abstract Enumerative geometry counts geometric objects satisfying a list of properties. An important method in the area is to obtain these counts as intersection numbers on a suitable moduli space Mbar. In the talk I explain how logarithmic intersection theory can be used in different examples to define intersection numbers which are independent of the precise choice of this space Mbar. After a discussion of (double) Hurwitz numbers, we'll also see a new class of invariants - called k-leaky double Hurwitz descendants - defined in joint work with Cavalieri and Markwig. I discuss some of their properties, show tropical formulas calculating them and present some questions on their enumerative interpretation.
Enumerative invariants from log intersection numbersread_more
HG G 19.2
* 25 September 2024
13:30-15:00 		William Newman
Ohio State University
Details

Algebraic Geometry and Moduli Seminar

Title Chow groups of moduli spaces via higher Chow groups
Speaker, Affiliation William Newman, Ohio State University
Date, Time 25 September 2024, 13:30-15:00
Location HG G 19.1
Abstract One can use Bloch's higher Chow groups to compute the usual Chow groups of moduli spaces. This involves first computing the necessary higher Chow groups, and then computing the connecting homomorphism of the localization exact sequence. I will explain general techniques for performing these computations and give examples for the integral Chow groups of moduli spaces of genus 1 curves.
Chow groups of moduli spaces via higher Chow groupsread_more
HG G 19.1
* 27 September 2024
16:00-17:30 		Max Schimpf
Universität Heidelberg
Details

Algebraic Geometry and Moduli Seminar

Title Stable pairs on local curves and Bethe roots
Speaker, Affiliation Max Schimpf, Universität Heidelberg
Date, Time 27 September 2024, 16:00-17:30
Location HG G 19.2
Abstract Local curves are an important class of threefolds which are indicative of the general behaviour of curve counting invariants. We give a closed formula for all descendent stable pair invariants of (absolute) local curves and use these to prove structure results conjectured by Pandharipande and Pixton. We then use our results to give a new approach to the Bethe ansatz story in physics/representation theory.
Stable pairs on local curves and Bethe rootsread_more
HG G 19.2
* 2 October 2024
13:30-15:30 		Jeremy Feusi
ETH Zürich
Details

Algebraic Geometry and Moduli Seminar

Title Complex abelian varieties and their moduli II
Speaker, Affiliation Jeremy Feusi, ETH Zürich
Date, Time 2 October 2024, 13:30-15:30
Location UZH Irchel
Abstract Toroidal compactifications and their cone stacks
Complex abelian varieties and their moduli IIread_more
UZH Irchel
9 October 2024
13:30-15:00 		Dr. Johannes Schmitt
ETH Zürich
Details

Algebraic Geometry and Moduli Seminar

Title Complex abelian varieties and their moduli III
Speaker, Affiliation Dr. Johannes Schmitt, ETH Zürich
Date, Time 9 October 2024, 13:30-15:00
Location HG G 43
Abstract Tropical abelian varieties and their moduli
Complex abelian varieties and their moduli IIIread_more
HG G 43
11 October 2024
16:00-17:30 		Prof. Dr. Georg Oberdieck
Universität Heidelberg
Details

Algebraic Geometry and Moduli Seminar

Title Refined curve counting on the Enriques surface
Speaker, Affiliation Prof. Dr. Georg Oberdieck, Universität Heidelberg
Date, Time 11 October 2024, 16:00-17:30
Location HG G 43
Abstract An Enriques surface is the quotient of a K3 surface by a fixed point free involution. There are many intriguing questions about curve counting on the Enriques surface. After giving an overview, we will zoom in on refined curve counting on the local Enriques surface. We discuss both K-theoretic refinement (following Nekrasov-Okounkov) and motivic refinements (following Kontsevich-Soibelman). In particular, we will see a refinement of the Klemm-Marino formula. This investigation leads to some concrete predictions about the moduli space of stable sheaves on Enriques surfaces.
Refined curve counting on the Enriques surfaceread_more
HG G 43
* 14 October 2024
15:30-17:00 		Dr. Adrian Sauvaget
CNRS and Université de Cergy-Pontoise
Details

Algebraic Geometry and Moduli Seminar

Title Several problems about spin classes
Speaker, Affiliation Dr. Adrian Sauvaget, CNRS and Université de Cergy-Pontoise
Date, Time 14 October 2024, 15:30-17:00
Location HG G 19.1
Abstract Many (partial) CohFTs in the moduli spaces of curves can be canonically lifted to the moduli space of spin structures. This leads to a refined study of these cohomology classes according to the sign (or Arf invariant) of the spin structure. We will review open problems and recent advances on the refined study of several partial CohFTs: Witten’s class, Double Ramification cycles, and strata of differentials.
Several problems about spin classes read_more
HG G 19.1
16 October 2024
13:30-15:30 		Dr. Sam Canning
ETH Zürich
Details

