We will talk about a paper by A. Moreira and J.C. Yoccoz, where they proved a conjecture by Palis according to which the arithmetic sums of generic pairs of regular Cantor sets on the line either has zero Lebesgue measure or contains an interval. 

Special room! MSTB 226!  We'll show you some of our favorite ways to use technology in the classroom.  In some classes it's more natural than others, but even for a class like Abstract Algebra, there are lots of possibilities! We might talk about Graphmatica, Doceri, Screencastomatic, Canvas, Wolfram Demonstrations Project.  We are always looking to learn about new resources, so please let us know about any favorites you have (or resources you've heard about but never tried).

This is the Fall 2015 intercampus Caltech-UCLA-UCI meeting.

Spatial heterogeneity of both humans and water may influence the spread of cholera, which is an infectious disease caused by an aquatic bacterium. To incorporate spatial effects, two models of cholera spread are proposed that both include direct (rapid) and indirect (environmental/water) transmission. The first is a multi-group model and the second is a multi-patch model. New mathematical tools from graph theory are used to understand the dynamics of both these heterogeneous cholera models, and to show that each model (under certain assumptions) satisfies a sharp threshold property, which de- termines whether cholera dies out or persists in the population. Specifically, Kirchhoff’s matrix tree theorem is used to investigate the dependence of the disease threshold on the patch connectivity and water movement (multi-patch model), and also to establish the global dynamics of both models. 

Multivariate polynomial optimization where variables and data are complex numbers is a non-deterministic polynomial-time hard problem that arises in various applications such as electric power systems, signal processing, imaging science, automatic control, and quantum mechanics. Complex numbers are typically used to model oscillatory phenomena which are omnipresent in physical systems. Thanks to recent advances in algebraic geometry, finding a global solution breaks down to solving a sequence of complex semidefinite programming relaxations that grow tighter and tighter. We’ll discuss Hermitian sums of squares and present numerical results on problems with several thousand complex variables. These consist of computing optimal power flows in the European high-voltage AC transmission network.