The Fall 2008 Math Colloquium will be held at Pomona College, Wednesdays at 4:00pm. Ellis Cumberbatch and Mario Martelli will continue as Colloquia co-chairs for 2008-09. September 3 will be the traditional Post Colloquium, Non-Colloquium Party to be held at Sprague Library, Harvey Mudd College.
September 10, Shahriar Shahriari, Pomona College
Title: "Matchings and Marriage, Chains and Dominance"
Abstract: The subsets of a finite set, the divisors of a positive integer, the subspaces of a finite dimensional vector space over a finite field, and the subgroups of a finite group are examples of finite partially ordered sets (poset). Now assume that you have a poset with 22 elements. What conditions on the poset would assure that you can partition the elements into four chains (totally ordered subsets) of sizes 6, 6, 6, and 4, as well as into five chains of sizes 5, 5, 5, 5, and 2.
Partitions of posets into chains have been the object of a number of long standing conjectures (two of them by Pomona alumnus Jerry Griggs).
In this talk, I will survey recent results on these conjectures, and propose a new and more general conjecture. My focus will be on a certain class of posets called normalized matching posets, and I will present a number of results obtained in collaboration with undergraduate students Elinor Escamilla, Andreea Nicolae, Andrew Pearsall, Paul Salerno, and Jordan Tirrell.
This talk has no prerequisite and should be accessible to all.
Click here for the flyer.
September 17, Student Research Poster Session
Summer undergraduate and graduate research poster session at the Marian Miner Cook Athenaeum, Claremont McKenna College, sponsored by REBMI and CCMS.
September 24, Robert J. Sacker, University of Southern California
Title: "Semigroups of Maps and Periodic Difference Equations"
Abstract: A collection M of monotonic maps from the positive reals to the positive reals is defined. Each map is linearly bounded, has non-negative Schwarzian and is either concave increasing or convex decreasing. It is shown that M is a semigroup under composition that contains the sub-semigroup of fractional linear maps and each function in M that is uni-linearly bounded has a globally attracting exponentially asymptotically stable fixed point. Thus we obtain a condition under which a periodic difference equation (mapping system) will have a periodic solution having the same properties. Certain restricted algebraic operations are valid in M and the structure of M is explored together with conjectures regarding the
interlacing of roots of a rational function in M.
Click here for the flyer.
October 1, Adolfo Rumbos, Pomona College
Title: "Periodic Solutions to a Piece-wise Linear Second Order Ordinary Differential Equation "
Abstract: Consider the problem of determining values of $\mu$ and $\nu$ for
which the second order ordinary differential equation (ODE)
\begin{equation}\label{AbsEqn1}
-u''=\mu u^+ - \nu u^-
\end{equation}
has non--trivial solutions of period $2\pi$, where $u^+$ and $u^-$
denote the positive and negative parts, respectively, of the
function $u\colon\mathbb{R}\to\mathbb{R}$.
The set of pairs $(\mu,\nu)$ for which the ODE in (\ref{AbsEqn1})
has non--trivial, $2\pi$--periodic solutions is called the {\em Fu\v
cik--Dancer spectrum} for boundary value problem (BVP)
\begin{equation}\label{AbsBvp1}
\left \{
\begin{array}{l}
-u'' =\mu u^+ - \nu u^- \qquad\mbox{for }0
Click here for the flyer.
October 8, Anna Bargagliotti, Univeristy of Memphis
Title: "Rating System Design: Transforming Individual Preferences to Rating Scores"
Abstract: We use rating systems in our daily lives to represent
people's opinions. At a university, we are asked to use a scale to
rate our professors, departments, and students. On-line, markets such
as Ebay or Amazon, depend on their rating systems to create a
trustworthy environment. Can these rating systems provide accurate
descriptions of our opinions? Why don't all markets use the same
rating system? Is one system better than the other? We show that
different rating systems may translate the same opinion to different
conclusions. Using simple mathematics, we characterize the differences
in the systems and provide simple tools to determine whether rating
systems are consistent.
Click here for the flyer.
October 15, Raanan Schul, University of California, Los Angeles
Title: "Harmonic Analysis and Analyzing Data"
Abstract: The topic of this talk lies on the interface between Harmonic Analysis or Geometric
Measure Theory and Applied Mathematics. In particular, in many cases, one is given
a large data set, represented as a subset of a metric space, such as R^d for a large
dimension d. One seeks to faithfully represent a large portion of this data set as a
subset of Rk for dimension k much smaller than d. We will discuss mathematical
aspects of three different methods of doing so.
Click here for the flyer.
October 22, Ali Nadim, Claremont Graduate University
Title: "tba"
Abstract: tba
October 29, David Costa, Univeristy of Nevada, Las Vegas
Title: "tba"
Abstract: tba
November 5, Glen Van Brummelen, Quest Univeristy of British Columbia
Title: "tba"
Abstract: tba
November 12, David Pengelley, New Mexico State Univeristy
Title: "tba"
Abstract: tba
November 19, Jo Hardin, Pomona College
Title: "tba"
Abstract: tba
December 3, Hongkai Zhao, Univeristy of California, Irvine
Title: "tba"
Abstract: tba
December 10, Aparna Higgins, Univeristy of Dayton
Title: "tba"
Abstract: tba
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