• Date:17TuesdayOctober 2017

    Dissecting a Three-Protein Brain: The Chemosensory Array of E. coli

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    Time
    10:00 - 11:00
    Location
    Nella and Leon Benoziyo Building for Biological Sciences
    Auditorium
    Lecturer
    Prof. John S. Parkinson
    Dept. of Biology - University of Utah
    Organizer
    Department of Biomolecular Sciences
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    Lecture
  • Date:17TuesdayOctober 2017

    Future climate change will reduce herbicide efficiency

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    Time
    11:30
    Location
    Nella and Leon Benoziyo Building for Biological Sciences
    Auditorium
    Lecturer
    Dr. Maor Matzrafi
    Department of Plant Sciences, University of California-Davis, USA
    Organizer
    Department of Plant and Environmental Sciences
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    Lecture
  • Date:17TuesdayOctober 2017

    Geometry and Topology Seminar

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    Time
    16:15 - 17:15
    Title
    Holography of traversing flows and its applications to the inverse scattering problems
    Location
    Jacob Ziskind Building
    Lecturer
    Gabriel Katz
    MIT
    Organizer
    Faculty of Mathematics and Computer Science, Department of Computer Science and Applied Mathematics, Department of Mathematics
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    AbstractShow full text abstract about We study the non-vanishing gradient-like vector fields $v$ o...»
    We study the non-vanishing gradient-like vector fields $v$ on smooth compact manifolds $X$ with boundary. We call such fields traversing.
    With the help of a boundary generic field $v$, we divide the boundary $d X$ of $X$ into two complementary compact manifolds, $d^ X(v)$ and $d^-X(v)$. Then we introduce the causality map $C_v: d^ X(v) o d^-X(v)$, a distant relative of the Poincare return map.
    Let $mathcal F(v)$ denote the oriented 1-dimensional foliation on $X$, produced by a traversing $v$-flow.
    Our main result, the Holography Theorem, claims that, for boundary generic traversing vector fields $v$, the knowledge of the causality map $C_v$ is allows for a reconstruction of the pair $(X, mathcal F(v))$, up to a homeomorphism $Phi: X o X$ which is the identity on the boundary $d X$. In other words, for a massive class of ODE's, we show that the topology of their solutions, satisfying a given boundary value problem, is rigid. We call these results ``holographic" since the $(n 1)$-dimensional $X$ and the un-parameterized dynamics of the flow on it are captured by a single correspondence $C_v$ between two $n$-dimensional screens, $d^ X(v)$ and $d^-X(v)$.
    This holography of traversing flows has numerous applications to the dynamics of general flows. Time permitting, we will discuss some applications of the Holography Theorem to the geodesic flows and the inverse scattering problems on Riemannian manifolds with boundary.
    Lecture