Dipartimento di Matematica -UTV-

Date	Type	Start	End	Room	Speaker	From	Title
08/05/24	Seminario	16:00	17:00	1201 Dal Passo	Roberto Conti	Sapienza Università di Roma	Operator Algebras Seminar Positive definite Fell bundle maps Abstract C-algebraic bundles (nowadays simply called Fell bundles) were introduced by Fell at the end of the sixties as yet another tool to deal with the representation theory of locally compact groups. The reason why the related literature is still growing is probably due to the fact that they fit pretty well with various aspects of the theory of (twisted) actions (and coactions) of groups (and groupoids) on C-algebras. For instance, many familiar constructions like group C-algebras and crossed products can be viewed as cross sectional C-algebras of suitable Fell bundles. In the talk we will introduce the concept of positive definite "multiplier" between Fell bundles and discuss some consequences and applications. Especially, a notion of amenability for Fell bundles naturally appears. Other applications are concerned with the construction of certain functors from the category of positive definite multipliers to the category of completely positive maps between C-algebras and with the existence of certain C-correspondences associated to left actions of Fell bundles on right Hilbert bundles. (Joint work with E. Bedos)
07/05/24	Seminario	14:30	15:30	1101 D'Antoni	Cinzia Casagrande	Università di Torino	Geometry Seminar Fano 4-folds con fibrazioni razionali su 3-folds Abstract Sia X una varietà di Fano liscia, complessa, di dimensione 4, e rho(X) il suo numero di Picard. Inizieremo discutendo il seguente risultato: se rho(X)>12, allora X è un prodotto di superfici di del Pezzo; se rho(X)=12, allora X ha una contrazione razionale X-->Y dove Y ha dimensione 3. Una contrazione razionale è una mappa data da una successione di flips seguita da un morfismo suriettivo a fibre connesse, vedremo degli esempi espliciti. Poi discuteremo le proprietà geometriche delle Fano 4-folds che hanno una contrazione razionale su una 3-fold. Un obiettivo è di determinare il massimo numero di Picard di X, ed eventualmente di classicare i casi con numero di Picard grande. Un altro obiettivo è di usare questa descrizione geometrica per costruire nuovi esempi con rho grande; questo è un progetto in corso con Saverio Secci. NB: This talk is part of the activity of the MIUR Department of Excellence Project MatMod@TOV (2023-2027)
03/05/24	Colloquium	15:00	16:00	1201 Dal Passo	Benjamin Schlein	Universität Zürich	Colloquium di Dipartimento Bogoliubov theory for dilute quantum systems Abstract In the setting of many-body quantum mechanics, I am going to present a rigorous and recently developed version of Bogoliubov theory. Furthermore, I am going to show how this theory can be applied, on the one hand to study the low-energy spectrum of dilute Bose gases (i.e. to determine the low-lying eigenvalues of their Hamilton operator) and, on the other hand, to approximate their time-evolution, capturing fluctuations around the nonlinear Gross-Pitaevskii equation describing the dynamics of the Bose-Einstein condensate. NB:This colloquium is part of the activity of the MIUR Excellence Department Project MATH@TOV CUP E83C23000330006
30/04/24	Seminario	16:00	17:00	1101 D'Antoni	Gianluca Pacienza	Institut Élie Cartan de Lorraine - Nancy	Geometry Seminar Regenerations and applications Abstract Chen-Gounelas-Liedtke recently introduced a powerful regeneration technique, a process opposite to specialization, to prove existence results for rational curves on projective K3 surfaces. In the talk I will present a joint work with G. Mongardi in which we show that, for projective irreducible holomorphic symplectic manifolds, an analogous regeneration principle holds and provides a very flexible tool to prove existence of uniruled divisors, significantly improving known results.
30/04/24	Seminario	14:30	15:30	1101 D'Antoni	Zhi Jiang	Fudan University, Shanghai	Geometry Seminar Irregular surfaces of general type with minimal holomorphic Euler characteristic Abstract We explain our recent work on the classification of surfaces of general type with p_g=q=2 or p_g=q=1. Our approach is based on cohomological rank functions, the Chen-Jiang decomposition/Fujita decomposition and Severi type inequalities. This talk is based on a joint work with Jiabin Du and Guoyun Zhang and a joint work in progress with Hsueh-Yung Lin.
