Past Seminars › Seminar Series

Topology Seminar (past)

Tue, 22/03/2011
02:15 		Kevin Costello (Northwestern) Topology Seminar Add to calendar L3
Factorization algebras and perturbative quantum field theory
I'll describe an approach to perturbative quantum field theorywhich is philosophically similar to the deformation quantization approachto quantum mechanics. The algebraic objects which appear in our approach –factorization algebras – also play an important role in some recent workin topology (by Francis, Lurie and others).  This is joint work with OwenGwilliam.
Mon, 07/03/2011
15:45 		Juan Souto (University of Michigan) Topology Seminar Add to calendar L3
Topology of hyperbolic 3-manifolds and rank of their fundamental groups
Mon, 07/03/2011
15:45 		Juan Souto Topology Seminar Add to calendar
To Be Announced
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
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
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, 21/02/2011
15:45 		Mustafa Korkmaz (METU Ankara) Topology Seminar Add to calendar L3
Curve complexes on nonorientable surfaces

The curve complex on an orientable surface, introduced by William Harvey about 30 years ago, is the abstract simplicial complex whose vertices are isotopy classes of simple close curves. A set of vertices forms a simplex if they can be represented by pairwise disjoint elements. The mapping class group of S acts on this complex in a natural way, inducing a homomorphism from the mapping class group to the group of automorphisms of the curve complex. A remarkable theorem of Nikolai V. Ivanov says that this natural homomorphism is an isomorphism. From this fact, some algebraic properties of the mapping class group has been proved. In the last twenty years, this result has been extended in various directions. In the joint work with Ferihe Atalan, we have proved the corresponding theorem for non-orientable surfaces: the natural map from the mapping class group of a nonorientable surface to the automorphism group of the curve compex is an isomorphism. I will discuss the proof of this theorem and possible applications to the structure of the mapping class groups.
Mon, 14/02/2011
15:45 		Martin Markl (Academy of Sciences of the Czech Republic) Topology Seminar Add to calendar L3
Deformations of algebras and their diagrams
Mon, 07/02/2011
15:45 		Roberto Frigerio (Universita di Pisa) Topology Seminar Add to calendar L3
Rigidity of manifolds without non-positive curvature
In this talk I describe some results obtained in collaboration with J.F. Lafont and A. Sisto, which concern rigidity theorems for a class of manifolds which are “mostly” non-positively curved, but may not support any actual non-positively curved metric. More precisely, we define a class of manifolds which contains non-positively curved examples. Building on techniques coming from geometric group theory, we show that smooth rigidity holds within our class of manifolds (in fact, they are also topologically rigid - i.e. they satisfy the Borel conjecture - but this fact won't be discussed in my talk). We also discuss some results concerning the quasi-isometry type of the fundamental groups of mostly non-positively curved manifolds.
Mon, 31/01/2011
17:00 		Misha Kapovich (University of California) Topology Seminar Add to calendar L3
RAAGs in Ham
I will explain how to embed arbitrary RAAGs (Right Angled Artin Groups) in Ham (the group of hamiltonian symplectomorphisms of the 2-sphere). The proof is combination of topology, geometry and analysis: We will start with embeddings of RAAGs in the mapping class groups of hyperbolic surfaces (topology), then will promote these embeddings to faithful hamiltonian actions on the 2-sphere (hyperbolic geometry and analysis).
Mon, 31/01/2011
15:45 		Hugo Parlier (University of Fribourg) Topology Seminar Add to calendar L3
Surfaces of large genus
Surfaces of large genus are intriguing objects. Their geometry has been studied by finding geometric properties that hold for all surfaces of the same genus, and by finding families of surfaces with unexpected or extreme geometric behavior. A classical example of this is the size of systoles where on the one hand Gromov showed that there exists a universal constant $ C $ such that any (orientable) surface of genus $ g $ with area normalized to $ g $ has a homotopically non-trivial loop (a systole) of length less than $ C log(g) $. On the other hand, Buser and Sarnak constructed a family of hyperbolic surfaces where the systole roughly grows like $ log(g) $. Another important example, in particular for the study of hyperbolic surfaces and the related study of Teichmüller spaces, is the study of short pants decompositions, first studied by Bers. The talk will discuss two ideas on how to further the understanding of surfaces of large genus. The first part will be about joint results with F. Balacheff and S. Sabourau on upper bounds on the sums of lengths of pants decompositions and related questions. In particular we investigate how to find short pants decompositions on punctured spheres, and how to find families of homologically independent short curves. The second part, joint with L. Guth and R. Young, will be about how to construct surfaces with large pants decompositions using random constructions.
Mon, 24/01/2011
15:45 		Andre Henriques (Universiteit Utrecht) Topology Seminar Add to calendar L3
A sampler of (algebraic) quantum field theory
Roughly speaking, a quantum field theory is a gadget that assigns algebraic data to manifolds. The kind of algebraic data depends on the dimension of the manifold.Conformal nets are an example of this kind of structure. Given a conformal net, one can assigns a von Neumann algebra to any 1-dimensional manifold, and (at least conjecturally) a Hilbert space to any 2-dimensional Riemann surfaces.I will start by explaining what conformal nets are. I will then give some examples of conformal net: the ones associated to loop groups of compact Lie groups. Finally, I will present a new proof of a celebrated result of Kawahigashi, Longo, andMueger:The representation category of a conformal net (subject to appropriate finiteness conditions) is a modular tensor category.All this is related to my ongoing research projects with Chris Douglas and Arthur Bartels, in which we investigate conformal nets from a categorytheoretical perspective.
Mon, 17/01/2011
15:45 		John MacKay (University of Illinois at Urbana-Champaign) Topology Seminar Add to calendar L3
Generic conformal dimension estimates for random groups

