September 11  December 20, 2023
Description: The program will bring together algebraic geometers working on different aspects of algebraic geometry with a focus on geometric applications to central classes of algebraic varieties. Special emphasis will be put on Hyperkähler, CalabiYau and Fano varieties, but the program aims at triggering new collaborations between the different directions in the title in a broad sense. We invite groups of early career researchers (Phd students, postdocs, junior faculty) to apply for the program, with the goal to pursue research within their group but also to collaborate with the other groups. The participants will be supported by the HIM to organize various activities (including seminars, a school, workshops) and are free to design a research environment that suits their research agenda best.
The program will be organized in collaboration with the ERC Synergy Project
The online application platform to participate in this trimester program has been closed.
PERSON 
AFFILIATION 
PERIOD OF STAY 
Anna Abasheva  Columbia University  10.09.2023 – 20.12.2023 
Younghan Bae  ETH Zürich  10.09.2023 – 20.12.2023 
Benjamin Bakker  University of Illinois at Chicago  14.11.2023 – 22.11.2023 
Anna Barbieri  Università di Verona  05.11.2023 – 16.11.2023 
Valeria Bertini  University of Genova  05.11.2023 – 16.11.2023 
Alessio Bottini  Università di Roma Tor Vergata  11.09.2023 – 20.12.2023 
Emma Brakkee  Leiden University  26.11.2023 – 05.12.2023 
Corey Brooke  Carleton College  27.11.2023 – 20.12.2023 
Riccardo Carini  Imperial College London  
Raymond Cheng  Gottfried Wilhelm Leibniz Universität Hannover  11.09.2023 – 20.12.2023 
Mark Andrea De Cataldo  Stony Brook University  03.12.2023 – 09.12.2023 
Philip Engel  Universität Bonn  
Andres Fernandez Herrero  Columbia University  10.09.2023 – 20.12.2023 
Soheyla Feyzbakhsh  Imperial College London  11.11.2023 – 03.12.2023 
Stefano Filipazzi  EPFL  12.11.2023 – 18.11.2023 
Sarah Frei  Dartmouth College  10.09.2023 – 14.10.2023 
Sarah Frei  Dartmouth College  05.11.2023 – 15.12.2023 
Roberto Fringuelli  University of Roma La Sapienza  03.12.2023 – 09.12.2023 
Richard Haburcak  Dartmouth College  10.09.2023 – 20.12.2023 
Moritz Hartlieb  Universität Bonn  
Jiexiang Huang  Universität Bonn  
Daniel Huybrechts  Universität Bonn  11.09.2023 – 20.12.2023 
Qingyuan Jiang  University of Edinburgh  10.09.2023 – 20.12.2023 
Martin Kalck  University of Graz  29.10.2023 – 11.11.2023 
Martin Kalck  University of Graz  26.11.2023 – 09.12.2023 
Tomohiro Karube  University of Tokyo  10.09.2023 – 28.11.2023 
Kohei Kikuta  Osaka University  10.09.2023 – 08.10.2023 
János Kollár  Princeton University  15.10.2023 – 27.10.2023 
Johannes Krah  Universität Bielefeld  10.09.2023 – 20.12.2023 
Dion Leijnse  Universiteit van Amsterdam  10.09.2023 – 20.12.2023 
Shengxuan Liu  University of Warwick  10.09.2023 – 20.12.2023 
Zhiyu Liu  Zhejiang University  20.10.2023 – 20.12.2023 
Pablo Magni  Universität Bielefeld  10.09.2023 – 20.12.2023 
Gebhard Martin  Universität Bonn  
Olivier Martin  Stony Brook University  18.11.2023 – 30.11.2023 
Luigi Martinelli  Université ParisSaclay  10.09.2023 – 20.12.2023 
Dominique Mattei  Universität Bonn  
Mirko Mauri  IST Austria  10.09.2023 – 20.12.2023 
Enrica Mazzon  Universität Regensburg  24.09.2023 – 08.10.2023 
Reinder Meinsma  Universität Bonn  
Giacomo Mezzedimi  Universität Bonn  
Noah Olander  University of Amsterdam  10.09.2023 – 20.12.2023 
Genki Ouchi  Nagoya University  11.09.2023 – 02.11.2023 
Hyeonjun Park  Korea Institute for Advanced Study  11.09.2023 – 20.11.2023 
Nebojsa Pavic  Leibniz Universität Hannover  11.09.2023 – 20.12.2023 
Laura Pertusi  Università degli Studi di Milano  01.10.2023 – 30.11.2023 
Jack Petok  Dartmouth College  10.09.2023 – 15.12.2023 
Xuqiang Qin  University of North Carolina at Chapel Hill  10.09.2023 – 20.12.2023 
Franco Rota  University of Glasgow  10.09.2023 – 20.12.2023 