Algebraic Geometry and Moduli Seminar

Title Complex abelian varieties and their moduli IV
Speaker, Affiliation Dr. Sam Canning, ETH Zürich
Date, Time 16 October 2024, 13:30-15:30
Location HG G 43
Abstract Degenerating abelian varieties
Complex abelian varieties and their moduli IVread_more
HG G 43
18 October 2024
16:00-17:30 		Prof. Dr. Yefeng Shen
University of Oregon and IHES
Details

Algebraic Geometry and Moduli Seminar

Title Quantum spectrum and Gamma structures for flips
Speaker, Affiliation Prof. Dr. Yefeng Shen, University of Oregon and IHES
Date, Time 18 October 2024, 16:00-17:30
Location HG G 43
Abstract Quantum spectrum and Gamma structures play key roles in Katzarkov-Kontsevich-Pantev-Yu’s proposal to extract birational invariants from quantum cohomology and Iritani's decomposition theorem for quantum D-modules of blowups. In this talk, we investigate these structures for standard flips in a much simpler setup, by restricting the quantum multiplication to a fiber curve direction. In this setup, we can show that both quantum spectrum and asymptotic behavior can be reduced from the local models, where the small I/J-functions are known explicitly. Using the asymptotic behavior of cohomology-valued Meijer G-functions, we obtain a decomposition of the cohomology of standard flips into asymptotic Gamma classes. This decomposition is compatible with the semi-orthogonal decomposition for standard flips constructed by Bondal-Orlov and Belmans-Fu-Raedschelders. The talk is based on work in progress joint with Mark Shoemaker.
Quantum spectrum and Gamma structures for flipsread_more
HG G 43
* 21 October 2024
17:30-19:00 		Dr. Naoki Koseki
University of Liverpool
Details

Algebraic Geometry and Moduli Seminar

Title Gopakumar-Vafa invariants of local curves
Speaker, Affiliation Dr. Naoki Koseki, University of Liverpool
Date, Time 21 October 2024, 17:30-19:00
Location Zoom
Abstract In the 1990s, two physisists, Gopakumar and Vafa, proposed an ideal way to count curves in a Calabi-Yau threefold, that is conjecturally equivalent to other curve counting theories such as Gromov-Witten theory. It is very recent that Maulik and Toda gave a mathematically rigorous definition of GV invariants. In this talk, I will review a recent progress on the GV theory, including chi-independence for GV invariants on local curves and degree two GW/GV equivalence for some smooth curves with generic normal bundles. This is based on a joint work with T. Kinjo and another work with B. Davison.
Gopakumar-Vafa invariants of local curvesread_more
Zoom
23 October 2024
13:30-15:00 		Aitor Iribar López
ETH Zürich
Details

Algebraic Geometry and Moduli Seminar

Title Complex abelian varieties and their moduli V
Speaker, Affiliation Aitor Iribar López, ETH Zürich
Date, Time 23 October 2024, 13:30-15:00
Location HG G 43
Abstract The toroidal compactifications of A_g
Complex abelian varieties and their moduli Vread_more
HG G 43
25 October 2024
16:00-17:30 		Dr. Yannik Schuler
ETH Zürich
Details

Algebraic Geometry and Moduli Seminar

Title Refined mirror symmetry of local P2
Speaker, Affiliation Dr. Yannik Schuler, ETH Zürich
Date, Time 25 October 2024, 16:00-17:30
Location HG G 43
Abstract I will report on joint work with Andrea Brini in which we establish expected properties of the refined Gromov-Witten generating series of local P2 coming from B-model heuristics: modularity, the extended holomorphic anomaly equation, orbifold regularity and the leading order conifold asymptotics. The first three statements generalise results of Lho-Pandharipande and Coates-Iritani while the proof of the last property is new even in the unrefined limit. I will start off explaining why these four features are expected in the first place and will mention some of their consequences. Afterwards I will discuss aspects of their proof mostly focusing on the arguments proving the leading order conifold asymptotics.
Refined mirror symmetry of local P2read_more
HG G 43
30 October 2024
13:30-15:00 		Lycka Drakengren
ETH Zürich
Details

Algebraic Geometry and Moduli Seminar

Title Complex abelian varieties and their moduli VI
Speaker, Affiliation Lycka Drakengren, ETH Zürich
Date, Time 30 October 2024, 13:30-15:00
Location HG G 43
Abstract The Torelli morphism and its extension to the moduli space of stable curves
Complex abelian varieties and their moduli VIread_more
HG G 43
1 November 2024
16:00-17:30 		Prof. Dr. Peter Patzt
Univ. of Oklahoma
Details

