We will continue reading Preiss's paper [Geometry of measures in R^n: Distribution, rectifiability, and densities]. We will first review some necessary notations and properties of uniformly distributed measure discussed last semester and then study whether a measure is flat or curved at infinity.

Title: Matrices with given row and column sums, II

Date: 02/14/2017

Time: 4:10 PM - 5:00 PM

Place: C304 Wells Hall

In this continuation of the first talk, I will discuss new results by Brualdi and myself where we impose various symmetry conditions on the desired matrix A via the action of the dihedral group of the square.

Title: Topological recursion for matrix models and abstract topological recursion (a course of 3 lectures)

Date: 02/15/2017

Time: 3:00 PM - 3:50 PM

Place: C304 Wells Hall

I will begin with the description of a generating function for numbers of
Grothendieck's dessins d'enfant, or Belyi pairs. This generating function
is given by a random matrix model integral, I describe what is a
topological expansion (AKA genus expansion) of such models. The method
allowing finding corrections in all orders of the genus expansion is
Topological Recursion formulated in its present form by Eynard, Orantin
and the speaker in 2005-2006. This method had already found numerous
applications in mathematics and mathematical physics, so I describe the
general construction underlying the topological recursion and present an
(incomplete) list of its applications. Very recently, this method was
developed into an abstract topological recursion by Kontsevich and
Soibelman. In my last lecture I explain their construction and our
interpretation of it (forthcoming paper by J.Andersen, G.Borot, L.Ch., and
N.Orantin).

Speaker: Maria del Rosario Zavala, San Francisco State University

Title: How does racial identity matter in the mathematics classroom?

Date: 02/15/2017

Time: 3:30 PM - 5:00 PM

Place: 252 EH

In this talk I will use contemporary research in mathematics learning as a racialized form of experience to take stock of where the field is in relation to the question of “How does racial identity matter in the mathematics classroom?” and examine where we are headed in research and classroom practice. One aspect of my talk is to complicate the master narrative of achievement motivation, which ascribes high achievement solely to effort, and analyze the racial dimensions of such narratives using examples from research with Latinx high school students.

First, I will give the definition of CAT(0) spaces. Then I will describe the boundary of these spaces and how the geodesic flow behave on these spaces.

Title: Non-equilibrium transitions between metastable patterns in populations of motile bacteria

Date: 02/16/2017

Time: 4:10 PM - 5:00 PM

Place: C304 Wells Hall

Active materials can self-organize in many more ways than their
equilibrium counterparts. For example, self-propelled particles whose
velocity decreases with their density can display motility-induced
phase separation (MIPS), a phenomenon building on a positive feedback
loop in which patterns emerge in locations where the particles slow
down. Here, we investigate the effects of intrinsic fluctuations in
the system's dynamics on MIPS, using a field theoretic description
building on results by Cates and collaborators. We show that these
fluctuations can lead to transitions between metastable patterns. The
pathway and rate of these transitions is analyzed within the realm of
large deviation theory, and they are shown to proceed in a very
different way than one would predict from arguments based on
detailed-balance and microscopic reversibility. Specifically, we show
that these transitions involve fluctuations in diffiusivity of the
bacteria followed by fluctuations in their population, in a specific
sequence. The methods of analysis proposed here, including their
numerical components, can be used to study noise-induced
non-equilibrium transitions in a variety of other non-equilibrium
set-ups, and lead to predictions that are verifiable experimentally.