Current and Recent Colloquia
Thursday, March 31, 2016, 1:00 pm, HH 3017
University of New Brunswick, Fredericton
Birational Classification of Noncommutative Varieties that are Finite over their Centres
Abstract: We introduce the problem of birational classification for usual commutative varieties as the algebraic problem of classifying fields of finite transcendence degree over the complex numbers using algebraic geometry. In particular a fintely generated field extension of the complex numbers of transcendence degree one corresponds to a unique compact smooth Riemann surface. We extend this problem to the classification of division algebras which are finite dimensional over their centres. The case of curves is a consequence of Tsen's Theorem, and surfaces were studied by Chan and myself in 2005, Recently, we solved this problem in all dimensions and the solution has applications to birational geometry beyond the original problem. This recent work is joint with Daniel Chan, Kenneth Chan, Louis de Thanhoffer de Volcsey, Kelly Jabbusch, Sandor Kovacs, Rajesh Kulkarni, Boris Lerner and Basil Nanayakkara.
Friday, March 18, 2016, 2:00 pm, HH 3017
University of Marburg
Abstract: Fomin-Kirillov algebras are certain quadratic algebras graded by the symmetric groups. They and related algebras have been introduced by Fomin and Kirillov in 1998. A particular subalgebra of the Fomin-Kirillov algebra is suitable for calculations with Schubert polynomials. Fomin-Kirillov algebras also appear naturally in the theory of pointed Hopf algebras. Nevertheless almost nothing is known about the structure of these algebras, not even their dimension or a linear basis. In the talk I will present some known facts and some new ideas.