Oxford

I will explain how to compute the symplectic cohomology of a manifold $M$ conical at infinity, whose Reeb flow at infinity arises from a Hamiltonian circle-action on $M$. For example, this allows one to compute the symplectic cohomology of negative line bundles in terms of the quantum cohomology, and (in joint work with Ivan Smith) via the open-closed string map one can determine the wrapped Fukaya category of negative line bundles over projective space. In this talk, I will show that one can explicitly compute the quantum cohomology and symplectic cohomology of Fano toric negative line bundles, which are in fact different cohomology groups, and surprisingly it is actually the symplectic cohomology which recovers the Jacobian ring of the Landau-Ginzburg superpotential.

 We'll discuss the connection between irreducibilty, D- and 
aD-spaces.

Noncommutative projective geometry is the study of quantum versions of projective space and other projective varieties.  Starting with the celebrated work of Artin, Tate and Van den Bergh on noncommutative projective planes, a substantial theory of noncommutative curves and surfaces has been developed, but the classification of noncommutative versions of projective three-space remains unknown.  I will explain how a portion of this classification can be obtained, via deformation quantization, from a corresponding classification of holomorphic foliations due to Cerveau and Lins Neto.  In algebraic terms, the result is an explicit description of the deformations of the polynomial ring in four variables as a graded Calabi--Yau algebra.

We produce new families of steady and expanding Ricci solitons
that are not of Kahler type. In the steady case, the asymptotics are
a mixture of the Hamilton cigar and the Bryant soliton paraboloid
asymptotics. We obtain some examples of Ricci solitons on homeomorphic
but non-diffeomorphic spaces. We also find numerical evidence of solitons
with more complicated topology.

I will start by introducing Somos sequences, defined by innocent-looking quadratic recursions which, surprisingly, always return integer values. I will then explain how they can be viewed in a much larger context, that of the Laurent phenomenon in the theory of cluster algebras. Some further steps take us to the the quantum cluster positivity conjecture of Berenstein and Zelevinski. I will finally explain how, following Nagao and Efimov, cohomological Donaldson-Thomas theory leads to a proof of this conjecture in some, perhaps all, cases. This is joint work with Davison, Maulik, Schuermann.

Computational structures---from simple objects like bits and qubits,

to complex procedures like encryption and quantum teleportation---can

be defined using algebraic structures in a symmetric monoidal

2-category. I will show how this works, and demonstrate how the

representation theory of these structures allows us to recover the

ordinary computational concepts. The structures are topological in

nature, reflecting a close relationship between topology and

computation, and allowing a completely graphical proof style that

makes computations easy to understand. The formalism also gives

insight into contentious issues in the foundations of quantum

computing. No prior knowledge of computer science or category theory

will be required to understand this talk.

Hrushovski-Martin-Rideau have proved rationality of Poincare series counting 
numbers of equivalence classes of a definable equivalence relation on the p-adic field (in connection to a problem on counting representations of groups). For this they have proved 
uniform p-adic elimination of imaginaries. Their work implies that these Poincare series are 
motivic. I will talk about their work.

I will introduce and motivate the concept of largeness of a group. I will then show how tools from different areas of mathematics can be applied to show that all free-by-cyclic groups are large (and try to convince you that this is a good thing).