The Fano Conference, , Univ. Such a set need not generate the ring of invariants. Thus it is desirable to solve certain classification problems for this algebra. We will describe higher frieze patterns, and how to generalise some of the classical combinatorial properties such as the quiddity sequence. Semi simple Exercises in Quantum Cohomology. Bridgeland Stability conditions on Threefolds II: Diane Maclagan University of Warwick:

Frobenius splitting of toric and T-varieties. Sue Sierra University of Edinburgh: In this talk I shall construct generalisations of the special biserial algebras introduced and studied by Pogorzaly and Skowronski. Over the last fifteen years there has been an explosion of work on varieties in this setting. You can find all my papers on the arXiv , on google scholar , and after a while on MathSciNet.

Polynomial Bridgeland stability conditions and the large volume limit.

This is joint work with Alexey Petukhov. Philipp Lampe Durham University: Colin Ingalls Carleton University: We will investigate different aspects of the Kontsevich integral, a strong knot invariant with roots in mathematical physics, algebraically related to the study of knots via singularity theory.

# Alice Rizzardo – University of Liverpool

Theses My PhD thesis on “Semisimple Quantum Cohomology, deformations of stability conditions and the derived category”, written under supervision of Yuri I. Matthew Woolf You can find all my papers on the arXivon google scholarand after a while on MathSciNet. For some of these classes a compatible cluster structure can be constructed. We no longer have unique factorization, cancellation, or the Noetherian property.

This suggests two conjectures: Determining the moduli space of deformations of a given Poisson bracket is typically thesiw difficult problem. Semisimple quantum cohomology and blowups. The seminar will normally take place in Mall 1 at Journalpublished online September We will describe higher frieze patterns, and how to generalise some of the classical combinatorial properties such as the thessi sequence.

This punctured sphere corresponds to the physicists’ stringy Kahler moduli space for a certain 3-dimensional surgery in algebraic geometry, and it gives us various predictions for the derived symmetry group, which is why we care. At the end, I will briefly explain some applications to noncommutative resolutions, to tilting theory, and to group actions.

I will discuss joint work with Felipe Rincon on a special class of “tropical” ideals in this semiring that is much better thesjs, and on the geometric side allows us to expand from varieties to schemes. In some cases, the compatible structure is a generalized cluster algebra, where the exchange relations are polynomial rather than binomial. Everything is encoded by choices of nodes in Dynkin diagrams. Such sections are called Frobenius splittings.

The Fano Conference,Univ. It ensures strong finiteness properties for the relevant deformation complex, making the deformation spaces computable in terms of topological invariants such as intersection cohomology.

We report on a joint work with Ana Garcia Elsener and Daniel Smertnig about the factorization theory of cluster algebras. Stability conditions on Kuznetsov components.

## Academic Commons

Intersections in Tits Cones, and Applications. Dimers with boundary, associated algebras and module categories Dimer models with boundary were introduced in joint work with King and Marsh as a natural generalisation of dimers. Sue Sierra University of Edinburgh: Then we discuss recent descriptions of McKay quivers of reflection groups by M. The deformation space is usually infinite-dimensional, highly obstructed, and extremely sensitive to singularities of the bracket. Enhancements in derived and triangulated categories.

## Arend Bayer

Post-docs mentored Current post-docs: Complement of spherical objects on K3 surfaces. One such generalisation, the higher frieze pattern, introduces a link to higher Auslander-Reiten theory.

In positive characteristic some standard tools of algebraic geometry stop working, such as Kodaira vanishing or resolution of singularities, but as a compensation we also obtain a very powerful new tool: