Topology Advanced Classes (past)

Mon, 05/03/2012 11:00	James Griffin (Cambridge)	Topology Advanced Classes	L3
	Cactus products and Outer space with generalised boundaries
	A cactus product is much like a wedge product of pointed spaces, but instead of being uniquely defined there is a moduli space of possible cactus products. I will discuss how this space can be interpreted geometrically and how its combinatorics calculates the homology of the automorphism group of a free product with no free group factors. Then I will reinterpret the moduli space with Outer space in mind: the lobes of the cacti now behave like boundaries and our free products can now include free group factors.

Mon, 06/02/2012 11:00	Leo Corry (Tel Aviv)	Topology Advanced Classes	L3
	Bourbaki and Categories: a story of incompatibilities

Mon, 30/01/2012 11:00	Andre Henriques (Utrecht)	Topology Advanced Classes	L3
	Three-tier CFTs I: Modular invariance and the cobordism hypothesis
	The idea of three-tier conformal field theory (CFT) was first proposed by Greame Segal. It is an extension of the functorial approach to CFT, where one replaces the bordism category of Riemann surfaces by a suitable bordism 2-category, whose objects are points, whose morphism are 1-manifolds, and whose 2-morphisms are pieces of Riemann surface. The Baez-Dolan cobordism hypothesis is a meta-mathematical principle. It claims that functorial quantum field theory (i.e. quantum field theory expressed as a functor from some bordism category) becomes simper once "you go all the way down to points", i.e., once you replace the bordism category by a higher category. Three-tier CFT is an example of "going all the way down to points". We will apply the cobordism hypothesis to the case of three-tier CFT, and show how the modular invariance of the partition function can be derived as a consequence of the formalism, even if one only starts with genus-zero data.

Mon, 16/01/2012 11:00	Gua Thiang, Robert Laugwitz, Jan Vonk	Topology Advanced Classes	L3
	Excursions in Algebraic Topology
	Three short talks by the authors of essays on topics related to c3 Algebraic topology: Whitehead's theorem, Cohomology of fibre bundles, Division algebras

Mon, 28/02/2011 12:00	Karin Valencia (Imperial College)	Topology Advanced Classes	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
11:00

Ulrike Tillmann (Oxford)

Topology Advanced Classes

SR2

What is persistent homology?

Persistent homology is a relatively new tool to analyse the topology of data sets.

We will give a brief introduction and tutorial as preparation for the third talk in the afternoon.

Mon, 23/02/2009 11:00	Neil Strickland (Sheffield)	Topology Advanced Classes	L3
	Revisiting the image of J
	I'll discuss my ongoing attempt to modernise the theory of the image of J. Some features that I would like to have are as follows: 1) Most of the spectra involved in the story should be E_\infty (or strictly commutative) ring spectra, and most of the maps involved should respect this structure. New machinery for dealing with E_\infty rings should be used systematically. 2) As far as possible the constructions used should not depend on arbitrary choices or on gratuitous localisation. 3) The Bernoulli numbers should enter via their primary definition as coefficients of a certain power series. 4) The image of J spectrum should be defined as the Bousfield localisation of S^0 with respect to KO, and other properties or descriptions should be deduced from this one. 5) There should be a clear conceptual explanation for the parallel appearance of Bernoulli numbers in the homotopy groups of J, K(Z) and in spectra related to surgery theory.

Wed, 11/06/2008 10:15	Dr. Marc Lackenby (Oxford)	Topology Advanced Classes	L3
	Topics in Geometry

Wed, 04/06/2008 10:15	Dr. Marc Lackenby (Oxford)	Topology Advanced Classes	L3
	Topics in Geometry

Wed, 28/05/2008 10:15	Dr. Marc Lackenby (Oxford)	Topology Advanced Classes	L3
	Topics in Geometry

Wed, 21/05/2008 10:15	Dr Marc Lackenby (Oxford)	Topology Advanced Classes	L3
	Topics in Geometry

Wed, 14/05/2008 10:15	Dr. Marc Lackenby (Oxford)	Topology Advanced Classes	L3
	Topics in Geometry

Wed, 07/05/2008 10:30	TBA	Topology Advanced Classes	L3
	To Be Announced

Wed, 30/04/2008 10:30	Dr M Lackenby	Topology Advanced Classes	L3
	Topics in Geometry

Mon, 24/10/2005 11:00		Topology Advanced Classes	L3
	To Be Announced

Mon, 25/04/2005 11:00	Graeme Segal (Oxford)	Topology Advanced Classes	L3
	Deformation Theory of Algebras and its connection to quantization I

Forthcoming Seminars

Mon, 20/05/2013 - 2:15pm

Eigenvalues of large random matrices, free probability and beyond.

Speaker: CAMILLE MALE
Mon, 20/05/2013 - 2:15pm

Four-manifolds, surgery and group actions

Speaker: Ian Hambleton
Mon, 20/05/2013 - 3:45pm

Fibering 5-manifolds with fundamental group Z over the circle

Speaker: Yang Su
Mon, 20/05/2013 - 3:45pm

Random Wavelet Series

Speaker: STEPHANE JAFFARD
Mon, 20/05/2013 - 4:00pm

The Hasse Principle for the Equation Polynomial=Norm: An Approach Using Sieve Theory

Speaker: Alastair Irving
Mon, 20/05/2013 - 5:00pm

Analysis of some nonlinear PDEs from multi-scale geophysical applications

Speaker: Bin Cheng
Tue, 21/05/2013 - 12:00pm

Quantum information processing in spacetime

Speaker: Ivette Fuentes (Nottingham)