Evgeny Shinder  Universität Bonn  
Fumiaki Suzuki  Leibniz Universität Hannover  01.10.2023 – 01.12.2023 
Roberto Svaldi  Università degli Studi di Milano  17.09.2023 – 08.12.2023 
Evgueni (Jenia) Tevelev  University of Massachusetts at Amherst  03.11.2023 – 13.11.2023 
Christoph Thiele  Universität Bonn  
Yukinobu Toda  Kavli IPMU, University of Tokyo  12.11.2023 – 18.11.2023 
Mauro Varesco  Universität Bonn  
Fei Xie  MPIM Bonn  11.09.2023 – 20.12.2023 
Ruijie Yang  HumboldtUniversität zu Berlin  11.09.2023 – 27.10.2023 
Shizhuo Zhang  MPIM Bonn  11.09.2023 – 20.12.2023 
Yu Zhao  Kavli IPMU  06.11.2023 – 10.11.2023 
Xiaolei Zhao  University of California, Santa Barbara  17.09.2023 – 01.12.2023 
PERSON 
AFFILIATION 
PERIOD OF STAY 
Anna Abasheva  Columbia University  10.09.2023 – 20.12.2023 
Younghan Bae  ETH Zürich  10.09.2023 – 20.12.2023 
Pietro Beri  Université Paris Cité  10.09.2023 – 15.09.2023 
Simone Billi  University of Bologna  10.09.2023 – 15.09.2023 
Alessio Bottini  Università di Roma Tor Vergata  11.09.2023 – 20.12.2023 
Ludovica Buelli  University of Genoa  10.09.2023 – 16.09.2023 
Chiara Camere  Università degli Studi di Milano  10.09.2023 – 17.09.2023 
Raymond Cheng  Gottfried Wilhelm Leibniz Universität Hannover  11.09.2023 – 20.12.2023 
Rodion Deev  Instytut Matematyczny PAN  10.09.2023 – 16.09.2023 
Hannah Dell  University of Edinburgh  10.09.2023 – 16.09.2023 
Andres Fernandez Herrero  Columbia University  10.09.2023 – 20.12.2023 
Alessandro Frassineti  Università di Bologna  10.09.2023 – 16.09.2023 
Sarah Frei  Dartmouth College  10.09.2023 – 14.10.2023 
Luca Giovenzana  Chemnitz University of Technology  10.09.2023 – 16.09.2023 
Franco Giovenzana  Université ParisSaclay  10.09.2023 – 16.09.2023 
Richard Haburcak  Dartmouth College  10.09.2023 – 20.12.2023 
Daniel Huybrechts  Universität Bonn  11.09.2023 – 20.12.2023 
Qingyuan Jiang  University of Edinburgh  10.09.2023 – 20.12.2023 
Tomohiro Karube  University of Tokyo  10.09.2023 – 28.11.2023 
Kohei Kikuta  Osaka University  10.09.2023 – 08.10.2023 
Johannes Krah  Universität Bielefeld  10.09.2023 – 20.12.2023 
Christian Lehn  TU Chemnitz  10.09.2023 – 14.09.2023 
Dion Leijnse  Universiteit van Amsterdam  10.09.2023 – 20.12.2023 
Shengxuan Liu  University of Warwick  10.09.2023 – 20.12.2023 
Irene Macías Tarrío  Universitat de Barcelona  10.09.2023 – 16.09.2023 
Pablo Magni  Universität Bielefeld  10.09.2023 – 20.12.2023 
Andreas Malmendier  Utah State University  
Luigi Martinelli  Université ParisSaclay  10.09.2023 – 20.12.2023 
Ana Victoria Martins Quedo  IMPA  10.09.2023 – 16.09.2023 
Mirko Mauri  IST Austria  10.09.2023 – 20.12.2023 
Martina Monti  University of Milano  11.09.2023 – 15.09.2023 
Stevell Muller  Saarland University  10.09.2023 – 16.09.2023 
Giacomo Nanni  Alma Mater Studiorum  Università di Bologna  10.09.2023 – 16.09.2023 
Erik Nikolov  Leibniz Universität Hannover  10.09.2023 – 15.09.2023 
Noah Olander  University of Amsterdam  10.09.2023 – 20.12.2023 
Genki Ouchi  Nagoya University  11.09.2023 – 02.11.2023 
Hyeonjun Park  Korea Institute for Advanced Study  11.09.2023 – 20.11.2023 
Nebojsa Pavic  Leibniz Universität Hannover  11.09.2023 – 20.12.2023 
Jack Petok  Dartmouth College  10.09.2023 – 15.12.2023 
Benedetta Piroddi  Università degli studi di Milano  10.09.2023 – 16.09.2023 
Wing Kei Poon  University of Bath  10.09.2023 – 16.09.2023 
Xuqiang Qin  University of North Carolina at Chapel Hill  10.09.2023 – 20.12.2023 
Nick Rekuski  Wayne State University  10.09.2023 – 16.09.2023 
Francesca Rizzo  Université Paris Cité  10.09.2023 – 16.09.2023 
Franco Rota  University of Glasgow  10.09.2023 – 20.12.2023 
Elena Sammarco  Università degli studi Roma Tre  10.09.2023 – 16.09.2023 
Sofia Tirabassi  Stockholm University  11.09.2023 – 15.09.2023 
Federico Tufo  Università degli studi di Bologna  10.09.2023 – 16.09.2023 
Alexandra Viktorova  KU Leuven  10.09.2023 – 16.09.2023 
