Seminars, 2017

  • May 9, 2017
    Quadrature Domains and Conformal Mappings
    Prof. Lavi Karp, ORT Braude College, Karmiel

    Newton showed that a ball with uniformly mass density gravitational attracts each point outside the ball as if all its mass were concentrated at the center of the ball (\textit{Philosophiæ Naturalis Principia Mathematica}). This property is equivalent to the mean value theorem of harmonic functions. Quadrature domains are a certain generalization of these properties.
    The talk will present examples of quadrature domains and discuss the construction of them by means of conformal mappings. We will also explore the Schwarz functions and some of its applications. The lecture will be held in introductory level and be accessible for students with background complex analysis.
  • April 18, 2017
    The Metric Dimension Problem
    Ron Adar, Department of Computer Science (PhD student), University of Haifa, Department of Mathematics

    Distances have significant roles in many optimization problem (both in theory and in "real life"). In this talk, I will present the metric dimension problem (and its weighted variant) which is an example of distances related graph optimization problem, and describe our work on calculating it on some specific graph classes. No previous background is required. Joint work with Leah Epstein.
  • March 21, 2017
    European Modelling Weeks and Study Groups with Industry
    Dr. Aviv Gibali, ORT Braude College

       The Mathematics for Industry Network (MI-NET) is a COST Action funded project which aims to facilitate more effective widespread application of mathematics to all industrial sectors, by encouraging greater interaction between mathematicians and industrialists. Two major activities are the Modelling Weeks and the Industrial Work shops.
       These events are week-long problem solving workshops, which provide a unique opportunity for interaction between mathematicians, statisticians, applied and computational scientists and industry. They bring together PhD Students, postdocs and professors to work intensively on real and diverse world problems.
       Since we plan to host a Modelling Week at the beginning of July 2017, in this presentation I wish to share some of my impressions regarding the industry problems we successfully approached in the last two Industrial Workshops I attended, the 118th and the 25th European Study Group with Industry (Dublin, Ireland, 4-8 July 2016, and Limassol, Cyprus, 5-9 December 2016).
  • February 6, 2017
    Modelling of the disease spread using cellular automaton computer simulations
    Prof. Jaroslav Ilnytskyi, Institute for Condensed Matter Physics of the National Academy of Sciences, Ukraine

    By means of the asynchronous cellular automata algorithm we study stationary states and spatial patterning in an SIS model, in which the individuals are attached to the vertices of a graph and their mobility is mimicked by varying the neighbourhood size q. Here we consider the following cases: q is fixed at certain value; and q is taken at random at each step and for each individual. The obtained numerical data are then mapped onto the solution of its version, corresponding to the limit q->infinity. This allows for deducing an explicit form of the dependence of the fraction of infected individuals on the curing rate. A detailed analysis of the appearance of spatial patterns of infected individuals in the stationary state is performed. We also consider a generalisation of this approach towards the model with multi-drug-resistant carriers and discuss future generalisations of the model to the case of the individuals on various types of networks.
  • January 10, 2017
    Spectral Analysis of a Complex Schrödinger Operator in the Semiclassical Limit
    Prof. Yaniv Almog, Department of Mathematics, Louisiana State University, USA

    We consider the operator −h2Δ+iV with either Dirichlet, Robin, or transmission boundary conditions, where V is a smooth real potential with no critical points, and the domain   is smooth as well.  We obtain the left margin of the  spectrum,in the semi-classical limit h→0.
    Joint works with Denis Grebenkov, Rapahael Henry and Bernard Helffer.