Seminars, 2014

  • December 31, 2014
    Matrix-Tree Theorems and Discrete Path Integration
    Dr.Yu. Burman, Independent University of Moscow and Higher School of Economics, Moscow, Russia
  • December 30, 2014
    Representations and Characters of Lie superalgebras
    Dr. Shifra Reif, University of Michigan, USA

    Lie superalgebras and their representations were introduced to mathematics to study supersymmetry in theoretical physics and have since been applicable in algebra, combinatroics, number theory and various other fields.
    In this talk we will discuss the structure and representation theory of Lie superalgebras. We shall focus on the Kac-Wakimoto formula for the characters of their representations, conjectured in 1994, and recently proved. Joint with Michael Chmutov and Crystal Hoyt.
  • December 23, 2014
    On a new type of conformality in R4 and bicomplex holomorphic functions
    Dr. Maria Elena Luna-Elizarraras, Instituto Politecnico Nacional, Mexico
  • December 16, 2014
    Deforming metrics on foliated manifolds
    Prof. Vladimir Rovenski, The University of Haifa
  • December 9, 2014
    Methane bubble growth in fine-grained muddy aquatic sediments: insights from modeling
    Dr. Regina Katsman, The University of Haifa
    Gassy sediments contribute to destabilization of aquatic infrastructure, air pollution, and global warming. In the current study a precise shape and size of the buoyant mature methane bubble in fine-grained muddy aquatic sediment is defined by numerical and analytical modeling, their results are in a good agreement. A closed-form analytical solution defining the bubble parameters is developed. It is found that the buoyant mature bubble is elliptical in its front view and resembles an inverted tear drop in its cross-section. The size and shape of the mature bubble strongly correlate with sediment fracture toughness. Bubbles formed in the weaker sediments are smaller and characterized by a larger surface-to-volume ratio that induces their faster growth and may lead to their faster dissolution below the sediment-water interface. This may prevent their release to the water column and to the atmosphere. Shapes of the bubbles in the weaker sediments deviate further from the spherical configuration, than those in the stronger sediments. Modeled bubble characteristics, important for the acoustic applications, are in a good agreement with field observations and lab experiments.
  • October 28, 2014
    A tale of quasimorphisms and quasi-states
    Prof. Tobias Hartnick, Technion
    In the 1950s Ulam suggested a new mathematical field of "quasi-algebra”, where algebraic definitions get modified by allowing algebraic conditions to hold only “up to a small error”. 
    Quasimorphisms are what you obtain when you “quasify” the notion of a group homomorphism. First examples of quasimorphisms arose already in the 4th century BC in Eudoxus' construction of the real numbers, but a conceptual framework for their study was only given more than 2300 years later. Quasimorphisms on Lie groups give rise to Lie quasi-states, a concept which played a major role in the early days of quantum mechanics. In this talk we will take a walk through the rich zoo of quasimorphisms and quasi-states and discuss some of their uses in different areas of mathematics.
  • September 18, 2014
    Proper group actions in complex geometry
    Prof. A. Isaev, Australian National University, Australia
    In their celebrated paper of 1939 Myers and Steenrod showed that the group of isometries of a Riemannian manifold acts properly on the manifold. This fact has many consequences. In particular, it
    implies that the group of isometries is a Lie group in the compact-open topology. This result triggered extensive studies of closed subgroups of the isometry groups of Riemannian manifolds. The peak of activities in this area occurred in the 1950s-70s, with many outstanding mathematicians involved: Kobayashi, Nagano, Yano, H.-C. Wang, I. P. Egorov, to name a few. In particular, Riemannian manifolds whose isometry groups possess subgroups of sufficiently high dimensions were explicitly determined.
    I will speak about proper actions in the complex-geometric setting. In this setting (real) Lie groups act properly by holomorphic transformations on complex manifolds. My general aim is to build a theory parallel to the theory that exists in the Riemannian case. In my lecture I will survey recent classification results for complex manifolds that admit proper actions of high-dimensional groups.
  • June 16, 2014
    A functional analytic approach to singular perturbation problems: a quasi-linear heat transmission problem in a periodic dilute two-phase composite
    Prof. Massimo Lanza de Cristoforis, University of Padova, Italy 

    We  consider a temperature transmission problem for a composite material which fills the Euclidean space. The composite has a periodic structure and consists of two materials. In each periodicity cell one material occupies  an inclusion of size ε, and the second material fills the remaining part of the cell. We assume that the thermal conductivities of the materials depend nonlinearly upon the temperature. We show that for ε small enough the problem has a solution, i.e., a pair of functions which determine the temperature distribution in the two materials. Then we analyze the behaviour of such a solution as ε approaches 0.