Pagina 3

Date | Type | Start | End | Room | Speaker | From | Title |
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08/05/20 | Seminario | 15:15 | 16:15 | 1101 D'Antoni | Roberto Svaldi | Ecole polytechnique fédérale de Lausanne | |

08/05/20 | Seminario | 14:30 | 15:30 | Parabolic
K-matrices for quantum groups- in streaming mode -
(see the instructions in the abstract)
Braided module categories provide a conceptual framework for the reflection equation, mimicking the relation between the Yang-Baxter equation and braided categories. Indeed, while the latter describes braids on a plane (type A), the former can be thought of in terms of braids on a cylinder (type B). In the theory of quantum groups, natural examples of braided module categories arise from quantum symmetric pairs (coideal subalgebras quantizing certain fixed point Lie subalgebra), where the action of type B braid groups is given in terms of a so-called universal K-matrix, constructed in finite-type by Balagovic-Kolb. In this talk, I will describe the construction of a family of "parabolic” K-matrices for quantum Kac-Moody algebras, which is indexed by Dynkin subdiagrams of finite-type and includes Balagovic-Kolb K-matrix as a special case. If time permits, I will explain how this construction could lead to a meromorphic K-matrix for quantum loop algebras. This is based on joint works with D. Jordan and B. Vlaar. Warning: the talk will be held in streaming, as a videoconference on-line; in order to join the videoconference, visit the web-page
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24/04/20 | Seminario | 15:15 | 16:15 | 1101 D'Antoni | Gabriele Benedetti | Heidelberg University | |

24/04/20 | Seminario | 14:30 | 15:30 | Real forms of complex Lie superalgebras and supergroups- in streaming mode -
(see the instructions in the abstract)
A real form of a complex Lie algebra is the subset of fixed points of some “real structure”, that is an antilinear involution; a similar description applies for real forms of complex (Lie or algebraic) groups. For complex Lie superalgebras, the notion of “real structure” extends in two different variants, called standard (a straightforward generalization) and graded (somewhat more sophisticated): the notion of “real form”, however, stands problematic in the graded case.
I will present the functorial version of “real structure” (standard or graded), and show that the notion of “real form” then properly extends, in both cases; along the same lines, I will introduce real structures and real forms for complex supergroups. Then, basing on a suitable notion of “Hermitian form” on complex superspaces, I will introduce unitary Lie superalgebras and supergroups (again standard or graded); any Lie superalgebra which embeds into a unitary one will then be called “super-compact” – and similary for supergroups. Finally, I will give nice existence/uniqueness results of super-compact real forms for complex Lie superalgebras which are simple of basic (or “contragredient”) type, and similarly for their associated connected simply-connected supergroups This is based on a joint work with Rita Fioresi. the talk will be held in streaming, as a videoconference on-line; in order to join the videoconference, go here and click on the link that you find there.Warning: | |||

17/04/20 | Seminario | 15:15 | 16:15 | 1101 D'Antoni | Giulia Saccà | Columbia University | |

17/04/20 | Seminario | 14:30 | 15:30 | The quest for bases of the intersection cohomology of Schubert varieties
- in streaming mode -
(see the instructions in the abstract)
The Schubert basis is a distinguished basis of the cohomology of a Schubert variety and it is a precious tool to study the ring structure of the cohomology.
When working with the intersection cohomology, we do not have a Schubert basis in general, and in fact understanding the intersection cohomology of a Schubert variety can be much more difficult. However, if one can understand well the related Kazhdan-Lusztig polynomials, one may often exploit their combinatorics and produce new bases in intersection cohomology which extend the original Schubert basis. In this talk I would like to talk about two (if time permits!) different cases where this is possible. The first one are Schubert varieties in the Grassmannian. Here we obtain bases by "lifting" the combinatorics of Dyck partitions. The second case, joint with Nicolás Libedinsky, is the affine Weyl group Ã_{2} . Here we realize our basis by defining a set of indecomposable light leaves.
the talk will be held in streaming, as a videoconference on-line; in order to join the videoconference, go here and click on the link that you find there.
Warning: | |||

03/04/20 | Seminario | 14:30 | 15:30 | Singularities of Schubert varieties within a right cell
- in streaming mode -
(see the instructions in the abstract)
We describe an algorithm which takes as input any pair of permutations and gives as output two permutations lying in the same Kazhdan-Lusztig right cell. There is an isomorphism between the Richardson varieties corresponding to the two pairs of permutations which preserves the singularity type. This fact has applications in the study of W-graphs for symmetric groups, as well as in finding examples of reducible associated varieties of sl_{n}-highest weight modules, and comparing various bases of irreducible representations of the symmetric group or its Hecke algebra. This is joint work with Peter McNamara. the talk will be held in streaming, as a videoconference on-line; in order to join the videoconference, go here and click on the link that you find there.
Warning: | |||

27/03/20 | Seminario | 15:15 | 16:15 | 1101 D'Antoni | Arvid Perego | Università di Genova | |

27/03/20 | Seminario | 14:30 | 15:30 | Orbit method via groupoid quantization - in streaming mode - (see the instructions in the abstract) The orbit method, in its most general form, can be seen as a general correspondence between symplectic leaves of a Poisson manifold and unitary irreducible representations of its quan-tization algebra. Properties of such correspondence should not depend on the choice of a specific quantization procedure. In this talk we will show how the so-called groupoid quantization allows to understand the correspondence for a wide family of quantum groups and their homogeneous spaces. the talk will be held in streaming, as a videoconference on-line; in order to join the videoconference, go
here and click on the link that you find there.
Warning: | |||

20/03/20 | Seminario | 15:15 | 16:15 | 1101 D'Antoni | Thomas Kraemer | Humboldt-Universität zu Berlin | A converse to Riemann's theorem on Jacobian varieties Jacobians of curves have been studied a lot since Riemann’s theorem, which says that their theta divisor is a sum of copies of the curve.
Similarly, for intermediate Jacobians of smooth cubic threefolds
Clemens and Griffiths showed that the theta divisor is a sum of two
copies of the Fano surface of lines on the threefold. We prove that
in both cases these are the only decompositions of the theta
divisor, extending previous results of Casalaina-Martin, Popa and
Schreieder. Our ideas apply to a much wider context and only rely on
the decomposition theorem for perverse sheaves and the
representation theory of reductive groups. |