Notiziario Scientifico

Notiziario dei seminari di carattere matematico
a cura del Dipartimento 'G. Castelnuovo'
Sapienza Università di Roma

Settimana dal 29 gennaio al 4 febbraio 2018

Lunedì 29 gennaio 2018
Ore 14:15, aula di Consiglio
seminario di Analisi Matematica
Daniele Bartolucci (Università di Roma Tor Vergata)
Uniqueness and a priori estimates of blow up solutions of mean field equations
We discuss a recent result, obtained in collaboration with A. Jevnikar, Y. Lee and W. Yang, concerning the uniqueness of blow up solutions of mean field type equations as ρn converges to 8πm, m being a postive integer. If u1,n and u2,n are two sequences of bubbling solutions with the same ρn and the same (non degenerate) blow up set, then u1,n=u2,n for sufficiently large n. The proof of the uniqueness requires a careful use of some sharp estimates for bubbling solutions of mean field equations and the analysis of suitably defined Pohozaev-type identities, as recently introduced by C.S. Lin and S. Yan in the study of the Chern-Simons-Higgs gauge field theory. In particular, motivated by the Onsager statistical description of two dimensional turbulence, we are bound to obtain a refined version of an estimate about ρn-8πm.

Martedì 30 gennaio 2018
Ore 11:00, aula di Consiglio
discussione tesi di Dottorato
Francesco Meazzini (Sapienza Università di Roma)
Model categories in deformation theory
The aim is the formalization of Deformation Theory in an abstract model category, in order to study several geometric deformation problems from a unified point of view. The main geometric application is the description of the DG-Lie algebra controlling infinitesimal deformations of a separated scheme over a field of characteristic 0.

Martedì 30 gennaio 2018
Ore 14:00, aula B
seminario di Geometria Algebrica
Kieran O'Grady (Sapienza Università di Roma)
Jacobiana intermedia di varietà hyperkaehler di tipo Kummer generalizzata, III
Se X è una varietà iperkaehler di tipo Kummer, il gruppo di coomologia H3(X) ha dimensione 8, e quindi la Jacobiana intermedia J3(X) è un toro complesso compatto di dimensione 4, proiettivo se X è proiettiva. Farò vedere come ricostruire esplicitamente J3(X) a partire dalla struttura di Hodge su H2(X). Seguirà anche che la varietà di Kuga-Satake di una X proiettiva è il prodotto di 4 copie di J3(X) e che, se X è proiettiva, allora J3(X) è una varietà abeliana di tipo Weil. Lo studio di J3(X) suggerisce come (tentare di) costruire famiglie esplicite localmente complete di varietà iperkaehler di tipo Kummer proiettive.

Martedì 30 gennaio 2018
Ore 14:30, aula 311, pal. C, Università di Roma Tre, largo san Leonardo Murialdo 1
seminario di Fisica Matematica
A. Efremov (Ecole Polytechnique, Palaiseau)
Renormalization in QFTs
The problem of perturbative renormalization of φ4 and Yang-Mills theories is studied in four dimensional Euclidean space. The analysis is based on the Functional Renormalization group. This is a unified approach which permits to study a large class of field theories without recourse to Feynman diagrams. An important part of the work consists in establishing upper bounds in momentum space on all vertex functions at all loop orders. These bounds have a very natural graphical interpretation in form of trees. In Yang-Mills theory introduction of ultraviolet(UV) and infrared(IR) cut-offs breaks BRST invariance. Thus it is essential to prove at all loop orders that the construction can be accomplished in such a way that BRST invariance is restored when the UV cut-off goes to infinity. As a useful application we derive the violated Slavnov Taylor identities for the effective action in the Maximal Abelian Gauge and show the existence of the gluon condensate in the effective low energy theory obtained in one loop. We also consider the renormalization of the stochastic singular PDE for the Gross-Neveu-Yukawa interaction in two dimensional Euclidean space using the theory of regularity structures.

