Faculty Talk Story: Rufus Willett @ Keller 401
Sep 29 @ 3:30 pm – 4:30 pm

Speaker: Rufus Willett

Title: Positive curvature and index theory.

Abstract: Starting with two-dimensional surfaces, I’ll introduce positive (scalar) curvature. I’ll then discuss the relationship of this to index theory, a theory that counts the number of solutions to certain partial differential equations. Finally, I’ll mention the relevance of K-theory, a way of generalizing the notion of dimension of a vector space from fields to arbitrary rings.

Applied Math Qualifying Exam
Oct 3 @ 9:00 am – 1:00 pm

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Analysis Seminar : Malik Younsi (University of Hawaii) @ Keller 402
Oct 3 @ 3:30 pm – 4:30 pm

Title : Conformal welding homeomorphisms.

Abstract : Conformal welding is a correspondence between circle homeomorphisms and curves in the plane. It has appeared over the years to be of considerable interest in several areas of mathematics and applications, such as Teichmüller Theory, Kleinian Groups, computer vision and pattern recognition, and so forth.

The uniqueness of conformal welding has been known for a long time to be closely related to the notion of conformal removability. In fact, many papers in the literature claim, using the same argument, that uniqueness is characterized precisely by the removability of the curve. In this talk, I will show that this argument is actually incorrect, so that the problem of characterizing uniqueness of conformal welding remains open.

Logic Seminar: Borel Determinacy I (Umar Gaffar) @ Keller 402
Oct 5 @ 2:55 pm – 3:55 pm

Title: Borel Determinacy I
Speaker: Umar Gaffar

We’re going through Ross Bryant’s presentation of Martin’s theorem (in ZFC) that Borel games are determined.

Colloquium: Pamela Harris (Williams)
Oct 6 @ 3:30 pm – 4:30 pm
Topology Qualifying Exam
Oct 10 @ 9:00 am – 1:00 pm

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Analysis Seminar : Austin Anderson (Kapi’olani Community College) @ Keller 402
Oct 10 @ 3:30 pm – 4:30 pm

Title: Composition semigroups on spaces of analytic functions

Abstract : A semigroup {phi_t}_{t geq 0} of analytic self-maps of the disk satisifies phi_t circ phi_s = phi_{t+s}, and induces a semigroup of composition operators. We study the maximal space of strong continuity when the composition operators act on spaces of analytic functions, particularly H^{infty}, BMOA, and the Bloch space. We show that not every composition semigroup is strongly continuous on BMOA, answering a question that had remained open in the literature since at least 1998. This is joint work with Wayne Smith and Mirjana Jovovic.

Logic Seminar: Borel Determinacy II (Khan) @ Keller 402
Oct 12 @ 2:55 pm – 3:55 pm