Harvard University Math Department

Talk begins at 4, reception begins at 5, snacks provided.

**Speaker:**Melody Chan (Brown)**Title:**Counting Trees**Abstract:**I will talk about counting trees, in the sense of graph theory---although this can be adjusted to the demands of the audience. No prerequisites.

**Speaker:**Rohini Ramadas (Harvard)**Title:**Dynamics of polynomials and rational functions**Abstract:**I will introduce polynomials as dynamical systems on the set of complex numbers and rational functions as dynamical systems on the Riemann Sphere (the complex numbers plus a point at infinity). I will discuss how the study of the dynamics of polynomials and rational functions leads to the study of higher dimensional dynamical systems. A famous example: If 'c' is a complex constant then the polynomial 'z goes to z^2+c' is a map from set of complex numbers to itself. How do the dynamics of this map depend on the complex number 'c'? This will be a very introductory talk.

**Speaker:**Wes Cain (Harvard)**Title:**Delay Equations**Abstract:**Time delays are associated with instabilities and oscillations in a wide array of phenomena in nature (e.g., oscillations in insulin/glucose levels). The desire to understand such phenomena leads naturally into the study of delay differential equations (DDEs). We'll begin by discussing some basic DDE-related notions (mainly via examples), at a level accessible to students who have completed a second semester calculus course (Math 1b or equivalent). Then, we'll delve into the theory of stability of equilibria for DDEs, drawing upon notions covered in courses in the 110-level (analysis) offered through Harvard's math department. I'll close by discussing a research project that I hope to complete in collaboration with one or more undergraduates: a functional analytic framework for stability of a special class of DDE (namely, neutral DDEs).

**Speaker:**Kathryn Mann (Brown)**Title:**Ordering Groups**Abstract:**The integers come with an operation (+) and an ordering (<) preserved by this, in the sense that a < b implies a+c < b+c. In this talk, I’ll introduce you to some rich and beautiful structures that generalize this: the theories of left-orderable and circularly-orderable groups. These structures are interesting algebraically, but also have connections to questions in topology and dynamics, which is how I came to use them in my research.

**Speaker:**Karen Edwards (Harvard)**Title:**TBA**Abstract:**TBA

**Speaker:**Heather Macbeth (MIT)**Title:**TBA**Abstract:**TBA

**Mailing list:** You can subscribe to the seminar mailing list here.

**Organizers:** Ana Balibanu (ana@math.harvard.edu) and Alison Miller (abmiller@math.harvard.edu)