Dipartimento di Matematica -UTV-

Date	Type	Start	End	Room	Speaker	From	Title
31/01/23	Seminario	16:00	17:00	1201 Dal Passo	Giulio Tiozzo	University of Toronto	Seminario congiunto di Equazioni Differenziali ed Analisi Complessa The harmonic measure for random walks on cocompact Fuchsian groups Abstract We consider random walks on groups of isometries of the hyperbolic plane, known as Fuchsian groups. It is well-known since Furstenberg that such random walks converge to the boundary at infinity, and the probability to reach a given subset of the boundary defines a hitting, or harmonic, measure on the circle. It has been a long-standing question whether this harmonic measure is absolutely continuous with respect to the Lebesgue measure. Conjecturally, this is never the case for random walks on cocompact, discrete groups. In the talk, based on joint work with Petr Kosenko, we settle the conjecture for nearest neighbour random walks on hyperelliptic groups. In fact, we show that the dimension of the harmonic measure for such walks is strictly less than one. This is also related to an inequality between entropy and drift.
25/01/23	Seminario	16:00	17:00	1201 Dal Passo	Roberto Conti	Sapienza University of Rome	Heat properties for groups Abstract Somewhat motivated by the original approach of J.-B. Fourier to solve the heat equation on a bounded domain, we formulate some new properties of countable discrete groups involving certain completely positive multipliers of the reduced group C*-algebra and norm-convergence of Fourier series. The stronger "heat property" implies the Haagerup property, while the "weak heat property" is satisfied by a much larger class of groups. Examples will be provided to illustrate the various aspects. In perspective, a challenging goal would be to obtain yet another characterization of groups with Kazhdan's property (T). (Based on joint work with E. Bédos.)
24/01/23	Seminario	16:00	17:00	1201 Dal Passo	Paolo Roselli	Università di Roma "Tor Vergata"	Seminario di Equazioni Differenziali Il paradosso del piano tangente e il rapporto incrementale vettoriale di un piano secante Abstract La retta tangente il grafico di una funzione sufficientemente regolare è la posizione limite di rette secanti il grafico. Ci si aspetterebbe che il piano tangente il grafico di una funzione a due variabili sufficientemente regolare sia la posizione limite di piani secanti il grafico in tre punti non collineari (a,f(a)), (b,f(b)) e (c,f(c)), ma così non è. Questo fenomeno paradossale è una versione locale del paradosso dell'area di una superficie curva (detto anche paradosso di Schwarz). In questo seminario visualizzerò il fenomeno paradossale, e mostrerò come il "coefficiente angolare vettoriale" di un piano secante possa esprimersi sia come combinazione vettoriale delle normali esterne al triangolo di vertici a, b e c, sia come rapporto vettoriale incrementale, quando il prodotto vettoriale è quello geometrico di Clifford. Se rimarrà tempo, accennerò anche a come modificare tale rapporto incrementale vettoriale per renderlo sempre convergente al gradiente di f.
17/01/23	Seminario	16:00	17:00	1201 Dal Passo	Liangjun Weng	Università di Roma "Tor Vergata"	A constrained mean curvature type flow Abstract In this talk, we will discuss the isoperimetric inequality and its high order version -- Alexandrov Fenchel inequality, which dates back to the Queen Dido in ancient Carthage era. We introduce the quermass integrals for compact hypersurfaces with capillary boundary. Then by using a constrained mean curvature type flow, one can obtain the Alexandrov-Fenchel inequality for compact hypersurfaces with capillary boundary.
