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Events
NoGAGS 2018 - North German Algebraic Geometry Seminar 2018

MPI für Mathematik in den Naturwissenschaften Leipzig

E1 05 (Leibniz-Saal)

conference

08.11.18 09.11.18

NoGAGS 2018 - North German Algebraic Geometry Seminar 2018

NoGAGS is a yearly mini conference in algebraic geometry. It gathers algebraic geometers from many different universities, primarily situated in northern Germany. Each year several speakers are invited. The structure of lectures as well as topics covered are reflected in previous NoGAGS events.

Speakers

Piotr Achinger

Instytut Matematyczny Polskiej Akademii Nauk

Dominic Bunnett

Freie Universität Berlin

Marco D'Addezio

Freie Universität Berlin

Rahul Pandharipande

ETH Zürich

Sam Payne

University of Texas at Austin

Jason van Zelm

Humboldt-Universität zu Berlin

Milena Wrobel

MPI MiS

Fei Xie

Bielefeld University

Ziyu Zhang

Leibniz Universität Hannover

Program

13:00 - 14:00	Rahul Pandharipande (ETH Zürich) Enumerative geometry and the holomorphic anomaly equation I will give a (gentle) introduction to the role of the holomorphic anomaly equation in curve counting problems starting with maps to elliptic curves, proceeding to local toric geometries, and concluding with the famous quintic 3-fold. Though I will discuss joint work with Hyenho Lho, much of what I will say is work of others (Pixton, Oberdieck-Pixton, Chen-Guo-Janda-Ruan, Jun Li and collaborators).
14:00 - 14:30	Coffee Break
14:30 - 15:30	Milena Wrobel (MPI MiS, Leipzig) The anticanonical complex - a combinatorial tool for Fano varieties Toric Fano varieties are in one to one correspondence with certain lattice polytopes, the so called Fano polytopes. Moreover classification of toric Fano varieties with respect to their singularity type turns out to be purely combinatorial: the position of lattice points in the Fano polytope determines the singularity type. The anticanonical complex has been introduced as a natural generalisation of the toric Fano polytope and so far has been succesfully used for the study of varieties with a torus action of complexity one. We enlarge the area of application of the anticanonical complex to Fano varieties with torus action of arbitrary complexity, for example arrangement varieties. In particular, we show that the possibility to apply the anticanonical complex to these varieties is connected to certain properties of their quotients.
15:30 - 16:00	Coffee Break
16:00 - 17:00	Dominic Bunnett (Freie Universität Berlin) Moduli of hypersurfaces in weighted projective space The moduli space of smooth hypersurfaces in projective space was constructed by Mumford in the 60’s using his newly developed classical (a.k.a. reductive) Geometric Invariant Theory. I wish to generalise this construction to hypersurfaces in weighted projective space (or more generally orbifold toric varieties). The automorphism group of a toric variety is in general non-reductive and I will use new results in non-reductive GIT, developed by F. Kirwan et al., to construct a moduli space of quasismooth hypersurfaces. I will give geometric characterisations of notions of stability arising from non-reductive GIT.
17:00 - 17:15	Coffee Break
17:15 - 18:15	Sam Payne (University of Texas at Austin) Top weight cohomology of M_g I will discuss the topology of a space of stable tropical curves of genus g with volume 1, whose reduced rational homology is canonically identified with the top weight cohomology of M_g and also with the homology of Kontsevich's graph complex. As one application, we show that H^{4g-6}(M_g) is nonzero for infinitely many g. This disproves a recent conjecture of Church, Farb, and Putman as well as an older, more general conjecture of Kontsevich. We also give an independent proof of a recent theorem of Willwacher, that homology of the graph complex vanishes in negative degrees, using the identifications above and known vanishing results for M_g. Joint work with M. Chan and S. Galatius.

09:15 - 10:15	Jason van Zelm (Humboldt-Universität zu Berlin) Computing classes of admissible covers 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.
10:15 - 10:45	Coffee Break
10:45 - 11:45	Ziyu Zhang (Leibniz Universität Hannover) Formality conjecture and moduli spaces of sheaves on K3 surfaces The formality conjecture for K3 surfaces, formulated by D.Kaledin and M.Lehn, states that on a complex projective K3 surface, the differential graded algebra RHom(F,F) is formal for any coherent sheaf F polystable with respect to an ample line bundle. In this talk, I will explain how to combine techniques from twistor spaces, dg categories and Fourier-Mukai transforms to prove this conjecture, and how to generalize it to derived objects. Based on joint work with Nero Budur.
11:45 - 12:45	Lunch
12:45 - 13:45	Fei Xie (Bielefeld University) Derived categories of fibrations of quintic del Pezzo surfaces I will provide two approaches for fining a semiorthogonal decomposition of the derived category of fibrations of quintic del Pezzo surfaces with RDP singularities. Similar to Kuznetsov’s work on sextic del Pezzo surfaces, the components of the semiorthogonal decomposition can be interpreted as the moduli spaces of semistable sheaves on fibers with fixed Hilbert polynomials. Alternatively, there is a rank 2 vector bundle on a quintic del Pezzo surface with RDP singularities that embeds the surface as a linear section of a Grassmannian. The semiorthogonal decomposition can be obtained by applying Homological Projective Duality. This is work in progress.
13:45 - 14:15	Coffee Break
14:15 - 15:15	Marco D'Addezio (Freie Universität Berlin) On the semi-simplicity conjecture for Qab We survey some old and new developments of the Grothendieck-Serre-Tate conjectures, with a particular attention to the semi-simplicity conjecture. We recall the role of Deligne's theory of weights for the semi-simplicity conjecture in positive characteristic. Then we switch to characteristic 0 and we explain some analogies with the previous situation.
14:30 - 15:30	Piotr Achinger (Instytut Matematyczny Polskiej Akademii Nauk) Serre-Tate theory for Calabi-Yau varieties Classical Serre–Tate theory describes deformations of ordinary abelian varieties. It implies that every such variety has a canonical lift to characteristic zero and equips the moduli space with a Frobenius lifting and canonical multiplicative coordinates. I will discuss a project, joint with Maciej Zdanowicz (EPFL), whose aim is to construct canonical liftings modulo $p^2$ of varieties with trivial canonical class which are ordinary in the weak sense that the Frobenius acts bijectively on the top cohomology of the structure sheaf. Consequently, we obtain a Frobenius lifting on the moduli space of such varieties. The quite explicit construction uses Frobenius splittings and a relative version of Witt vectors of length two. Attention: this event is cancelled.

