Colloquium

The Mathematics of the Bluegrass Banjo

03/26/2008 - 4:15pm
03/26/2008 - 5:15pm
Speaker: 
Joti Rockwell (Pomona College, Music Department)
Abstract: 

The musical characteristics of the bluegrass-style banjo, a five-stringed instrument played with three picks on the right hand, can be explained in part through basic mathematical concepts. This talk will begin by articulating some set-theoretic properties of bluegrass banjo style, after which point it will invoke group theory to describe rhythmic patterns. The talk will conclude with analysis of specific banjo performances, discussing how the permutational logic of the banjo interacts with the prototypical rhythmic organization of a bluegrass ensemble. No background in abstract algebra is required to follow the talk.

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

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

#CANCELLED# The Fractal Geometry of the Mandelbrot Set

03/05/2008 - 4:15pm
03/05/2008 - 5:15pm
Speaker: 
Robert Devaney (Boston University)
Abstract: 

In this lecture we describe several folk theorems concerning
the Mandelbrot set. While this set is extremely complicated
from a geometric point of view, we will show that, as long as
you know how to add and how to count, you can understand this
geometry completely. We will encounter many famous mathematical
objects in the Mandelbrot set, like the Farey tree and the
Fibonacci sequence. And we will find many soon-to-be-famous
objects as well, like the "Devaney" sequence. There might
even be a joke or two in the talk.

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

Due to unforeseen circumstances, colloquium speaker Prof. Devaney has had to cancel his trip to Claremont. Therefore the colloquium has been cancelled for this Wednesday, March 5.

TBA

02/27/2008 - 4:15pm
02/27/2008 - 5:15pm
Speaker: 
Harish Bhat
Abstract: 

TBA

Where: 
Beckman Auditorium, B126, Harvey Mudd College

TBA

02/20/2008 - 4:15pm
02/20/2008 - 5:15pm
Speaker: 
Susan Martonosi
Abstract: 

TBA

Where: 
Beckman Auditorium, B126, Harvey Mudd College

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
*********************************************************
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
**************************

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
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