Stability conditions in triangulated categories Wall-Crossing and birational geometry of moduli spaces Donaldson-Thomas invariants, Stacky Gromov-Witten invariants Graduate students Current students: These results are obtained via the study of the local cohomology with support at an arrangement of linear subspaces naturally arising from the action. Sira Gratz University of Glasgow: Pyramids and their applications In this talk, we define the category of pyramids over an additive category. For some of these classes a compatible cluster structure can be constructed. Then I will present a generalisation of Payne’s results to so-called T-varieties.

Holonomic Poisson manifolds and deformations of elliptic algebras. I will describe joint work with Travis Schedler, in which we introduce a natural new nondegeneracy condition for Poisson brackets, called holonomicity. It ensures strong finiteness properties for the relevant deformation complex, making the deformation spaces computable in terms of topological invariants such as intersection cohomology. Buchweitz applying results of Lusztig on McKay quivers to understand the relations of the basic model of the skew group ring. For a finite group acting linearly on a vector space, a separating set is simply a set of invariants whose elements separate the orbits o the action. Stability conditions, wall-crossing and weighted Gromov-Witten invariants.

I will describe joint work with Travis Schedler, in which we introduce a natural new nondegeneracy condition for Poisson brackets, called holonomicity.

After the seminar we will have biscuits and tea and coffee in the common room.

# Alice Rizzardo – University of Liverpool

This suggests two conjectures: Mathematically, they are spatially localised structures that solve certain PDEs, and quantum mechanics also comes in. Amit Hazi University of Leeds: You can read more about our research group on the Edinburgh Hodge Institute webpage. Gizzardo a strict monoidal structure is enclosed over the additive category, the strictness will be preserved when the monidal structure is lifted to the category of pyramids avoiding any use rizzarfo direct sums.

And a strict monoidal action can be also defined on the homotopy category of pyramids. Diletta Martinelli My official school page has more contact information. Exotic cluster algebras on simple Lie groups. You can find all my papers on the arXivon google scholarand after a while on MathSciNet. Pyramids and their applications In this talk, we define the category of pyramids over an additive category.

Selecta Mathematica New Seriespublished online November Threefold flops, matrix factorisations, and noncommutative algebras. Such a set need not generate the ring of invariants. Nef divisors for moduli spaces of complexes with compact support. Michael Wemyss University of Glasgow: Matthew Woolf Diane Maclagan University of Warwick: Instead it will be mainly about the geometrical structure of the Skyrmions.

## Mathematics Genealogy Project

Then we discuss recent descriptions of McKay quivers of reflection groups by M. A short proof of the deformation property of Bridgeland stability conditions. Stability conditions in families. Here are brief lecture notes on Bridgeland stability conditions intended for graduate students interested in the topic. As a corollary, we reprove and extend a classification of factoriality for cluster algebras of Dynkin type.

As an application, we establish the deformation-invariance of some families of noncommutative algebras introduced by Sklyanin and Feigin–Odesskii. We briefly present the history of McKay quivers and their applications in geometry and representation theory. Thus it is desirable to solve certain classification problems for this algebra.

Arnaud Mortier Dublin City University: 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.

Frieze patterns have an interesting combinatorial structure, as studied by Conway and Coxeter.

Lewis, and work with E. Enhancements in derived and triangulated categories. Rizaardo 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.

Poisson Lie groups are classified by the Belavin-Drinfeld classification of solutions to the classical Yang Baxter equation. Joint with Alastair Craw and Ziyu Zhang: