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Mathematics Department

Basic Notions Seminar

Fall 2013

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

  • Nov
    06
  • A brief introduction to cooperative game theory
    Prof. Nelson Uhan
    USNA
    Time: 01:00 AM

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    Cooperative game theory provides a mathematical framework for determining "fair" ways of sharing the costs of cooperating and participating in a joint enterprise. In this talk, I will introduce some basic concepts from cooperative game theory, present a few classic results, and discuss their connections to polyhedral combinatorics, matroids, and linear programming duality. In addition, I will describe some applications, and if time permits, some of my recent research in this area.
  • Oct
    30
  • Turbulence modeling
    Prof. Evelyn Lunasin
    USNA

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    The prediction of turbulent flows by direct numerical simulation of the Navier-Stokes equations (NSE) remains prohibitively expensive due to the wide range of spatial and temporal scales that need to be resolved when simulating turbulent flows. To avoid this problem one may consider regularizing the NSE either by adding artificial dissipation or by modifying the nonlinearity before performing any numerical discretization. This talk is an overview of a certain family of sub-grid-scale turbulence models. We will start with some historical background and then discuss their advantages in certain physical applications.
  • Oct
    23
  • From Pappus to Caley, and Bach(arach)
    Prof. Will Traves
    USNA
    Time: 01:00 AM

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    I'll introduce Pappus's Theorem and its generalizations, leading to my recent work, some of which will appear in December's Math Monthly. The topic is an interesting blend of advanced (but very accessible!) geometry.
  • Oct
    16
  • Permutation statistics and q,t-Catalan numbers
    Prof. Nick Loehr
    USNA
    Time: 01:00 AM

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    This talk gives an introduction to a part of algebraic combinatorics that relates algebraic objects (specifically, the Hilbert series of certain vector spaces defined by taking quotients of polynomial rings) to combinatorial objects (specifically, permutations and lattice paths weighted by appropriate statistics). The first half of the talk shows how the inversion and major index statistics on S_n encode information about a certain ring of coinvariants. The next part introduces the q,t-Catalan numbers, which give a surprising unification of seemingly unrelated concepts in various areas: word combinatorics, lattice path combinatorics, representation theory, algebraic geometry, symmetric functions, partition theory, and Macdonald polynomials.
  • Oct
    09
  • 0/1 constraint-satisfaction problems and Pfaffian circuits
    Prof. Susan Margulies
    USNA
    Time: 01:00 AM

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    The notion of a Pfaffian circuit arises from L. Valiant's work with "holographic algorithms" and J. Cai and V. Choudhary's subsequent lifting of "holographic algorithms" to the language of tensor products and tensor contraction networks. The essence of L. Valiant's famous Holant Theorem is that there exists an equation where the left-hand side is evaluated in exponential-time, but the right-hand side is evaluated in polynomial-time. The notion of a Pfaffian circuit mimics the idea of L. Valiant's Holant Theorem by again identifying two quantities with differing evaluation times: the first is a particular tensor product (computable in exponential-time), and the second is the Pfaffian of a carefully constructed matrix (computable in polynomial-time). In this talk, I will introduce tensor contraction networks and their relationship to #CSP problems, as well as the notion of a Pfaffian circuit.
  • Sep
    23
  • Ergodic theorem and Poincare recurrence
    Prof. Kostya Medynets
    USNA
    Time: 01:00 AM

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    We will talk about two the most fundamental results of ergodic theory---the pointwise ergodic theorem and the Poincare recurrence lemma. Most of the talk will be devoted to applications of these results in various branches of mathematics.
  • Sep
    16
  • Arithmetic modulo primes and quadratic rational maps
    Dr. Brian Stout
    USNA
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