Seminari/Colloquia
Pagina 30
Date  Type  Start  End  Room  Speaker  From  Title 

29/10/21  Seminario  16:00  17:00  1201 Dal Passo  "Partial and global representations of finite groups"  in live & streaming mode  (see the instructions in the abstract) N.B.: this talk is part of the activity of the MIUR Excellence Department Project CUP E83C18000100006
The notions of partial actions and partial representations have been extensively studied in several algebraic contexts in the last 25 years. In this talk we introduce these concepts and give a short overview of the results known for finite groups.
We will briefly show how this theory extends naturally the classical global theory, in particular in the important case of the symmetric group. This is joint work with William Hautekiet, Paolo Saracco and Joost Vercruysse. N.B.: please click HERE to attend the talk in streaming  
29/10/21  Seminario  14:30  15:30  1201 Dal Passo  "Soergel diagrammatics in modular representation theory"  in live & streaming mode  (see the instructions in the abstract)
We provide an elementary introduction to EliasWilliamson’s Soergel diagrammatics and pKazhdanLusztig theory and discuss the applications in representation theory. In particular we will discuss the recent proof of (generalised versions of) LibedinskyPatimo’s conjecture, which states that certain simple characters of affine Hecke algebras are given in terms of pKazhdanLusztig polynomials and of BerkeschGriffethSam’s conjecture which states that the unitary representations admit cohomological constructions via BGG resolutions.
This is joint work with Anton Cox, Amit Hazi, Emily Norton, and Jose Simental. N.B.: please click HERE to attend the talk in streaming  
27/10/21  Seminario  14:00  14:59  1201 Dal Passo  Erik Tonni  SISSA  Modular Hamiltonians for the massless Dirac field in the presence of a boundary or of a defect
 in blended mode  Microsoft Teams link in the abstract.
The reduced density matrix of a spatial subsystem can be written as the exponential of the modular Hamiltonian, hence this operator contains a lot of information about the entanglement of the corresponding spatial bipartition. First we consider the massless Dirac field on the halfline, imposing the most general boundary conditions that ensure the global energy conservation. This leads to two inequivalent phases where either the vector or the axial symmetry is preserved. In these two phases, we discuss the analytic expressions for the modular Hamiltonians of an interval on the halfline when the system is in its ground state, for the corresponding modular flows of the Dirac field and for the corresponding modular correlators. The method allows to obtain analytic expressions also for the modular Hamiltonians, the modular flows and the modular correlators for two disjoint equal intervals at the same distance from a pointlike defect characterised by a unitary scattering matrix, that allows both reflection and transmission.
Microsoft Teams Link 
26/10/21  Seminario  14:30  15:30  1201 Dal Passo 
Campana proposed a series of conjectures relating algebrogeometric and complexanalytic properties of algebraic varieties and their arithmetic. The main ingredient is the definition of the class of special varieties, which is the key for a new functorial classification of algebraic varieties, that is more suitable to answer arithmetic questions. In the talk we will review the main conjectures and constructions, and we will discuss some recent results that give evidence for some of these conjectures. This is joint work with E. Rousseau and J. Wang.
 
20/10/21  Seminario  16:00  17:00  1201 Dal Passo  JeanLuc Sauvageot  Institut de Mathématiques de Jussieu  Misurabilità, densità spettrali e tracce residuali in geometria non commutativa
We introduce, in the dual Macaev ideal of compact operators of a Hilbert space, the spectral weight rho(L) of a positive, selfadjoint operator L having discrete spectrum away from zero. We provide criteria for its measurability and unitarity of its Dixmier traces (
rho(L) is then called a spectral density) in terms of the growth of the spectral multiplicities of L and in terms of the asymptotic continuity of the eigenvalue counting function NL. Existence of meromorphic extensions and residues of the zetafunction zeta L of a spectral density are provided, under summability conditions on the spectral multiplicities. The hypertrace property of the states Omega L(·) = Tr omega(· rho(L)) on the norm closure of the Lipschitz algebra AL follows if the relative multiplicities of L vanish faster then its spectral gaps or if, at least, NL is asymptotically regular.

