Mathematics Department

Basic Notions Seminar

Spring 2016

All talks are from 3:45-4:45 p.m. in the Seminar room, unless otherwise specified.

  • May
    02
  • Symbolic Dynamics on Graded Graphs
    Kostya Medynets
    Location: CH320
    Time: 03:45 PM

    View Abstract

    In the talk we will explore the role of Bratteli diagrams, infinite graded graphs, in the study of symbolic dynamical systems. We will discuss how combinatorial properties of these graphs and their asymptotic growth rate impact dynamical behavior of the systems, including invariant measures and entropy. We will describe the construction of Bratteli diagrams for several classes of dynamical systems, including cutting sequences of Billiards and substitution dynamical systems. This talk should be accessible to a wide audience.
  • Apr
    25
  • The Riemann-Roch Theorem for Graphs
    Caroline Melles
    USNA
    Time: 03:45 PM

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    The Riemann-Roch theorem is one of the fundamental results on algebraic curves. In 2007, Baker and Norine formulated and proved a Riemann-Roch theorem for graphs. Central to their proof is the notion of a non-special divisor on a graph. Non-special divisors can be created by certain combinatorial procedures. The number of equivalence classes of non-special divisors on a graph is the value of the Tutte polynomial of the graph evaluated at (1,0). The Riemann-Roch theorem for graphs will be discussed, with emphasis on the role of non-special divisors in the proof.
  • Apr
    18
  • Successes and Failures of Linearization (Surprising Misbehavior of Piece-wise Smooth Systems)
    Irina Popovici
    USNA
    Time: 12:00 PM

    View Abstract

    1. A few standard results from non-linear ODEs associated with hyperbolic cases (when linearization works), and when small perturbations in the underlying system do not change the behavior of trajectories. 2. Standard results addressing the existence of cycles (linearization and perturbations of systems may lead to different trajectories). 3. Difficulties associated with systems that lack the C1 smoothness (only piece-wise smooth).

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