ERC Synergy Grant

Winter 2022/23

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• Joint working group (Bonn-Paris): Topics in hyperkähler geometry. 

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Friday 14:00-16:00. The seminar will be organized as a hybrid event. Typically we will have two speakers with talks of 50 min each. In Bonn, the talks will be delivered/streamed in Lipschitz Saal, Endenicher Allee 60.

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14 October: This session will be replaced by the seminar talk by Chenyu Bai on Thursday 13 October:

Applications d'Abel--Jacobi des familles lagrangiennes, 14:00 in the Séminaire de géométrie algébrique

21 October: LLV algebra acting in Chow: Talks by G. Oberdieck and Y. Kim (Bonn)

28 October: No seminar (school holidays in France)

04 November: No seminar (school holidays in France)

11 November: This session will be replaced by the seminar talk by Pietro Beri on Thursday 10 November

Kodaira dimension of some moduli spaces of polarized hyperkähler manifolds 14:00 in the Séminaire de géométrie algébrique

18 November: Cones and birational maps. Talks by Francesco Denisi & Yajnaseni Dutta/Dominique Mattei

​25 November: Filtration of Chow groups: Talks by Charles Vial & Zhiyuan Li

02 December: André motives of hyperkähler varieties: Talks by Salvatore Floccari & Andrey Soldatenkov

​09 December: Giulia Saccà: cancelled

 

 

​12 & 13 January: Special Paris addition:

 

 Thursday

 E. Shinder (14:00, ENS, salle W): Motivic invariants of birational maps

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Abstract: I explain how exceptional divisors of birational maps can be assembled into invariants taking values in the Grothendieck ring of varieties and in the Kontsevich-Tschinkel ring. Using these invariants we prove new results about the structure of the groups of birational isomorphisms; in particular, we prove that various Cremona groups are not generated by regularizable elements. This is joint work with Hsueh-Yung Lin.

 

Rui-jie Yang (16:00, ENS, salle W): The Riemann-Schottky problem via singularities of theta divisors

Abstract: The Riemann-Schottky problem is the problem of determining which principally polarized abelian varieties (PPAV) arise as Jacobians of curves. Riemann showed that the theta divisor on the Jacobian of a hyperelliptic curve has singularity of codimension three. A hundred years later, Debarre conjectured that any irreducible PPAV with such property must come from hyperelliptic curves. In this talk, I will discuss a refinement of this conjecture by Casalaina-Martin and provide a partial solution. To achieve this, we develop a complete theory of higher multiplier ideals for Q-divisors, using Sabbah-Schnell's theory of complex Hodge modules. This is joint work with Christian Schnell.

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Friday

Alessio Bottini (10:00, Jussieu, salle 411, 15-16): Towards a modular construction of OG10

 

Abstract: Moduli spaces of sheaves on holomorphic symplectic surfaces are examples of hyper-Kähler manifolds. Sheaves on higher dimensional hyper-Kähler manifolds have proven much more difficult to study, although it is believed that their moduli spaces could lead to new examples. Recently, the introduction of modular and atomic sheaves has lead to developments in this subject. They are special classes of sheaves on hyper-Kähler manifolds with beautiful properties, and they make good candidates to have well-behaved moduli spaces. In this talk, I will go over these notions and give the first example of a non-rigid atomic stable bundle on a hyper-Kähler fourfold whose moduli space is birational to OG10.

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Gianluca Pacienza (11:00, Jussieu, salle 411, 15-16): On the cone conjecture for Enriques manifolds. 

Abstract: Enriques manifolds are non simply connected manifolds whose universal cover is irreducible holomorphic symplectic, and as such they are natural generalizations of Enriques surfaces. In this talk I will report on a joint work in progress with Alessandra Sarti in which  we study the Morrison-Kawamata cone conjecture for such manifolds using the analogous result (established by Amerik-Verbitsky) for their universal cover.

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zoom: https://uni-bonn.zoom.us/j/62174064883?pwd=TUZiWWFXUXpXcUJIRlJBdzBQUDFyQT09

Meeting-ID: 621 7406 4883

Kenncode: 111260

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Winter 2021/22

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• Joint working group (Bonn-Paris): Topics in hyperkähler geometry. 

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Friday 10:00-12:00 The seminar will be organized as a hybrid event. In Bonn, the talks will be delivered/streamed in Lipschitz Saal, Endenicher Allee 60.

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19 November: Gushel-Mukai varieties I (Pietro Beri & Dominique Mattei) notes

26 November: Derived categories of Gushel-Mukai varieties (Dmitrii Pirozhkov) notes

3 December: Gushel-Mukai varieties II  (Pietro Beri & Olivier Debarre) notes

10 December: Characteristic foliations (Fabrizio Anella & Daniel Huybrechts) notes

17 December: Dual fibrations (Thorsten Beckmann & Daniel Huybrechts) notes

14 January: Vector bundles on hyperkähler manifolds (Alessio Bottini & Emanuele Macrì)

21 January: Integral Hodge conjecture (Ignacio Barros & Claire Voisin)

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Zoom: https://uni-bonn.zoom.us/j/99037487887?pwd=TVZkNm9sTXZzMkJPMjNKZjdnTExrUT09

Meeting-ID: 990 3748 7887

Kenncode: 596770

Summer 2021

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• Joint working group (Bonn-Paris): Topics in hyperkähler geometry

 

The notes of the talks can be downloaded here.

 

Friday 10:00-12:00

16 April: F. Anella & D. Huybrechts: Semipositive line bundles (Campana-Peternell-Oguiso and Verbitsky)

23 April: A. Bottini: Looijenga-Lunts algebra and Verbitsky's theorem

30 April: P. Beri & O. Debarre: Betti numbers (Guan, Salamon,...)

14 May: M. Varesco & C. Voisin: Kuga-Satake (classical theory and work of Markman-O'Grady)

21 May: T. Beckmann: Derived categories and derived monodromy (work of Taelman)

4 June: D. Huybrechts & M. Mauri: Lagrangian fibrations (Matsushita, Shen & Yin) 

11 June: G. Oberdieck & J. Song: Representation theory and cohomology (Green-Kim-Laza-Robles)

      

 

• SAG (Bonn)

• SAGA (Orsay)

• SGA (Paris)