Colloquium

TBA

02/13/2008 - 4:15pm
02/13/2008 - 5:15pm
Speaker: 
Carlos Castillo-Chavez
Abstract: 

TBA

Where: 
Beckman Auditorium, B126, Harvey Mudd College

OSCILLATIONS AND DELAYS IN DRUG

02/06/2008 - 4:15pm
02/06/2008 - 5:15pm
Speaker: 
Jacques Belair
Abstract: 

Temporal fluctuations are naturally observed in a number of physiological measurements.

When drugs are administered to redress abnormal conditions, it is natural to try to reproduce these fluctuations, and thus oscillations in plasma concentration are desired, over periods of variable time durations. We review recent examples where such oscillations were modelled, including a technological application in which the oscillations are generated by the delayed response of the permeability of a membrane at the boundary of a reaction chamber. We perform a complete qualitative analysis of the ensuing system of delay-differential equations (stability of equilibrium, Hopf bifurcation), and provide conditions for multiple mode instabilities (double Hopf bifurcations) to occur.

Where: 
Beckman B126 (Harvey Mudd College)
Misc. Information: 

Coffee & cookies at 4:00pm
Wine and cheese after the talk
Olin B161, HMC
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The dinner will be hosted by John Milton
If interested in attending, call Ext. 70024

Phase Models with Time Delay

01/30/2008 - 4:15pm
01/30/2008 - 5:35pm
Speaker: 
Sue Ann Campbell (University of Waterloo, Canada)
Abstract: 

Coupled oscillators are ubiquitous in nature and engineering, and have been a focus of intense mathematical study for over 300 years, since Huygens noticed that two pendulum clocks hung on the same wall would begin to run in perfect synchrony. Major questions still remain unanswered, however.

In this talk we consider a network of neurons with time delayed connections where the neurons are inherently oscillatory. We show how this may be reduced to a phase model network and how the time delay enters into the reduced model. For the case of two neurons, we show how the time delay may affect the stability of the periodic solution leading to stability switching between synchronous and antiphase solutions as the delay is increased. Results for two different types of oscillators are compared.

Where: 
Beckman Auditorium, B126, Harvey Mudd College
Misc. Information: 

Coffee & cookies at 4:00pm Wine and cheese after the talk Olin B161, HMC

The dinner will be hosted by Ami Radunskaya If interested in attending, call Ext. 18715

Beaucoup de Sudoku

11/28/2007 - 4:15pm
11/28/2007 - 5:15pm
Speaker: 
Michael Krebs (California State University, Los Angeles)
Abstract: 

In this talk I plan to apply the ideas of the paper Groups and mini-Sudokus to the problem of deciding when two mini-Sudokus are essentially the same. Along the way, we may use Lagrange's theorem, equivalence relations, the Burnside's lemma, as well as the ubiquitous technique of finding invariants that distinguish equivalence classes of objects.

Where: 
Millikan 134 Pomona College
Misc. Information: 

Coffee & cookies at 4:00 p.m.
Wine and cheese after the talk.
Harry Mullikin Room, Millikan 209
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The dinner will be hosted by Art Benjamin
If interested in attending, call Ext. 18688

Banach Algebras of continuous functions and measures, and their second duals

11/19/2007 - 4:15pm
11/19/2007 - 5:15pm
Speaker: 
H.G. Dales (Leeds College, UK)
Abstract: 

For every Banach algebra $ A $, there are two products on the second dual space $ A'' $ that make $ A'' $ into a Banach algebra; they may or may not coincide. A lot of information about the orginal algebra $ A $ comes easily by looking at these second duals. We shall first give the basic definitions and some (old and new) examples.

The first detailed example is the case where $ A $ is $ C_{\Omega} $, an algebra of continuous functions on a locally compact space Omega.

Next, let $ G $ be a locally compact group, and let $ L^1(G) $ and $ M(G) $ be the group algebra and the measure algebra on $ G $, respectively. We shall describe the scond duals $ L^1(G)'' $ and $ M(G)'' $, giving some classical results, some new results, and some open questions.

Where: 
Millikan 134 Pomona College
Misc. Information: 

Coffee & cookies at 4:00 p.m.
Wine and cheese after the talk.
Harry Mullikin Room, Millikan 209
**************************

The dinner will be hosted by Sandy Grabiner
If interested in attending, call Ext. 18707

Compressive Sampling

11/14/2007 - 4:15pm
11/14/2007 - 5:15pm
Speaker: 
Prof. Emmanuel Candes, California Institute of Technology
Abstract: 

One of the central tenets of signal processing is the Shannon-Nyquist sampling theory: the numbers of samples needed to reconstruct a signal without error is dictated by its bandwith, namely the shortest interval which contains the support of the spectrum of the signal under study. Veryrecently, an alternative sampling or sensing theory has emerged which goes against the conventional wisdom. This theory allows the faithfulrecovery of signals and images from what appear to be highly incomplete sets of data, i.e. from far fewer data that tradinal methods use. Underlying this methodology is a concrete protocol for sensing and compressing data simultaneously.
This talk will present the key mathematical ideas underlying this new sampling or sensing theory, and will survey some of the most important results. We will argue that this is a robust mathematical theory; not only it is possible to recover signals accurately from just an incomplete sets of measurements, but it is also possible to do so when the measurements are unrealiable and corrupted by noise.

