Colloquium  

Spring 2014

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

  • May 06
    An Algorithm for Advancing Slow Features in Fast-Slow Systems without Separation - A Young Measure Approach Prof. Edriss Titi Weizmann Institute of Science (Israel) and UC Irvine Abstract

  • Apr 14
    Optimizing the Societal Benefits of the Annual Influenza Vaccine: A Stochastic Programming Approach Prof. Andrew Schaefer University of Pittsburgh Abstract

  • Apr 09
    A new method for finding solutions to certain Galois embedding problems Prof. Andy Schultz Wellesley College

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    One of the major open problems in Galois theory is the inverse Galois problem: for a given group G and field F, how does one detect if F has an extension L whose Galois group is G? One can approach this problem inductively when G has a nontrivial quotient Q by using the short exact sequence from Galois theory; this leaves us with a relativized version of the inverse Galois problem which is called a Galois embedding problem. Typically one analyzes embedding problems by performing calculations in second cohomology. For a certain class of groups, we describe a new technique that relies instead on basic linear algebra. This allows us to give precise enumeration results for a wide class of embedding problems and puts fairly severe restrictions on the structure of absolute Galois groups.
  • Apr 04
    The Ghost effect, thermal creep, and Hilbert's 6th problem Prof. Marshall Slemrod University of Wisconsin

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    In this talk my goal is to show how a project originally begun by J.C. Maxwell shortly before his death in 1879 helps us understand one aspect of Hilbert's 6th problem. In particular I claim the rigorous derivation of the Euler equations of gas dynamics from the Boltzmann equation of statistical physics cannot be achieved.
  • Mar 26
    Characteristic $p$ methods in commutative algebra Prof. Craig Huneke University of Virginia

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    Since the early 1970s, reduction to characteristic $p$ has been one of the most successful tools in commutative algebra. This talk will focus on one or two classical problems to illustrate this method. Let $R$ be a polynomial ring over the complex numbers in $d$-variables. If $P$ is a prime ideal, the $n$th symbolic power of $P$ is the set of all polynomials which vanish to order $n$ along $P$. An amazing result, proved by Ein, Lazarsfeld and Smith around 2000, proves that functions vanishing to order $dn$ along $P$ can be always written as sums of products of $n$-functions vanishing at $P$. We will describe this result, and related more recent work, and show how reduction to characteristic $p$ is done in this specific case.
  • Mar 19
    Recent progress on Gomory and Johnson's infinite group problem Prof. Amitabh Basu Johns Hopkins University

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    Ralph Gomory and Ellis Johnson introduced the so-called infinite group problem in the 70s as an elegant infinite dimensional abstraction of general mixed-integer optimization problems. Since then it has played a very important role in polyhedral combinatorics - a key tool for solving general mixed-integer optimization problems. In recent years powerful tools from analysis, convex geometry, and combinatorics have come together to make significant breakthroughs in this problem. We review recent results for the infinite group problem, and discuss the many challenging open problems that still remain.
  • Mar 05
    Webs and Springer varieties Prof. Heather Russell Washington College

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    Webs are oriented, trivalent, planar graphs that diagrammatically encode information about intertwining maps between certain representations. They can be used to explain the Jones polynomial as well as other well-known quantum knot invariants. The combinatorics of webs have recently been used to study Springer varieties. In particular, they reveal information about the structure of irreducible components and how components intersect one another. In this talk, we will introduce webs, define Springer varieties, and discuss the interplay between the two.
  • Feb 26
    An introduction to calculus of functors and its applications to knots and links Prof. Ismar Volic Wellesley College

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    The goal of this talk is to give an introduction to manifold calculus of functors, a theory which "categorifies" the ordinary Taylor series of a function, and discuss how this theory can in particular be used for studying knots and links. I will go over the basic construction of the Taylor tower of approximations for the space of knots and explain how this leads to a new point of view on finite type invariants of knots that have received much attention in the last fifteen years. A generalization to links and braids, which is joint work with B. Munson, will also be discussed.
  • Jan 13
    Finite Number of Determining Parameters for the Navier-Stokes Equations with Applications into Feedback Control and Data Assimilations Prof. Edriss Titi Weizmann Institute of Science (Israel) and UC Irvine Abstract

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