TBA

04/25/2018 - 4:15pm
04/25/2018 - 5:15pm
Speaker:
Abstract:

TBA

Where:
Kravis 62, CMC

Geometric Properties of Noncommutative Symmetric Spaces of Measurable Operators and Unitary Matrix Ideals

02/07/2018 - 4:15pm
02/07/2018 - 5:15pm
Speaker:
Anna Kaminska (U of Memphis)
Abstract:

This is a survey lecture presenting a number of geometric properties of  noncommutative symmetric spaces of measurable operators $E\Mtau$ and unitary matrix ideals $C_E$, where $\M$ is a von Neumann algebra with  a semi-finite, faithful  and normal trace $\tau$, and  $E$ is a (quasi)Banach function and a sequence lattice, respectively. We provide   auxiliary  definitions, notions,  examples and we discuss a number of properties  that are most often used in studies  of local and global geometry of (quasi) Banach spaces.  We  interpret  the general spaces $E\Mtau$  in the case when $E=L_p$ obtaining $L_p\Mtau$ spaces, and in the case when $E$ is a sequence space we  explain how the unitary matrix space $C_E$ can be in fact identified with the  symmetric  space of measurable operators $G\Mtau$ for some Banach function lattice $G$.  We present the results on (complex) extreme points, (complex) strict convexity, strong extreme points and midpoint local uniform convexity, $k$-extreme points and $k$-convexity,  (complex or local) uniform convexity, smoothness and strong smoothness, (strongly) exposed points, (uniform) Kadec-Klee properties, Banach-Saks properties, Radon-Nikod\'ym property and stability in the sense of Krivine-Maurey. We also present some open problems.

Where:
Freeberg Forum, LC 62, Kravis Center, CMC

field meeting

01/17/2018 - 4:15pm
01/17/2018 - 5:15pm
Speaker:
field meeting
Abstract:

Please come to discuss course offerings and other synergistic items.

Where:
HMC SkyCube (Shanahan 3460)

A Moment Closure Technique for a Stochastic Predator-Prey Model

11/08/2017 - 4:15pm
11/08/2017 - 5:15pm
Speaker:
Jenny Switkes (Cal Poly Pomona)
Abstract:
The classical deterministic Lotka-Volterra predator-prey model famously leads to closed curves in the predator-prey phase plane. A stochastic version of this model has the form of a simple birth-death process, with the expected values governed by a system of differential equations almost identical in form to the deterministic system, the difference in rate function for each species being proportional to the time-dependent covariance of the populations of the two species. We explore the impact of this covariance term, using a moment closure technique to obtain a closed system of differential equations for the expected values, variances, and covariance of the populations.  This talk will be accessible to students with a background in differential equations; some experience with probability is helpful but not required.

Where:
Argue Auditorium, Millikan, Pomona College

Model Theory and Continuous Logic

10/25/2017 - 4:15pm
10/25/2017 - 5:15pm
Speaker:
Victoria Noquez (HMC)
Abstract:

Do you think that considering the abstract notion of a vector space is more fun than doing computations with matrices? Have you ever wondered how you can make that even more abstract? Are you now wondering why anyone ever would?  In this talk we will discuss the kinds of questions which model theorists seek to answer, some applications of these types of results to other branches of math, and ways in which we can generalize the ordinary framework of classical logic to allow for an even wider variety of applications.

Where:
Argue Auditorium, Millikan, Pomona College

Etudes of Spectral Theory

10/18/2017 - 4:15pm
10/18/2017 - 5:15pm
Speaker:
Victor Ivrii (University of Toronto, visiting Caltech now)
Abstract:

I briefly describe five old but still actively explored problems of the Spectral Theory of Partial Differential Equations

1.  How eigenvalues are distributed (where eigenvalues often mean squares of the frequencies in the mechanical or electromagnetic problems
or energy levels in the quantum mechanics models) and the relation to the behaviour of the billiard trajectories.
2.  Equidistribution  of eigenfunctions and connection to ergodicity of billiard trajectories
(a quantum chaos and  a classical chaos).

3.  Can one hear the shape of the drum?
4.  Nodal lines and Chladni plates.
5.  Strange spectra of quantum systems.

Where:
Argue Auditorium, Millikan, Pomona College

Trust your gut: the physics and mathematics behind maintenance of the gastric pH gradient.

10/11/2017 - 4:15pm
10/11/2017 - 5:15pm
Speaker:
Owen Lewis (U of Utah )
Abstract:

The gastric mucus layer is widely recognized to serve a protective function, shielding your stomach wall from the extremely low pH and digestive enzymes present in the stomach lumen. Often described as a "diffusion barrier," the mucus is believed to hinder the transport of small diffusive species from the stomach interior (lumen), to the wall (mucosa). However, there is no consensus on the mechanism by which the mucus layer hinders lumen-to-wall transport while allowing acid and enzymes secreted from the mucosa unimpeded transport to the lumen. Using simple physical principles, we develop a mathematical description of electro-diffusion within the stomach, and use it to test physiological hypotheses that are beyond current experimental techniques. Furthermore, we explore what regulatory mechanisms are necessary to segregate an acidic stomach interior from a neutral stomach wall.

Where:
Argue Auditorium, Millikan, Pomona College

seminar canceled

10/07/2010 - 4:15pm
10/07/2010 - 5:15pm
Speaker:
Mark Hansen, UCLA
Abstract:

TBA

Where:
Harvey Mudd College 3rd floor Sprague. Refreshments at 4pm.

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