04/29/2014 - 4:15pm

Speaker:

Timothy Hsu (San Jose State University)

Abstract:

The *Virtual Haken Conjecture* was, until recently, probably the biggest open problem in --manifolds

(-dimensional geometry). Then in March 2012, Ian Agol proved the conjecture by completing a key part of Dani Wise's program of studying *nonpositively curved cube complexes*. So how did questions in -dimensional geometry end up being resolved using spaces made from (very high--dimensional) cubes? We'll give an overview explaining the connection and describe the speaker's joint work with Wise that is part of the emerging and rapidly growing subject of cube complexes.

Background: This talk is meant to be accessible to students who have had one semester of abstract algebra. No background in topology is required, and we will give at least cartoon definitions of the relevant technical terms (e.g., -manifold).

Where:

Shanahan 3460 (the SkyCube), Harvey Mudd College

Misc. Information:

Refreshments at 3:45 p.m. 3rd Floor North Patio of Shanahan & wine and cheese after the talk on the 3rd Floor North Patio of Shanahan

03/11/2014 - 4:15pm

03/11/2014 - 5:15pm

Speaker:

H. G. Dales (Lancaster University)

Abstract:

Let be a locally compact space. Then is the Banach algebra of all continuous,

complex-valued functions on that vanish at infinity, taken with the pointwise algebraic

operations and uniform norm . The maximal modular ideals of have the

form , where . We see that each of these maximal

ideals has a contractive approximate identity: this is a net in

with and for each .

Now suppose that is a Banach function algebra on such that each maximal modular

ideal has such a contractive approximate identity. Must we have ? Or can you

think of such an algebra with ? How close does the group algebra of

a locally compact group come to having the above properties?

This is joint work with Ali Ülger of Istanbul

Where:

Seeley G. Mudd Science Library 126, Pomona College

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