The 49th ARTIN meeting will take place at Lancaster University on the afternoon of Thursday 10th and morning of Friday 11th November 2016. It will be funded by the London Mathematical Society and the Glasgow Mathematical Journal Trust.
-- Kenny de Commer (Brussels)
-- David Jordan (Edinburgh)
-- Iva Halacheva (Lancaster)
-- Kevin de Laet (Antwerp)
-- Alice Rizzardo (Edinburgh)
Alice Rizzardo (Edinburgh) - From Fourier transforms to Fourier-Mukai functors
10th November 2016, 1:00pm to 1:50pm Lab 2, Postgraduate Statistics Centre, Lancaster University -- Show/hide abstractAbstract: Starting from familiar concepts coming from analysis and classical algebraic geometry, I will introduce Fourier-Mukai functors in the context of derived categories. I will explain what makes them useful, and talk about which functors between derived categories can be expressed in Fourier-Mukai form. This is joint work with Michel Van den Bergh.
Kevin de Laet (Antwerp) - Representation theory of Sklyanin algebras at points of finite order
10th November 2016, 2:00pm to 2:50pm Lab 2, Postgraduate Statistics Centre, Lancaster University -- Show/hide abstractAbstract: Sklyanin algebras form a 2-dimensional family of noncommutative algebras and they form deformations of the commutative polynomial ring. They depend on an elliptic curve E and a point t of E. In the case that t is a torsion point, Tate and Van den Bergh showed that such a Sklyanin algebra is a finite module over its center. However, except in the 3-dimensional and in the 4-dimensional case, the PI-degree and a description of the center is not known. After recalling the connection between fat point modules and irreducible representations for Sklyanin algebras, I will show that Sklyanin algebras at points of order 2 of odd global dimension n are Clifford algebras over a polynomial ring in n variables, which gives the PI-degree in this special case. For n=5 in this special case, the ramification locus is calculated, as well as the correspondence between fat points and points projective 4-space.
Tea and coffee
10th November 2016, 3:00pm to 3:30pm B Floor Social Area, Postgraduate Statistics Centre, Lancaster University
Kenny de Commer (Brussels) - Torsion-freeness for discrete quantum groups
10th November 2016, 3:30pm to 4:20pm A54 Lecture Theatre, Postgraduate Statistics Centre, Lancaster University -- Show/hide abstractAbstract: In order to formulate the Baum-Connes conjecture in the setting of discrete quantum groups, R. Meyer introduced a notion of torsion-freeness for them. In this talk, we define torsion-freeness for rigid tensor C*-categories and fusion rings. As an application, we then show that the discrete duals of the free unitary quantum groups of Wang and Van Daele are torsion-free, answering a question of C. Voigt. This is joint work with Y. Arano.
10th November 2016, 7:00pm to 9:00pm Paulo Gianni's, 15 New Street, Lancaster LA1 1EG, UK
Iva Halacheva (Lancaster) - The cactus group, crystals, and shift of argument algebras
11th November 2016, 9:30am to 10:20am Lab 2, Postgraduate Statistics Centre, Lancaster University -- Show/hide abstractAbstract: Two objects arising from a finite-dimensional reductive Lie algebra g and its representation theory are the cactus group defined using the Dynkin diagram of g, and crystals encoding the information of g-representations. We define an action of the cactus group on any crystal, which can be realized both combinatorially and geometrically. On one hand, it can be described in terms of Schützenberger involutions. On the other hand, it is the monodromy action for a covering of a certain moduli space, coming from a family of maximal commutative subalgebras of U(g) known as the shift of argument algebras.
Tea and coffee
11th November 2016, 10:30am to 11:00am B Floor Social Area, Postgraduate Statistics Centre, Lancaster University
David Jordan (Edinburgh) - The quantum Springer sheaf
11th November 2016, 11:00am to 11:50am A54 Lecture Theatre, Postgraduate Statistics Centre, Lancaster University -- Show/hide abstractAbstract: In classical Springer theory, one is constructing representations of the Weyl group W of a reductive group, exploiting the geometry of the flag variety. Hotta and Kashiwara gave a striking reformulation of classical Springer theory, in terms of equivariant D-modules on the Lie algebra g (i.e. systems of differential equations on g, with strong symmetry properties). In this talk, I'll review Hotta and Kashiwara's construction, and explain some joint work with Monica Vazirani to define and compute analogs of Hotta-Kashiwara's D-modules in the setting of quantum groups.
Please register if you plan to attend, using the following link:
This will help us to organise refreshments, plan the conference dinner, and manage the budget.
We have reserved 15 rooms on campus for the night of Thursday 10th November, which can be booked by visiting the website
and using the code ARTIN49. Please note that this code will only work for the night of Thursday 10th; should you wish to book for more than one night, you should not use the code. Please contact the organiser in the event of any difficulties.
The designated funding for post-docs and PhD students is spent, but nevertheless get in touch if you want to come and need funding, in case we can find more.
There will be a conference dinner on Thursday night, at a location to be announced.
The details will be updated on the ARTIN webpage
If you have any questions, please contact Jan Grabowski (firstname.lastname@example.org).