Notiziario Scientifico

Settimana dal 18 al 24 maggio 2015

Lunedì 18 maggio 2015
Ore 14:30, aula di Consiglio
Colloquium di Analisi Matematica
Felix Otto (Max Planck Institute for Mathematics in the Sciences, Leipzig)
A quantitative theory of stochastic homogenization
The topic of stochastic homogenization of elliptic partial differential equations in divergence form is classical. It is about the homogeneous large-scale behavior of heterogeneous media, like conductive media or elastic media, that are characterized in stochastic terms. Our interest grew out of quantifying the error scaling in the engineer's concept of a 'representative volume element', which allows to approximately extract the homogeneous coefficients. Meanwhile, the connections with classical regularity theory (attached to the names De Giorgi, Nash, Campanato, Meyers...) and with concepts of concentration of measure (as for instance captured by the Logarithmic Sobolev Inequalities) have emerged in a clearer way. Not only is the regularity theory for uniformly elliptic coefficient fields A a key ingredient, but stochastic homogenization sheds a new light on a generic large-scale behavior of A-harmonic functions - which is more regular than suggested by the classical counter-examples. We also advocate to exploring more the synergies between the treatment of quenched noise (like the random coefficients in stochastic homogenization) and thermal noise (like in statistical mechanics or stochastic partial differential equations).

Martedì 19 maggio 2015
Ore 14:00, aula 311, Unversità di Roma Tre (largo s. Leonardo Murialdo)
Seminario di Probabilità
Yinon Spinka (Tel Aviv)
Long-range order in random 3-colorings
We study the anti-ferromagnetic 3-state Potts model of statistical physics. In this model, one samples a random coloring of a box in Z^d with 3 colors, with the probability of a coloring f being proportional to exp(-β N(f)), where β>0 is a parameter (representing the inverse temperature) and N(f) is the number of edges connecting vertices colored with the same color. Our main result is that in high dimensions and low temperature (large β), a sampled coloring will typically exhibit long-range order, placing the same color at most of either the even or odd vertices of the box. This extends previous work of Galvin, Kahn, Peled, Randall and Sorkin. The main ingredient in our proof is a new structure theorem for 3-colorings which characterizes the ways in which different 'phases' may interact, putting special emphasis on the role of edges connecting vertices of the same color. We also discuss several related conjectures. No background in statistical physics will be assumed and all terms will be explained. Joint work with Ohad Feldheim.

Martedì 19 maggio 2015
Ore 14:30, aula Dal Passo, Università di Roma Tor Vergata
Seminario di Equazioni Differenziali
Juncheng Wei (UBC Vancouver)
Nondegeneracy of sign-changing solutions to Yamabe problem and its applications
We first establish the existence of a sequence of nondegenerate, in the sense of Duyckaerts-Kenig-Merle, nodal solutions to the critical Yamabe problem

-ΔQ=|Q|^4/(N-2)Q, Q ∈ D^1,2(R^N)
Then we use it to construct sign-changing bubbling solutions to the slightly super-critical Bahri-Coron problem in a bounded domain with nontrivial topology.

Martedì 19 maggio 2015
Ore 15:00, aula di Consiglio
Seminaio di Modellistica Differenziale Numerica
Emiliano Cristiani (IAC-CNR)
Blended numerical schemes for the advection equation
In this talk we discuss a method to couple two or more explicit numerical schemes approximating the same equation, in order to create new schemes which inherit advantages and drawbacks of the original ones. In the lucky cases, the combination allows to increase the accuracy of all the original schemes but the price to pay is a larger computational time.
For illustrative purposes, we focus on the coupling of two schemes only. We couple both two macroscopic (Eulerian) schemes and a microscopic (Lagrangian) with a macroscopic one. In the latter case we get a new kind of multiscale numerical method. As a test problem, we consider the advection equation.

Mercoledì 20 maggio 2015
Ore 14:30, aula di Consiglio
Seminario di Algebra e Geometria
Alessandro Valentino (Bonn)
Central extensions of mapping class groups from characteristic classes
I will discuss a functorial construction of extensions of mapping class groups of smooth manifolds which are induced by extensions of (higher) diffeomorphisms groups via the group stack of automorphisms of manifolds equipped with higher degree topological structures. The problem of constructing such extensions arises naturally in the study of topological quantum field theories, in particular in 3d Chern-Simons theory. Joint work with Domenico Fiorenza and Urs Schreiber.