What is a random group? What does it look like? In Gromov's few relator
and density models (with density < 1/2) a random group is a hyperbolic
group whose boundary at infinity is homeomorphic to a Menger curve.
Pansu's conformal dimension is an invariant of the boundary of a
hyperbolic group which can capture more information than just the
topology. I will discuss some new bounds on the conformal dimension of the
boundary of a small cancellation group, and apply them in the context of
random few relator groups, and random groups at densities less than 1/24.
Mon, 22/11/2010
15:45 		Nicholas Touikan (Oxford) Topology Seminar Add to calendar L3
To Be Announced
Mon, 15/11/2010
15:45 		Pierre Pansu (Orsay) Topology Seminar Add to calendar L3
$ L^p $ cohomology and pinching
We prove that no Riemannian manifold quasiisometric to complex hyperbolic plane can have a better curvature pinching. The proof uses cup-products in $ L^p $-cohomology.
Mon, 08/11/2010
15:45 		Alexandra Pettet (Oxford) Topology Seminar Add to calendar
The fundamental group of $ \text{ Hom}(\bb Z^k,G) $
Let $ G $ be a compact Lie group, and consider the variety $ \text {Hom} (\bb Z^k,G) $ of representations of the rank $ k $ abelian free group $ \bb Z^k $ into $ G $. We prove that the fundamental group of $ \text {Hom} (\bb Z^k,G) $ is naturally isomorphic to direct product of $ k $ copies of the fundamental group of $ G $. This is joint work with Jose Manuel Gomez and Juan Souto.
Mon, 01/11/2010
15:45 		Tom Leinster (Glasgow) Topology Seminar Add to calendar L3
Analogues of Euler characteristic
There is a close but underexploited analogy between the Euler characteristic of a topological space and the cardinality of a set. I will give a quite general definition of the "magnitude" of a mathematical structure, framed categorically. From this single definition can be derived many cardinality-like invariants (some old, some new): the Euler characteristic of a manifold or orbifold, the Euler characteristic of a category, the magnitude of a metric space, the Euler characteristic of a Koszul algebra, and others. A conjecture states that this purely categorical definition also produces the classical invariants of integral geometry: volume, surface area, perimeter, .... No specialist knowledge will be assumed.
Mon, 25/10/2010
03:45 		Udo Hertrich-Jeromin (Bath) Topology Seminar Add to calendar L3
Discrete differential geometry: constant mean curvature surfaces
The is the second part of the Analysis and Geometry Seminar today.

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

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