## ALICE RIZZARDO THESIS

Amit Hazi University of Leeds: The seminar will normally take place in Mall 1 at 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. Instructions for submission by email. Triangles in cluster categories and punctured skein relations We describe triangles in the cluster category of type D, and show the relation between them and punctured skein relations arising from Teichmuler theory. Instead it will be mainly about the geometrical structure of the Skyrmions.

Chain conditions in the enveloping algebra of the Witt algebra The Witt algebra W is the Lie algebra of vector fields on the complex torus. Triangles in cluster categories and punctured skein relations. Reduction for negative Calabi-Yau triangulated categories Iyama and Yoshino introduced a tool, now known as Iyama-Yoshino reduction, which is very useful in studying the generators and decompositions of positive Calabi-Yau triangulated categories. My official school page has more contact information. Curto and Morrison have also given an efficient and explicit description of the first two families via matrix factorisations, and they conjecture that this can be done generally.

Semisimple quantum cohomology and blowups. This is joint work with Piotr Achinger and Nathan Ilten.

Stability conditions in families. As a corollary, we reprove and extend a classification of factoriality for cluster algebras of Dynkin type. Silting theory and stability spaces.

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. Using the notion of compatibility between Poisson brackets and cluster algebras in the coordinate rings of simple complex Lie groups, Gekhtman Shapiro and Vainshtein conjectured a correspondence between the two.

We report on a joint work with Ana Garcia Elsener and Daniel Smertnig about the factorization theory of cluster algebras. In this talk I will introduce the notion of silting objects and mutation of silting objects.

Joint with Tom Bridgeland: For example, if there exists a section of this morphism we get back the Kodaira vanishing theorem.

A probably slightly outdated CV.

Instructions for submission by email. Mori cones of holomorphic symplectic varieties of K3 type.

# University of Leeds Algebra Seminar

I will explain the grounds of knot theory, what a 1-cocycle is in this context, riizzardo what we can expect from such a tool. Annales scientifiques de l’Ecole Normale Superieure, 48 4 Selecta Mathematica New Seriespublished online November We also show that any factor of Rizzaedo W by an order 2 element has finite GK-dimension.

The talk begins with an introduction to class groups and cluster algebras. As an application, we prove that every simple transitive 2-representation of the 2-category of projective bimodules over a finite dimensional algebra is equivalent to a cell 2-representation.

## Mathematics Genealogy Project

Joint with Chunyi Li: Algebra, Geometry and Skyrmions Skyrmions arise in a model devised to explain atomic nuclei. Thesiz divisors for moduli spaces of complexes with compact support. The Leeds Algebra Group. Such a set need not generate the ring of invariants. I will present some possibly new results about the weight diagrams, and say something about what this implies for the physics. Such sections are called Frobenius splittings.

## Arend Bayer

Kontsevich invariants in knot theory. Chain conditions in the enveloping algebra of the Witt algebra The Witt algebra W is the Lie algebra of vector fields on the complex rizzagdo. Factoriality and class groups of cluster algebras. Stability conditions in triangulated categories Wall-Crossing and birational geometry of moduli spaces Donaldson-Thomas invariants, Stacky Gromov-Witten invariants Graduate students Current students: This suggests two conjectures: Bridgeland Thedis conditions on Threefolds II: In particular, I will show how a certain discreteness of this mutation theory enables one to employ techniques of Qiu and Woolf to obtain the contractibility of the space of stability conditions for a class of mainstream algebraic examples, the so-called silting-discrete algebras.

Derived and triangulated categories are a fundamental object of study for many mathematicians, both allice geometry and in topology.