Sep

21

Thu

Title: Measure-Risking Arguments in Recursion Theory

Abstract: By way of introducing the idea of measure-risking, I will present a proof of Kurtz’s theorem that the Turing upward closure of the set of 1-generic reals is of full Lebesgue measure. Then I will show how a stronger form of the theorem (due originally to Kautz) can be obtained by framing the proof as a “fireworks argument”, following a recent paper of Bienvenu and Patey.

Sep

29

Fri

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.

Oct

3

Tue

View your event at https://www.google.com/calendar/event?action=VIEW&eid=N3NsdWpobDZwMnI2ZmJqbjliN2dyOGVpbm8gaGF3YWlpLmVkdV9hcGdwazdtbzE0ZDNpc3JxajA4Ym1rbmIyMEBn.

View your event at https://www.google.com/calendar/event?action=VIEW&eid=N3NsdWpobDZwMnI2ZmJqbjliN2dyOGVpbm8gaGF3YWlpLmVkdV9hcGdwazdtbzE0ZDNpc3JxajA4Ym1rbmIyMEBn.

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.

Oct

5

Thu

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.

## University of Hawaiʻi at Mānoa