The 45th ARTIN meeting will take place at the University of Edinburgh on the 11th and 12th of September 2015. All talks will be in the James Clerk Maxwell Building, room 6206.
The theme of the meeting is noncommutative ring theory, with an emphasis on noncommutative algebraic geometry.
- Martina Balagovic (Newcastle)
- Charlie Beil (Bristol)
- Alexey Petukhov (Manchester)
- Dennis Presotto (Hasselt)
- Ana Rovi (Glasgow/Newcastle)
- Spela Spenko (Edinburgh)
Friday 11 September
|1300-1400||Dennis Presotto|| |
Noncommutative versions of some classical birational transformations
In the paper 'arXiv:1410.5207' (to appear in Journal of Noncommutative Geometry) Michel Van den Bergh and I generalize some classical birational transformations to the noncommutative setting. In particular we show that 3-dimensional quadratic Sklyanin algebras (noncommutative projective planes) and 3-dimensional cubic Sklyanin algebras (non-commutative quadrics) have the same function field. In the same vein we construct an analogue of the Cremona transform for noncommutative projective planes.
In this talk I will explain the approach and motivation for our paper. The motivation is based on the construction of the Cremona transform (in the commutative setting) using linear systems. I will also recapitulate some relevant facts about noncommutative surfaces and Artin-Schelter regular (Z-)algebras.
|1430-1530||Charlie Beil|| |
Noncommutative resolutions of nonnoetherian singularities and the nature of time
Quantum nonlocality is the strange phenomenon where two entangled particles can affect each other instantaneously, regardless of how far apart they are. I will explain how this phenomenon can be described geometrically as a nonnoetherian singularity in spacetime. I will then introduce the notion of a noncommutative resolution of such a singularity, and describe how this notion fits into the quantum world.
|1530-1630||Tea and coffee|
|1630-1730||Spela Spenko|| |
Non-commutative resolutions of quotient singularitiesSlides
This is joint work with Michel Van den Bergh. We generalize standard results about non-commutative resolutions of quotient singularities for finite groups to arbitrary reductive groups. We show in particular that quotient singularities for reductive groups always have non-commutative resolutions in an appropriate sense.
We discuss a number of examples, both new and old, that can be treated using our methods; twisted non-commutative crepant resolutions exist in previously unknown cases for determinantal varieties of symmetric and skew-symme- tric matrices.
1830- Conference Dinner, Kalpna (2-3 St. Patrick Square, Edinburgh EH8 9EZ).
Saturday 12 September
|0900-1000||Ana Rovi|| |
Lie algebroids in the Loday-Pirashvili category
We describe Lie--Rinehart algebras in the tensor category of linear maps in the sense of Loday and Pirashvili and construct a functor from Lie-Rinehart algebras (in the category of linear maps) to Leibniz algebroids.
|1015-1115||Martina Balagovic|| |
Universal K-matrices via quantum symmetric pairsSlides
The construction of the universal R-matrix for quantum groups produces solutions of the Yang-Baxter equation on tensor products of representations of that quantum group. This gives an action of the braid group of type A, endowing the category of finite dimensional Uq(g)-representations with a structure of a braided tensor category.
I will explain how the theory of quantum symmetric pairs allows an analogous construction of a universal K-
|1115-1200||Tea and coffee|
|1200-1300||Alexey Petukhov|| |
Birational commutative and non-commutative geometry
In my talk I will construct a functor from some class of skew fields to some class of commutative fields with map \( Q( C[x, \partial_x]) \to Q (C[x, y]) \) as the main example. I will also provide some link between this construction and some known results and conjectures on skew fields.
While not part of the official program, attendees might be interested in the M. C. Escher exhibit at the Scottish National Gallery of Modern Art. There may be a semi-organised outing to the exhibit on Saturday afternoon.
The ARTIN meeting will take place in the James Clerk Maxwell Building at the University of Edinburgh King's Buildings. This is about 2.5 miles south of the city centre. Directions are here: http://www.maths.ed.ac.uk/contact/travel-directions
Please register here if you plan to attend: http://goo.gl/forms/4kFBgvXpc4