Seminari/Colloquia

Pagina 24


DateTypeStartEndRoomSpeakerFromTitle
03/05/22Seminario16:0017:001201 Dal PassoFrancesco FidaleoUniversità di Roma Spectral actions for q-particles and their asymptotic
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For spectral actions made of the average number of particles and arising fromopen systems made of general free q-particles (including Bose, Fermi and classical ones corresponding to q= pm 1 and 0, respectively) in thermal equilibrium, we compute the asymptotic expansion with respect to the natural cut-off. We treat both relevant situations relative to massless and massive particles, where the natural cut-off is 1/eta=k_eta T and  1//sqrt{eta}, respectively. We show that the massless situation enjoys less regularity properties than the massive one. We also consider the passage to the continuum describing infinitely extended open systems in thermal equilibrium. We briefly discuss the appearance of condensation phenomena occurring for Bose-like q-particles, for which qin (0,1], after passing to the continuum. We also compare the arising results for the finite volume situation (discrete spectrum) with the corresponding infinite volume one (continuous spectrum).
NB:This talk is part of the activity of the MIUR Excellence Department Project MATH@TOV CUP E83C18000100006
22/04/22Seminario16:0017:001201 Dal Passo
Andrea APPEL
Università di Parma
Algebra & Representation Theory Seminar (ARTS)
"Schur-Weyl duality for quantum affine symmetric pairs"
- in live & streaming mode -
( please click HERE to attend the talk in streaming )
N.B.: This talk is part of the activity of the MIUR Excellence Department Project MATH@TOV CUP E83C18000100006

  In the work of Kang, Kashiwara, Kim, and Oh, the Schur-Weyl duality between quantum affine algebras and affine Hecke algebras is extended to certain Khovanov-Lauda-Rouquier (KLR) algebras, whose defining combinatorial datum is given by the poles of the normalised R-matrix on a set of representations.
  In this talk, I will review their construction and introduce a "boundary" analogue, consisting of a Schur-Weyl duality between a quantum symmetric pair of affine type and a modified KLR algebra arising from a (framed) quiver with a contravariant involution. With respect to the Kang-Kashiwara-Kim-Oh construction, the extra combinatorial datum we take into account is given by the poles of the normalised K-matrix of the quantum symmetric pair.
  N.B.: please click HERE to attend the talk in streaming.
22/04/22Seminario14:3015:301201 Dal Passo
Lleonard RUBIO y DEGRASSI
Università di Verona
Algebra & Representation Theory Seminar (ARTS)
"Maximal tori in HH1 and the homotopy theory of bound quivers"
- in live & streaming mode -
( please click HERE to attend the talk in streaming )
N.B.: This talk is part of the activity of the MIUR Excellence Department Project MATH@TOV CUP E83C18000100006

  Hochschild cohomology is a fascinating invariant of an associative algebra which possesses a rich structure. In particular, the first Hochschild cohomology group HH1(A) of an algebra A is a Lie algebra, which is a derived invariant and, among selfinjective algebras, an invariant under stable equivalences of Morita type. This establishes a bridge between finite dimensional algebras and Lie algebras, however, aside from few exceptions, fine Lie theoretic properties of HH1(A) are not often used.
  In this talk, I will show some results in this direction. More precisely, I will explain how maximal tori of HH1(A), together with fundamental groups associated with presentations of A, can be used to deduce information about the shape of the Gabriel quiver of A. In particular, I will show that every maximal torus in HH1(A) arises as the dual of some fundamental group of A. By combining this, with known invariance results for Hochschild cohomology, I will deduce that (in rough terms) the largest rank of a fundamental group of A is a derived invariant quantity, and among self-injective algebras, an invariant under stable equivalences of Morita type. Time permitting, I will also provide various applications to semimonomial and simply connected algebras.
  This is joint work with Benjamin Briggs.
  N.B.: please click HERE to attend the talk in streaming.
19/04/22Seminario16:0017:001201 Dal PassoQing HanUniversity of Notre DameSingular harmonic maps and the mass-angular momentum inequality
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Motivated by studies of axially symmetric stationary solutions of the Einstein vacuum equations in general relativity, we study singular harmonic maps from domains of the 3-dimensional Euclidean space to the hyperbolic plane, with bounded hyperbolic distance to extreme Kerr harmonic maps. We prove that every such harmonic map has a unique tangent map at the black hole horizon. As an application, we establish an explicit and optimal lower bound for the ADM mass in terms of the total angular momentum, in asymptotically flat, axially symmetric, and maximal initial data sets for the Einstein equations with multiple black holes. The talk is based on joint work with Marcus Khuri, Gilbert Weinstein, and Jingang Xiong.
NB:This talk is part of the activity of the MIUR Excellence Department Project MATH@TOV CUP E83C18000100006
12/04/22Seminario16:0017:001201 Dal PassoValerio AssenzaHeidelberg University
Seminario di Equazioni Differenziali
     Magnetic Curvature and Closed Magnetic Geodesic  
     (MS Teams link for the streaming at the end of the abstract)  

