"Conferinţele Facultăţii de Matematică" este o serie de expuneri adresate unui public larg de matematicieni, cu subiecte din diverse ramuri ale matematicii sau conexe acestora, realizate de personalităţi ale domeniului.

Programul colocviului

Vineri 30 mai 2025, ora 14:30 (Amfiteatrul Al. Myller)

• Cristinel MARDARE, Sorbonne Universite, Paris, Franţa, Approximations of the best constants.

Abstract: A classical theorem of Liouville about mappings from an Euclidean space into itself states that if such a mapping is sufficiently smooth and its gradient is a field of orthogonal matrices, then the mapping is necessarily affine. A quantitative version of this theorem, due to Friesecke, James & Muller, states that the W^1,p(Ω)-distance, 1 < p < +∞, between a mapping u : Ω -> Rⁿ and the set of all affine mappings from Ω into Rⁿ is bounded above by the L^p-distance between the gradient field ∇u : Ω -> R^n×n and the set of all matrix fields from Ω into the set of special orthogonal matrices of order n.

We will discuss the applications of this result in nonlinear elasticity.

Vineri 14 martie 2025, ora 14 (Amfiteatrul Al. Myller)

• Liviu IGNAT, IMAR Bucureşti, Approximations of the best constants.

Abstract: In this talk we consider some well known quotients related with either eigenvalue problems, Sobolev or Hardy’s inequality. We consider the infimum of these quotients and their discrete analogous in a finite element subspace. We estimate the difference between the best constants above as the discretization parameter goes to zero and obtain sharp convergence rates.

Vineri 22 martie 2024, ora 16 (Amfiteatrul Al. Myller)

• Philippe GILLE, Universite Claude Bernard Lyon 1, Franţa & IMAR, Forme pătratice algebrice şi u-invariantul.

Abstract: Prima parte va fi o introducere în teoria algebrică a formelor pătratice, i.e. formele pătratice peste un corp arbitrar K, de caracteristică diferită de 2 (Gauss, Sylvester, Witt, Milnor,…). Un important invariant al corpului K este u-invariantul, notat cu u(K) (Kaplansky). Este definit ca supremumul dimensiunilor formelor pătratice anizotropice peste k, i.e. acele forme pătratice care se anulează doar la 0. Studiul invariantului u(K) are o istorie destul de surprinzatoare. Vom încheia cu unele rezultate recente privind u(K) datorate lui Parimala-Suresh şi vom discuta unele aspecte conexe.

Vineri 29 septembrie 2023, ora 16 (Sala de Conferinţe a Observatorului Astronomic)

• CS I Mirel Bîrlan, Institutul Astronomic al Academiei Romane, membru al Academiei Internationale de Astronautica, Astronomia asteroizilor: aspectul si structura lor interna.

Vineri 12 mai 2023, ora 17 (Amfiteatrul Al. Myller)

• Prof. dr. Aurel RĂŞCANU, membru corespondent al Academiei Române, Professor Emeritus Universitatea "Al. I Cuza" din Iaşi, Elemente de calcul stochastic şi aplicaţii la ecuaţii diferenţiale cu derivate parţiale.

Abstract: Formula Feynman–Kac surprinde legatura puternica dintre ecuatiile diferentiale stochastice si ecuatiile diferentiale cu derivate partiale de ordinul doi (eliptice, parabolice) in intreg spatiul, sau pe domenii marginite cu conditii la frontiera de tip Dirichlet-Neumann.
Dupa o scurta expunere a catorva elemente de calcul stochastic:
- miscarea browniana,
- integrala stochastica Ito,
- formula Ito
se prezinta faimoasa formula Feynman–Kac. Sunt trecute in revista cateva aplicatii ale acestei formule in reprezentarea solutiilor unor EDP.

Miercuri 19 octombrie 2022, ora 16 (Amfiteatrul I.3)

• Prof. dr. Liviu ORNEA, Universitatea Bucureşti, Despre geometria varietatilor Hopf.

Abstract: Varietăţile Hopf sunt câturi ale lui Cⁿ-{0} prin acţiunea unei contracţii olomorfe, inversabile cu centrul în 0. Voi descrie structura complexă şi structura metrică ale acestor varietăţi, combinând tehnici de geometrie şi analiză. Expunerea se bazează pe articole în colaborare cu Misha Verbitsky.

Vineri 2 aprilie 2021, ora 16 (online: Zoom Meeting)

• Prof. dr. Sorin DASCALESCU, Universitatea Bucuresti, On the classification of finite dimensional Hopf algebras.

Abstract: We present some fundamental facts about the structure of Hopf algebras, and discuss the state of the classification of finite dimensional Hopf algebras, with an emphasis on the pointed and semisimple cases.

Vineri 19 februarie 2021, ora 16 (online: Zoom Meeting)

• Prof. dr. Constantin ZALINESCU, Academia Romana & Universitatea "Alexandru Ioan Cuza", On entropy optimization and Lagrange multipliers.

Abstract: I shall speak about the use of the Lagrange multipliers method for obtaining the optimal solutions of entropy optimization problems.

Vineri 15 ianuarie 2021, ora 18 (online: Zoom Meeting)

• Prof. dr. Daniel TATARU, University of California, Berkeley, Free boundary problems for a compressible gas.

Abstract: This talk is concerned with the evolution of an inviscid, compressible gas with a vacuum boundary, e.g. a gaseous star.
This is a degenerate hyperbolic free boundary problem of interest to both mathematicians and physicists. The goal will be to describe a new, Eulerian approach for the study of the local well-posedness for this problem. This is joint work with Mihaela Ifrim, and, in part, with Marcelo Disconzi.

Vineri 11 decembrie 2020, ora 15 (online: Zoom Meeting)

• Prof. dr. Liviu NICOLAESCU, University of Notre Dame, Spectral perestroika.

Abstract: I will describe how to reconstruct the geometry of a Riemann manifold from the knowledge of eigenvalues and eigenfunctions of the scalar Laplacian and then I will explain the probabilistic flavour of this perestroika.

Joi 14 mai 2020, ora 16 (online: Zoom Meeting)

• Acad. Viorel BARBU, Academia Romana Nonlinear Fokker-Planck equations and trend to equilibrium in statistical mechanics.

Abstract: One surveys a few recent results on well-posedness and longtime behaviour (H-theorem) of solutions to nonlinear Fokker-Planck equations.