Friday, February 19, 3pm - 4pm
William Riley Casper (CSUF)
Commuting differential and integral operators and the adelic Grassmannian
Beginning with the work of Landau, Pollak and Slepian in the 1960s on time-band limiting, commuting pairs of integral and differential operators have played a key role in signal processing, random matrix theory and integrable systems. In this talk, we will describe a close connection between commuting integral and differential operators and points in the adelic Grassmannian, which provides a commuting pair for each self-adjoint point in the Grassmannian. Central to this relationship is the Fourier algebra, a certain algebra of differential operators isomorphic to the algebra of differential operators on a line bundle over a rational curve.
Friday, March 5, 3pm - 4pm
Dan Volok (Kansas State U.)
Zeros of discrete analytic polynomials
We shall discuss some basic interpolation results for discrete analytic (in the sense of J. Ferrand and R.J. Duffin) functions on the integer lattice in the complex plane.
Friday, March 12, 3pm - 4pm
Mario Stipčić (U. of Zagreb)
L^p estimates for dyadic singular integral forms associated with hypergraphs and for ergodic-martingale paraproducts
We will identify T(1)-type conditions and other characterizations of L^p boundedness of entangled multilinear singular integrals associated with hypergraphs. After that, we will examine the convergence of ergodic-martingale paraproducts in the Lebesgue spaces with respect to the range of exponents.
Friday, April 16, 3pm - 4pm
Annina Iseli (UCLA)
Thurston maps with four postcritical points
A Thurston map is a branched covering map of the 2-sphere which is not a homeomorphism and for which every critical point has a finite orbit under iteration of the map. Frequently, a Thurston map admits a description in purely combinatorial-topological terms. In this context it is an interesting question whether a given map can (in a suitable sense) be realized by a rational map with the same combinatorics. This question was answered by Thurston in the 1980's in his celebrated characterization of rational maps. Thurston's Theorem roughly says that a Thurston map is realized if and only if it does not admit a Thurston obstruction, which is an invariant multicurve that satisfies a certain growth condition. However, in practice it can be very hard to verify whether a given map has no Thurston obstruction, because, in principle, one would need to check the growth condition for infinitely many curves.