Algebraic Geometry and Moduli Seminar

Title Unstable cohomology of SL(n,Z) and Hopf algebras
Speaker, Affiliation Prof. Dr. Peter Patzt, Univ. of Oklahoma
Date, Time 1 November 2024, 16:00-17:30
Location HG G 43
Abstract I want to give a survey about the rational cohomology of SL_n Z. This includes recent developments of finding Hopf algebras in the direct sum of all cohomology groups of SL_n Z for all n. I will give a quick overview about Hopf algebras and what this structure implies for the cohomology of SL_n Z. If time permits, I will explain a connection to graph homology.
Unstable cohomology of SL(n,Z) and Hopf algebrasread_more
HG G 43
8 November 2024
16:00-17:30 		Dr. Sergej Monavari
EPFL
Details

Algebraic Geometry and Moduli Seminar

Title Tetrahedron instantons in Donaldson-Thomas theory
Speaker, Affiliation Dr. Sergej Monavari, EPFL
Date, Time 8 November 2024, 16:00-17:30
Location HG G 43
Abstract Tetrahedron instantons were recently introduced by Pomoni-Yan-Zhang in string theory, as a way to describe systems of D0-D6 branes with defects. We propose a rigorous geometric interpretation of their work by the point of view of Donaldson-Thomas theory. We will explain how to naturally construct the moduli space of tetrahedron instantons as a Quot scheme, parametrizing quotients of a torsion sheaf over a certain singular threefold, and how to construct a virtual fundamental class in this setting using quiver representations and the recent machinery of Oh-Thomas (which is in principle designed for moduli spaces of sheaves on Calabi-Yau 4-folds). Furthermore, we will show how to formalize mathematically the invariants considered by Pomoni-Yan-Zhang (initially defined via supersymmetric localization in Physics) and how to rigorously compute them, solving some open conjectures. Joint work with Nadir Fasola.
Tetrahedron instantons in Donaldson-Thomas theoryread_more
HG G 43
13 November 2024
13:30-15:00 		Prof. Dr. Alexander Polishchuk
Univ. of Oregon and FIM
Details

Algebraic Geometry and Moduli Seminar

Title Equations of some birational models of M_g,n.
Speaker, Affiliation Prof. Dr. Alexander Polishchuk, Univ. of Oregon and FIM
Date, Time 13 November 2024, 13:30-15:00
Location HG G 43
Abstract I will discuss examples of birational models of M_{g,n} that on the one hand are given as GIT-quotients for torus actions on explicit affine schemes, and on the other hand admit modular descriptions. I’ll focus mostly on cases g=0 and g=1.
Equations of some birational models of M_g,n.read_more
HG G 43
15 November 2024
16:00-17:30 		Dr. Simon Telen
MPI Leipzig
Details

Algebraic Geometry and Moduli Seminar

Title Adjoints and canonical differential forms 
Speaker, Affiliation Dr. Simon Telen, MPI Leipzig
Date, Time 15 November 2024, 16:00-17:30
Location HG G 43
Abstract The adjoint hypersurface of a simple convex polytope is uniquely defined by interpolation conditions. Its defining equation is the numerator of a meromorphic volume form associated to the polytope, called its canonical form. That form has applications in optimization and particle physics. We extend these assertions to amplituhedra in the Grassmannian of lines in three-space. Joint work with Kristian Ranestad and Rainer Sinn. 
Adjoints and canonical differential forms read_more
HG G 43
* 27 November 2024
14:30-16:00 		Dr. Younghan Bae
Univ. of Michigan
Details

Algebraic Geometry and Moduli Seminar

Title Complex abelian varieties and their moduli VII
Speaker, Affiliation Dr. Younghan Bae, Univ. of Michigan
Date, Time 27 November 2024, 14:30-16:00
Location Zoom
Abstract Fourier-Mukai transformations on compactified Jacobians
Complex abelian varieties and their moduli VIIread_more
Zoom
* 29 November 2024
15:00-16:30 		Prof. Dr. Longting Wu
SUST Shenzhen
Details

