15.00 Gather in the Maths common room, JCMB 5212, for tea.
Talks will take place in JCMB, Lecture Theatre B
15.30 Stephane Launois (Kent) Efficient recognition of totally nonnegative cells.
In this talk, I will explain how one can use tools develop to study the prime spectrum of quantum matrices in order to study totally nonnegative matrices.16.30 Adrien Brochier (Edinburgh) On finite type invariants for knots in the solid torus.
Finite type knot invariants are those invariants vanishing on the nth piece of some natural filtration on the space of knots. This notion was introduced by Vassiliev and it turns out that most of known numerical invariants are of finite type. Kontsevich proved the existence of a "universal" invariant, taking its values in some combinatorial space, of which every finite type invariant is a specialization. This result involves some complicated integrals, but can be made combinatorial using the theory of Drinfeld associators. We will review this construction and explain why the naive generalization of this theory for knot in thickened surfaces fails. We will suggest a general way of overcoming this obstruction, and prove an analog of Kontsevich theorem in this framework for the case M=C^*, i.e. for knots in a solid torus. Time permitting, we will give an explicit construction of specializations of our invariant using quantum groups.
09.30 Oleg Chalykh (Leeds) Calogero-Moser spaces for algebraic curves.
I will discuss two existing definitions of Calogero-Moser spaces for curves: one in terms of Cherednik algebras, another - in terms of deformed preprojective algebras, the link between them, and explain how one can compute geometric invariants of these spaces, such as the Euler characteristic and Deligne-Hodge polynomial.11.00 Michele D'Adderio (University Libre de Bruxelles) A geometric theory of algebras.
I will introduce some classical notions of geometric group theory (like growth and amenability) in the setting of associative algebras, and I will show how they interact with other classical invariants (like the Gelfand-Kirillov dimension and the lower transcendence degree).12.00 Wendy Lowen (Antwerp) On compact generation of deformed schemes.
We discuss a theorem which allows to prove compact generation of derived categories of Grothendieck categories, based upon certain coverings by localizations. This theorem follows from an application of Rouquier's cocovering theorem in the triangulated context, and it implies Neeman's Result on compact generation of quasi-compact separated schemes. We give an application of our theorem to non-commutative deformations of such schemes.