Joint with Brendan Hassett and Yuri Tschinkel: You can find all my papers on the arXiv , on google scholar , and after a while on MathSciNet. For a simple complex Lie group G and a Belavin-Drinfeld class, one can define a corresponding Poisson bracket on the ring of regular functions on G. My research has been recognized by the University of Cambridge Adams prize , shared with Tom Coates , by the Whitehead prize awarded by the London Mathematical Society, and the Whittaker prize by the Edinburgh Mathematical Society. Such a set need not generate the ring of invariants. Nef divisors for moduli spaces of complexes with compact support.

We no longer have unique factorization, cancellation, or the Noetherian property. Stability conditions in families. The Fano Conference, , Univ. As a corollary, we reprove and extend a classification of factoriality for cluster algebras of Dynkin type. Recently, I have been awarded an ERC consolidator grant.

# On Fourier-Mukai type functors | Academic Commons

In this talk, we establish a Calabi-Yau reduction theorem for this class of categories. Then we discuss recent descriptions of McKay quivers of reflection groups by M. Joint with Charles Cadman: Threefold flops in algebraic geometry were classified rzzardo 6 families by Katz and Morrison using the length invariant.

In this talk, we give lower bounds on rizzxrdo size of separating sets based on the geometry of the action. Their structure is however in many ways insufficient, and usually an enhancement is needed to carry on many important constructions on them.

Separating invariants and local cohomology The study of separating invariants is a rizzzardo trend in Invariant Theory and a return to its roots: Alice Rizzardo This structure was later found to illustrate many of the properties of basic cluster algebras, and several generalisations of frieze patterns have since appeared in the literature and expanded on this connection.

## Academic Commons

Journal of Algebraic Geometry 23 MMP for moduli of sheaves on K3s via wall-crossing: We use these to derive certain infinite dimensional algebras and consider idempotent subalgebras w. Nick Manton University of Cambridge: The latter is biequivalent to the category of complexes and this biequivalence can be induced onto the corresponding homotopy categories. In some cases, the compatible structure is a generalized cluster algebra, where the exchange relations are polynomial rather than binomial.

Some generalisations of special biserial algebras. We will describe higher frieze patterns, and how to generalise some of the classical combinatorial properties such as the quiddity sequence. Pyramids and their applications In this talk, we define the category of pyramids over an additive category.

## Arend Bayer

In this talk I will introduce the notion of silting objects and mutation of silting objects. Raphael Bennett-Tennenhaus University of Leeds: Stability conditions in triangulated categories Wall-Crossing and birational geometry of moduli spaces Donaldson-Thomas invariants, Stacky Gromov-Witten invariants Graduate students Current students: Complement of spherical objects on K3 surfaces.

Joint with Jack Jeffries. Everything is encoded by choices of nodes in Dynkin diagrams. Silting theory and stability spaces. Polynomial Bridgeland stability conditions and the large volume limit. 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. Joint with Brendan Hassett and Yuri Tschinkel: Recently, I have been awarded an ERC consolidator grant.

We no longer have unique factorization, cancellation, or the Noetherian property. Derived automorphism groups of K3 surfaces of Picard rank 1.

Matthew Woolf Some related SAGE code. One such generalisation, the higher frieze pattern, introduces a link to higher Auslander-Reiten theory. Mori cones of holomorphic symplectic varieties of K3 type. Kontsevich invariants in knot theory.