Tomasz Wawak  Jagiellonian University  10.09.2023 – 15.09.2023 
Fei Xie  MPIM Bonn  11.09.2023 – 20.12.2023 
Ruijie Yang  HumboldtUniversität zu Berlin  11.09.2023 – 27.10.2023 
Shizhuo Zhang  MPIM Bonn  11.09.2023 – 20.12.2023 
Vanja Zuliani  Université ParisSaclay / SiSSA  10.09.2023 – 16.09.2023 
PERSON 
AFFILIATION 
PERIOD OF STAY 
Anna Abasheva  Columbia University  10.09.2023 – 20.12.2023 
Younghan Bae  ETH Zürich  10.09.2023 – 20.12.2023 
Anna Barbieri  Università di Verona  05.11.2023 – 16.11.2023 
Arend Bayer  The University of Edinburgh  05.11.2023 – 11.11.2023 
Marcello Bernardara  Institut de Mathématiques de Toulouse  Université Toulouse 3 Paul Sabatier  05.11.2023 – 09.11.2023 
Valeria Bertini  University of Genova  05.11.2023 – 16.11.2023 
Rudradip Biswas  University of Warwick  05.11.2023 – 11.11.2023 
Omer Bojan  Tel Aviv University (TAU)  05.11.2023 – 11.11.2023 
Lev Borisov  Rutgers University  05.11.2023 – 11.11.2023 
Alessio Bottini  Università di Roma Tor Vergata  11.09.2023 – 20.12.2023 
Igor Burban  University of Paderborn  05.11.2023 – 08.11.2023 
Sebastian CasalainaMartin  University of Colorado  06.11.2023 – 10.11.2023 
Raymond Cheng  Gottfried Wilhelm Leibniz Universität Hannover  11.09.2023 – 20.12.2023 
Francesco Denisi  Paris  
Daniele Faenzi  Université de Bourgogne  06.11.2023 – 11.11.2023 
Andres Fernandez Herrero  Columbia University  10.09.2023 – 20.12.2023 
Sarah Frei  Dartmouth College  05.11.2023 – 15.12.2023 
Annalisa Grossi  Paris  
Richard Haburcak  Dartmouth College  10.09.2023 – 20.12.2023 
James Hotchkiss  Columbia University  05.11.2023 – 11.11.2023 
Daniel Huybrechts  Universität Bonn  11.09.2023 – 20.12.2023 
Chen Jiang  Fudan University  06.11.2023 – 10.11.2023 
Qingyuan Jiang  University of Edinburgh  10.09.2023 – 20.12.2023 
Martin Kalck  University of Graz  29.10.2023 – 11.11.2023 
Tomohiro Karube  University of Tokyo  10.09.2023 – 28.11.2023 
Johannes Krah  Universität Bielefeld  10.09.2023 – 20.12.2023 
Dion Leijnse  Universiteit van Amsterdam  10.09.2023 – 20.12.2023 
Shengxuan Liu  University of Warwick  10.09.2023 – 20.12.2023 
Zhiyu Liu  Zhejiang University  20.10.2023 – 20.12.2023 
Pablo Magni  Universität Bielefeld  10.09.2023 – 20.12.2023 
Luigi Martinelli  Université ParisSaclay  10.09.2023 – 20.12.2023 
Mirko Mauri  IST Austria  10.09.2023 – 20.12.2023 
Noah Olander  University of Amsterdam  10.09.2023 – 20.12.2023 
Angela Ortega  Humboldt Universität  05.11.2023 – 10.11.2023 
Hyeonjun Park  Korea Institute for Advanced Study  11.09.2023 – 20.11.2023 
Nebojsa Pavic  Leibniz Universität Hannover  11.09.2023 – 20.12.2023 
Laura Pertusi  Università degli Studi di Milano  01.10.2023 – 30.11.2023 
Jack Petok  Dartmouth College  10.09.2023 – 15.12.2023 
Matthew Pressland  University of Glasgow  
Xuqiang Qin  University of North Carolina at Chapel Hill  10.09.2023 – 20.12.2023 
Franco Rota  University of Glasgow  10.09.2023 – 20.12.2023 
David Rydh  KTH Royal Institute of Technology  05.11.2023 – 10.11.2023 
Paolo Stellari  Universita' degli Studi di Milano  05.11.2023 – 10.11.2023 
Fumiaki Suzuki  Leibniz Universität Hannover  01.10.2023 – 01.12.2023 
Roberto Svaldi  Università degli Studi di Milano  17.09.2023 – 08.12.2023 
Evgueni (Jenia) Tevelev  University of Massachusetts at Amherst  03.11.2023 – 13.11.2023 
Giancarlo Urzúa  Pontificia Universidad Católica de Chile  05.11.2023 – 10.11.2023 
Filippo Viviani  University of Rome Tor Vergata  05.11.2023 – 08.11.2023 
Michael Wemyss  University of Glasgow  05.11.2023 – 09.11.2023 
Fei Xie  MPIM Bonn  11.09.2023 – 20.12.2023 
Shizhuo Zhang  MPIM Bonn  11.09.2023 – 20.12.2023 
Yu Zhao  Kavli IPMU  06.11.2023 – 10.11.2023 
Xiaolei Zhao  University of California, Santa Barbara  17.09.2023 – 01.12.2023 
PERSON 
AFFILIATION 
PERIOD OF STAY 
Anna Abasheva  Columbia University  10.09.2023 – 20.12.2023 
Younghan Bae  ETH Zürich  10.09.2023 – 20.12.2023 
