Thu, 10 Feb 2011
17:00
L3

Games and Structures at aleph_2

Philip Welch
(Bristol)
Abstract

Games are ubiquitous in set theory and in particular can be used to build models (often using some large cardinal property to justify the existence of strategies). As a reversal one can define large cardinal properties in terms of such games.

We look at some such that build models through indiscernibles, and that have recently had some effect on structures at aleph_2.

Thu, 10 Feb 2011
17:00
L3

tba

Philip Welch
(Bristol)
Tue, 26 Oct 2010

14:30 - 15:30
L3

When not knowing can slow you down

Raphael Clifford
(Bristol)
Abstract

Combinatorial pattern matching is a subject which has given us fast and elegant algorithms for a number of practical real world problems as well as being of great theoretical interest. However, when single character wildcards or so-called "don't know" symbols are introduced into the input, classic methods break down and it becomes much more challenging to find provably fast solutions. This talk will give a brief overview of recent results in the area of pattern matching with don't knows and show how techniques from fields as disperse FFTs, group testing and algebraic coding theory have been required to make any progress. We will, if time permits, also discuss the main open problems in the area.

Thu, 21 Oct 2010

16:00 - 17:00
L3

Almost prime points on homogeneous varieties

Dr A Gorodnik
(Bristol)
Abstract

Given a polynomial function f defined on a variety X,

we consider two questions, which are non-commutative analogues

of the Prime Number Theorem and the Linnik Theorem:

- how often the values of f(x) at integral points in X are almost prime?

- can one effectively solve the congruence equation f(x)=b (mod q)

with f(x) being almost prime?

We discuss a solution to these questions when X is a homogeneous

variety (e.g, a quadratic surface).

Thu, 04 Nov 2010
17:00
L3

Vopenka's Principle: a useful large cardinal axiom

Andrew Brooke-Taylor
(Bristol)
Abstract

Vopenka's Principle is a very strong large cardinal axiom which can be used to extend ZFC set theory. It was used quite recently to resolve an important open question in algebraic topology: assuming Vopenka's Principle, localisation functors exist for all generalised cohomology theories. After describing the axiom and sketching this application, I will talk about some recent results showing that Vopenka's Principle is relatively consistent with a wide range of other statements known to be independent of ZFC. The proof is by showing that forcing over a universe satisfying Vopenka's Principle will frequently give an extension universe also satisfying Vopenka's Principle.

Tue, 27 Oct 2009

14:30 - 15:30
L3

The simple harmonic urn

Stanislav Volkov
(Bristol)
Abstract

The simple harmonic urn is a discrete-time stochastic process on $\mathbb Z^2$ approximating the phase portrait of the harmonic oscillator using very basic transitional probabilities on the lattice, incidentally related to the Eulerian numbers.

This urn which we consider can be viewed as a two-colour generalized Polya urn with negative-positive reinforcements, and in a sense it can be viewed as a “marriage” between the Friedman urn and the OK Corral model, where we restart the process each time it hits the horizontal axes by switching the colours of the balls. We show the transience of the process using various couplings with birth and death processes and renewal processes. It turns out that the simple harmonic urn is just barely transient, as a minor modification of the model makes it recurrent.

We also show links between this model and oriented percolation, as well as some other interesting processes.

This is joint work with E. Crane, N. Georgiou, R. Waters and A. Wade.

Subscribe to Bristol