Seminars, 2017

Lectures:
  • December 12, 2017
    Finding the closest pair of points on two polyhedra 
    Dr. Zilin Jiang, Technion

    Abstract
    Given two disjoint convex polyhedra, we look for a pair of points, one in each polyhedron, attaining the minimum distance between the sets. We propose a process based on projections onto the half-spaces defining the two polyhedra. This is a joint work with Ron Aharoni and Yair Censor.
  • November 28, 2017
    Introduction to Geometric Structures and Classification of Generalized Cusps on Convex Projective Manifolds 
    Dr. Arielle Leitner, Technion

    Abstract
    The first half of the talk will be an introduction to geometric structures in the sense of Thurston. We will also review a bit of projective geometry, and take a virtual tour with computer visualizations through some interesting types of geometry. 
     
    In the second part of the talk, we will discuss conditions for deforming properly convex projective structures to get new properly convex projective structures. A necessary condition is that the ends of the manifold have the structure of generalized cusps. I have classified these in dimension 3, and together with Sam Ballas and Daryl Cooper, we have classified generalized cusps in dimension n.  We will discuss the geometry, volume, and classification by lattices, and deformation theory of generalized cusps.
  • July 25, 2017
    Forman's Ricci curvature and its applications to Complex Networks 
    Dr. Emil Saucan, Technion - Israel Institute of Technology, Israel

    Abstract
    Traditionally, network analysis is based on local properties of vertices, like their degree or clustering coefficient, and their statistical behavior across the network in question, thus concentrating on the elements of the network (nodes), rather than on their interrelations (edges), that define, in effect, the network.
    We propose an alternative edge-based approach. The geometric tool that enables us to do this is Forman's discretization of Ricci curvature, initially devised for quite general weighted CW complexes. We show that in the limit case of 1-dimensional complexes, i.e. networks (or graphs) this notion is still powerful and expressive enough to allow us to capture not only local, but also global properties of networks, both weighted and unweighted, directed as well as undirected. We show the robustness of this notion and compare it to other, more classical, graph invariants and network descriptors, both on standard model networks and on a variety of real-life networks.
    Furthermore, we develop a fitting Ricci flow, and we apply it in the analysis of dynamic networks, and employ it to such tasks as change detection, denoising and clustering of experimental data, as well as to the extrapolation of network evolvement.
    Moreover, we consider not only the pairwise correlations in networks, but also the higher order ones, that are especially important in biological and social networks, and apply Forman's original notion to the resulting complexes (hyper-networks) together with an adapted Ricci flow.
    This represents joint work with Juergen Jost, Melanie Weber and Areejit Samal.

    Presentation

     

  • June 27, 2017
    Statistical mechanics approach to modeling of the soft condensed matter: Fundamentals and applications
    Prof. Andrij Trokhymchuk, Institute for Condensed Matter Physics of the National Academy of Sciences of Ukraine

    Abstract
    Soft condensed matter is a complex system composed of huge number of atoms and/or molecules. A goal of the modeling of matter in general, and the soft condensed matter in particular is to predict the observed or macroscopic properties. The properties vary depending of both the composition (is it a single atom component, compound, solution or mixture of many different chemical species) as well as the external parameters like temperature, pressure, volume of the system. Statistical mechanics fulfills this task by providing relations between the observable properties of the system and forces acting between the microscopic constituents of the soft condensed matter system. In this lecture, I will present the most important of these relations and will discuss the examples of mathematical issues that are appearing on this way, including those that have been already solved and those that still are in the process.
  • June 20, 2017
    Partition relations equiconsistent with high rank measurable
    cardinals
    Prof. Yechiel M. Kimchi, CS Faculty, Technion, Israel

  • June 13, 2017
    Data Science and its applications
    Eitan Lifshits, Cyberint, Israel

    Abstract
    Data science today is one of the most evolving and widely used areas. Involving mathematics, statistics and computer science, it has a wide range of applications, such as Machine Learning, Natural Language Processing, Image Processing and many more.
    In the lecture we go through data related domains and roles in industry as well as desired skills and knowledge.
    A second part will describe few text analysis examples, from Machine Learning to Near Duplicates problem.
  • June 6, 2017
    THE GARSIDE GROUPS AND SOME OF THEIR PROPERTIES
    Dr. Fabienne Chouraqui, Oranim College, Israel

    Abstract
    Garside groups have been first introduced by P Dehornoy and L.Paris in 1990. In many aspects, Garside groups extend braid groups and more generally finite-type Artin groups. These are torsion-free groups with a word and conjugacy problems solvable, and they are groups of fractions of monoids with a structure of lattice with respect to left and right divisibilities. It is natural to ask if there are additional properties Garside groups share in common with the intensively investigated braid groups and finite-type Artin groups. In this talk, I will introduce the Garside groups in general, and a particular class of Garside groups, that arise from certain solutions of the Quantum Yang Baxter equation. I will describe the connection between these theories arising from different domains of research, present some of the questions raised for the Garside groups and give some partial answers to these questions.
  • June 1, 2017
    Multi-point Schwarz-Pick lemma and its applications
    Prof. Toshiyuki Sugawa, Tohoku University, Japan

    Abstract
    A multi-point Schwarz-Pick lemma was first asserted by Beardon and Minda in their 2004 paper published in J. Anal. Math. We deduce several useful inequalities from the lemma and apply them to Geometric Function Theory. For instance, we obtain a sharp coefficient inequality for analytic self-maps of the unit disk with a prescribed fixed point.