Santa Clara University

Mathematics and Computer Science department

SCU Mathematics/CS Colloquium Series

Spring 2009

All talks are Tuesdays at 4:00 pm in O'Connor 105, unless otherwise announced.

April 14: Thomas Russell, Dept. of Economics, SCU

Title: Sympleconomics—Additive Separability, Optimization, and Trivial Webs

Abstract: In this talk,  we show that two seemingly unrelated problems in economics, the hypothesis of integrability and the hypothesis of additive separability are linked by the absence of curvature of connections on webs naturally associated with each problem.

April 21: Pascale Garaud, UC Santa Cruz

Title: Puzzles in Astrophysical and Geophysical fluid dynamics. Abstract: I will describe two problems of interest in fluid dynamics, and ways in which they are studied using applied mathematical tools.

The first one stems from helio-seismic observations of the solar interior. The interior of the Sun is observed to have a peculiar rotation profile, which remains unexplained to this day. I will present the problem, together with analytical and numerical attempts to study it.

The second problem stems from measurements of the depth-dependence of salinity and temperature in the upper region of the tropical ocean. There, peculiar formations known as "thermohaline staircases" are often observed. The origin of these staircases remained a puzzle for 5 decades, but we have recently been able to shed light on the problem using a combination of analytical and numerical tools.

April 28: Kent Morrison, Cal Poly, San Luis Obispo

Title: The Median is the Message or Where's the Hub?

Abstract: The original shipping strategy of FedEx is to fly all packages to a hub location during the afternoon and evening, sort them there, and then fly them to their destinations during the night for delivery the next day. This talk deals with the problem of finding the optimal hub.

May 5: No colloquium. Pi Mu Epsilon initiation.

May 12: Jean Pedersen, SCU

Title:  Mathematics, Models, and Magz


Abstract:  We will first look at some theorems about binomial coefficients that involve 2-dimensional geometry.  Then we will look for possible 3-dimensional analogues to these theorems, beginning with a result due to G. L. Alexanderson and V. E. Hoggatt Jr., which was published in the Fibonacci Quarterly in 1971.  In order to help us to see and understand the relevant geometry in 3-dimensions, we implement the discussion with models made from the popular Magz toys (see http://www.magz.com/ ).  Some surprising results occur, and many natural questions arise.  Many of the natural questions will be answered during the talk — the remaining questions will be left for the interested members of the audience to explore. 
All that is required to understand this talk is some knowledge of elementary algebra and geometry.

May 19: Kathleen O'Reilly, SCU

Title: Harmonic 1-Cycles in Reflection Tilings

Abstract: It is known that non-trivial harmonic 1-cycles exist in reflection tilings of hyperbolic space, but finding explicit examples can be challenging.  In this talk, I will present a brief introduction to both ordinary- and l2-homology, and reflection tilings of hyperbolic space. I will then describe, in the context of a particular reflection tiling, the procedure Professor Rick Scott and I found this summer for calculating the harmonic representative of a given 1-cycle.


May 26: Victor Quintanar-Zilinskas, Santa Clara University


Title: Computational Neuroscience and Biology


Abstract: Biology and neuroscience both pose exciting questions that require math in the pursuit of their answers.  At this talk, there will first be an overview of the ‘set of questions’ in mathematical biology/neuroscience and the math that matches to these questions.  We will then examine a selection of some of the highest-impact recent work that is important both biologically and mathematically—audience participation will be a part of this process.  We will also (briefly) discuss the mathematical bio/neuro paradigm’s implications for the organization of scientific knowledge, funding policy, scientific workflow and work practices, pedagogy, and society.

June 2:  Stephanie Somersille, UC Berkeley

Title: Game Theory and Using Games to Solve Partial Differential Equations

Abstract: Some games have optimal strategies.  In other cases, finding an optimal strategy is an open problem and all we can do is discover whether a player has a winning strategy. We will examine several games that illustrate this. Finally, we will discuss the very simple "biased tug-of-war" game and how this leads to solutions of a not-so-simple partial differential equation involving the infinity Laplacian operator.

There will be refreshments before each talk in O'Connor 31 starting at 3:45pm.

If you have a disability and require a reasonable accommodation, please call or email Frank Farris 408-554-4430 or ffarris@scu.edu .

Abstracts of previous talks are available here.
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