24/04/24	Seminario	16:00	17:00	1201 Dal Passo	Alex Bols	ETH Zürich	Operator Algebras Seminar The anyon sectors of Kitaev's quantum double models Abstract In this talk I will explain how to extract an 'anyon theory' (braided tensor category) from a gapped ground state of an infinite two-dimensional lattice spin system. Just as in the DHR formalism from AQFT, the anyon types correspond to certain superselection sectors of the observable algebra of the spin system. We apply this formalism to Kitaev's quantum double model for finite gauge group G, and find that the anyon types correspond precisely to the representations of the quantum double algebra of G. The Operator Algebra Seminar schedule is here: https://sites.google.com/view/oastorvergata/home-page?authuser=0
23/04/24	Seminario	16:00	17:00	1201 Dal Passo	Philippe Souplet	Université Sorbonne Paris Nord & CNRS	Seminario di Equazioni Differenziali Liouville-type theorems, singularities and universal estimates for nonlinear elliptic and parabolic problems Abstract The Cauchy-Liouville theorem (1844) states that any bounded entire function of a complex variable is necessarily constant. In the realm of PDE's, by a Liouville-type theorem, one usually means a statement asserting the nonexistence of solutions in the whole space (or a suitable unbounded domain). Numerous results of this kind have appeared over the years and many far-reaching applications have arisen, conferring Liouville-type theorems an important role in the theory of PDE's and revealing strong connections with other mathematical areas (calculus of variations, geometry, fluid dynamics, optimal stochastic control). After a brief historical detour (minimal surfaces - Lagrange, Bernstein, de Giorgi, Bombieri,… and regularity theory for linear elliptic systems - Giaquinta, Necas, ...), we will recall the developments of the 1980-2000's on nonlinear elliptic problems, leading to powerful tools for existence and a priori estimates for Dirichlet problems (Gidas, Spruck, Caffarelli, ...), based on the combination of Liouville type theorems and renormalization techniques. In a more recent period, this line of research has also led to much progress in the study of singularities of solutions, both for stationary (elliptic) and evolution PDEs. In particular, in the case of power like nonlinearities, we will recall the equivalence between Liouville type theorems and universal estimates, based on a method of doubling-rescaling (joint work with P. Polacik and P. Quittner, 2007). Then we will present recent developments which show that these renormalization techniques can be applied to nonlinearities without any scale invariance, even asymptotically, with applications to initial and final blowup rates or decay rates in space and/or time. Note: This talk is part of the activity of the MIUR Department of Excellence Project MatMod@TOV (2023-2027)
23/04/24	Seminario	14:30	16:00	1101 D'Antoni	Lukas Branter	University of Oxford	Deformations and lifts of Calabi-Yau varieties in characteristic p Abstract Homotopy theory allows us to study formal moduli problems via their tangent Lie algebras. We apply this general paradigm to Calabi-Yau varieties Z in characteristic p. First, we show that if Z has torsion-free crystalline cohomology and degenerating Hodge-de Rham spectral sequence (and for p=2 a lift to W/4), then its mixed characteristic deformations are unobstructed. This generalises the BTT theorem from characteristic 0 to characteristic p. If Z is ordinary, we show that it moreover admits a canonical (and algebraisable) lift to characteristic zero, thereby extending Serre-Tate theory from abelian varieties to Calabi-Yau varieties. This is joint work with Taelman, and generalises results of Achinger-Zdanowicz, Bogomolov-Tian-Todorov, Deligne-Nygaard, Ekedahl–Shepherd-Barron, Iacono-Manetti, Schröer, Serre-Tate, and Ward.
22/04/24	Seminario	16:00	17:00	1201 Dal Passo	Andrew Clarke	UPC Barcelona	Seminario di Sistemi Dinamici Chaotic properties of billiards in circular polygons Abstract Circular polygons are closed plane curves formed by concatenating a finite number of circular arcs so that, at the points where two arcs meet, their tangents agree. These curves are strictly convex and C1, but not C2. We study the billiard dynamics in domains bounded by circular polygons. We prove that there is a set accumulating on the boundary of the domain in which the return dynamics is semiconjugate to a transitive shift on infinitely many symbols. Consequently the return dynamics has infinite topological entropy. In addition we give an exponential lower bound on the number of periodic orbits of large period, and we prove the existence of trajectories along which the angle of reflection tends to zero with optimal linear speed. These results are based on joint work with Rafael Ramírez-Ros. Note: This talk is part of the activity of the MIUR Department of Excellence Project MatMod@TOV (2023-2027)
22/04/24	Seminario	14:30	15:30	1201 Dal Passo	Anna Miriam Benini	Università di Parma	Seminario di Sistemi Dinamici Wandering Domains and Non Autonomous Dynamics on the disk Abstract In one dimensional complex dynamics we have an increasingly detailed knowledge about stable components which are periodic and preperiodic. On the other hand, stable components which elude being (pre)periodic (aka wandering domains) also elude our full understanding and are currently an active topic of research. While much of the current research focuses on constructing examples showing a great variety of possibilities, in our work we propose an actual classification of wandering domains according to the behaviour of their internal orbits. This seamlessly leads us to analyzing nonautonomous dynamics for self-maps of the unit disk. For autonomous iteration of inner functions (self-maps of the disk whose radial extension is a self map of the boundary a.e.) there is a remarkable dichotomy due to Aaronson, Doering and Mañé, according to which the internal dynamics of the map determines the dynamical properties of its boundary extension: either (almost all) boundary orbits converge to a single point, or (almost all) boundary orbits are dense. In the nonautonomous setting the situation is more complicated. However, we present a generalization of this dichotomy which is, in a specific sense, optimal. This is joint work with Vasso Evdoridou, Nuria Fagella, Phil Rippon, and Gwyneth Stallard. Parts of this work are still in progress. Note: This talk is part of the activity of the MIUR Department of Excellence Project MatMod@TOV (2023-2027)