Dipartimento di Matematica -UTV-

Date	Type	Start	End	Room	Speaker	From	Title
22/04/22	Seminario	16:00	17:00	1201 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 Abstract 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.
22/04/22	Seminario	14:30	15:30	1201 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 Abstract 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.
19/04/22	Seminario	16:00	17:00	1201 Dal Passo	Qing Han	University of Notre Dame	Singular harmonic maps and the mass-angular momentum inequality ( MS Teams Link for the streaming ) Abstract 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
12/04/22	Seminario	16:00	17:00	1201 Dal Passo	Valerio Assenza	Heidelberg University	Seminario di Equazioni Differenziali Magnetic Curvature and Closed Magnetic Geodesic (MS Teams link for the streaming at the end of the abstract) 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
12/04/22	Seminario	13:00	14:00	2001	Deepesh Toshniwal	Delft University of Technology	Quadratic unstructured splines Abstract 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.
08/04/22	Seminario	16:30	17:30	1201 Dal Passo	Paolo PAPI	"Sapienza" Università di Roma	Algebra & Representation Theory Seminar (ARTS) "Collapsing levels for affine W-algebras" - in live & streaming mode - ( click HERE* to attend the talk in streaming )* Abstract 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.
08/04/22	Seminario	14:00	15:00	1201 Dal Passo	Vincenzo MORINELLI	Università di Roma "Tor Vergata"	Algebra & Representation Theory Seminar (ARTS) "About Lie theory in Algebraic Quantum Field Theory" - in live & streaming mode - ( click HERE* to attend the talk in streaming )* Abstract 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.
05/04/22	Seminario	16:00	17:00	1201 Dal Passo	Luca Battaglia	Università di Roma Tre	Blow-up phenomena for a curvature problem in a disk ( MS Teams Link for the streaming ) Abstract 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
05/04/22	Seminario	14:30	15:30	1201 Dal Passo	Luca Tasin	Universita' di Milano	Geometry Seminar Sasaki-Einstein metrics on spheres. Abstract 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.
01/04/22	Seminario	15:30	16:30	1200 Biblioteca Storica	Alessia Caponera	EPFL	Nonparametric Estimation of Covariance and Autocovariance Operators on the Sphere Abstract We propose nonparametric estimators for the second-order central moments of spherical random fields within a functional data context. We consider a measurement framework where each field among an identically distributed collection of spherical random fields is sampled at a few random directions, possibly subject to measurement error. The collection of fields could be i.i.d. or serially dependent. Though similar setups have already been explored for random functions defined on the unit interval, the nonparametric estimators proposed in the literature often rely on local polynomials, which do not readily extend to the (product) spherical setting. We therefore formulate our estimation procedure as a variational problem involving a generalized Tikhonov regularization term. The latter favours smooth covariance/autocovariance functions, where the smoothness is specified by means of suitable Sobolev-like pseudo-differential operators. Using the machinery of reproducing kernel Hilbert spaces, we establish representer theorems that fully characterize the form of our estimators. We determine their uniform rates of convergence as the number of fields diverges, both for the dense (increasing number of spatial samples) and sparse (bounded number of spatial samples) regimes. We moreover validate and demonstrate the practical feasibility of our estimation procedure in a simulation setting. Based on a joint work with Julien Fageot, Matthieu Simeoni and Victor M. Panaretos. This talk is part of the activity of the MIUR Excellence Department Project CUP E83C18000100006.