13/12/22	Seminario	16:00	17:00	1201 Dal Passo	Cristiana De Filippis	Università di Parma	Seminario di Equazioni Differenziali Schauder estimates for any taste Abstract So-called Schauder estimates are a standard tool in the analysis of linear elliptic and parabolic PDE. They have been originally obtained by Hopf (1929, interior case), and by Schauder and Caccioppoli (1934, global estimates). The nonlinear case is a more recent achievement from the ’80s (Giaquinta & Giusti, Ivert, Lieberman, Manfredi). All these classical results hold in the uniformly elliptic framework. I will present the solution to the longstanding problem, open since the ‘70s, of proving estimates of such kind in the nonuniformly elliptic setting. I will also cover the case of nondifferentiable functionals and provide a complete regularity theory for a new double phase model. From joint work with Giuseppe Mingione (University of Parma). Note: This talk is part of the activity of the MIUR Department of Excellence Project MATH@TOV CUP E83C18000100006
06/12/22	Seminario	16:00	17:00	1201 Dal Passo	Marco Ghimenti	Università di Pisa	Compactness and blow up for Yamabe boundary problem Abstract In 1992 Escobar extended the well known Yamabe problem to manifolds with boundary. The case of the scalar flat target manifold is particularly interesting since it also represents a generalization to Riemann mapping theorem to higher dimensions. In this talk we discuss when the solutions of the Yamabe boundary problem are a compact set, or when they form a blowing up sequence, underlining the affinities and the differences with the classical Yamabe problem. NB:This talk is part of the activity of the MIUR Excellence Department Project MATH@TOV CUP E83C18000100006
29/11/22	Seminario	16:00	17:00	1201 Dal Passo	Francesco Esposito	Università della Calabria	Symmetry results for singular solutions to the p-Laplace equation Abstract In this talk we will consider positive singular solutions to semilinear or quasilinear elliptic problems. We will deduce symmetry and monotonicity results of the solutions via a careful adaptation of the moving plane procedure of Alexandrov-Serrin. NB:This talk is part of the activity of the MIUR Excellence Department Project MATH@TOV CUP E83C18000100006
25/11/22	Seminario	16:00	17:00	1201 Dal Passo	Alessandro IRACI	Università di Pisa	Algebra & Representation Theory Seminar (ARTS) "Delta and Theta operators expansions" N.B.: This talk is part of the activity of the MIUR Excellence Department Project MATH@TOV CUP E83C18000100006 Abstract Delta and Theta operators are two families of operators on symmetric functions that show remarkable combinatorial properties. Delta operators generalise the famous nabla operator by Bergeron and Garsia, and have been used to state the Delta conjecture, an extension of the famous shuffle theorem proved by Carlsson and Mellit. Theta operators have been introduced in order to state a compositional version of the Delta conjecture, with the idea, later proved successful, that this would have led to a proof via the Carlsson-Mellit Dyck path algebra. We are going to give an explicit expansion of certain instances of Delta and Theta operators when t=1 in terms of what we call gamma Dyck paths, generalising several results including the Delta conjecture itself, using interesting combinatorial properties of the forgotten basis of the symmetric functions.
25/11/22	Seminario	14:30	15:30	1201 Dal Passo	Giovanni GAIFFI	Università di Pisa	Algebra & Representation Theory Seminar (ARTS) "Combinatorial aspects of the cohomology of compactifications of toric arrangements" N.B.: This talk is part of the activity of the MIUR Excellence Department Project MATH@TOV CUP E83C18000100006 Abstract I will describe how to construct monomial bases for the integer cohomology rings of compact wonderful models of toric arrangements. In the description of the monomials various combinatorial objects come into play: building sets, nested sets, and the fan of a suitable toric variety. In particular, I will focus on the case of the toric arrangements associated with root systems of type A. Here the combinatorial description of these basis offers a geometrical point of view on the relation between some eulerian statistics on the symmetric group. This is a joint work with Oscar Papini and Viola Siconolfi.
22/11/22	Seminario	16:00	18:00	1200 Biblioteca Storica	Dario Fasino	Università degli Studi di Udine	Metodi matriciali nell'analisi di reti complesse Abstract Breve panoramica sulla scienza delle reti. Concetti classici di centralità basati su cammini minimi. Misure di centralità, somiglianza e distanza tra nodi basate su tecniche spettrali e funzioni di matrici. Catene di Markov a tempo discreto: Percorsi casuali classici e non-retrocedenti. Tecniche matriciali per la localizzazione di clusters, strutture core-periphery o quasi-bipartite. Introduzione ai percorsi casuali del secondo ordine: Tensori stocastici, PageRank nonlineare. Il seminario fa parte delle attività del Progetto MIUR Dipartimento d'Eccellenza CUP E83C18000100006 e del centro RoMaDS.