19/10/21  Seminario  14:30  15:30  1201 Dal Passo  Laura Pertusi  University of Milano 
Stability conditions on the Kuznetsov component of a Fano threefold of Picard rank 1, index 1 and 2 have been constructed by Bayer, Lahoz, Macrì and Stellari, making possible to study moduli spaces of stable objects and their geometric properties. In this talk we investigate the action of the Serre functor on these stability conditions. In the index 2 case and in the case of GM threefolds, we show that they are Serreinvariant. Then we prove a general criterion which ensures the existence of a unique Serreinvariant stability condition and applies to some of these Fano threefolds. Finally, we apply these results to the study of moduli spaces in the case of a cubic threefold X. In particular, we prove the smoothness of moduli spaces of stable objects in the Kuznetsov component of X and the irreducibility of the moduli space of stable Ulrich bundles on X. These results come from joint works with Song Yang and with Soheyla Feyzbakhsh and in preparation with Ethan Robinett.
These talks are part of the activity of the MIUR Excellence Department Project MATH@TOV CUP E83C18000100006. 
15/10/21  Seminario  16:00  17:00  1201 Dal Passo  "On degeneration and extensions of symplectic and orthogonal quiver representations"  in live & streaming mode  (see the instructions in the abstract)
Motivated by linear degenerations of flag varieties, and the study of 2nilpotent Borbits for classical groups, I will review the representation theory of symmetric quivers, initiated by Derksen and Weyman in 2002. I will then focus on the problem of describing the orbit closures in this context and how to relate it to the orbit closures for the underlying quivers. In collaboration with M. Boos we have recently given an answer to this problem for symmetric quivers of finite type. I believe that this result is a very special case of a much deeper and general result that I will mention in the form of conjectures and open problems.
The talk is based on the preprint version of my paper with Boos available on the arXiv as 2106.08666. N.B.: please click HERE to attend the talk in streaming  
15/10/21  Seminario  14:30  15:30  1201 Dal Passo  "Symmetric groups, tensor powers and extended powers of a topological space"  in live & streaming mode  (see the instructions in the abstract)
The nth cohomology of the symmetric group S_{n} on n objects with coefficients in the nth tensor power of a vector space V on a field k, is endowed with an extremely rich algebraic structure. Indeed, their direct sum for all n ∈ N is an example of what goes under the name of "Hopf ring".
First I will recall and review the definition of Hopf ring, then I will explicitly describe the cohomology algebras above, and finally I will briefly discuss the link with extended powers and other topological spaces interesting for homotopy theorists. The content of this talk stems from an ongoing collaboration with Paolo Salvatore and Dev Sinha. N.B.: please click HERE to attend the talk in streaming  
12/10/21  Seminario  14:30  15:30  1201 Dal Passo  Daniele Agostini  Max Planck Institute for Mathematics in the Sciences in Leipzig 
The theta function of the Jacobian of a projective curve induces a solution of an infinite series of partial differential equations, the KP hierarchy. These solutions are packaged into the socalled tau function in integrable systems theory. I will recall the wellknown picture in the case of smooth curves, and I will present some new results in the case of singular curves, focusing on those curves for which the theta function is actually polynomial. This is joint work with T. Çelik and J. Little.
This talk is part of the activity of the MIUR Excellence Department Project MATH@TOV CUP E83C18000100006. 
06/10/21  Seminario  14:00  15:00  1201 Dal Passo  Edoardo D'Angelo  Universita' di Genova  Role of the relative entropy in the entropy of dynamical black holes
Since the discovery of the BekensteinHawking formula, there had been many attempts to derive the entropy of black holes from the entanglement between the degrees of freedom of matter fields inside and outside the event horizon. The entanglement is usually measured in terms of the entanglement entropy, which is obtained from the von Neumann entropy tracing over the degrees of freedom outside the black hole. However, the entanglement entropy is divergent in the continuum limit, and its regularizationdependence is in contrast with the universality of the BekensteinHawking formula.
In a recent paper, Hollands and Ishibashi adopted a different measure for the matter entropy: the relative entropy, which is welldefined also for continuum theories such as QFT. Hollands and Ishibashi showed that it reproduces the BekensteinHawking formula for Schwarzschild black holes.
In this talk I present a generalization of the work of Hollands and Ishibashi for the case of dynamical, spherically symmetric black holes. Using the backreaction of a free, scalar quantum field on the metric, I showed that a variation in the relative entropy between coherent states of the field produces a variation of onequarter of the black hole horizon area, thus finding that the black hole entropy is naturally defined as S = A/4 also in the dynamical case.

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