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Herbstsemester 2024

Datum / Zeit Referent:in Titel Ort
* 16. September 2024
15:30-17:00 		Dr. Sam Canning
ETH Zürich
Details

Algebraic Geometry and Moduli Seminar

Titel The tautological ring of the moduli space of stable curves is rarely Gorenstein
Referent:in, Affiliation Dr. Sam Canning, ETH Zürich
Datum, Zeit 16. September 2024, 15:30-17:00
Ort 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

Titel Complex abelian varieties and their moduli I
Referent:in, Affiliation Aitor Iribar López, ETH Zürich
Datum, Zeit 18. September 2024, 13:30-15:00
Ort 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

Titel Enumerative invariants from log intersection numbers
Referent:in, Affiliation Dr. Johannes Schmitt, ETH Zürich
Datum, Zeit 20. September 2024, 16:00-17:30
Ort 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

Titel Chow groups of moduli spaces via higher Chow groups
Referent:in, Affiliation William Newman, Ohio State University
Datum, Zeit 25. September 2024, 13:30-15:00
Ort 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

Titel Stable pairs on local curves and Bethe roots
Referent:in, Affiliation Max Schimpf, Universität Heidelberg
Datum, Zeit 27. September 2024, 16:00-17:30
Ort 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. Oktober 2024
13:30-15:30 		Jeremy Feusi
ETH Zürich
Details

Algebraic Geometry and Moduli Seminar

Titel Complex abelian varieties and their moduli II
Referent:in, Affiliation Jeremy Feusi, ETH Zürich
Datum, Zeit 2. Oktober 2024, 13:30-15:30
Ort UZH Irchel
Abstract Toroidal compactifications and their cone stacks
Complex abelian varieties and their moduli IIread_more
UZH Irchel
9. Oktober 2024
13:30-15:00 		Dr. Johannes Schmitt
ETH Zürich
Details

Algebraic Geometry and Moduli Seminar

Titel Complex abelian varieties and their moduli III
Referent:in, Affiliation Dr. Johannes Schmitt, ETH Zürich
Datum, Zeit 9. Oktober 2024, 13:30-15:00
Ort HG G 43
Abstract Tropical abelian varieties and their moduli
Complex abelian varieties and their moduli IIIread_more
HG G 43
11. Oktober 2024
16:00-17:30 		Prof. Dr. Georg Oberdieck
Universität Heidelberg
Details

Algebraic Geometry and Moduli Seminar

Titel Refined curve counting on the Enriques surface
Referent:in, Affiliation Prof. Dr. Georg Oberdieck, Universität Heidelberg
Datum, Zeit 11. Oktober 2024, 16:00-17:30
Ort 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. Oktober 2024
15:30-17:00 		Dr. Adrian Sauvaget
CNRS and Université de Cergy-Pontoise
Details

Algebraic Geometry and Moduli Seminar

Titel Several problems about spin classes
Referent:in, Affiliation Dr. Adrian Sauvaget, CNRS and Université de Cergy-Pontoise
Datum, Zeit 14. Oktober 2024, 15:30-17:00
Ort 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. Oktober 2024
13:30-15:30 		Dr. Sam Canning
ETH Zürich
Details

Algebraic Geometry and Moduli Seminar

Titel Complex abelian varieties and their moduli IV
Referent:in, Affiliation Dr. Sam Canning, ETH Zürich
Datum, Zeit 16. Oktober 2024, 13:30-15:30
Ort HG G 43
Abstract Degenerating abelian varieties
Complex abelian varieties and their moduli IVread_more
HG G 43
18. Oktober 2024
16:00-17:30 		Prof. Dr. Yefeng Shen
University of Oregon and IHES
Details

Algebraic Geometry and Moduli Seminar

Titel Quantum spectrum and Gamma structures for flips
Referent:in, Affiliation Prof. Dr. Yefeng Shen, University of Oregon and IHES
Datum, Zeit 18. Oktober 2024, 16:00-17:30
Ort 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. Oktober 2024
17:30-19:00 		Dr. Naoki Koseki
University of Liverpool
Details