Participants

Piotr Achinger

Instytut Matematyczny Polskiej Akademii Nauk

Daniele Agostini

Humboldt-Universität zu Berlin

Klaus Altmann

FU Berlin

Edgar Ayala

Leibniz Universität Hannover

Patrick Bloß

Leibniz Universität Hannover

Dominic Bunnett

Freie Universität Berlin

Alberto Cattaneo

Leibniz Universität Hannover

Türkü Özlüm Çelik

Max Planck Institute for Mathematics in the Sciences

Alexandru Constantinescu

Freie Universität Berlin

Marco D'Addezio

Freie Universität Berlin

Wolfgang Ebeling

Leibniz Universität Hannover

Gavril Farkas

Humboldt Universität zu Berlin

Amelie Flatt

FU Berlin

Mauro Fortuna

Leibniz Universität Hannover

Tim Gabele

Hamburg University

Francesco Galuppi

MPI MiS

Tatiana Gateva-Ivanova

MPI MIS and AUBG

Paul Görlach

Max Planck Institute MIS Leipzig

Christian Haase

FU Berlin

Paul Helminck

University of Bremen

Christoff Hische

Universität Tübingen

Kyusik Hong

Korea Institute for Advanced Study

Violeta Ivanova-Rohling

Bulgarian Academy of Sciences

Hanieh Keneshlou

mpi MiS

Thomas Krämer

Humboldt-Universität zu Berlin

Herbert Kurke

Humboldt Universitaet zu Berlin

Jun Ho Lee

Mokpo National University

Christian Lehn

Technische Universität Chemnitz

Daniel Litt

Institute for Advanced Study

Michael Lönne

Universität Bayreuth

Carlos Maestro Pérez

Berlin Mathematical School, Humboldt-Universität zu Berlin

Giacomo Mezzedimi

Leibniz Universität Hannover

Mateusz Michalek

Max-Planck-Institut für Mathematik in den Naturwissenschaften

Chenqi Mou

Beihang University, China

Rahul Pandharipande

ETH Zürich

Marta Panizzut

TU Berlin

Sam Payne

University of Texas at Austin

Marco Portioli

University of Bologna

Yue Ren

MPI MIS Leipzig

Karin Schaller

Freie Universität Berlin

Matthias Schütt

Leibniz Universität Hannover

Emre Sertöz

MPI MiS

Tim Seynnaeve

Max Planck Institute for Mathematics in the Sciences

Andrey Soldatenkov

Humboldt-Univetsität zu Berlin

Bernd Sturmfels

Max Planck Institute for Mathematics in the Sciences

Jason van Zelm

Humboldt-Universität zu Berlin

Charles Vial

Universität Bielefeld

Lena Walter

FU Berlin

Milena Wrobel

MPI MiS

Fei Xie

Bielefeld University

Ziyu Zhang

Leibniz Universität Hannover

Scientific Organizers

Mateusz Michalek

Max-Planck-Institut für Mathematik in den Naturwissenschaften

Administrative Contact

Saskia Gutzschebauch

Max-Planck-Institut für Mathematik in den Naturwissenschaften Contact via Mail

NoGAGS 2018 - North German Algebraic Geometry Seminar 2018

Links

Speakers

Piotr Achinger

Dominic Bunnett

Marco D'Addezio

Rahul Pandharipande

Sam Payne

Jason van Zelm

Milena Wrobel

Fei Xie

Ziyu Zhang

Program

Participants

Piotr Achinger

Daniele Agostini

Klaus Altmann

Edgar Ayala

Patrick Bloß

Dominic Bunnett

Alberto Cattaneo

Türkü Özlüm Çelik

Alexandru Constantinescu

Marco D'Addezio

Wolfgang Ebeling

Gavril Farkas

Amelie Flatt

Mauro Fortuna

Tim Gabele

Francesco Galuppi

Tatiana Gateva-Ivanova

Paul Görlach

Christian Haase

Paul Helminck

Christoff Hische

Kyusik Hong

Violeta Ivanova-Rohling

Hanieh Keneshlou

Thomas Krämer

Herbert Kurke

Jun Ho Lee

Christian Lehn

Daniel Litt

Michael Lönne

Carlos Maestro Pérez

Giacomo Mezzedimi

Mateusz Michalek

Chenqi Mou

Rahul Pandharipande

Marta Panizzut

Sam Payne

Marco Portioli

Yue Ren

Karin Schaller

Matthias Schütt

Emre Sertöz

Tim Seynnaeve

Andrey Soldatenkov

Bernd Sturmfels

Jason van Zelm

Charles Vial

Lena Walter

Milena Wrobel

Fei Xie

Ziyu Zhang

Scientific Organizers

Mateusz Michalek

Administrative Contact

Saskia Gutzschebauch