Martedì 30 gennaio 2018
Ore 16:00, aula D'Antoni, dipartimento di Matematica, Università di Roma Tor Vergata, viale della Ricerca Scientifica 1
seminario di Analisi Complessa
Lorenzo Guerini (University of Amsterdam)
Random local dynamics
The study of the dynamics of an holomorphic map near a fixed point is a central subject in complex dynamics. In this talk we will consider the corresponding random setting: given a probability measure μ with compact support on the space of germs of holomorphic maps fixing the origin, we study the iterates fn•...•f1, where each fi is chosen with probability μ. We will see, as in the non-random case, that the stability of the family of the random iterates can be studied by looking at the linear part of the germs in the support of the measure and, in particular, at some quantities commonly known as Lyapunov indexes. A particularly interesting case occurs when all Lyapunov indexes vanish. When this happens stability is equivalent to simultaneous linearizability of all germs in supp(μ).

Mercoledì 31 gennaio 2018
Ore 11:30, aula 211, pal. C, Università di Roma Tre, largo san Leonardo Murialdo 1
seminario di Fisica Matematica
M. Capanna (Università de L'Aquila)
Turing instability in a model with two interacting Ising lines
In [1], the author introduces a reaction-diffusion system to model the pattern formation phenomenon present in morphogenesis. Under the assumption that the reaction part of the system is stable around an equilibrium point, he finds conditions over the diffusion coefficients under which the hole system is unstable due to the amplification of non-zero Fourier modes. This phenomenon is known as Turing instability. In this talk, we introduce an interacting particle system at which the latter phenomenon is present. The system is a continuous-time Markov process that has two coupled discrete toruses with Ising spins as state-space. The evolution in each torus responds to macroscopic ferromagnetic Kac's potentials, while the spins in different toruses interact in a local attractive-repulsive way. About this model, we prove hydrodynamic limit, and find conditions that guarantee the occurence of Turing instability. In the Turing instability regime, we analyze the fluctuations of the density fields around the equilibrium point (0,0) by studying the limiting behaviour of the discrete Fourier modes of the system. More precisely, we prove that, at a time at which the process is infinitesimal, and under the proper spatial scaling, the unstable Fourier modes converge to a normal distribution while the rest of the modes vanish. We finally give a result about pattern formation at a time that converges to the critical one at which the process starts to be finite.
[1] A. M. Turing, The chemical basis of morphogenesis.

Mercoledì 31 gennaio 2018
Ore 15:00, aula Seminari, RM004, Dipartimento di Scienze di Base e Applicate per Ingegneria (SBAI), via A. Scarpa 16
seminario di Analisi Matematica
Maria Medina (Pontificia Universidad Catolica de Chile)
A first example of nondegenerate sign-changing solution for the Yamabe problem with maximal rank
In this talk we will construct a sequence of nondegenerate (in the sense of Duyckaerts-Kenig-Merle) nodal nonradial solutions to the critical Yamabe problem -Δu=[n(n-2)]/4 |u|4/(n-2)u, u∈D1,2(Rn), which, for n=4, provides the first example in the literature of a solution with maximal rank. This is a joint work with M. Musso and J. Wei.

Mercoledì 31 gennaio 2018
Ore 16:15, aula Seminari, RM004, Dipartimento di Scienze di Base e Applicate per Ingegneria (SBAI), via A. Scarpa 16
seminario di Analisi Matematica
Benedetta Pellacci (Università della Campania Luigi Vanvitelli)
Nonlinear Helmholtz equations: some existence results
The aim of this talk is to present some existence results of radially symmetric oscillating solutions for a class of nonlinear autonomous Helmholtz equations and in particular to analyse their exact asymptotic behavior at infinity. Some generalizations to non-autonomous radial equations as well as existence results for non-radial solutions will be discussed. These results are linked with the existence of standing waves solutions of nonlinear wave equations with large frequencies. Joint work with Rainer Mandel (Karlsruher Institut fur Technologie) and Eugenio Montefusco (Sapienza Università di Roma).