Benjamin Bakker  University of Illinois at Chicago  14.11.2023 – 22.11.2023 
Alessio Bottini  Università di Roma Tor Vergata  11.09.2023 – 20.12.2023 
Cinzia Casagrande  Università di Torino  19.11.2023 – 24.11.2023 
Raymond Cheng  Gottfried Wilhelm Leibniz Universität Hannover  11.09.2023 – 20.12.2023 
Stéphane Druel  Université Claude Bernard Lyon 1  20.11.2023 – 25.11.2023 
Gavril Farkas  Humboldt Universität zu Berlin  19.11.2023 – 24.11.2023 
Andres Fernandez Herrero  Columbia University  10.09.2023 – 20.12.2023 
Soheyla Feyzbakhsh  Imperial College London  11.11.2023 – 03.12.2023 
Sarah Frei  Dartmouth College  05.11.2023 – 15.12.2023 
Lie Fu  University of Strasbourg  19.11.2023 – 24.11.2023 
Osamu Fujino  Kyoto University  19.11.2023 – 25.11.2023 
Cécile Gachet  HumboldtUniversität zu Berlin  19.11.2023 – 25.11.2023 
Francois Greer  Michigan State University  
Richard Haburcak  Dartmouth College  10.09.2023 – 20.12.2023 
Daniel Huybrechts  Universität Bonn  11.09.2023 – 20.12.2023 
Qingyuan Jiang  University of Edinburgh  10.09.2023 – 20.12.2023 
Junpeng Jiao  Tsinghua University  19.11.2023 – 25.11.2023 
Tomohiro Karube  University of Tokyo  10.09.2023 – 28.11.2023 
Tasuki Kinjo  Kyoto University  19.11.2023 – 25.11.2023 
Johannes Krah  Universität Bielefeld  10.09.2023 – 20.12.2023 
Dion Leijnse  Universiteit van Amsterdam  10.09.2023 – 20.12.2023 
Shengxuan Liu  University of Warwick  10.09.2023 – 20.12.2023 
Zhiyu Liu  Zhejiang University  20.10.2023 – 20.12.2023 
Eduard Looijenga  University of Chicago  19.11.2023 – 25.11.2023 
Pablo Magni  Universität Bielefeld  10.09.2023 – 20.12.2023 
Olivier Martin  Stony Brook University  18.11.2023 – 30.11.2023 
Luigi Martinelli  Université ParisSaclay  10.09.2023 – 20.12.2023 
Davesh Maulik  MIT  17.11.2023 – 22.11.2023 
Mirko Mauri  IST Austria  10.09.2023 – 20.12.2023 
Noah Olander  University of Amsterdam  10.09.2023 – 20.12.2023 
Hyeonjun Park  Korea Institute for Advanced Study  11.09.2023 – 20.11.2023 
Nebojsa Pavic  Leibniz Universität Hannover  11.09.2023 – 20.12.2023 
Laura Pertusi  Università degli Studi di Milano  01.10.2023 – 30.11.2023 
Jack Petok  Dartmouth College  10.09.2023 – 15.12.2023 
Brent Pym  McGill University  19.11.2023 – 21.11.2023 
Xuqiang Qin  University of North Carolina at Chapel Hill  10.09.2023 – 20.12.2023 
Franco Rota  University of Glasgow  10.09.2023 – 20.12.2023 
Junliang Shen  Yale University  19.11.2023 – 25.11.2023 
Fumiaki Suzuki  Leibniz Universität Hannover  01.10.2023 – 01.12.2023 
Roberto Svaldi  Università degli Studi di Milano  17.09.2023 – 08.12.2023 
Sho Tanimoto  Nagoya University  19.11.2023 – 24.11.2023 
Salim Tayou  Harvard University  19.11.2023 – 25.11.2023 
Michael Temkin  Hebrew University  19.11.2023 – 23.11.2023 
Claire Voisin  Institut de mathématiques de JussieuParis rive gauche  19.11.2023 – 24.11.2023 
Fei Xie  MPIM Bonn  11.09.2023 – 20.12.2023 
Ziquan Yang  University of WisconsinMadison  19.11.2023 – 25.11.2023 
Shizhuo Zhang  MPIM Bonn  11.09.2023 – 20.12.2023 
Xiaolei Zhao  University of California, Santa Barbara  17.09.2023 – 01.12.2023 
Venue: HIM lecture hall, Poppelsdorfer Allee 45, Bonn
Organizers: Raymond Cheng, Sarah Frei, Mirko Mauri, Laura Pertusi
September 21, 2023 (CEST)
10:30  11:30 am Mauro Varesco
Title: Algebraicity of Hodge similitudes and the Hodge conjecture for Kum^2type varieties
Abstract: In this talk, we will introduce the notion of Hodge similitudes between polarized Hodge structures of K3type. After recalling the construction of KugaSatake varieties associated to polarized Hodge structures of K3type, we will prove that it is functorial with respect to Hodge similitudes. This will be used to deduce the algebraicity of Hodge similitudes of transcendental lattices of hyperkähler manifolds of generalized Kummer type. As a corollary, we will show how this implies the Hodge conjecture for Kum^2type varieties. This last application is product of a joint work with Floccari Salvatore.