Where: 
TBA

Sphere Packing, Lattices, and Epstein zeta function

11/07/2007 - 4:05pm
11/07/2007 - 5:00pm
Category: 
Colloquium
Speaker: 
Lenny Fukshansky, Claremont McKenna College
Abstract: 

The sphere packing problem in dimension N asks for an arrangement of non-overlapping spheres of equal radius which occupies the largest porportion of the corresponding Euclidean space.

Where: 
Pomona College, Millikan 214

The backward shift on Dirichlet-type spaces

09/17/2007 - 4:15pm
09/17/2007 - 5:15pm
Category: 
Analysis Seminar
Speaker: 
Stephan Garcia (Pomona College)
Abstract: 

The Dirichlet-type spaces are Hilbert spaces of analytic functions on the unit disk which encompass many of the standard spaces (e.g., Hardy, Bergman, Dirichlet). We discuss a few aspects of the backward shift operator (i.e., shift the sequence of Taylor coefficients backward one step) on these spaces. This talk will be mostly expository (i.e., no difficult proofs) and is aimed at introducing these fascinating spaces to general analysts.

Where: 
Davidson Lecture Hall at Claremont McKenna College
Misc. Information: 

Direction:
To reach Claremont McKenna College (CMC) from the 10 freeway, exit at Indian Hill, go north, turn right (east) on 10th street and proceed to Columbia, take a right on Columbia, and then left on 9th: CMC is on your right, and Davidson Lecture Hall is on the lower level of Adams Hall. To reach CMC from the 210 freeway, if traveling east, exit at Towne Avenue, turn right (south) on Towne, turn left (east) on Foothill Blvd, and turn right (south) onto Dartmouth Avenue. If traveling West on the 210 freeway, exit at Baseline/Padua, turn right (west) onto Baseline, turn left (south) onto Padua at the first light, turn right (west) onto Foothill Blvd at the third light, turn left (south) onto Dartmouth Avenue. For a map of the area, go on Google Maps, and search for the address 850 Columbia Avenue, Claremont, CA 91711. Parking on many streets near the campus is free (for instance, on Dartmouth Avenue, College Avenue, etc.)

Why Did Lagrange Prove the Parallel Postulate?

09/19/2007 - 4:00pm
09/19/2007 - 6:00pm
Category: 
Colloquium
Speaker: 
Dr. Judith Grabiner (Pitzer College)
Abstract: 

In 1806, Joseph-Louis Lagrange (1736-1813) read a memoir proving Euclid's parallel postulate to the Institut de France in Paris, but stopped, as the story goes, saying "I have to think about this some more." We'll look at Lagrange's still unpublished Paris manuscript on this subject, and place this activity in the context of his mathematical career. We will look also at how the ideas in this manuscript are related to Lagrange's philosophy of mathematics, Newton's physics, and Leibniz's Principle of Sufficient Reason. Finally, we will reflect on what this episode tells us about eighteenth-century attitudes toward geometry, space, and the universe.

Where: 
Seaver North Auditorium 645 N. College Avenue, Pomona College
Misc. Information: 

Coffee & cookies at 4:00 p.m.
Wine and cheese after the talk, Harry Mullikin Room, Millikan 209

The dinner will be hosted by Jim Hoste. If interested in attending, call Ext. 73258

Optimization of a delay-differential model of the immune response to cancer vaccines

09/26/2007 - 4:00pm
09/26/2007 - 7:00pm
Category: 
Colloquium
Speaker: 
Dr. Ami Radunskaya ( Pomona College )
Abstract: 

Can mathematical models be truly helpful in medical applications? In this talk I will present a new mathematical model developed with immunologist Sarah Hook that uses delay-differential equations to model the immune kinetics in response to tumor antigen. Differential equations with delays occur in many applications, and, mathematically,

they pose considerable challenges in their analysis. In particular, the introduction of delays makes it difficult to analytically apply control techniques to this problem.

The aim of this work is to model the T cell immune response to a vaccine with the goal that the model can be used to aid in the optimisation of vaccine-induced cellular immune responses. Since these responses are much more difficult to measure than antibody levels, often the only option available for researchers and clinicians is the "Goldilocks'' approach to cancer vaccination: give not too much of the vaccine, or too little and give it not too often or too few times.

In this talk I will discuss some of the mathematical difficulties presented by delay-differential models, and will describe several mathematical methods that can be used to suggest immunization protocols that would optimize the immune response.

No previous knowledge of immunology or control theory will be assumed.

Where: 
The Founder's Room* in Honnold Library *Directions: Enter the library under the bridge. Just inside the door there is a Welcome Desk. Tell the staff member that you're there for the Math Colloquium, and he/she will direct you.
Misc. Information: 

Coffee & cookies at 4:00 p.m.

Wine and cheese after the talk.

Due to Prof. Radunskaya's schedule, there will be no dinner after the talk.

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