26/10/21  Seminario  14:30  15:30  1201 Dal Passo  Amos Turchet  University of Roma Tre  Geometry Seminar
Campana’s program and special varieties
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  Geometry Seminar
Serreinvariant stability conditions and cubic threefolds
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  Giovanni CERULLI IRELLI  “Sapienza” Università di Roma 
Algebra & Representation Theory Seminar (ARTS)
"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  Lorenzo GUERRA  Scuola Normale Superiore  Pisa 
Algebra & Representation Theory Seminar (ARTS)
"Symmetric groups, tensor powers and extended powers of a topological space"
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(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  Geometry Seminar
Theta functions and tau functions of algebraic curves
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.

05/10/21  Seminario  14:30  15:30  1101 D'Antoni  Claudio Onorati  Tor Vergata  Geometry Seminar
Remarks on sheaves on hyperKahler manifolds
The geometry of moduli spaces of sheaves on K3 surfaces is very rich and led to very deep results in the last decades. Moreover, under certain hypotheses, these varieties are smooth projective and have a hyperKahler structure, providing nontrivial examples of compact hyperKahler manifolds. In higher dimensions the situation is much more complicated, nevertheless in the '90s Verbitsky introduced a set of sheaves on hyperKahler manifolds, called hyperholomorphic, whose moduli spaces are singular hyperKahler (but not compact in general). Recently O'Grady proved that such sheaves belong to a larger set of sheaves for which there exists a good wallandchamber decomposition of the ample cone. This suggests an analogy between the study of moduli spaces of hyperholomorphic sheaves on hyperKahler manifolds and the study of moduli spaces of sheaves on K3 surfaces. After having recalled the needed definitions and results, in this talk I will face the formality problem for such set of sheaves. In particular, I will extend the notion of hyperholomorphic to complexes of locally free sheaves, and show how the associated dg Lie algebra of derived endomorphism is formal, namely quasiisomorphic to its cohomology. As a corollary one gets a different proof of a quadraticity result of Verbitsky. This is a joint work in progress with F. Meazzini (INdAM).
This talk is part of the activity of the MIUR Excellence Department Project MATH@TOV CUP E83C18000100006.

28/09/21  Seminario  14:30  15:30  1101 D'Antoni  Rick Miranda  Colorado State University  Geometry Seminar
Moduli spaces for rational elliptic surfaces (of index 1 and 2)
Elliptic surfaces form an important class of surfaces both from the theoretical perspective (appearing in the classification of surfaces) and the practical perspective (they are fascinating to study, individually and as a class, and are amenable to many particular computations). Elliptic surfaces that are also rational are a special subclass. The first example is to take a general pencil of plane cubics (with 9 base points) and blow up the base points to obtain an elliptic fibration; these are socalled Jacobian surfaces, since they have a section (the final exceptional curve of the sequence of blowups). Moduli spaces for rational elliptic surfaces with a section were constructed by the speaker, and further studied by Heckman and Looijenga. In general, there may not be a section, but a similar description is possible: all rational elliptic surfaces are obtained by taking a pencil of curves of degree 3k with 9 base points, each of multiplicity k. There will always be the kfold cubic curve through the 9 points as a member, and the resulting blowup produces a rational elliptic surface with a multiple fiber of multiplicity m (called the index of the fibration). A. Zanardini has recently computed the GIT stability of such pencils for m=2; in joint work with her we have constructed a moduli space for them via toric constructions. I will try to tell this story in this lecture.
This talk is part of the activity of the MIUR Excellence Department Project MATH@TOV CUP E83C18000100006.

24/09/21  Seminario  14:00  15:00  1201 Dal Passo  Christian Gass  Uni Goettingen  Renormalization in stringlocalized field theories: a microlocal analysis
Stringlocalized quantum field theory (SL QFT) provides an alternative to gauge theoretic approaches to QFT. In the last oneandahalf decades, many conceptual benefits of SL QFT have been discovered. However, a renormalization recipe for loop graphs with internal SL fields was not at hand until now.
In this talk, I present a proof that the problem of renormalization remains a pure short distance problem in SL QFT. This happens in spite of the delocalization of SL fields and the analytic complexity of their propagators – provided that one takes care in how to set up perturbation theory in SL QFT. As a result, the improved shortdistance behavior of SL fields remains a meaningful notion, which indicates that there can exist renormalizable models in SL QFT whose pointlocalized counterparts are nonrenormalizable.
The talk is based on arXiv:2107.12834. 