21:00 – 22:00 pm Mirko Mauri
Title: On the geometric P=W conjecture
Abstract: The geometric P = W conjecture is a conjectural description of the asymptotic behavior of a celebrated correspondence in nonabelian Hodge theory. In a joint work with Enrica Mazzon and Matthew Stevenson, we establish the full geometric conjecture for compact Riemann surfaces of genus one, and obtain partial results in arbitrary genus: this is the first nontrivial evidence of the conjecture for compact Riemann surfaces. To this end, we employ nonArchimedean, birational and degeneration techniques to study the topology of the dual boundary complex of certain character varieties.
September 26, 2023 (CEST)
3:00 – 4:00 pm Reinder Meinsma
Title: Derived equivalence for elliptic K3 surfaces and Jacobians
Abstract: We present a detailed study of FourierMukai partners of elliptic K3 surfaces. One way to produce FourierMukai partners of elliptic K3 surfaces is by taking Jacobians. We answer the question of whether every FourierMukai partner is obtained in this way. This question was raised by Hassett and Tschinkel in 2015. We fully classify elliptic fibrations on FourierMukai partners in terms of Hodgetheoretic data, similar to the Derived Torelli Theorem that describes FourierMukai partners. This classification has an explicit computable form in Picard rank two, building on the work of Stellari and Van Geemen. We prove that for a large class of Picard rank 2 elliptic K3 surfaces all FourierMukai partners are Jacobians. However, we also show that there exist many elliptic K3 surfaces with FourierMukai partners which are not Jacobians of the original K3 surface. This is joint work with Evgeny Shinder.
September 27, 2023 (CEST)
2:00 – 3:00 pm
September 28, 2023 (CEST)
10:30 – 11:30 am Noah Olander
Title: Fully faithful functors and dimension
Abstract: Can one embed the derived category of a higher dimensional variety into the derived category of a lower dimensional variety? The expected answer was no. We give a simple proof and prove new cases of a conjecture of Orlov along the way.
September 25, 27, 29; 2023 (CEST)
3:00 – 4:00 pm Philip Engel
Title: Compact moduli of K3 surfaces
Abstract: For each d > 0, there is a 19dimensional moduli space F_{2d} of K3 surfaces, with an ample line bundle of degree 2d. Choosing an ample divisor in a canonical way on each such K3 surface, the minimal model program provides a "KSBA" compactification of F_{2d}. On the other hand, the Hodge theory of K3 surfaces implies that F_{2d}=Γ\D is a Type IV arithmetic quotient/orthogonal Shimura variety. In this capacity, it has a variety of compactifications: BailyBorel, toroidal, semitoroidal. Can these two types of compactifications ever be identified?
The first lecture will introduce K3 surfaces and their oneparameter degenerations, in particular, semistable (aka Kulikov) models. In analogy with how stable graphs encode degenerations of curves, we will describe a way to combinatorially encode the data of a degeneration, using integralaffine structures on the sphere.
The second lecture will focus on the geometry of moduli spaces F_{2d} and their compactifications, from both the Hodgetheoretic and MMP perspectives. We will discuss degeneration of the period map, and give some explicit examples of (semi)toroidal compactifications, for F_{2} and for moduli of elliptic K3 surfaces.
The third lecture will introduce the notion of a "recognizable divisor". These are divisors chosen on the generic polarized K3 surface whose KSBA compactifications are Hodgetheoretic. We will give examples for F_{2} and for moduli of elliptic K3 surfaces. Then we will discuss the general theory of recognizable divisors, and how it can be applied to compactify F_{2d}.
October 10, 2023 (CEST)
3:00  4:00 pm Raymond Cheng
Title: qbic hypersurfaces
Abstract: Let’s count: 1, 2, q+1. The eponymous objects are special projective hypersurfaces of degree q+1, where q is a power of the positive ground field characteristic. This talk will sketch an analogy between the geometry of qbic hypersurfaces and that of quadric and cubic hypersurfaces. For instance, the moduli spaces of linear spaces in qbics are smooth and themselves have rich geometry. In the case of qbic threefolds, I will describe an analogue of result of Clemens and Griffiths, which relates the intermediate Jacobian of the qbic with the Albanese of its surface of lines.
October 11, 2023 (CEST)
1:30  2:30 pm Lisa Marquand
Title: An overview of the LSV construction
October 12, 2023 (CEST)
10:30  11:30 am Genki Ouchi
Title: Cubic fourfolds and K3 surfaces with large automorphism groups
Abstract: Relations between cubic fourfolds and K3 surfaces are described by Hodge theory and derived categories. Using Hodge theory and derived
categories, we can show that cubic fourfolds and associated K3 surfaces
share their symmetries, which are related with Mathieu groups and Conway
groups. In this talk, we find pairs of a cubic fourfold and a K3 surface
sharing large symplectic automorphism groups via Bridgeland stability
conditions on K3 surfaces.
October 9, 11, 13; 2023 (CEST)
3:00  4:00 pm Hyeonjun Park
Title: Shifted Symplectic Structures
Abstract: This minicourse aims to introduce shifted symplectic structures in derived algebraic geometry and their applications to DonaldsonThomas theory of CalabiYau varieties.
