04/25/2018 - 4:15pm

04/25/2018 - 5:15pm

Speaker:

Adrin Gharakhani

Abstract:

TBA

Where:

Kravis 62, CMC

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

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)

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

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

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

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

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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