Joint Analysis Seminar

Introducing The Joint Analysis Seminar! This seminar is co-organized by Ciprian Demeter, Norm Levenberg, and Michael R. Pilla. We’re kicking off this semester on Wednesday, September 9th and will meet weekly at 4:15pm. The Zoom Room will open at 4pm. This is a joint seminar with the goal of having talks accessible to a general analysis audience. If you are interested, please contact me for joining information!

You will find the (soon to be updated!) schedule below:

09/09/2020: Michael R. Pilla, IU Bloomington

Title: A Generalized Cross Ratio

Abstract: In this talk, we define a generalized cross ratio and determine some of its basic properties. In particular, by defining linear fractional maps in several complex variables, we have a class of maps that obey similar transitivity properties as in one variable, under some more restrictive conditions.

09/16/2020: Norm Levenberg, IU Bloomington

Title: Polynomials Associated to Non-Convex Bodies

Abstract: Polynomial spaces associated to a convex body C in {R^+)^d have been the object of recent studies. We first recall this  setting and then we consider polynomial spaces associated to possibly non-convex C. This is done in order to discuss quantitative  Runge-type polynomial approximation results using relatively sparse families of polynomials. Joint work-in-progress with Franck Wielonsky.

09/23/2020: Chris Judge, IU Bloomington (CANCELED)

Title: On the Schwartz kernel theorem

09/30/2020: Yen Do, University of Virginia

Title: The number of real roots for random trigonometric polynomials: universality and non-universality of the variance

Abstract: We study the number of real roots of random trigonometric polynomials with iid coefficients of mean zero and bounded moments. We show that the variance of this number is asymptotically linear in terms of the expectation. This result extends a prior work of Bally, Caramellino, and Poly (where some smoothness conditions are required for the coefficient distributions). In particular, our methods work for discrete trigonometric polynomials. Joint work with Hoi Nguyen (Ohio State) and Oanh Nguyen (UIUC).

10/06/2020: Ian Charlesworth, UC Berkeley (NOTE DIFFERENCE IN DATE)

10/14/2020: Ching Wei Ho, IU Bloomington