5 jun 2022 - 10 jun 2022
Trento/Levico Terme
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Dear colleagues,
we are organising an in-person school/workshop on Moduli Spaces and Stability Conditions to be held in Trento/Levico Terme, Italy, on 5-10 June, 2022 (with arrival on Sunday 5th before dinner and departure on Friday 10th after lunch), in the framework of the CIRM scientific program ( https://cirm.fbk.eu/).
The mini-courses of the school will be scheduled from Monday June 6th to Thursday morning June 9th. Participants are expected to have a solid background in abstract Algebraic Geometry, but no previous exposure to Bridgeland stability conditions is required. Please find below the preliminary program of the school.
Enrico Arbarello: Introduction to Bridgeland stability conditions.
Abstract: Definitions and basic properties. The wall and chamber structure. Stability
conditions on K3 surfaces. The (\alpha, \beta)-plane. Computation of walls and
wall-crossing in specific examples. Applications to classical problems for curves
and K3 surfaces.
Emanuele Macrì: Bridgeland stability conditions on higher dimensional varieties
and applications.
Abstract: The construction of Bridgeland stability conditions on higher dimensional
varieties is an open question, already in the threefold case. There are though many
examples where such existence is known and this already turned out to have
interesting applications, for example to Clifford-type bounds for vector bundles on
curves and to counting invariants. We will review the basic framework to show
existence of stability conditions, by using the notion of tilt-stability, state the main
conjectural inequality which would imply the existence in the threefold case, and
present examples where such inequality is proved, in particular the quintic
threefold. Finally, we will discuss the applications.
Laura Pertusi: Residual components for Fano threefolds and fourfolds.
Abstract: As shown by Kuznetsov, the bounded derived category of a prime Fano
variety admits a semiorthogonal decomposition whose non-trivial residual
component encodes much information about the geometry of the variety. In this
mini-course we will focus on the case of prime Fano threefolds of index 1 and 2, on
cubic fourfolds and Gushel--Mukai fourfolds. We will discuss the construction of
Bridgeland stability conditions on their residual components, the geometry of the
associated moduli spaces and some applications.
Giulia Saccà: Wall-crossing and local structure of moduli spaces on K3 surfaces.
Abstract: In this course I will survey the theory of Bayer-Macrì describing wall-
crossing on moduli spaces of Bridgeland stable objects on K3 surfaces and then
focus on the local structure of singular moduli spaces that arise in this context.
The workshop will take place on Thursday afternoon June 9th and on Friday
morning June 10th. The speakers will be Soheyla Feyzbakhsh, Alexander
Kuznetsov (to be confirmed), Alexander Perry, Xiaolei Zhao.
Due to Covid restrictions, there will be a maximum number of participants. If you are interested in attending the school/workshop, please send an email to modulicirm(AT)gmail.com no later than February 28th, 2022. There are also a few grants available to cover full board (but not travel) expenses to young participants. If you wish to apply for a grant, please attach an updated scientific CV to your email. We will confirm your participation and provide you with all the details needed for reservation by writing back to you no later than March 15th, 2022. Finally, we point out that in the following week (13-17 June, 2022) the CIRM conference New Perspectives on Hyperkähler Manifolds. A Celebration of Dimitri Markushevich's 60+2nd Birthday will take place in the same location. For further information please check the web page https://indico.cs.dm.unipi.it/event/13/.
Best regards,
The Scientific Committee
Gilberto Bini and Claudio Fontanari
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