All talks will take place in Frank Adams seminar room 1, Alan Turing Building. You can find directions here.
Tea and coffee will be on the first level Atrium Bridge in the Alan Turing Building.
10.15 – 11.00

Tea, Coffee and Biscuits 
11.00 – 12.00 
Ramón Vera (University of Durham) Nearsymplectic 2nmanifolds In this talk, I will explain the generalization of two concepts from lowdimensional topology in higher dimensions: nearsymplectic manifolds and overtwisted contact structures. By nearsymplectic it is meant a closed 2form that is nondegenerate, or symplectic, outisde a submanifold where it is singular. This approach uses some simple mappings coming from singularity theory called broken Lefschetz fibrations. It seems that a similar phenomena occurring in low dimensions appears also in higher dimensions: a nearsymplectic 2nmanifold induces a contact structure on a codimension 1 submanifold, which is PSovertwisted. 
12:00 – 14:00

LUNCH 
14:00 – 15:00

Nick Gurski (University of Sheffield) Semistrict higher categories (Joint with John Bourke) Strict higher categories admit a very simple inductive definition, with ncategories just being categories enriched over (n1)categories. These are not general enough for many purposes, for example it is known that strict ngroupoids do not model homotopy ntypes. Many definitions of weak higher categories have been given, but very few definitions of semistrict higher categories (i.e., not strict, but not entirely weak either) are known. I will discuss an inductive approach to semistrict higher categories using machinery very familiar to topologists: the cofibrantly generated factorization system given by the inclusion of boundary spheres into disks. 
15.00 – 15.30 
Tea, Coffee and Biscuits 
15:30 –16:30  Alexander Vishik (University of Nottingham) Unstable operations in Algebraic Cobordism
Algebraic Cobordism of LevineMorel is an algebraic analogue of the complex oriented cobordism theory in topology. In particular, it is the universal oriented theory, and has the same coefficient ring as MU. It provides an important invariant of algebraic varieties which is much richer than the classical Chow groups or K_0. The structure (as in topology) is provided here by cohomological operations. The stable ones among them are LandweberNovikov operations. These can be constructed using universality, and have various applications in algebraic geometry. But for some time it was observed that to get sharp results on rationality of algebraic cycles one needs unstable operations. Unfortunately, no general methods to construct such operations were known up to recently. The new technique permits to describe and construct all (unstable) additive operations from any theory obtained from algebraic cobordism by change of coefficients to any other theory. As applications we get: 1) The description of multiplicative operations as morphisms of the respective formal group laws ; 2) The construction of T.tom Dieck style Steenrod operations in Algebraic Cobordism; 3) The construction of integral (!) Adams operations in the mentioned theories, which specialize to classical Adams operations in K_0; 4) The construction of Symmetric Operations for all primes (have applications to rationality of cycles). 
Everyone who wishes to participate is welcome, particularly postgraduate students. We shall operate the usual criteria for assistance with travel expenses. Beneficiaries will need to complete the standard forms (available from the main TTT page), and should come with NI numbers and details of UK bank accounts if they want to complete the form on the day.