Winter School

Geometry, Algebra and Combinatorics of Moduli Spaces and Configurations III

Dobbiaco (Toblach), February 17-22, 2019

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

Timetable

	Monday 18/2	Tuesday 19/2	Wednesday 20/2	Thursday 21/2	Friday 22/2
14:30	Frediani	Caselli		Frediani	Routis

15:30		Frediani			Caselli

16:30	Coffee break	Coffee break		Coffee break	Coffee break

17:00	Caselli	De Sole		Caselli	De Sole
			Gandini Melani
18:00				De Sole

19:00
21:00			Cifani
21:45			Fleming

22:30

Mini-courses

Fabrizio Caselli, Università di Bologna, Bruhat intervals, Coxeter matroids and related polytopes [Slides]
Alberto De Sole, Sapienza Università di Roma, W-algebre classiche e quantistiche e applicazioni [Slides 1] [Slides 2][Slides 3]
Paola Frediani, Università di Pavia, Second fundamental form of the Torelli map and special subvarieties of A_g [Slides]

Talks:

Maria Gioia Cifani, Università di Pavia, Monodromy of projective hypersurfaces (Wed 20/2 h. 21:00).[Slides] [show abstract]
Abstract: Let X be a irreducible, reduced, non developable, projective hypersurface over the complex numbers; consider the linear projection of X from a point p not in X that is a finite map of degree d=deg(X). To it we can associate the monodromy group, that is a transitive subgroup of the symmetric group S_d. It is known that for a general point, the monodromy group associated to the projection from it is S_d. We say that a point with monodromy group S_d is uniform. We prove that X admits at most a finite number of non uniform points (this is a j.w.w. A.Cuzzucoli and R.Moschetti). [Hide abstract]
Aeran Fleming, University of Liverpool, Multipoint Seshadri constants and explicit Kähler packings of projective complex manifolds (Wed 20/2 h. 21:45).[Slides] [show abstract]
Abstract: In this talk I will start by introducing the concept of multipoint Seshadri constants and discuss their relationship with Nagata's conjecture. I will then introduce the notion of a Kähler packing and show that there is a direct connection between the multipoint Seshardi constant and the existence of Kähler packings. To end I will provide an example of a Kahler packing of a toric variety which highlights a connection between Kahler packings of certain polytopes and their corresponding varieties. [Hide abstract]
Jacopo Gandini, Università di Pisa, Variations on the Bruhat order (Wed 20/2 h. 17:30). [show abstract]
Abstract: Let G be a simple algebraic group G and B a Borel subgroup of G. If X is a B-variety which decomposes into finitely many orbits, the Bruhat order on X is the partial order among the B-orbits given by the inclusion of their closures. I will explain how to describe combinatorially the Bruhat order in two (related) cases: that of the Hermitian symmetric varieties of G, and that of the abelian ideals of the Lie algebra of B. The talk is based on joint works with A. Maffei, P. Moseneder-Frajria and P. Papi. [Hide abstract]
Valerio Melani, Università di Pisa, TBA (Wed 20/2 h. 18:20).
Evangelos Routis, Max Planck Institute, Bonn, Complete Complexes and Spectral Sequences (Fri 22/2 h. 14:30). [show abstract]
Abstract: (joint with M. Kapranov) The space of complete collineations is an important and beautiful chapter of algebraic geometry, which has its origins in the classical works of Chasles, Giambieli, Hirst, Schubert, Tyrell and others, dating back to the 19th century. It provides a `wonderful compactification' (i.e. smooth with normal crossings boundary) of the space of full-rank maps between two (fixed) vector spaces. More recently, the space of complete collineations has been studied intensively and has been used to derive groundbreaking results in diverse areas of mathematics. One such striking example is L. Lafforgue's compactification of the stack of Drinfeld's shtukas, which he subsequently used to prove the Langlands correspondence for the general linear group. In joint work with M. Kapranov we look at these classical spaces from a modern perspective: a complete collineation is simply a spectral sequence of two-term complexes of vector spaces. We then develop a theory involving more full-fledged (simply graded) spectral sequences of complexes of vector bundles with arbitrarily many terms. We prove that the set of such spectral sequences has the structure of a smooth projective variety, the `variety of complete complexes', which provides a desingularization, with normal crossings boundary, of the `Buchsbaum-Eisenbud variety of complexes', i.e. a `wonderful compactification' of the union of its maximal strata. [Hide abstract]

[Click here for a list of registered participants]

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 18, 2019.

Registration and support

Participants are required to register by contacting the organizers at the following email address: toblach.configurations2019@gmail.com.

Application for financial support is not possible anymore.

The participants who are financially supported by the organization will be hosted by Hotel Union and Casa Alpina. Both are very close to the Kulturzentrum. The other participants are encouraged to book in advance their room.

This workshop is supported by:

University of Pisa