A Magnetic System describes the motion of a charged particle moving on a Riemannian Manifold under the influence of a magnetic field. Trajectories for this dynamics are called Magnetic Geodesics and one of the main tasks in the theory is to investigate the existence of Magnetic Geodesic which are closed. In general this depends on the magnetic system taken into account and on the topology of the base space. Inspired by the work of Bahri and Taimanov, I will introduce the notion of Magnetic Curvature which is a perturbation of the standard Riemannian curvature due to the magnetic interaction. We will see that Closed Magnetic Geodesic exist when the Magnetic Curvature is positive, which happens , for instance, when the magnetic field is sufficiently strong.

MS Teams Link for the streaming
Note: This talk is part of the activity of the MIUR Department of Excellence Project MATH@TOV CUP E83C18000100006
12/04/22Seminario13:0014:002001Deepesh ToshniwalDelft University of TechnologyQuadratic unstructured splines

Isogeometric Analysis generalizes classical finite element analysis and intends to integrate it with the field of Computer-Aided Design. A central problem in achieving this objective is the reconstruction of analysis-suitable models from Computer-Aided Design models, which is in general a non-trivial and time-consuming task. This talk will present an overview of new piecewise-quadratic spline constructions that enable model reconstruction, as well as simulation of high-order PDEs on the reconstructed models. In particular, we will discuss splines on unstructured meshes in both two and three dimensions. This talk is part of the activity of the MIUR Excellence Department Project CUP E83C18000100006.
08/04/22Seminario16:3017:301201 Dal Passo
Paolo PAPI
"Sapienza" Università di Roma
Algebra & Representation Theory Seminar (ARTS)
"Collapsing levels for affine W-algebras"
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  I will discuss some projects in collaboration with D. Adamovic, V. Kac and P. Moseneder-Frajria regarding affine W-algebras. I will concentrate on the notion of collapsing level for not necessarily minimal W-algebras and I will illustrate some applications to the representation theory of affine algebras and, if time allows, to our conjectural classification of unitary representations for minimal W-algebras.
  N.B.: please click HERE to attend the talk in streaming.
08/04/22Seminario14:0015:001201 Dal Passo
Vincenzo MORINELLI
Università di Roma "Tor Vergata"
Algebra & Representation Theory Seminar (ARTS)
"About Lie theory in Algebraic Quantum Field Theory"
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( click HERE to attend the talk in streaming )

  The relation between the geometric and the algebraic structure in algebraic quantum field theory is an intriguing topic that has been studied through several mathematical areas. A fundamental concept in Algebraic Quantum Field Theory (AQFT) is the relation between the localization property and the geometry of models. In the recent work with K.-H. Neeb, we rephrased and generalized some aspects of this relation by using the language of Lie theory.
  We will start the talk introducing fundamental algebraic features of AQFT, in particular the Haag-Kastler axioms and the one particle formalism, and the presenting algebraic construction of the free field due to R.Brunetti, D. Guido and R. Longo. We will explain how this picture can be generalized. Firstly, how to determine some fundamental localization region, called wedge regions, at the Lie theory level and how a general Lie group can support a generalized AQFT. Then we show a classification of the simple Lie algebras supporting abstract wedges in relation with some special wedge configurations. The construction is possible for a large family of Lie groups and provides several new models in a generalized framework. Such a description of AQFT model generalization does not need a supporting manifold even if it is a desirable object. Time permitting, we will comment on recent developments about symmetric manifolds such models.
  Based on V. Morinelli and K.-H. Neeb, Covariant homogeneous nets of standard subspaces, Commun. in Math. Phys 386 (1), 305-358 (2021).
  N.B.: please click HERE to attend the talk in streaming.
05/04/22Seminario16:0017:001201 Dal PassoLuca Battaglia Università di Roma TreBlow-up phenomena for a curvature problem in a disk
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We consider the problem of prescribing Gaussian and geodesic curvatures for a conformal metric on the unit disk, which is equivalent to a Liouville-type PDE with nonlinear Neumann boundary conditions. We build a family of solutions which blow up on the boundary at a critical point of a functional which is a combination of the curvatures we are prescribing. The talk is based on joint works with M. Medina and A. Pistoia.
NB:This talk is part of the activity of the MIUR Excellence Department Project MATH@TOV CUP E83C18000100006
05/04/22Seminario14:3015:301201 Dal PassoLuca Tasin
Universita' di Milano
Geometry Seminar
Sasaki-Einstein metrics on spheres.

I will report on a joint work with Yuchen Liu and Taro Sano in which we construct infinitely many families of Sasaki-Einstein metrics on odd-dimensional spheres that bound parallelizable manifolds, proving in this way conjectures of Boyer-Galicki-Kollar and Collins-Szekelyhidi. The construction is based on showing the K-stability of certain Fano weighted orbifold hypersurfaces.

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