The Fall 2009 Math Colloquium will be held at Pomona College, Millikan 134, Wednesdays at 4:15pm. Mario Martelli and Asuman Aksoy are Colloquia co-chairs for Fall 2009; Asuman Aksoy and Susan Martonosi will co-chair the Spring 2010 Colloquium. Archived Colloquia can be found on the CCMS website.
December 9, 2009, Winston Ou, Scripps College
Title: "tba"
Abstract: tba
December 2, 2009, Kevin Woods, Oberlin College and Conservatory
Title: "tba"
Abstract: tba
November 18, 2009, Mark Huber, Claremont McKenna College
Title: "Better numerical integration through randomness"
Abstract: Numerical integration in one dimension is easy, even the
simpler methods like the trapezoidal rule or Simpson's rule suffice
for most problems. However, higher dimensional integrals present a serious difficulty. To
approximate them using methods like Simpson's
rule requires exponential time in the dimension, an effect known as
"The Curse of Dimensionality".
However, problems of this type are common
in statistics and combinatorics and integration methods are needed to
obtain numerical solutions with the necessary level of accuracy.
In this talk I'll present a new approach, called TPA, that uses random choices.
I have designed the method and I will discuss some of its applications.
Click here for the flyer.
November 11, 2009, Benjamin Sudakov, Univeristy of California, Los Angeles
Title: "Extremal Graph Theory and its Applications"
Abstract: In a typical extremal problem one wants to determine maximum cardinality of discrete structure with certain prescribed properties. Probably the earliest such result was obtained 100 years ago by Mantel who computed the maximum number of edges in a triangle free graph on n vertices. This was generalized by Turan for all complete graphs and became a starting point of Extremal Graph Theory. In this talk we survey several classical problems and results in this area and present some interesting applications of Extremal Graph Theory to other areas of mathematics. We also describe a recent surprising generalization of Turan's theorem which was motivated by a question in Computational Complexity.
Click here for the flyer.
November 4, 2009, Charles Doran, University of Alberta and University of Washington
Title: "Reflexive Polygons, Complex Tori, and Elliptic Curves"
Abstract: We'll start by investigating the combinatorial properties of certain special pairs of
polygons defined on a planar lattice. By reinterpreting these, after Isaac Newton, we
will relate them to algebraic equations. The variables in the algebraic equations are
naturally complex numbers and they describe a “complex torus”. The vanishing loci
of the algebraic equations are elliptic curves, whose basic geometric and topological
properties we will discuss. If time permits, we may also describe an application to
string theory.
Click here for the flyer.
October 28, 2009, Andrew Bernoff, Harvey Muddd College
Title: "An Introduction to Surface Tension (Or Why Raindrops are Spherical)"
Abstract: A common misconception is that raindrops take the form of teardrops. In fact, they tend to be nearly spherical due to surface tension forces. This is an example of how at small scales fluid molecules' tendency to adhere to each other is the dominate effect driving a fluid's motion. In this talk we will explain how surface tension arises from intermolecular forces. We will also examine some examples of the behavior that can occur at small scales due to the balance between fluid-fluid and fluid-solid forces, with applications as varied as understanding how detergents help clean clothes to the design of fuel tanks in zero gravity environments.
Click here for the flyer.
October 21, 2009, Ashish Bhan, Claremont Graduate University and Keck Graduate Institute
Title: "Who's Mining the Text?"
Abstract: The Internet and the World Wide Web have led to a massive increase in the amount of data publicly available for researchers to analyze. This has resulted in the growth of new fields of study like Data Mining and Machine Learning. A hot topic these days is the field of Text Mining. In this talk I'll give an introduction to some ideas and techniques in Text Mining that span a variety of disciplines including the humanities (Literature and History) and the sciences (Functional Genomics and Bioinformatics).
Click here for the flyer.
