Seminars, 2010
  • December 27, 2010

    Mathematical Models in General Insurance
    Dr. Alex Segal, Head of Insurance Risks Section, P&C Actuarial Department


    In this talk we will cover some of the fundamental aspects of the theory of insurance, concentrating on the part of this theory related to general insurance.
    We will explain main ideas involved in reinsurance and illustrate these ideas using an example of excess of loss treaty.
    Finally, we will exhibit the problem of optimal pricing of a heterogeneous insurance portfolio.

  • December 13, 2010

    Mathematical methods in digital image processing. Geometric distortion correction and mosaic image creation
    Dr. Karelin Irina, Algorithm Manager, DenCT Company


    Creation of mosaic image whose parts are small images is widely used idea. Usually these small images suffer from many problems such as different types of noises, geometric distortion, intensity discrepancies of one to another etc. To create resulted image of high quality it is necessary to achieve smooth seamless stitching between its small parts. These problems are solved by different mathematical methods which will be discussed.

  • November 22, 2010

    Remarks on the Bohr and Rogosinski phenomena for power series
    Prof. Lev Aizenberg, Bar-Ilan University


    The following problems are discussed in this work.
    1. The Bohr and Rogosinski radii for Hardy classes of functions holomorphic in the disk.
    2. Neither Bohr nor Rogosinski radius exists for functions holomorphic in an annulus, with natural basis
    3. Asymptotics of the majorant function in the Reinhardt domains in Cn.
    4. The Bohr and Rogosinski radii for the mappings of the Reinhardt domains into Reinhardt domains.

  • November 8, 2010

    Modeling infectious disease dynamics
    Dr. Haggai (Guy) Katriel, Biomathematics Unit in the Faculty of Life Sciences, Tel-Aviv University


    The aim of mathematical and computational epidemiology is to develop models that will help us to understand and predict the spread of infectious diseases in populations. I will give an overview of some of these efforts, focusing on recent work studying influenza epidemics.

  • September 13, 2010

    Infinitely divisible laws in the free probability and Nevanilnna -Pick analytic function
    Prof. M. Bozejko, University of Wroclaw, Poland


    We consider the free additive convolution of probability measures on the real line introduced by Dan Voiculescu and we will presented the main results on infinitely divisible laws in that convolution done by H. Bercovici and D.Voiculescu in his paper in Pacific J.Math.1992 .Also Bercovici-Pata bijection between classical infinitely divisible measures on the real line and the free case will be done, see important paper of H.Bercovici and V.Pata in Ann.of Math.149, (1999), 1023-1060.
    The Levy-Khinchine theorem for free additive convolution will be recalled, which is in the language of Voiculescu R-transform is done by Nevanilnna -Pick theorem for analytic functions mapping upper half-plane C^{+} into C^{+}.
    We also present our last results with Anshelevich, Belinschi,Lehner,Speicher and myself, that classical Normal law N(0,1) and q-Gaussian laws(i.e. theta one function of Jacobi) are infinitely divisible in the free convolution, for details see our papers in arXiv or in Math.Res.Lett. 17(2010), 909-920.
    Relations with recent papers of A.Connes and D.Kreimer and W.Bryc and A.Dembo and T.Jiang on generalized gaussian processes and random matrices will be also in the lecture.

  • August 11, 2010

    Sub-Riemannian geometry in examples
    Prof. I. Markina, University of Bergen, Norway


    Sub-Riemannian manifolds and the geometry introduced by bracket generating distributions of smoothly varying $k$-plains is widely studied, interesting subject, that has applications in control theory, quantum physics, C-R geometry, and other areas. We present all necessary definitions and several examples and applications where sub-Riemannian geometry naturally arises.
    Among them we consider parallel parking problem, rolling motion, qubits, nilpotent Lie groups and odd dimensional spheres.

  • August 11, 2010

    Applications of moduli method to extremal problems for conformal homeomorphisms of the unit disk
    Prof. A. Vasiliev, University of Bergen, Norway


    We consider extremal problems which involve angular derivatives of conformal homeomorphisms of the unit disk at its boundary. We show a geometric approach based on reduced moduli of digons and triangles. Relations to semigroups of conformal homeomorphisms of the unit disk will be discussed.

  • July 05, 2010

    Local exponential estimates for h-pseudodifferential operators with operator-valued symbols and tunneling for waveguides
    V. S. Rabinovich, National Polytechnic Institute, Mexico


    Abstract (Link)