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Spring Semester 2018

Date / Time Speaker Title Location
21 February 2018
13:30-15:00 		Johannes Schmitt
ETH Zürich
Details

Algebraic Geometry and Moduli Seminar

Title Log geometry: introduction and motivation
Speaker, Affiliation Johannes Schmitt, ETH Zürich
Date, Time 21 February 2018, 13:30-15:00
Location HG G 43
Abstract A log structure on a scheme X is some additional data we can add to X recording some "hidden smoothness", even if X itself is singular. Logarithmic geometry is a large research field which in particular has applications to the theory of moduli spaces. In this reading seminar we will particularly focus on these aspects of the theory. In the first talk I will introduce some basic notions and try to give some motivation for how log structures can be useful.
Log geometry: introduction and motivationread_more
HG G 43
23 February 2018
16:00-17:15 		Junliang Shen
ETH Zürich
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Algebraic Geometry and Moduli Seminar

Title K3 categories, cubic fourfolds, and the Beauville-Voisin filtration
Speaker, Affiliation Junliang Shen, ETH Zürich
Date, Time 23 February 2018, 16:00-17:15
Location HG G 43
Abstract We discuss recent progress on the connection between 0-cycles of holomorphic symplectic varieties and structures of K3 categories. We propose that there exists a sheaf/cycle correspondence for any K3 category, which controls the geometry of algebraically coisotropic subvarieties of certain holomorphic symplectic varieties. We will first review the case of the derived category of a K3 surface (joint with Qizheng Yin and Xiaolei Zhao). Then we discuss the sheaf/cycle correspondence of Kuznetsov's noncommutative K3 category of a cubic 4-fold and its applications. This is joint work with Qizheng Yin.
K3 categories, cubic fourfolds, and the Beauville-Voisin filtrationread_more
HG G 43
28 February 2018
13:30-15:00 		Alberto Merici
Uni. Zürich
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Algebraic Geometry and Moduli Seminar

Title Log geometry: definitions and basic properties of log schemes
Speaker, Affiliation Alberto Merici, Uni. Zürich
Date, Time 28 February 2018, 13:30-15:00
Location HG G 43
Log geometry: definitions and basic properties of log schemes
HG G 43
2 March 2018
16:00-17:15 		Johannes Schmitt
ETH Zürich
Details

Algebraic Geometry and Moduli Seminar

Title Tautological points on the moduli space of stable curves
Speaker, Affiliation Johannes Schmitt, ETH Zürich
Date, Time 2 March 2018, 16:00-17:15
Location HG G 43
Abstract Tautological zero cycles form a one-dimensional subspace of the set of all algebraic zero-cycles on \M_g,n. The latter can in general be infinite-dimensional, so not all points of the moduli space will represent a tautological class. In the talk, we will present geometric conditions ensuring that a pointed curve does define a tautological point. On the other hand, we show that given any point Q in \M_g,n we can find other points P_1, ..., P_m such that Q+P_1+ ... + P_m is tautological. The necessary number m is uniformly bounded in terms of g,n, but the question of its minimal value is open. This is joint work with R. Pandharipande.
Tautological points on the moduli space of stable curvesread_more
HG G 43
7 March 2018
13:30-15:00 		Dr. Ulrike Riess
ETHZ-ITS
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Algebraic Geometry and Moduli Seminar

Title Log differentials, smoothness, and deformations
Speaker, Affiliation Dr. Ulrike Riess, ETHZ-ITS
Date, Time 7 March 2018, 13:30-15:00
Location HG G 43
Log differentials, smoothness, and deformations
HG G 43
9 March 2018
16:00-17:15 		Dr. Hyenho Lho
ETH Zürich
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Algebraic Geometry and Moduli Seminar

