Wed, 27 Nov 2013

17:00 - 18:00
L2

The fascination of what's difficult: Mathematical aspects of classical water wave theory from the past 20 years

Professor John Toland
(Newton Institute)
Abstract
Experimental observations about steady water waves have famously challenged mathematicians since Stokes and Scott-Russell in the 19th century and modern methods of global analysis are inadequate to answer the simplest of questions raised by careful numerical experiments in the 20th century. This lecture concerns mathematical advances that have emerged since Brooke's untimely death in 1995 and elucidates important challenges that remain to the present day. All are warmly invited to attend the lecture and reception that follows.
Tue, 08 Feb 2011
17:00
L2

On a conjecture of Moore

Dr Ehud Meir
(Newton Institute)
Abstract

Abstract:

this is joint work with Eli Aljadeff.

Let G be a group, H a finite index subgroup. Moore's conjecture says that under a certain condition on G and H (which we call the Moore's condition), a G-module M which is projective over H is projective over G. In other words- if we know that a module is ``almost projective'', then it is projective. In this talk we will survey cases in which the conjecture is known to be true. This includes the case in which the group G is finite and the case in which the group G has finite cohomological dimension.

As a generalization of these two cases, we shall present Kropholler's hierarchy LHF, and discuss the conjecture for groups in this hierarchy. In the case of finite groups and in the case of finite cohomological dimension groups, the conjecture is proved by the same finiteness argument. This argument is straightforward in the finite cohomological dimension case, and is a result of a theorem of Serre in case the group is finite. We will show that inside Kropholler's hierarchy the conjecture holds even though this finiteness condition might fail to hold.

We will also discuss some other cases in which the conjecture is known to be true (e.g. Thompson's group F).

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