The first lecture will cover the background on derived algebraic geometry. Heuristically, derived moduli spaces are infinitesimal thickening of moduli spaces whose cotangent complexes govern the higherorder deformation theory. We will present various derived moduli spaces and their cotangent complexes, including the moduli spaces of sheaves (or complexes), stable maps, Gbundles, and Higgs bundles.
The second lecture will focus on the shifted symplectic geometry. There are natural extensions of symplectic structures, Lagrangians, Lagrangian fibrations, and Lagrangian correspondences in the shifted symplectic setting. We will provide various examples of these structures arising in moduli spaces and local structure theorems for them. I will also explain how to pushforward symplectic fibrations along base changes, which allows us to construct symplectic quotients and symplectic zero loci.
The last lecture will provide applications to DonaldsonThomas theory. For CalabiYau 3folds, moduli spaces of sheaves are locally critical loci, and their perverse sheaves of vanishing cycles glue globally. This gives us categorical DT3 invariants, which are related to the singularity of moduli spaces. For CalabiYau 4folds, moduli spaces of sheaves carry special cycle classes which are heuristically the fundamental cycles of Lagrangians. This gives us numerical DT4 invariants, which are invariant along the deformations of CalabiYau 4folds for which the (0,4)Hodge pieces of the second Chern characters remain zero.
Degeneration seminar
October 14, 2023 (CEST)
October 13, 20, 27; 2023 (CEST)
November 3, 17; 2023 (CET)
December 8, 15; 2023 (CET)
10:30 – 12:00
For more informations: Schedule and Abstracts
Monday October 16, 15:0016:00, HIM lecture hall
Speaker: Tudor Ciurca
Title: Irrationality of cubic threefolds in characteristic 2
Abstract: In 1972 Clemens and Griffiths gave a formidable proof that a smooth cubic threefold over C is irrational. The proof was soon after adapted to any algebraically closed field of characteristic not 2 using algebraic methods. I will finish the story by extending the proof to the case of characteristic 2. As arithmetic applications, we answer a question of Deligne regarding arithmetic Torelli maps and establish the Shafarevich conjecture for cubic threefolds over function fields of characteristic 2.
Wednesday October 18, 13:3014:30, HIM lecture hall
Speaker: Jack Petok
Title: LSV: Hyperkahler structure
Friday October 20, 15:0016:00, HIM lecture hall
Speaker: Fei Xie
Title: Quadric bundles over smooth surfaces
Abstract: For a flat quadric bundle of relative even dimension with fibers of corank at most 1, there is a well established relation between its derived category and its relative Hilbert scheme of maximal isotropic subspaces (or its relative moduli of spinor bundles). For a smooth 2mfold with the structure of a quadric bundle over a smooth surface, there is a finite number of fibers with corank 2 and this relation fails. I will discuss how to fix the relation in this case.
Monday October 23, 15:0016:00, HIM lecture hall
Speaker: Fumiaki Suzuki
Title: Maximal linear spaces for pencils of quadrics and rationality
Abstract: Over an arbitrary field k of odd characteristic, let X be a smooth complete intersection of two quadrics in P^{2g+1}. For every g at least 2, we show that the existence of a (g1)plane, defined over k, on X may be characterized by krationality of a certain 3dimensional subvariety of the Fano scheme of (g2)planes on X, generalizing the g = 2 case due to HassettTschinkel and BenoistWittenberg. We also present a related result on krationality of the Fano schemes of nonmaximal linear spaces on X. This is joint work in progress with Lena Ji.
Wednesday October 25, 13:3014:30, HIM lecture hall
Speaker: Moritz Hartlieb
Title: LSV: Pfaffians and OG10 type
Friday October 27, 15:0016:00, HIM lecture hall
Speaker: Shengxuan Liu
Title: A note on spherical bundles on K3 surfaces
Abstract: Let S be a K3 surface with the bounded derived category D^b(S). Let E be a spherical object in D^b(S). Then there always exists a nonzero object F satisfying RHom(E,F)=0. Further, there exists a spherical bundle E on some K3 surfaces that is unstable with respect to all polarization on S. Also we “count” spherical bundles with a fixed Mukai vector. These provide (partial) answers to some questions of Huybrechts. This is a joint work with Chunyi Li.
Tuesday October 31, 15:0016:00, HIM lecture hall
Speaker: Jack Petok
Title: Zeta function of the K3 category of a cubic
Abstract: We study the arithmetic of the K3 category associated to a cubic fourfold over a nonalgebraically closed field k. We start by constructing the Mukai structure of this K3 category with a natural action of Galois. For k a finite field, this lets us define the zeta function of a K3 category, an invariant under FMequivalence of K3 categories. We provide a characterization of those cubic fourfolds whose K3 category has zeta function arising from a K3 surface defined over k. One interesting outcome is that the zeta function does not always detect the geometricity of the K3 category. This is joint work with Asher Auel.
Wednesday November 2, 13:3014:30, HIM lecture hall
Speaker: Xuqiang Qin
Title: LLSvS Eightfolds
Thursday November 2, 10:3011:30, HIM lecture hall
Speaker: Franco Rota
Title: Noncommutative deformations and contractibility of rational curves
Abstract: When can we contract a rational curve C? The situation is much more complicated for threefolds than it is for surfaces: Jimenez gives examples of (3,1)rational curves neither contract nor move. Their behaviour is controlled by the functor of noncommutative deformations of C, which conjecturally controls exactly their contractibility.
