Forthcoming Seminars

Mon, 28/02/2011
12:00 		Karin Valencia (Imperial College) Topology Advanced Classes Add to calendar L3
The Topology of DNA-Protein Interactions

The central axis of the famous DNA double helix can become knotted
or linked as a result of numerous biochemical processes, most notably
site-specific recombination. Site-specific recombinases are naturally
occurring enzymes that cleave and reseal DNA molecules in very precise ways.
As a by product of their main purpose, they manipulate cellular DNA in
topologically interesting and non-trivial ways. So if the axis of the DNA
double helix is circular, these cut-and-seal mechanisms can be tracked by
corresponding changes in the knot type of the DNA axis.  In this talk, I'll
explain several topological strategies to investigate these biological
situations. As a concrete example, I will disscuss my recent work, which
predics what types of DNA knots and links can arise from site-specific
recombination on DNA twist knots.
Mon, 28/02/2011
14:15 		Ron Doney Stochastic Analysis Seminar Add to calendar Eagle House
First passage times for random walks and Levy processes
The behaviour of the tail of the distribution of the first passage time over a fixed level has been known for many years, but until recently little was known about the behaviour of the probability mass function or density function. In this talk we describe recent results of Vatutin and Wachtel, Doney, and Doney and Rivero which give such information whenever the random walk or Levy process is asymptotically stable.
Mon, 28/02/2011
14:15 		Dorothy Buck (Imperial College London) Topology Seminar Add to calendar L3
The Classification of Rational SubTangle Adjacencies, with Applications to Complex Nucleoprotein Assemblies.

Many proteins cleave and reseal DNA molecules in precisely orchestrated
ways. Modelling these reactions has often relied on the axis of the DNA
double helix
being circular, so these cut-and-seal mechanisms can be
tracked by corresponding changes in the knot type of the DNA axis.
However, when the DNA molecule is linear, or the
protein action does not manifest itself as a change in knot type, or the
knots types are not 4-plats, these knot theoretic models are less germane.

We thus give a taxonomy of local DNA axis configurations. More precisely, we
characterise
all rational tangles obtained from a given rational tangle via a rational
subtangle
replacement (RSR). This builds on work of Berge and Gabai. 
We further determine the sites for these RSR of distance greater than 1.
Finally, we classify all knots in lens spaces whose exteriors are
generalised Seifert fibered spaces and their lens space surgeries, extending work of
Darcy-Sumners.

Biologically then, this classification is endowed with a distance that
determines how many protein reactions
of a particular type (corresponding to steps of a specified size) are
needed to proceed from one local conformation to another.
We conclude by discussing a variety of biological applications of this
categorisation.

Joint work with Ken Baker
Mon, 28/02/2011
15:45 		Greg Gyurko Stochastic Analysis Seminar Add to calendar Eagle House
"Rough paths of inhomogeneous degree of smoothness and applications"

"Rough paths of inhomogeneous degree of smoothness (Pi-rough paths) can be treated as p-rough paths (of homogeneous degree of
smoothness) for a sufficiently large p. The theory of integration with respect to p-rough paths can be applied to prove existence and uniqueness of solutions of differential equations driven by Pi-rough paths. However the required conditions on the one-form determining the differential equation are too strong and can be weakened. The talk proves the existence and uniqueness under weaker conditions and explores some applications of Pi-rough paths
Mon, 28/02/2011
15:45 		Michael Farber (University of Durham) Topology Seminar Add to calendar L3
Stochastic Algebraic Topology

Topological spaces and manifolds are commonly used to model configuration
spaces of systems of various nature. However, many practical tasks, such as
those dealing with the modelling, control and design of large systems, lead
to topological problems having mixed topological-probabilistic character
when spaces and manifolds depend on many random parameters.
In my talk I will describe several models of stochastic algebraic topology.
I will also mention some open problems and results known so far.
Mon, 28/02/2011
16:00 		Markus Hanselmann (Oxford) Junior Number Theory Seminar Add to calendar SR1
Rational points on (quartic) hypersurfaces
Mon, 28/02/2011
17:00 		Jacek Brodzki (Southampton University) Topology Seminar Add to calendar L1
Geometry and topology of data sets

Coarse geometry provides a very useful organising point of view on the study
of geometry and analysis of discrete metric spaces, and has been very
successful in the context of geometric group theory and its applications. On
the other hand, the work of Carlsson, Ghrist and others on persistent
homology has paved the way for applications of topological methods to the
study of broadly understood data sets. This talk will provide an
introduction to this fascinating topic and will give an overview of possible
interactions between the two.

