Dipartimento di Matematica -UTV-

Date	Type	Start	End	Room	Speaker	From	Title
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.
22/11/22	Seminario	16:00	17:00	1201 Dal Passo	Massimiliano Berti	SISSA Trieste	Seminario di Equazioni Differenziali Benjamin-Feir instability of Stokes waves Abstract A classical subject in fluid mechanics regards the spectral instability of traveling periodic water waves, called Stokes waves. Benjamin, Feir, Whitam and Zhakarov predicted, through experiments and formal arguments, that Stokes waves in sufficiently deep water are unstable, finding unstable eigenvalues near the origin of the complex plane, corresponding to small Floquet exponents $mu$ or equivalently to long-wave perturbations. The first rigorous mathematical results have been given by Bridges-Mielke (’95) in finite depth and by Nguyen-Strauss (’20) in infinite depth. On the other hand, it has been found numerically that when the Floquet number $mu$ varies, two eigenvalues trace an entire figure-eight. I will present a novel approach to prove this conjecture fully describing the unstable spectrum. This is joint work with A. Maspero and P. Ventura. Note: This talk is part of the activity of the MIUR Department of Excellence Project MATH@TOV CUP E83C18000100006.
22/11/22	Seminario	14:00	16:00	1200 Biblioteca Storica	Enrico Bozzo	Università degli Studi di Udine	Sistemi dinamici lineari su grafi Abstract Argomenti: Grafi e matrici: concetti di connettività, matrice di adiacenza, matrici non negative, matrici primitive, teoria di Perron-Frobenius. Matrici stocastiche e substocastiche, problema del consenso. Matrici Laplaciane e di Metzler, punti di equilibrio e consenso nel caso continuo, cenno ai sistemi compartimentali. Il seminario fa parte delle attività del Progetto MIUR Dipartimento d'Eccellenza CUP E83C18000100006 e del centro RoMaDS.