I will report on work in progress with M. Wemyss, and reinterpret some of Jimenez's examples in terms of noncommutative deformations.
Friday November 3 and November 17, 14:1516:00 (with 15 minutes break), HIM lecture hall
Speaker: Nebojsa Pavic
Title: Derived categories and singularities
Abstract: In this minicourse, we discuss the current state of the art on semiorthogonal decompositions of derived categories of singular varieties. We define notions such as categorical absorptions and Kawamata type semiorthogonal decompositions and we give examples and obstructions to such decompositions.
In the first lecture we give a short introduction to the topic by providing explicit examples of semiorthogonal decompositions of curves and surfaces with mild isolated singularities. Along the way, we introduce the notions categorical absorptions and Kawamata type semiorthogonal decompositions. We then proceed by recalling the singularity category of a variety, state general properties about this category and discuss necessary conditions for a projective variety admitting a Kawamata type decomposition in terms of the singularity category. We then rephrase the necessary assumption on the singularity category in terms Grothendieck groups. As a consequence, we show that the defect of a projective variety with certain singularity types is an obstruction to Kawamata type decompositions.
In the second lecture, we explain the relation between the derived category of a singular variety and its resolution and we state the BondalOrlov localization conjecture. Moreover, we explain how the localization conjecture descends to a semiorthogonal decomposition on the singularity. We then talk about sufficient conditions on resolutions of nodal ndimensional singularities and ndimensional quotient singularities of type 1/n(1^n), such that a "nice" categorical absorption, respectively Kawamata type decomposition is induced on the singularity. We explain briefly the idea of the proofs and we give examples.
Abstracts
Monday 13 November and Wednesday 15 November, 10:3011:30, 15:0016:00, HIM lecture hall
Speaker: Tudor Padurariu and Yukinobu Toda
Title: QuasiBPS categories
Tuesday 14 November, 15:0016:00, HIM lecture hall
Speaker: Stefano Filipazzi
Title: On the boundedness of elliptic CalabiYau threefolds
Abstract:
In this talk, we will discuss the boundedness of CalabiYau threefolds admitting an elliptic fibration. First, we will review the notion of boundedness in birational geometry and its weak forms. Then, we will switch focus to CalabiYau varieties and discuss how the KawamataMorrison cone conjecture comes in the picture when studying boundedness properties for this class of varieties. To conclude, we will see how this circle of ideas applies to the case of elliptic CalabiYau threefolds. This talk is based on work joint with C.D. Hacon and R. Svaldi.
Wednesday November 15, 13:3014:30, HIM lecture hall
Speaker: Richard HaburcakAufklappText
Thursday November 16, 10:3011:30, HIM lecture hall
Speaker: Andres Fernandez Herrero
Title: Towards curve counting on the classifying stack BGL_n
Friday November 17, 14:1516:00 (with 15 minutes break), HIM lecture hall
Speaker: Nebojsa Pavic
Title: Derived categories and singularities (second lecture)
Abstract: In this minicourse, we discuss the current state of the art on semiorthogonal decompositions of derived categories of singular varieties. We define notions such as categorical absorptions and Kawamata type semiorthogonal decompositions and we give examples and obstructions to such decompositions.
In the first lecture we give a short introduction to the topic by providing explicit examples of semiorthogonal decompositions of curves and surfaces with mild isolated singularities. Along the way, we introduce the notions categorical absorptions and Kawamata type semiorthogonal decompositions. We then proceed by recalling the singularity category of a variety, state general properties about this category and discuss necessary conditions for a projective variety admitting a Kawamata type decomposition in terms of the singularity category. We then rephrase the necessary assumption on the singularity category in terms Grothendieck groups. As a consequence, we show that the defect of a projective variety with certain singularity types is an obstruction to Kawamata type decompositions.
In the second lecture, we explain the relation between the derived category of a singular variety and its resolution and we state the BondalOrlov localization conjecture. Moreover, we explain how the localization conjecture descends to a semiorthogonal decomposition on the singularity. We then talk about sufficient conditions on resolutions of nodal ndimensional singularities and ndimensional quotient singularities of type 1/n(1^n), such that a "nice" categorical absorption, respectively Kawamata type decomposition is induced on the singularity. We explain briefly the idea of the proofs and we give examples.
No. 
Author(s) 
Title 
Preprint 
Publication 
2023c01  Lin, X.; Zhang, S.  Serre algebra, matrix factorization and categorical Torelli theorem for hypersurfaces  2310.09927  
2023c02  Auel, A.; Haburcak, R.; Larson, H.  Maximal BrillNoether loci via the gonality stratification  2310.09954 

2023c03  Arena, V.; Canning, S.; Clader, E.; Haburcak, R.; Li, A.Q.; Mok, S.C.; Tamborini, C.  Holomorphic forms and nontautological cycles on moduli spaces of curves  2402.03874  
2023c04  Bayer, A.; Chen, H.; Jiang, Q. 
