Mathematical Colloquium

PROGRAM

PROGRAM ZA MAJ 2017.

ČETVRTAK, 04.05.2017. u 15:15, Sala 301f, MI SANU, Kneza Mihaila 36
Ilijas Farah, York University, Toronto
LOGIKA I ALGEBRE OPERATORA
Proucavanje algebri operatora na Hilbertovom prostoru je zapocelo 30tih godina dvadesetog veka i od tada se ono prosirilo na mnoge oblasti moderne matematike, ukljucujuci geometriju, teoriju brojeva, ergodicku teoriju, matematicku fiziku, i topologiju. Zbog njihove konkretne prirode, misljenje da su problemi nastali u izucavanju algebri operatora "imuni" od skupovnoteoretske nezavisnosti je bilo opsteprihvaceno medju ekspertima. Ovo misljenje je promenjeno razvojem u poslednjih desetak godina, i to ce biti tema ovog predavanja.

PETAK, 05.05.2017. u 14:15, Sala 301f, MI SANU, Kneza Mihaila 36
Sandro Coriasco, Faculty of Mathematics, University of Torino
SOLUTIONS OF A CLASS OF NONLINEAR STOCHASTIC EQUATIONS ON Rⁿ: A MICROLOCAL APPROACH
We study random field and function-valued solutions of certain hyperbolic stochastic partial differential equations, involving linear partial differential operators with polynomially bounded coefficients. We first analyze linear equations, and provide conditions on the initial data and on the stochastic terms, so that a random field solution exists and is unique. We will then illustrate the case of some associated semilinear equations, and discuss an analogous existence and uniqueness result of a function-valued solution. This is joint work with A. Ascanelli and A. Suss.

PONEDELJAK, 08.05.2017. u 14:15, Sala 301f, MI SANU, Kneza Mihaila 36
Theodore Popelensky, MGU, Moscow
ON COMBINATORIAL RICCI FLOW ON SURFACES
After R. Hamilton's paper "Three-manifolds with positive Ricci curvature" (1982), a natural question about properties of the Ricci flow on surfaces arose. In this dimension the long-time existence and convergence were proved more or less easy: in 1986, R. Hamilton announced and in 1988 published the proof of convergence of the Ricci flow to the metric of constant curvature for arbitrary initial metric for any closed surface different form the sphere; in 1991, B. Chow closed the question by proving the same statement for two-dimensional sphere.
In 2003 B. Chow and F. Luo investigated on of possible "discretization" of the Ricce flow. Fixed data consists of a closed surface, its triangulation, and weights on the edges of the triangulations. For this object one has so called "circle packing metrics", corresponding curvatures, and Ricci flow. This version of discretization is important due to the circle packings which were investigated by Thurston in his unpublished book "Geometry and topology of 3-manifolds".
Chow and Luo showed that under certain conditions on the weight function the Ricci flow converges exponentially fast to the metric of constant curvature. One of the important conditions consists in non-negativity of the weights.
Recently R. Pepa and me were able to weaken some of the Clow-Luo conditions. Namely some weights can be negative but still should satisfy some conditions. Also we show that the weakening the conditions cannot be unlimited. We found examples of triangulation of surfaces and weights on the edges of the triangulation such that there exists saddle points of the Ricci flow.
In the talk I give the exposition of old results and present some new ones.

PETAK, 12.05.2017. u 14:15, Sala 301f, MI SANU, Kneza Mihaila 36
Boban Veličković, Department of Mathematics, University of Paris VII
SPEKTRUM L_{\omega_1,\omega} TEORIJA
Za datu teoriju T u nekoj logici L, spektar, spec(T), je klasa kardinala kapa za koje postoji model od T kardinalnosti kapa. Zbog teoreme Lowenheim-Skolem-a za logiku prvog reda pitanje pripadnosti spektru od T je interesantno samo za konacne kardinale. U ovom predavanju razmatracemo pitanje spektra za logiku L_{\omega_1,\omega}. Ova logika se dobija tako sto se familija atomskih formula zatvori za negacije, prebojive konjunkcije i disjunkcije i kvantifikacije po konacno mnogo promenljivih. Analiza spektra spec(fi) za tvrdjenja fi u L_{\omega_1,\omega} logici vodi zanimljivim pitanjima na preseku izmedju teorije skupova u teorije modela. U predavanju cemo dati pregled poznatih i predstaviti par novih rezultata. Takodje cemo spomenuti nekoliko otvorenih problema u ovoj oblasti.

PETAK, 26.05.2017. u 14:15, Sala 301f, MI SANU, Kneza Mihaila 36
Vladlen Timorin, HSE, Moscow
LAMINATIONAL MODELS FOR SPACES OF POLYNOMIALS
This is a joint work with Alexander Blokh, Lex Oversteegen and Ross Ptacek. We will discuss combinatorial structure of spaces of complex polynomials. The latter are viewed as dynamical systems. A classic example is the Mandelbrot set which parameterizes complex quadratic polynomials with "interesting dynamics" up to affine conjugacy. A combinatorial model for the Mandelbrot set, which is also a conjectural topological model, is known. We address the issue of finding combinatorial models for spaces of higher degree polynomials. As in the quadratic case, it is useful first to model individual polynomials (combinatorial models for polynomials are provided by Thurston's laminations), and then use appropriate spaces of laminations to model the corresponding spaces of polynomials.