Seminars, 2016

  • November 29, 2016
    Representation theory of Lie superalgebras
    Dr. Crystal Hoyt, Weizmann Institute

    What are possible matrix solutions of the following equation XY +  YX = 1?   One approach to answering such a question is to study Lie superalgebras and their representations.  Lie superalgebras first appeared in physics in the 70s in the theory of supersymmetry, and since then they have been studied extensively.  In 1977, Victor Kac classified all finite-dimensional simple Lie superalgebras. A nice class of Lie superalgebras, the “Kac-Moody superalgebras”, can be presented by generators and relations, however these are not finite dimensional in general. In joint work with Vera Serganova, I classified the Kac-Moody superalgebras of "finite growth".  In my talk, I will discuss these Lie superalgebras and their representations.
  • June 14, 2016
    Randomized Algorithms for Matrix Decomposition
    Dr. Yariv Aizenbud, Tel-Aviv University

    Matrix decompositions, and especially SVD, are very important tools in data analysis. When big data is processed, the computation of matrix decompositions becomes expensive and impractical. In recent years, several algorithms, which approximate matrix decomposition, have been developed. These algorithms are based on metric conservation features for linear spaces of random projections. We present a randomized method based on sparse matrix distribution that achieves a fast approximation with bounded error for low rank matrix decomposition.
  • May 31, 2016
    Reflection spaces - classical and not so classical
    Prof. Tobias Hartnick, Technion

    Reflection spaces were introduced by Ottmar Loos in the late 60’s as generalizations of Euclidean and hyperbolic spaces. We will survey the classical theory of smooth reflection spaces, starting from reflections in Euclidean space and leading   to a beautiful theorem of Loos which characterizes affine symmetric manifolds axiomatically. We will then discuss various more recent generalizations of the classical theory, in particular to infinite dimensions. We explain how to find a representation of a  finite reflection group inside a classical Riemannian symmetric space. We then show that certain geometric representations of infinite reflection groups admit similar globalizations into reflection spaces, albeit with slightly bizarre and unexpected properties. This latter part is based on ongoing joint work with W. Freyn, M. Horn and R. Köhl. Since we start from reflections in R^n, no previous knowledge of symmetric spaces is required.
  • May 24, 2016
    Superdimension of Lie superalgebra representations
    Dr. Shifra Reif, ORT Braude College

    We shall discuss the notion of superdimension and methods to compute it for simple modules of basic Lie superalgebras. We give a superdimension formula for modules over the general linear Lie superalgebra and propose ideas on how one should approach the general case. Joint with Chmutov and Karpman.
  • May 10, 2016
    Mathematical billiards in the eye of symplectic
    Prof. Yaron Ostrover, Tel-Aviv University

    Mathematical billiards describe the motion of a massless particle in a domain with elastic reflections from the boundary. Despite the simplicity of the model, mathematical billiards present a broad variety of dynamical behaviors, from complete integrability to chaotic motion. Furthermore, the study of billiard dynamics has vast applications to different fields such as mathematical physics, number theory, acoustics, optics, etc.
    In this talk we will highlight some of the geometric aspects of billiard dynamics. In particular, we will explain how a certain symplectic invariant on the classical phase space can be used to obtain bounds and inequalities on the length of the shortest periodic billiard trajectory, and the relation of billiard dynamics to
    a 75 years-old open conjecture from convex geometry known as Mahler Conjecture. 
    No previous knowledge in symplectic geometry is assumed.
    The talk is based on a joint work with Shiri Artstein-Avidan and Roman Karasev.
  • April 12, 2016
    On a Class of Starlike Functions
    Prof. Nikola Tuneski, Ss. Cyril and Methodius University in Scopje, R. Macedonia

  • April 12, 2016
    Epidemic Modeling
    Dr. Rami Yaari, The Gertner Institute for Epidemiology and Health Policy Research, Tel-Hashomer Department of Statistics, Haifa University

    An epidemic model is a mathematical formulation of the manner an infectious disease spreads in a population. Given values to the model parameters and initial conditions, the model provides a description for the state of the disease spread over time (and space – if it is a spatial model).  In a deterministic formulation, the model provides the same description for a given set of parameter values, while in a stochastic formulation, the model will provide different possible descriptions for the same set of parameter values. Epidemic models are used as a tool in both theoretical (qualitative) and quantitative epidemiological research. In a theoretical research, the model is used to obtain general insights regarding the studied processes and to evaluate the behavior of a system under different regions of the parameter space. In a quantitative research, the model is fitted to epidemiological data collected during an epidemic in order to obtain estimates for the model parameters, and use these estimates to examine the dynamics of the epidemic and the factors that shaped it. The advantages of using a mathematical model as a research tool over a research based on an analysis of observations are the ability to study the effect of a given factor in an isolated manner, as well as the ability to repeat an experiment numerous times. A qualitative model can also provide forecasts to the way an epidemic would unfold and can be used as a tool to study the effectiveness of various mitigation strategies for an epidemic. The lecture will focus on a common type of models called compartmental models, in which the population is divided into groups that differ in terms of their potential/state of infection, while the model describes the transition of individuals from one group to another. We will go over important concepts such as the basic reproductive number (R0), the effective reproductive number (Re), the generation interval of the disease and ”herd immunity”. Finally, we will get a taste of two quantitative researches using epidemic modeling: a study of the spread of the 2009 influenza pandemic in Israel (“the swine flu”), and a study of the silent epidemic of polio among the Bedouin population of southern Israel in 2013.
  • March 29, 2016
    C^0 symplectic geometry
    Dr. Lev Buhovski, Tel-Aviv University

    I will try to give an overview of some topics from the field: Function theory on symplectic manifolds, C^0 Hamiltonian dynamics, C^0 rigidity and flexibility of smooth submanifolds.