• Title: Uniform distributed measures over R^n
• Date: 02/13/2017
• Time: 1:40 PM - 3:00 PM
• Place: C517 Wells Hall
• Speaker: Shiwen Zhang, MSU

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: Flipped Calculus Classes in a Large Lecture Setting
• Date: 02/13/2017
• Time: 4:10 PM - 5:00 PM
• Place: C109 Wells Hall
• Speaker: Ryan Maccombs, MSU

Ryan will discuss his experiences with teaching MTH 132 in a flipped-classroom setting in a large lecture format during the Fall of 2016.

• Title: Matrices with given row and column sums, II
• Date: 02/14/2017
• Time: 4:10 PM - 5:00 PM
• Place: C304 Wells Hall
• Speaker: Bruce Sagan, MSU

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
• Speaker: Leonid Chekov, Steklov Institute and MSU

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).

• Title: How does racial identity matter in the mathematics classroom?
• Date: 02/15/2017
• Time: 3:30 PM - 5:00 PM
• Place: 252 EH
• Speaker: Maria del Rosario Zavala, San Francisco State University

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.

• Title: Formal Groups
• Date: 02/16/2017
• Time: 11:30 AM - 12:20 PM
• Place: C117 Wells Hall
• Speaker: Nicholas Ovenhouse, MSU

No abstract available.

• Title: Geodesic flow on CAT(0) Spaces
• Date: 02/16/2017
• Time: 3:00 PM - 3:50 PM
• Place: C304 Wells Hall
• Speaker: Samuel Lin, MSU

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
• Speaker: Eric Vanden-Eijnden, NYU

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.