Santa Clara University

Mathematics and Computer Science department

Colloquium Series

Winter 2013

Unless otherwise noted, talks will be at 3:50 PM in Daly Science 201.  Also, there will be refreshments before each talk in O'Connor 31 at 3:30 PM.



Tuesday January 22nd, Daly Science 201

Speaker: Alissa Crans, Loyola Marymount U, Current Director of Educational Outreach Activities at MSRI

Title: "Quandles, Braids, and Tangles, oh my!"

Abstract:  While it may sound surprising, algebra and topology actually have a very close relationship!  One way to demonstrate this connection is through the language of "quandles".  A quandle is a set equipped with two binary operations satisfying axioms that capture the essential properties of group conjugation and algebraically encode the three Reidemeister moves.
Moreover, a cohomology theory of quandles exists and the cocycles serve as a source of invariants for knots and knotted surfaces.  After examining examples of quandles, we will illustrate their connection to knot theory, and in particular, to these Reidemeister moves.  We will also explore the method which enables us to associate a quandle to a given knot.  Finally, we will consider the collection of quandle homomorphisms and discuss preliminary results about the structure of this "hom quandle".

 


Tuesday, February 5th, Daly Science 201

Speaker: Frank Sottile, Texas A&M

Title: "Galois groups of Schubert problems"

Abstract:  Building on work of Jordan from 1870, in 1979 Harris showed that a geometric monodromy group associated to a problem in enumerative geometry is equal to the Galois group of an associated field extension.   Vakil gave a geometric-combinatorial criterion that implies a Galois group contains the alternating group.  With Brooks and Martin del Campo, we used Vakil's criterion to show that all Schubert problems involving lines have at least alternating Galois group.

My talk will describe this background and sketch a current project to systematically determine Galois groups of all Schubert problems of moderate size on all small classical flag manifolds, investigating at least several million problems.  This will use supercomputers employing several overlapping methods, including combinatorial criteria, symbolic computation, and numerical homotopy continuation, and require the development of new algorithms and software.


Tuesday, February 19th, Daly Science 201

Speaker: Carol Meyers, Lawrence Livermore National Lab

Title: Working for a National Laboratory in Operations Research, ‘The Science of Better’

Abstract: Are you curious as to the kind of work that is done at a national laboratory?  Have you heard of the field of operations research, or are you interested in learning about it and how it is applied to real problems?  In this talk I will describe the kinds of math I use in my job at Lawrence Livermore National Laboratory, as well as giving an introduction to the discipline of operations research.  The talk will focus primarily on two projects I have worked on.  The first of these involves using optimization techniques to assess policy options for downsizing the US nuclear weapons stockpile.  We discuss consolidation of the weapons complex in general, and our implementation of a mixed-integer linear programming model that is currently being used to evaluate policy alternatives.  The second topic addresses using supercomputers to help solve energy grid planning problems, based on ongoing work with energy stakeholders in the state of California.  With the increased introduction of renewable resources into the grid, planning models must account for increased intermittency of generation, which leads to larger and more complex optimization problems.  We demonstrate how such problems can be solved much more quickly via the use of supercomputing.

Tuesday, February 26th, Daly Science 201

Speaker: Brandyn Lee, Santa Clara University

Title: Generalizations of the Hermitian eigenvalue problem

Abstract: Dating back to the nineteenth century, the classic Hermitian eigenvalue problem asks what can be said about the eigenvalues of a sum of two Hermitian matrices, in terms of the eigenvalues of the summands.  In this talk, I will give discuss the history of this problem and the solution given by A. Klyachko in the '90's.  We will see that the classic problem is connected to the intersection theory, or Schubert calculus, of certain homogenous spaces (Grassmannians) associated to the special linear group.  By considering other semisimple complex algebraic groups (e.g., the special orthogonal or symplectic group) and their corresponding homogenous spaces, generalizations of the classic problem naturally arise.  If time permits, I'll mention results from my thesis.


Tuesday, March 5th, Daly Science 201

Speaker: Ben Ford, Sonoma State University

Title: The Mathematics of Traffic Jams

Abstract: Ever been stuck in traffic and wondered what caused the jam? While some seem to be caused by particular events - accidents, sights along the side of the road, etc. - many appear out of nowhere in otherwise smoothly-flowing traffic. We'll explore various models that are used to model traffic flow, and see if any of them can help you get around faster!


If you have a disability and require a reasonable accommodation,
please call/email Rick Scott 408-554-4460/rscott at scu dot edu (or
use 1-800-735-2929 TTY—California Relay).

Abstracts of previous talks are available here.
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