October 14, 2009, Jen-Mei Chang, California State University, Long Beach
Title: "An Introduction to Geometric Data Analysis and its Possible
Applications"
Abstract: The analysis of patterns in data has typically been a subject in
statistics and engineering. Recently, however, fundamental mathematical
theory in areas such as linear algebra and differential geometry have
provided a new mathematical framework and insights for understanding large
data sets residing in spaces of large ambient dimensions. In this talk, we
will explore a wide range of applications that are natural under the linear
algebra and differential geometry framework. In particular, applications in
image compression, handwritten digit and face recognition, image
reconstruction from noisy and missing data will be discussed.
Click here for the flyer.
October 7, 2009, Gerald Beer, California State University, Los Angeles
Title: "Between Compactness and Completeness"
Abstract: In this expository talk we look at look at two classes of metric spaces lying between the compact metric spaces and the complete metric spaces. The first is the well-known class of UC spaces, best known as the class of spaces on which each continuous function with values in a metric space is uniformly continuous. The second is the class of cofinally complete metric spaces, best known as the class of spaces in which each ``cofinally Cauchy'' sequence has a cluster point. We show how these classes are in many ways parallel universes, and explain why.
Click here for the flyer.
September 30, 2009, Robert Rovetti, Loyola Marymount University
Title: "The Game of Life (and Sudden Death): Predicting Cardiac Instabilties at Multiple Scales with Nonlinear Stochastic Models"
Abstract: Cardiac cells have a surprisingly complex architecture, and dynamic
instabilities within them may lead to ventricular fibrillation, the
leading cause of sudden cardiac death. The principle contractile
signal, calcium release, must rise and fall in a controlled fashion,
yet is a result of the random action of thousands of subcellular "Calcium
Release Units" (CRUs). How does the cardiac cell produce an orderly
signal from a seemingly random process, and what causes this system to
break down?
We will first examine the dynamics of a single CRU represented as a
Birth-Death (Markov) Process with multiple "fixed points". At a
higher scale, we consider a network of such CRUs, encoding their properties
into a Cellular Automata scheme. We analyze the average (ensemble)
behavior of the system with an iterated map function and find
sufficient conditions under which calcium release undergoes a period-2 bifurcation to instability.
Click here for the flyer.
September 23, 2009, Ruben Hersh, University of New Mexico
Title: "Alvin White and Humanistic Mathematics"
Abstract: Alvin's life in mathematics is exemplary for two reasons: he insisted, and he persisted. He insisted that mathematics is something that people do, it is inseparable from people. And he persisted and persisted! In the spirit of Alvin's example, I will try to lead an informal conversation, linking two well-known controversies:
The first controversial issue is about the many different approaches and styles to college math teaching. Noteworthy examples are Emil Artin, Alonzo Church, William Feller, Robert Lee Moore, Richard Courant, George Polya, and Clarence Stephens.
On the other hand, there is a controversy in the philosophy of mathematics about the nature of mathematical entities or ``objects.'' Mathematical entities might actually be self-subsisting, external, outside of space and time (``Platonism''). Or they might just be arrangements of arbitrary symbols to form ``patterns'' (formalism, structuralism). Or they might be concepts, shared by thinking human beings (humanism).
Is there an important linkage between these two controversies, about the teaching of mathematics and the nature of mathematics?
Note: This talk will be hed at Platt Campus Center, Green Room, HMC
Click here for the flyer.
September 16, 2009, Claremont Colleges' 2009 Summer Mathematics Students
Title: "REBMI Poster Session"
Abstract: The colloquium is replaced this week by the Poster Session, please join us.
Click here for the flyer and here for the abstracts.
September 9, 2009, Sam Nelson, Claremont McKenna College
Title: "The Combinatorial Revolution in Knot Theory"
Abstract: Much as our concept of `number' has evolved over time,
what we mean by `knots' has recently undergone its own evolutionary
generalization. We will explore new types of generalized knots
including virtual knots, singular knots, flat virtual knots and more.
These new knot types motivate related algebraic structures such
as kei, quandles, racks and biquandles. This talk is based on an
article scheduled to appear in Notices of the AMS in 2010.
Click here for the flyer.
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