Algebraic Geometry and Moduli Seminar

Title Poincaré polynomials of moduli spaces of 1-dimensional sheaves on the projective plane
Speaker, Affiliation Prof. Dr. Longting Wu, SUST Shenzhen
Date, Time 29 November 2024, 15:00-16:30
Location NO E 39
Abstract The geometry of moduli spaces of one-dimensional sheaves on the projective plane has attracted a lot of study recently. In this talk, I will give a new calculation of the Betti numbers of the moduli spaces of one-dimensional sheaves on the projective plane using Gromov-Witten invariants of local P^2 and local curves. The new calculation is based on the refined sheaves/GW correspondence established by Bousseau and all genus local/relative correspondence given by Bousseau-Fan-Guo-Wu. It can be used to prove the divisibility property of Poincaré polynomials of moduli spaces of one-dimensional sheaves on projective plane conjectured by Choi-van Garrel-Katz-Takahashi, and can also be used to recover the asymptotic behaviour of the Betti numbers established by Yuan. This is a work in progress with Shuai Guo.
Poincaré polynomials of moduli spaces of 1-dimensional sheaves on the projective planeread_more
NO E 39
4 December 2024
13:00-15:00 		Jeremy Feusi
ETH Zürich
Details

Algebraic Geometry and Moduli Seminar

Title Complex abelian varieties and their moduli VIII
Speaker, Affiliation Jeremy Feusi, ETH Zürich
Date, Time 4 December 2024, 13:00-15:00
Location HG G 43
Abstract Introduction to log abelian varieties
Complex abelian varieties and their moduli VIIIread_more
HG G 43
11 December 2024
13:30-15:00 		Dr. Pim Spelier
Utrecht University
Details

Algebraic Geometry and Moduli Seminar

Title The moduli space of log abelian varieties
Speaker, Affiliation Dr. Pim Spelier, Utrecht University
Date, Time 11 December 2024, 13:30-15:00
Location HG G 43
Abstract There are many compactifications of the moduli space of abelian varieties. In a series of papers by Kajiwara, Kato and Nakayama, they construct a particularly nice modular compactification, consisting of log abelian varieties, certain proper group objects in the category of log spaces. In this talk, I will recall the definitions of a tropical abelian variety and a log abelian variety, and give an overview of the moduli space of log abelian varieties (with level structure). I will also explain how it compares to the toroidal compactifications, such as the second Voronoi compactification. I will also discuss how classical constructions like duality and the Poincare bundle generalise to the logarithmic setting.
The moduli space of log abelian varietiesread_more
HG G 43
13 December 2024
16:00-17:30 		Dr. Pim Spelier
Utrecht University
Details

Algebraic Geometry and Moduli Seminar

Title Gluing logarithmic curves: the logarithmic double ramification cycle and logarithmic Gromov-Witten invariants
Speaker, Affiliation Dr. Pim Spelier, Utrecht University
Date, Time 13 December 2024, 16:00-17:30
Location HG G 43
Abstract The gluing maps on the moduli space of curves are integral to much of the enumerative geometry of curves. For example, Gromov-Witten invariants satisfy recursive relations with respect to the gluing maps. For log GW invariants, counting maps with tangency conditions, this fails, as gluing maps do not respect the logarithmic structure hence the pullback is not well-defined. I will describe a certain logarithmic enhancement of Mgn that does admit gluing maps. For the logarithmic double ramification cycle, a certain curve count controlling the log Gromov-Witten invariants of toric varieties, a formula for the pullback along the separating gluing map was known. I will present a formula for pulling back the log DR cycle along the non-separating gluing map in terms of smaller log DR cycles and piecewise polynomials, and explain how this gives a formula for the classical pullback of the classical double ramification cycle. I will sketch how this story extends to logarithmic Gromov-Witten invariants.
Gluing logarithmic curves: the logarithmic double ramification cycle and logarithmic Gromov-Witten invariantsread_more
HG G 43
* 17 December 2024
16:00-17:30 		Dr. Denis Nesterov
ETH Zürich
Details

Algebraic Geometry and Moduli Seminar

Title Stable maps and admissible covers 
Speaker, Affiliation Dr. Denis Nesterov, ETH Zürich
Date, Time 17 December 2024, 16:00-17:30
Location HG G 19.1
Abstract Moduli spaces of stable maps and admissible covers of a curve give rise to interesting cycles on moduli spaces of stable curves. The talk will be about a wall-crossing formula relating these two types of cycles. Based on a joint work with Max Schimpf. 
Stable maps and admissible covers read_more
HG G 19.1
18 December 2024
13:30-15:00 		Dr. Sam Canning
ETH Zürich
Details

Algebraic Geometry and Moduli Seminar

Title Cycles on moduli spaces of curves and abelian varieties
Speaker, Affiliation Dr. Sam Canning, ETH Zürich
Date, Time 18 December 2024, 13:30-15:00
Location HG G G43
Abstract I will show how the study of non-tautological classes on the moduli space of abelian varieties helps explain the structure of the tautological ring of the moduli space of curves of compact type. On the curves side, this is joint work with Hannah Larson and Johannes Schmitt, and on the abelian varieties side, it is joint with Dragos Oprea and Rahul Pandharipande.
Cycles on moduli spaces of curves and abelian varietiesread_more
HG G G43

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