This seminar marks the start of the Fall 2017 TA training program.  After outlining the main features of the training, we will discuss the profile of the students we are serving at UCI, and move on to a discussion of mathematical mindsets.

In collaboration with Dominik Wodarz, we would like to announce a new NSF funded project, and are hoping to interest students to join the team. This will provide the opportunity to perform novel mathematical work in the field of virus dynamics, and at the same time to apply the mathematical work to experimental and clinical data in the context of human immunodeficiency virus (HIV). The evolution of the virus within patients is an important determinant of the disease process, and is also an important reason why treatments and vaccines can fail. Recent experimental data indicate that “social interactions” among different HIV mutants within the same patient can determine evolutionary outcomes, and this has so far not been investigated mathematically, in the context of evolutionary theory. The aim of the funded project is to fill this gap. This will provide new information that will be crucial to advance our understanding of the disease, and to design more effective vaccination approaches.

Peer observation of teaching is an excellent way to receive concrete, fact-based feedback on what it's like in your classroom.  This spring quarter the math department will run peer observation among 1st and 2nd year grad students, and this meeting will introduce that.  It is also open to more advanced grad students.  In particular, any student eventually needing a teaching-focused letter of recommendation (which is required for almost all postdocs) is strongly encouraged to attend this session.  Our set-up will be based on Danny Mann's talk in fall quarter.

Graduate students may wonder how the muscle power of mathematics can be used to solve, or at least shed light, on serious concerns from other disciplines.  In this expository presentation, I offer some examples.  The first is how orbits of symmetry groups can resolve a range of long-standing puzzles coming from voting to statistics to …  A second is how related ideas introduce new insights about the compelling “dark matter” mystery from astronomy.

In 1932 von Neumann proposed classifying the statistical behavior of measure preserving diffeomorphisms of the torus, In joint work with B. Weiss I prove this is impossible (in a convincing and rigorous sense) even in the simplest and most concrete case: the 2-torus. 

By luck our work has accidental, but far-reaching consequences inside ergodic theory.  It establishes a “global structure theorem” for ergodic measure preserving transformations that gives heretofore unknown and surprising examples of diffeomorphisms of the torus.