Seminari/Colloquia
Pagina 4
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  Positive definite Fell bundle maps
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  Fano 4folds con fibrazioni razionali su 3folds
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 4folds che hanno una contrazione razionale su una 3fold. 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 (20232027) 
03/05/24  Colloquium  15:00  16:00  1201 Dal Passo  Benjamin Schlein  Universität Zürich  Bogoliubov theory for dilute quantum systems
In the setting of manybody 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 lowenergy spectrum of dilute Bose gases (i.e. to determine the lowlying eigenvalues of their Hamilton operator) and, on the other hand, to approximate their timeevolution, capturing fluctuations around the nonlinear GrossPitaevskii equation describing the dynamics of the BoseEinstein 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  Regenerations and applications
ChenGounelasLiedtke 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  Irregular surfaces of general type with minimal holomorphic Euler characteristic
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 ChenJiang 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 HsuehYung Lin.

24/04/24  Seminario  16:00  17:00  1201 Dal Passo  Alex Bols  ETH Zürich  The anyon sectors of Kitaev's quantum double models
In this talk I will explain how to extract an 'anyon theory' (braided tensor category) from a gapped ground state of an infinite twodimensional 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/homepage?authuser=0 
23/04/24  Seminario  16:00  17:00  1201 Dal Passo  Philippe Souplet  Université Sorbonne Paris Nord & CNRS  Liouvilletype theorems, singularities and universal estimates for nonlinear elliptic and parabolic problems
The CauchyLiouville theorem (1844) states that any bounded entire function of a complex variable is necessarily constant. In the realm of PDE's, by a Liouvilletype 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 farreaching applications have arisen, conferring Liouvilletype 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 19802000'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 doublingrescaling (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 (20232027) 
23/04/24  Seminario  14:30  16:00  1101 D'Antoni  Lukas Branter  University of Oxford  Deformations and lifts of CalabiYau varieties in characteristic p
Homotopy theory allows us to study formal moduli problems via their tangent Lie algebras. We apply this general paradigm to CalabiYau varieties Z in characteristic p. First, we show that if Z has torsionfree crystalline cohomology and degenerating Hodgede 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 SerreTate theory from abelian varieties to CalabiYau varieties. This is joint work with Taelman, and generalises results of AchingerZdanowicz, BogomolovTianTodorov, DeligneNygaard, Ekedahl–ShepherdBarron, IaconoManetti, Schröer, SerreTate, and Ward.

22/04/24  Seminario  16:00  17:00  1201 Dal Passo  Andrew Clarke  UPC Barcelona  Chaotic properties of billiards in circular polygons
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 RamírezRos.
Note: This talk is part of the activity of the MIUR Department of Excellence Project MatMod@TOV (20232027) 
22/04/24  Seminario  14:30  15:30  1201 Dal Passo  Anna Miriam Benini  Università di Parma  Wandering Domains and Non Autonomous Dynamics on the disk
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 selfmaps of the unit disk. For autonomous iteration of inner functions (selfmaps 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 (20232027) 
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