Mercoledì 20 maggio 2015
Ore 15:15, aula di Consiglio
Seminario di Algebra e Geometria
Ghislain Fourier (Glasgow)
Quantum PBW filtrations and monomial ideals
Our aim is to define a PBW-type filtration for quantum groups, following the framework from recent years in the non-quantum setup. For this we recall main properties of this classical filtration which guideline us towards a quantum PBW filtration. In type A_n we obtain an appropriate degree function via dimensions of homomorphism space of the corresponding oriented quiver. By specializing to q=1, we obtain a new filtration on the universal enveloping algebra and hence on any simple module. We can give a basis for the associated graded module and see that the annihilating ideal is monomial, in contrast to the standard PBW filtration. We finish with exploring the relations to flag varieties, Schubert varieties, quiver Grassmanian and their degenerations to toric varieties. This is joint work with X. Fang and M. Reineke

Mercoldì 20 maggio 2015
Ore 16:00, aula F, Università di Roma Tre (largo s. Leonardo Murialdo)
Colloquium di Matematica
Juncheng Wei (University of British Columbia)
On Serrin's over-determined problem and a conjecture of Berestycki-Caffarelli-Nirenberg
In 1972, Serrin proved that the only bounded domain such that the overdetermined problem

Δ u + f(u)=0 in Ω, u=0 and ∂_νu= C on ∂Ω
admits a solution are balls. When the domain Ω becomes unbounded and Ω^c is connected, in 1997, Berestycki, Caffarelli and Nirenberg conjectured that Ω is either a half-space, or a cylinder Ω=B_k⊕R^n-k, or the complement of a ball or a cylinder. We discuss recent progress on this conjecture.

Mercoledì 20 maggio 2015
Ore 16:30, aula di Consiglio
Seminario di Fisica Matematica
Paolo Antonelli (GSSI, L'Aquila)
Analysis of finite energy weak solutions for some systems in quantum fluid dynamics
In this talk I will review some global existence results for the quantum hydrodynamic system. Such systems arise in the description of superfluids, Bose-Einstein condensates and in the modeling of semiconductor devices. The analysis is done by avoiding the WKB ansatz and it allows the presence of nodal regions, namely the regions where the mass density vanishes: this is interesting also from the physical point of view because it is the region where the quantized vortices (of the superfluid) are located. I will then present some new results for systems describing Bose condensed gases at finite temperatures, where the quantum fluid is coupled to a classical fluid.

Mercoldì 20 maggio 2015
Ore 17:00, aula Dal Passo, Università di Roma Tor Vergata
Makoto Yamashita (Ochanomizu University, Tokyo)
Poisson boundary of monoidal categories
Motivated by by the theory of dimension for tensor categories by Longo and Roberts, and also by the theory of noncommutative Poisson boundary by Izumi, we define the notion of categorical Poisson boundary for rigid C^*-tensor categories with irreducible unit. We recover many known constructions in the theory of subfactors and quantum groups as a part of this categorical boundary. In the so called weakly amenable case, we prove that the Poisson boundary has a universality property for the amenable dimension function, which has implications both to subfactors and to quantum groups. This talk is based on joint work with S. Neshveyev.

Giovedì 21 maggio 2015
Ore 11:15, aula Dal Passo, Università di Roma Tor Vergata
Colloquium dei dottorandi in Matematica di Roma I, Roma II e Roma III
Rocio Isabel Paez (Università di Roma Tor Vergata)
Perturbation theory for Trojan motion
Trojan motion is a classical subject of Celestial Mechanics, from both analytical and numerical points of view. Its main problem is due to the existence of singularities corresponding to close encounters between the Trojan and primary bodies. While numerical approaches can easily overcome this issue, analytical treatments face convergence problems that pose obstructions to representing Trojan motions in terms of series expansions. The talk will focus on introducing the Trojan problem as a particular case of the Restricted 3-Body Problem. Furthermore, we will present a set of basic tools of Perturbation Theory, used to the study of problems in Celestial Mechanics via a Hamiltonian Formulation and reduction to normal forms by Lie transformations. We will also show some novel approaches for bypassing the convergence problem.