Title Generalized holomorphic anomaly equation on 4-folds
Speaker, Affiliation Dr. Hyenho Lho, ETH Zürich
Date, Time 9 March 2018, 16:00-17:15
Location HG G 43
Abstract Holomorphic anomaly equation is some recursive equation on the Gromov-Witten invariants of Calabi-Yau 3-fold predicted by Physics B-model. In this talk, I will try to generalise H.A.E. for some Calabi-Yau 4-fold. I will introduce two CohFT which are related to Gromov-Witten theory of local P3 and Sextic 4-fold and prove some generalised version of Holomorphic anomaly equations.
Generalized holomorphic anomaly equation on 4-foldsread_more
HG G 43
14 March 2018
13:30-15:00 		Prof. Dr. Chenyang Xu
Peking University
Details

Algebraic Geometry and Moduli Seminar

Title Volume and stability of singularities
Speaker, Affiliation Prof. Dr. Chenyang Xu, Peking University
Date, Time 14 March 2018, 13:30-15:00
Location HG G 43
Abstract One guiding principle for the class of kawamata log terminal (klt) singularities is that it is the local analogue of Fano varieties. In this talk, I will discuss our work (joint with Chi Li) on establishing an algebraic stability theory, which is the analogue to the K-stability of Fano varieties, for a klt singularity. This is achieved by using Chi Li’s definition of normalised volumes on the ’non-archimedean link'. The conjectural picture can be considered as a purely local construction which algebrizes the metric tangent cone in complex geometry. As an application, we solve Donaldson-Sun’s conjecture.
Volume and stability of singularitiesread_more
HG G 43
21 March 2018
13:30-15:00 		Simone Chiarello
Université de Genève
Details

Algebraic Geometry and Moduli Seminar

Title The P=W conjecture on the moduli space of rank 2 Higgs bundles
Speaker, Affiliation Simone Chiarello, Université de Genève
Date, Time 21 March 2018, 13:30-15:00
Location HG G 43
Abstract The cohomology ring of the moduli space of stable Higgs bundles over a Riemann surface is endowed with two filtrations: the weight filtration of mixed Hodge theory and the perverse filtration coming from the Hitchin system. The fact that these two filtrations coincide was proved by De Cataldo, Hausel and Migliorini in 2012 for the rank 2 case using geometric methods, while for higher ranks it is still unproven. In recent joint work with Hausel and Szenes, we give a new enumerative proof for rank 2 case. These methods might be extended to any rank. I will illustrate the main ideas of the proof and the problems that arise.
The P=W conjecture on the moduli space of rank 2 Higgs bundlesread_more
HG G 43
28 March 2018
13:30-15:00 		Dr. Longting Wu
ETH Zürich
Details

Algebraic Geometry and Moduli Seminar

Title Log smooth curves and their moduli
Speaker, Affiliation Dr. Longting Wu, ETH Zürich
Date, Time 28 March 2018, 13:30-15:00
Location HG G 43
Log smooth curves and their moduli
HG G 43
11 April 2018
13:30-15:00 		Johannes Schmitt
ETH Zürich
Details

Algebraic Geometry and Moduli Seminar

Title Log geometry: d-semistable varieties
Speaker, Affiliation Johannes Schmitt, ETH Zürich
Date, Time 11 April 2018, 13:30-15:00
Location HG G 43
Abstract We will discuss criteria for normal-crossing varieties to embed in smooth varieties or to admit semistable smoothings in terms of log structures.
Log geometry: d-semistable varietiesread_more
HG G 43
18 April 2018
13:30-15:00 		Jakob Oesinghaus
Uni. Zürich
Details

Algebraic Geometry and Moduli Seminar

Title Log geometry: stacks of logarithmic structures
Speaker, Affiliation Jakob Oesinghaus, Uni. Zürich
Date, Time 18 April 2018, 13:30-15:00
Location HG G 43
Log geometry: stacks of logarithmic structures
HG G 43
25 April 2018
13:30-15:00 		Dr. Thomas Preu
Details

Algebraic Geometry and Moduli Seminar

Title Log geometry: log deformation theory
Speaker, Affiliation Dr. Thomas Preu,
Date, Time 25 April 2018, 13:30-15:00
Location HG G 43
Log geometry: log deformation theory
HG G 43
2 May 2018
13:30-15:00 		Dr. Honglu Fan
ETH Zürich
Details

