Geometry, Algebra and Combinatorics of Moduli Spaces and Configurations V

This is the fifth edition of the winter school held in Toblach in winter 2017, winter 2018, winter 2019 and winter 2020. There will be three 5 hours minicourses, some talks and ample time for discussion.

Mini-courses

• Stephen Coughlan, Institute of Mathematics, Polish Academy of Sciences, Krakow Branch, Poland, Weighted projective spaces and Cox coordinates (notes).
• Peter Fiebig, Friedrich-Alexander-Universität, Algebraic and quantum tilting modules.
• Mario Salvetti, Università di Pisa, Around the K(π, 1) conjecture for Artin groups (first part, second part, third part).

Talks:

• Martina Lanini, Università di Roma 'Tor Vergata'. Symmetric quivers and symmetric varieties. [show abstract]

  Abstract: In this talk I will report on ongoing joint work with Ryan Kinser and Jenna Rajchgot on varieties of symmetric quiver representations. These varieties are acted upon by a reductive group via change of basis, and it is natural to ask for a parametrisation of the orbits, for the closure inclusion relation among them, for information about the singularities arising in orbit closures. Since the Eighties, same (and further) questions about representation varieties for type A quivers have been attacked by relating such varieties to Schubert varieties in type A flag varieties (Zelevinsky, Bobinski-Zwara, ...). I will explain that in the symmetric setting it is possible to interpret the above questions in terms of certain symmetric varieties. More precisely, we show that singularities of an orbit closure of a symmetric quiver representation variety are smoothly equivalent to singularities of an appropriate Borel orbit closure in a symmetric variety. [Hide abstract]

• Roberto Pagaria, Università di Bologna. Decomposition theorem for Hitchin fibrations and non-integral partition poset. [show abstract]

  Abstract: In this talk, we will introduce the moduli space of semistable Higgs bundles on a compact Riemann surface and the associated Hitchin fibration. The intersection complex of this moduli space depends on certain local systems supported on some subvarieties. We explicitly describe the support, the rank, and the monodromy of these local systems in terms of the non-integral partitions posets. The talk will focus on this combinatorial description: we count integral points in graphical zonotopes, prove the shellability of the aforementioned posets and finally prove an identity between representations. [Hide abstract]

Schedule


You can download a pdf with the schedule of the winter school here.

Patercipants:

• Evienia Bazzocchi, Università di Bologna
• Houcine Ben Dali, Université de Lorraine/Université de Paris
• Simone Billi, Università di Bologna
• Margot Bruneaux, École Normale Supérieure of Paris
• Luca Bruni, Scuola Normale
• Jacopo Burelli, Università di Pisa
• Nicoletta Cantarini, Università di Bologna
• Luigi Caputi, Czech Academy of Sciences
• Luca Casarin, Università di Roma 'La Sapienza'
• Fabrizio Caselli, Università di Bologna
• Azzurra Ciliberti, Università di Roma 'La Sapienza'
• Elena Collacciani, Università di Padova
• Martina Costa Cesari, Università di Padova
• Stephen Coughlan, University of Bayreuth
• Michele D'Adderio, Università di Pisa
• Sabino Di Trani, Università di Roma 'La Sapienza'
• Giacomo Hermes Ferraro, Università di Roma 'La Sapienza'
• Peter Fiebig, Friedrich-Alexander-Universität
• Marco Franciosi, Università di Pisa
• Luca Francone, Université de Lyon 1
• Giovanni Gaiffi, Università di Pisa
• Nikita Geldhauser, LMU Munich
• Felix Göbler, Goethe University Frankfurt
• Davide Gori, Università di Roma 'La Sapienza'
• Giovanni Giuseppe Grimaldi, Università 'Federico II' di Napoli
• Paolo Grossi, Università di Pavia
• Lorenzo Guerra, Università di Roma 'Tor Vergata'
• Giovanni Interdonato, Università di Pisa/Scuola normale
• Alessandro Iraci, Università di Pisa
• Martina Lanini, Università di Roma 'Tor Vergata'
• Federico Lazzeri, Università di Pisa
• Fabio Lischka, Universität Erlangen-Nürnberg
• Luca Migliorini, Università di Bologna
• Roberto Pagaria, Università di Bologna
• Paolo Papi, Università di Roma 'La Sapienza'
• Francesca Pratali, Université Sorbonne Paris Nord
• Fabio Renda, Università di Ferrara
• Roberto Riccardi, Scuola normale
• Nikola Sadovek, FU Berlin
• Mario Salvetti, Università di Pisa
• Prajwal Samal, Polskiej Akademii Nauk
• Parth Shimpi, University of Glasgow
• Viola Siconolfi, Università di Pisa
• Balázs Szendroi, University of Vienna
• Marco Trevisiol, Università di Roma 'La Sapienza'
• Luca Vai, Università di Pavia
• Lorenzo Vecchi, Università di Bologna
• Lorenzo Venturello, Università di Pisa
• Shilun Wang, Università di Padova
• Nicholas Wawrykow, University of Michigan

Venue

The school will be held in Dobbiaco (Toblach) at the Kulturzentrum Grand Hotel Centro Culturale, in "La Sala degli Specchi". Kulturzentrum Grand Hotel Centro Culturale is located in front of Toblach train station (see the map).

The first talk will start on Monday February 20, 2023.

Registration and support

Participants are required to register by contacting the organizers at the following email address: toblachconfigurations2023@gmail.com.

Limited funding will be available to cover the local expenses (lodging and meals) of some PhD students. Participants who want to apply for financial support should send an email with their CV to toblachconfigurations2023@gmail.com. The deadline is December 10, 2022.

The participants who are financially supported by the organization will be hosted by the Guesthouse of the Kulturzenturm. The other participants are encouraged to book in advance their room.

This workshop is supported by:

PRA_2022_10, "Spazi di moduli, rappresentazioni e strutture combinatorie", University of Pisa.

Prin 2017, Moduli and Lie Theory, University of Pisa.

Teoria delle rappresentazioni e applicazioni, Ateneo 2020, Sapienza Università di Roma.

GNSAGA, INDAM.

Organizers: Michele D'Adderio , Marco Franciosi , Giovanni Gaiffi , Alessandro Iraci , Paolo Papi , and Viola Siconolfi