Giovedì 21 maggio 2015
Ore 12:00, aula Dal Passo, Università di Roma Tor Vergata
Colloquium dei dottorandi in Matematica di Roma I, Roma II e Roma III
Ruggero Bandiera (Sapienza Università di Roma)
Gruppoidi di Deligne superiori
Nel corso del colloquium rivedremo la costruzione, dovuta a Getzler, del gruppoide di Deligne superiore di una dg Lie algebra, e il suo ruolo in teoria delle deformazioni e in teoria dell'omotopia razionale. Data una dg Lie algebra (o più in generale una L-infinity algebra) pronilpotente L, il gruppoide di Deligne superiore di L è l'insieme simpliciale delle cocatene di Maurer-Cartan sul simplesso cosimpliciale standard a coefficienti in L. Per dg Lie algebre concentrate in gradi non negativi questo generalizza il gruppoide di Deligne ordinario (da cui l'importanza in teoria delle deformazioni), mentre ristretto alla categoria delle dg Lie algebre concentrate in gradi strettamente negativi realizza l'equivalenza di Quillen tra questa categoria modulo quasi-isomorfismi e la categoria degli spazi connessi e semplicemente connessi modulo equivalenze omotopiche razionali. Descriveremo alcune applicazioni alla teoria dell'omotopia razionale di spazi non necessariamente connessi (e.g., mapping spaces). Infine, tempo permettendo, illustreremo il teorema di discesa di Hinich per gruppoidi di Deligne ordinari e il suo ruolo in teoria delle deformazioni, e mostreremo come segue da un più generale teorema di discesa per gruppoidi di Deligne superiori.

Giovedì 21 maggio 2015
Ore 15:00, aula 1B1, Dipartimento SBAI
Seminario di Geometria
Giovanni Cerulli Irelli (Sapienza Università di Roma)
Introduzione alla teoria delle algebre cluster
Motivati dalla teoria delle basi canoniche di Lusztig, e con lo scopo di descriverne gli elementi esplicitamente, Sergei Fomin e Andrei Zelevinsky hanno scoperto (almeno congetturalmente) una struttura algebrica sull'anello delle coordinate di certe varietà di interesse (ad esempio Grassmanniane, sottogruppi unipotenti di Gruppi algebrici, varietà di bandiere..) che hanno chiamato algebra cluster. La definizione di un'algebra cluster si basa sulla definizione di mutazione di un polinomio di Laurent. In questo seminario introduttivo alla teoria, discuterò il concetto di mutazione e la definizione di algebra cluster attraverso esempi espliciti. Parlerò poi dei teoremi principali della teoria e delle congetture ancora aperte.

Giovedì 21 maggio 2015
Ore 15:00, aula F, Università di Roma Tre (largo s. Leonardo Murialdo)
Beyond Logic Hypothetical Reasoning in Philosophy of Science, Informatics, and Law
15:00 Luiz Carlos Pereira (PUC Rio de Janeiro), TBA
16:15 Cesare Cozzo (Sapienza Univ. Roma), Dummett on inference
17:30 Arnaud Valence (Univ. Roma Tre), Dewey's Logic Revisited

Venerdì 22 maggio 2015
Ore 09:30, aula 311, Università di Roma Tre (largo s. Leonardo Murialdo)
Beyond Logic Hypothetical Reasoning in Philosophy of Science, Informatics, and Law
09.30 Jean Fichot (IHPST, Univ. Paris 1), Principles(s) of conservativity
10:45 Jean-Baptiste Joinet (Univ. Lyon 3), Actional processes, individuals and identity criteria
12:00 Paolo Pistone (Univ. Roma Tre & Aix-Marseille Univ.), Untyped validity: completeness through parametricity

Venerdì 22 maggio 2015
Ore 15:00, aula 211, Università di Roma Tre (largo s. Leonardo Murialdo)
Beyond Logic Hypothetical Reasoning in Philosophy of Science, Informatics, and Law
15:00 Mael Pegny (IHPST, Univ. Paris 1), Constructivity and the Church-Turing thesis
16:15 Thomas Piecha (Univ. Tubingen), Inversion of logical rules
17:30 Peter Schroeder-Heister (Univ. Tubingen), Proof-theoretic semantics and the sequent calculus

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