Mon, 28/02/2011
17:00 		Matthias Röger (Technische Universität Dormund) Partial Differential Equations Seminar Add to calendar Gibson 1st Floor SR
Stochastic perturbations of the Allen-Cahn equation
In this talk we will first consider the Allen-Cahn action functional that controls the probability of rare events in an Allen-Cahn type equation with additive noise. Further we discuss a perturbation of the Allen-Cahn equation by a stochastic flow. Here we will present a tightness result in the sharp interface limit and discuss the relation to a version of stochastically perturbed mean curvature flow. (This is joint work with Luca Mugnai, Leipzig, and Hendrik Weber, Warwick.)
Tue, 01/03/2011
11:00 		Athanasios Tsanas (Mathematics (Oxford)) Applied Dynamical Systems and Inverse Problems Seminar Add to calendar DH 3rd floor SR
Dimensionality Reduction
Tue, 01/03/2011
14:15 		Dr Frank Kwasniok (Mathematics and Physical Sciences (University of Exeter)) Geophysical and Nonlinear Fluid Dynamics Seminar Add to calendar Dobson Room, AOPP
Nonlinear stochastic low-order models of atmospheric low-frequency variability using an empirical regime-weighted closure scheme
Tue, 01/03/2011
15:45 		Vivek Shende (Princeton) Algebraic and Symplectic Geometry Seminar Add to calendar L3
Cohomology of Hilbert schemes of plane curve singularities and the triply graded Khovanov-Rozansky homology of their links
I describe a conjecture equating the two items appearing in the title.
Tue, 01/03/2011
17:00 		Markus Riedle (Manchester) Functional Analysis Seminar Add to calendar L3
Stochastic integration in Banach spaces and radonifying operators
One of the cores in modern probability theory is the stochastic integral introduced by K. Ito in the 1940s. Due to the randomness and the irregularity of typical stochastic integrators (such as the Wiener process) one can not follow a classical approach as in calculus to define the stochastic integral. For Hilbert spaces Ito's theory of stochastic integration in finite dimensions can be generalised. There are several even quite early attempts to tackle stochastic integration in more general spaces such as Banach spaces but none of them provides the generality and powerful tool as the theory in Hilbert spaces. In this talk, we begin with introducing the stochastic integral in Hilbert spaces based on the classical theory and with explaining the restriction of this approach to Hilbert spaces. We tackle the problem of stochastic integration in Banach spaces by introducing a stochastic version of a Pettis integral. In the case of a Wiener process as an integrator, the stochastic Pettis integrability of a function is related to the extensively studied class of $ \gamma $-radonifying operators. Surprisingly, it turns out that for more general integrators which are non-Gaussian and discontinuous (Levy processes) such a relation can still be established but with another subclass of radonifying operators.
Tue, 01/03/2011
17:00 		Prof. Martin Kassabov (Southampton) Algebra Seminar Add to calendar L2
Bounding the residual finiteness of free groups (joint work with Francesco Matucci
We analyze the question of the minimal index of a normal subgroup in a free group which does not contain a given element. Recent work by BouRabee-McReynolds and Rivin give estimates for the index. By using results on the length of shortest identities in finite simple groups we recover and improve polynomial upper and lower bounds for the order of the quotient. The bounds can be improved further if we assume that the element lies in the lower central series.
Wed, 02/03/2011
11:30 		Algebra Kinderseminar Add to calendar
No Seminar
Wed, 02/03/2011
16:00 		John Mackay (Oxford University) Junior Geometric Group Theory Seminar Add to calendar SR2
Analysis on boundaries of hyperbolic groups
We'll survey some of the ways that hyperbolic groups have been studied using analysis on their boundaries at infinity.
Wed, 02/03/2011
16:00 		Henk Bruin (University of Surrey) Analytic Topology in Mathematics and Computer Science Add to calendar L3
Cancelled
Thu, 03/03/2011
11:00 		Adam Harris (Oxford) Advanced Class Logic Add to calendar SR2
"Model theory of j-invarian"

For any corrections/updates to these listings, please contact seminars [-at-] maths [dot] ox [dot] ac [dot] uk.

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