Algebraic Geometry and Moduli Seminar

Titel Gopakumar-Vafa invariants of local curves
Referent:in, Affiliation Dr. Naoki Koseki, University of Liverpool
Datum, Zeit 21. Oktober 2024, 17:30-19:00
Ort 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. Oktober 2024
13:30-15:00 		Aitor Iribar López
ETH Zürich
Details

Algebraic Geometry and Moduli Seminar

Titel Complex abelian varieties and their moduli V
Referent:in, Affiliation Aitor Iribar López, ETH Zürich
Datum, Zeit 23. Oktober 2024, 13:30-15:00
Ort HG G 43
Abstract The toroidal compactifications of A_g
Complex abelian varieties and their moduli Vread_more
HG G 43
25. Oktober 2024
16:00-17:30 		Dr. Yannik Schuler
ETH Zürich
Details

Algebraic Geometry and Moduli Seminar

Titel Refined mirror symmetry of local P2
Referent:in, Affiliation Dr. Yannik Schuler, ETH Zürich
Datum, Zeit 25. Oktober 2024, 16:00-17:30
Ort 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. Oktober 2024
13:30-15:00 		Lycka Drakengren
ETH Zürich
Details

Algebraic Geometry and Moduli Seminar

Titel Complex abelian varieties and their moduli VI
Referent:in, Affiliation Lycka Drakengren, ETH Zürich
Datum, Zeit 30. Oktober 2024, 13:30-15:00
Ort 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

Titel Unstable cohomology of SL(n,Z) and Hopf algebras
Referent:in, Affiliation Prof. Dr. Peter Patzt, Univ. of Oklahoma
Datum, Zeit 1. November 2024, 16:00-17:30
Ort 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

Titel Tetrahedron instantons in Donaldson-Thomas theory
Referent:in, Affiliation Dr. Sergej Monavari, EPFL
Datum, Zeit 8. November 2024, 16:00-17:30
Ort 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

Titel Equations of some birational models of M_g,n.
Referent:in, Affiliation Prof. Dr. Alexander Polishchuk, Univ. of Oregon and FIM
Datum, Zeit 13. November 2024, 13:30-15:00
Ort 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

Titel Adjoints and canonical differential forms 
Referent:in, Affiliation Dr. Simon Telen, MPI Leipzig
Datum, Zeit 15. November 2024, 16:00-17:30
Ort 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

Titel Fourier-Mukai transformations on compactified Jacobians
Referent:in, Affiliation Dr. Younghan Bae, Univ. of Michigan
Datum, Zeit 27. November 2024, 14:30-16:00
Ort Zoom
Fourier-Mukai transformations on compactified Jacobians
Zoom
* 29. November 2024
15:00-16:30 		Prof. Dr. Longting Wu
SUST Shenzhen
Details

Algebraic Geometry and Moduli Seminar

Titel Poincaré polynomials of moduli spaces of 1-dimensional sheaves on the projective plane
Referent:in, Affiliation Prof. Dr. Longting Wu, SUST Shenzhen
Datum, Zeit 29. November 2024, 15:00-16:30
Ort HG ?
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
HG ?
11. Dezember 2024
13:30-15:00 		Dr. Pim Spelier
Utrecht University
Details

Algebraic Geometry and Moduli Seminar

Titel Title T.B.A.
Referent:in, Affiliation Dr. Pim Spelier, Utrecht University
Datum, Zeit 11. Dezember 2024, 13:30-15:00
Ort HG G 43
Title T.B.A.
HG G 43
13. Dezember 2024
16:00-17:30 		Dr. Pim Spelier
Utrecht University
Details

Algebraic Geometry and Moduli Seminar

Titel Title T.B.A.
Referent:in, Affiliation Dr. Pim Spelier, Utrecht University
Datum, Zeit 13. Dezember 2024, 16:00-17:30
Ort HG G 43
Title T.B.A.
HG G 43
16. Dezember 2024
15:00-16:30 		Dr. Denis Nesterov
ETH Zürich
Details

Algebraic Geometry and Moduli Seminar

Titel Title T.B.A.
Referent:in, Affiliation Dr. Denis Nesterov, ETH Zürich
Datum, Zeit 16. Dezember 2024, 15:00-16:30
Ort
Title T.B.A.

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