Notiziario Scientifico

Settimana dal 16 al 22 giugno 2014

Lunedì 16 giugno 2014
Ore 11:00, Aula Dal Passo, Università di Roma II
Minicorso
J. Weyman (University of Connecticut)
Local Cohomology supported in determinantal varieties, I
In the first lecture the basic notions will be introduced, in the second one two recent papers by C.Raicu and E. Witt will be discussed.

Martedì 17 giugno 2014
Ore 14:30, Aula 211, Università di Roma III
Seminario di Geometria
Sebastian Casalaina-Martin (University of Colorado)
Prym varieties and applications
Prym varieties are abelian varieties obtained from connected, etale double covers of curves. They were introduced by Mumford (1974) in connection with the study the intermediate Jacobian of a cubic threefold, and were later used by Beauville (1977) to extended Mumford's construction to the case of arbitrary fibrations in odd dimensional quadrics. In this talk, I will review these constructions, and then discuss a few recent projects building on this work. This will include degenerations of intermediate Jacobians, extensions of the Prym map, and the cohomology of fibrations in quadrics over the rational numbers. This is joint work with (in various combinations) S. Grushevsky, K. Hulek, R. Laza and J. Achter.

Martedì 17 giugno 2014
Ore 16:00, Aula 211, Università di Roma III
Seminario di Geometria
Ana-Maria Castravet (Ohio University)
Birational geometry of moduli spaces of stable rational curves
I will report on joint work with Tevelev on the birational geometry of the Grothendieck-Knudsen moduli space of stable rational curves with n markings. We prove that for n > 133 this space is not a Mori Dream Space, thus answering a question of Hu and Keel.

Mercoledì 18 giugno 2014
Ore 14:30, Aula di Consiglio
Seminario di Algebra e Geometria
Jerzy Weyman (University of Connecticut)
Local cohomology supported in determinantal varieties
I will discuss the joint work with Claudiu Raicu and Emily Witt on the local cohomology of determinantal varieties. Let S be a polynomial ring K[X_[i,j]]_[1 < = i < = m,1 < = j < = n] where the variables are the entries of a generic mtimes n matrix X=(X_[i,j]). Let I_p be a determinantal ideal generated by the ptimes p minors of the matrix X. The main result is the calculation of the local cohomology modules H^i_[I_p](S). We give the decompostion of these modules into the irreducible representations of the group GL_mtimes GL_n acting on S by row and column operations. We also calculate their D-module structure. Similar results can be obtained for some of the other spherical representations.

Mercoledì 18 giugno 2014
Ore 16:00, Aula F, Università di Roma III
Colloquium di Matematica
Nick Shepherd-Barron (King's College, Londra)
Henon maps and Feistel ciphers: Cremona transformations in dynamics and cryptography
We explore the fact that similar Cremona transformations are used, for opposite reasons, in dynamics and in cryptography.

Giovedì 19 giugno 2014
Ore 14:30, Aula 211, Università di Roma III
Seminario di Geometria
Nick Shepherd-Barron (King's College, Londra)
Algebraic groups, log resolutions of elliptic singularities and del Pezzo surfaces
Brieskorn, Springer and Grothendieck found an association between the simultaneous resolution of a rational double points and the corresponding simple algebraic group. Elliptic singularities have a simultaneous log resolution in which del Pezzo surfaces appear; we describe an association between this picture and stacks of principal bundles over elliptic curves. This is joint work with Ian Grojnowski.

Giovedì 19 giugno 2014
Ore 14:30, Aula C
Seminario di Probabilità
Alessandra Bianchi (Università di Padova)
A random walk in a Levy random environment

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