Brill–Noether Theory of Hilbert Schemes of Points on Surfaces 
2304.12016 
International Mathematics Research Notices (2023), rnad263, https://doi.org/10.1093/imrn/rnad263 
2023c05  Hu, X.; Krah, J.  Autoequivalences of BlowUps of Minimal Surfaces  2310.17938  
2023c06  Li, C.; Liu, S.  A Note on Spherical Bundles on K3 Surfaces  2310.10842  
2023c07  Dell, H.; Jacovskis, A.; Rota, F.  Cyclic covers: Hodge theory and categorical Torelli theorems  2310.13651  
2023c08  Fan, C.; Liu, Z.; Ma, S.K.  Stability manifolds of Kuznetsov components of prime Fano threefolds  2310.16950  
2023c09  Moschetti, R.; Rota, F.; Schaffler, L.  The nondegeneracy invariant of Brandhorst and Shimada families of Enriques surfaces  2309.14981 

2023c10  Bae, Y.; Maulik, M.; Shen, J.; Yin, Q.  On generalized Beauville decompositions  2402.08861 

2023c11  Bud, A.; Haburcak, R.  Maximal BrillNoether loci via degenerations and double covers  2404.15066 
September 11  15, 2023
Venue: HIM lecture hall (Poppelsdorfer Allee 45, Bonn)
Organizers: Sarah Frei (Dartmouth), Richard Haburcak (Dartmouth), Genki Ouchi (Nagoya), Jack Petok (Dartmouth), and Xuqiang Qin (UNC)
Lecturers:
 Chiara Camere (Milano)
 Daniel Huybrechts (Bonn)
 Christian Lehn (TU Chemnitz)
 Sofia Tirabassi (Stockholm)
Description: The focus of the school will be K3 surfaces, hyperkähler manifolds, and cubic fourfolds. A major problem in the geometry of classical algebraic varieties is the rationality problem for cubic hypersurfaces of dimension 4. While it remains to be seen whether all cubic fourfolds are rational, a rich framework of theorems and conjectures has been developed to study this problem, relating cubic fourfolds with K3 surfaces as well as other hyperkähler manifolds. Some of these relationships are described by classical algebraic geometric constructions, and in the last few decades tools such as Hodge theory, derived categories, and moduli theory have proven indispensable in studying these connections.
The school aims to introduce participants to this circle of ideas, and will consist of 4 expository minicourses and short introductory talks from some participants of the Junior Trimester Program. The lectures will be aimed at advanced graduate students and postdocs with a background in algebraic geometry.
November 06  10, 2023
Venue: HIM lecture hall, Poppelsdorfer Allee 45, Bonn
On November 8th different location! Endenicher Allee 60, Raum 1.016 (LipschitzSaal)
Organizers: Martin Kalck (Graz), Laura Pertusi (Milano), Shizhuo Zhang (Bonn)
Speakers:
 Anna Barbieri
 Arend Bayer
 Marcello Bernardara
 Lev Borisov
 Igor Burban
 Sebastian CasalainaMartin
 Daniele Faenzi
 James Hotchkiss
 Chen Jiang
 Johannes Krah
 Zhiyu Liu
 Angela Ortega
 Nebojsa Pavic
 David Rydh
 Evgeny Shinder
 Paolo Stellari
 Jenia Tevelev
 Giancarlo Urzua
 Filippo Viviani
 Michael Wemyss
Description: The study of derived categories has a central role in algebraic geometry. A celebrated theorem by Bondal and Orlov states that smooth projective varieties with ample (anti)canonical bundle and equivalent bounded derived categories are isomorphic. This statement is not true in general, but weaker formulations involving the notion of semiorthogonal decomposition have been proved in many interesting geometric contexts. Furthermore, moduli spaces of stable objects in the derived category provide a way to construct new smooth projective varieties and to study their birational geometry by wallcrossing. In the framework of resolutions of singularities, derived categories can be used to characterize the singularity of a variety. The aim of this workshop is to bring together experts working in these fields to discuss the recent developments in the theory and exchange new ideas.
November 20  24, 2023
Venue: HIM lecture hall, Poppelsdorfer Allee 45, Bonn
Organizers: Raymond Cheng (Hannover), Mirko Mauri (ISTA), Roberto Svaldi (Milan)
Speakers:
 Benjamin Bakker (tbc)
 Cinzia Casagrande
 Stéphane Druel
 Gabi Farkas
 Lie Fu
 Osamu Fujino
 Cécile Gachet
 Jiao Junpeng
 Tasuki Kinjo
 Eduard Looijenga
 Davesh Maulik
 Brent Pym
 Junliang Shen
 Sho Tanimoto
 Salim Tayou
 Michael Temkin
 Claire Voisin
 Ziquan Yang
Description: Breakthroughs in algebraic geometry are often achieved after a dramatic change of viewpoint, or by exporting powerful techniques from one field of research to the other, thus providing a new perspective and applications of the original tools. For instance, in the 1980s Mori showed the existence of complex rational curves on Fano varieties via reduction to positive characteristic, the celebrated BendandBreak. The theory of foliations was used by Bogomolov and later McQuillan to provide new significant evidence of the GreenGriffiths Conjecture. More recently, Hodge theoretic techniques are reshaping our understanding of hyperkaehler geometry. These are just a few examples among numerous fruitful synergies that have significantly advanced the field.
The workshop will survey several area of algebraic geometry with the goal of fostering interactions between different research groups. The program will focus on the following themes: birational geometry, foliations, hyperkahler geometry, Hodge theory, stacks, and positive characteristic methods.