Giovedì 1 febbraio 2018
Ore 10:00, aule 5,6, Dipartimento di Scienze di Base e Applicate per Ingegneria (SBAI), via A. Scarpa 16
Discretaly, a workshop in Discrete Mathematics
10:00 D. Jungnickel On block codes of Steiner triple systems
10:50 A. Burgess On 2-factorization problems, from Oberwolfach to Hamilton and Waterloo, and beyond
11:45 G. Rinaldi Spanning tree decompositions of complete graphs orthogonal to 1-factorizations
12:00 A. Wassermann q-analogs of Group divisible designs
12:15 E. Brugnoli The golden cow construction
14:10 S. Ball On Sylvester problems for point sets in real space
15:00 L. Storme Cameron-Liebler sets in geometrical settings
16:15 S. Costa New 2-designs via strong difference families
16:30 F. Zullo MRD-codes and a new criteria for generalized twisted Gabidulin codes
16:45 M. Cavaleri Wreath product of graphs: spectrum and topological indices

Giovedì 1 febbraio 2018
Ore 11:00, aula B
seminario Giovani Ricercatori
Marco Olivieri
The Mathematical theory of Mechanics: between Classical and Quantum
At a first sight the theories of Classical and Quantum Mechanics have really different Mathematical natures, and these differences arise when one consider, for example, the observable quantities of a system. If in Classical Mechanics they can be described by measurable functions on the phase space, the Quantum Mechanics needs instead the functional analysis to study them as self-adjoint operators on appropriate Hilbert spaces. The aim of this talk is twofold: at first, to state the relation between the non-commutativity of the algebra of the observables and the arising of quantum effects in the system. Secondly, to present, despite the different approaches, a correspondence principle (that, operatively speaking, is a limit of scale) between the objects of the two theories. This allows to think to Classical and Quantum Mechanics just as two parts included in the same unique theory of Mechanics, and to obtain internal coherence thanks to Hamiltonian formalism. The seminar will be introductive to the argument and the attention will be focused for the most only to the case of a simple system of a finite number of particles, avoiding in this way too much generality and mathematical rigour but, hopely, giving a more clear and explanatory approach.

Venerdì 2 febbraio 2018
Ore 09:30, aule 5,6, Dipartimento di Scienze di Base e Applicate per Ingegneria (SBAI), via A. Scarpa 16
Discretaly, a workshop in Discrete Mathematics
09:30-10:10 O. Serra Linear analogues of additive theorems
10:20-11:00 J. Truss Ehrenfeucht-Fraissé games on linear orders
11:40-12:20 K. Alladi A partition theorem of Gollnitz and a new dual
12:30-12:45 S. Pagani Regions of uniqueness in discrete tomography
14:10-14:50 M. Primc Some new combinatorial identities related to representations of affine Lie algebras
15:00-15:40 J. Lepowsky tba
16:15-16:30 A. Svob Strongly regular graphs and groups
16:30-16:45 F. Pavese Strongly regular graphs from classical generalized quadrangles
16:45-17:00 S. Mattheus The forbidden configuration problem for polar triangles
17:00-17:15 D.A. Jaume Combinatorial interpretation of the Drazin inverse of trees

Venerdì 2 febbraio 2018
Ore 12:00, aula di Consiglio
seminari MoMa
Giorgio Parisi (Sapienza Università di Roma)
The physics of glasses form the viewpoint of theoretical physicists
Glassy materials are characterized by being solid (for all practical purpose) at low temperature in absence of a sharp transition from the liquid phase to the solid state. They are ubiquitous in nature: among them, we find window glasses, wax, honey, mozzarella cheese... In spite of the very strong experimental and theoretical effort done in the last century, there are many questions that are opened. During this seminar, I would also stress some progress that has been done in the recent years on hard spheres models of glasses.

Venerdì 2 febbraio 2018
Ore 16:00, aula Picone
Seminario per insegnanti (Piano Lauree Scientifiche)
Emiliano Ippoliti (Sapienza Università di Roma)
Il ragionamento euristico in matematica

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