Meredith Sargent

John Akeryod (January 30): An invitation to extend Beurling’s Theorem.

Abstract: We review Beurling’s Theorem and its proof, and mention results that are related to it. There are some important open questions in this context that we carefully outline.

Alan Sola (January 23): Singularities of rational inner functions in dimension two and higher.

Abstract: I will present recent joint work with K. Bickel (Bucknell) and J.E. Pascoe (U Florida) concerning rational inner functions and their singularities. Our focus will be on integrability of derivatives as well as geometry of unimodular level surfaces. As we will see, the two-dimensional case is relatively well understood, while the situation in higher dimensions is much more complicated.

September 5: Chao Ding

Classical Maxwell Equations and a Generalized Maxwell Operator

September 12: cancelled

September 19: Chao Ding

Special Bases for Solutions of the Generalized MaxwellEquation in 3-dimensional Space

September 26:

October 3:

October 10: Meredith Sargent

Old Results and New Observations for Optimal Approximants on the Bidisk

Abstract: In recent years, optimal polynomial approximants have been used to study cyclicity of functions in Dirichlet-type spaces on the complex unit disk, with particular interest being paid to the connection between the location of the zero sets of the optimal approximants and cyclicity, as well as a correspondence between optimal approximants and orthogonal polynomials. Some progress has been made to extend these ideas to the bidisk, where this question was also studied by electrical engineers for polynomials in the Hardy space. In this talk, the engineering results are reviewed, and new observations regarding zero sets and cyclic functions are discussed.

October 17: John Ryan

Towards a double layer potential operator for the Maxwell operator, 1

Abstract: We will first set up the Maxwell equation in n dimensional Euclidean space. We will establish that the equation is conformally invariant in degree one. We then use the conformal invariance of this Maxwell equation to introduction a Poisson kernel in upper half space and a double layer potential operator over a Lipschitz graph.
This is joint work with Chao Ding.

October 24: Minh Nguyen

U(n) Seiberg-Witten Equations

Special Visitor Seminar October 29, 1:00-1:50​ in SCEN 322:  Benjamin Steinhurst (McDaniel college)

Laplacians and Spectra on Laakso Spaces

Abstract: Laakso spaces are a family of fractal spaces that are constructed from a sequence of approximations via a projective (inverse) limit. This gives rise to a direct limit of the associated function spaces, ($L^{2}$, $Dom(\\\\Delta)$, $\\\\ldots$). The virtue of this is that the Laplacian is very well understood and has an explicitly computable spectrum and eigenspaces. We construct all of these objects and discuss how the spectrum changes in response to small changes in the geometry of the fractal.

October 31: Caleb Parks

Interpolation in Analytic Tent Spaces.

Abstract:Introduced by Coifman, Meyer, and Stein, the tent spaces have seen wide applications in Harmonic Analysis. Their analytic cousins have seen some applications involving the derivatives of Hardy space functions. Moreover, the tent spaces have been a recent focus of research. We introduce the concept of interpolating sequences for analytic tent spaces analogously to the same concepts for Bergman spaces. We then characterize such sequences in terms of Seip’s upper uniform density. We accomplish this by exploiting a kind of M\\”obius invariance for the tent spaces.

November 7: John Ryan

Towards a double layer potential operator for the Maxwell operator, 2

Abstract: we will continue to look at the Maxwell equation as an analog of the Laplace equations in n-dimensional Euclidean space. This leads us to some representation theory for the group SO(n) and to Rartitta-Schwinger/Stein-Weiss first order operators.

November 14: Bill Feldman

November 21: John Akeroyd

November 28: Thanksgiving

December 5: Zachary Bradshaw