Algebraic Geometry and Moduli Seminar

Title Log geometry: twisted curves and log twisted curves
Speaker, Affiliation Dr. Honglu Fan, ETH Zürich
Date, Time 2 May 2018, 13:30-15:00
Location HG G 43
Log geometry: twisted curves and log twisted curves
HG G 43
9 May 2018
13:30-15:00 		Junliang Shen
ETH Zürich
Details

Algebraic Geometry and Moduli Seminar

Title Log geometry: log stable maps
Speaker, Affiliation Junliang Shen, ETH Zürich
Date, Time 9 May 2018, 13:30-15:00
Location HG G 43
Log geometry: log stable maps
HG G 43
18 May 2018
16:00-17:15 		Prof. Dr. Angelo Vistoli
SNS Pisa
Details

Algebraic Geometry and Moduli Seminar

Title Chow rings of some moduli spaces of smooth curves
Speaker, Affiliation Prof. Dr. Angelo Vistoli, SNS Pisa
Date, Time 18 May 2018, 16:00-17:15
Location HG G 43
Abstract There is by now an extensive theory of rational Chow rings of moduli spaces of smooth curves. The integral version of these Chow rings is not as well understood. I will survey what is known, including some recent developments.
Chow rings of some moduli spaces of smooth curvesread_more
HG G 43
23 May 2018
13:30-15:00 		PD Dr. Thorsten Weist
Universität Wuppertal
Details

Algebraic Geometry and Moduli Seminar

Title Homological invariants of quiver moduli spaces
Speaker, Affiliation PD Dr. Thorsten Weist, Universität Wuppertal
Date, Time 23 May 2018, 13:30-15:00
Location HG G 43
Abstract We consider moduli spaces attached to quivers and their representations and investigate methods which can be used to compute their homological invariants. With these methods it can be shown that the Euler characteristics of moduli spaces of point configurations in projective spaces, which can be identified with quiver moduli spaces, coincide with Gromov-Witten invariants counting certain rational curves in the projective plane. Moreover, using that both kind of invariants can be obtained by counting certain combinatorial objects, several formulas for these invariants can be derived.
Homological invariants of quiver moduli spacesread_more
HG G 43
25 May 2018
16:00-17:15 		Dr. Grégoire Menet
Université de Bourgogne
Details

Algebraic Geometry and Moduli Seminar

Title Global Torelli theorem for irreducible symplectic orbifolds
Speaker, Affiliation Dr. Grégoire Menet, Université de Bourgogne
Date, Time 25 May 2018, 16:00-17:15
Location HG G 43
Abstract Since the Bogomolov decomposition theorem, irreducible symplectic manifolds play an important role in algebraic geometry. They can be considereted as elementary bricks among the Kähler manifolds with a trivial first Chern class. In 2011, Verbitsky has proved a fundamental tool in the field: the global Torelli theorem. The idea is to be able to recover the geometry of the manifold from the Hodge structure of its second cohomology group. An orbifold is a generalization of manifold obtained by gluing quotients of opens of C^n by finite groups. In this talk, we will see, how the global Torelli theorem can be extended to irreducible symplectic orbifolds.
Global Torelli theorem for irreducible symplectic orbifoldsread_more
HG G 43
1 June 2018
16:00-17:15 		Dr. Jason van Zelm
Humboldt Universität Berlin
Details

Algebraic Geometry and Moduli Seminar

Title Computing classes of spaces of admissible covers
Speaker, Affiliation Dr. Jason van Zelm, Humboldt Universität Berlin
Date, Time 1 June 2018, 16:00-17:15
Location HG G 43
Abstract Let Adm(g,h,d) be the space of degree d admissible covers C → D of a genus h curve D by genus g curves C. There is a natural map f : Adm(g,h,d) → Mgnbar into the moduli space of stable curves taking the source curve of an admissible cover and forgetting everything else. When the class [f(Adm(g,h,d))] is tautological we can try to express this class in terms of a known basis for the tautological ring of Mgnbar. We will discuss several strategies for making these computations and give a number of examples.
Computing classes of spaces of admissible coversread_more
HG G 43

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