3/6, UFRJ. Sala C 116
Jethro van Ekeren (UFF),
Indicators of Heisenberg Groups.|
Resumo. Consider a module M over some type of algebra for which the notion of `dual module' makes sense (e.g., compact groups, Lie algebras, vertex algebras, etc). To say that M is self-dual is the same as to give an invariant bilinear form on M. Schur's lemma implies at once that such a form is either symmetric or else skew-symmetric, and one defines the Frobenius-Schur (FS) indicator of M to be +1 or -1 in these respective cases.
The motivation for this talk comes from vertex algebras, where calculation of FS indicators is (or has been) a notoriously delicate and slippery matter. The actual content of the talk, however, will have to do with finite Heisenberg groups: I will present a new and elementary calculation of some FS indicators in this context using finite quadratic spaces and the 2-adic lattice genus. Aside from streamlining the most technical part of several existing vertex algebra constructions, this calculation suggests the start of a nice story involving lattice automorphisms, Weil representations, arithmetic, and braided tensor categories.
Simone Marchesi (UNICAMP),
The existence of monads on projective varieties.|
Resumo. We will generalize Floystad's criterion for the existence of monads and we will study the properties of the sheafs defined by their cohomology. In particular we will study whenever it is locally free, simple, stable and we will describe the set of pairs of morphisms which define the monad and the moduli space of the cohomology sheaves.
This is a joint work with Pedro Macias Marques and Helena Soares.