Time and location
The OttawaCarleton joint algebra seminar meets during the academic year approximately once per week at either The University of Ottawa or Carleton University. Unless otherwise indicated, the seminar takes place on Fridays,
14:30–15:30 at the following location:
 University of Ottawa: KED B015
 Carleton University: HP 4369
For information on the seminar in past semesters, click here. To schedule a talk, please contact Hadi Salmasian.
Talks
For a complete listing of all talks at the University of Ottawa, click here.
Date
 Speaker
 Title (click on titles to show/hide abstracts)

Jul. 10 (O) 
Changlong Zhong (SUNY Albany) 
Generalized Hecke algebras. 11:30–12:30 in KED B015
Abstract:
In this talk I will review the algebraic definition of formal affine Hecke algebra, and its relation with equivariant oriented cohomology of Steinberg variety. Moreover, I will also briefly mention a parallel work, which shows that the elliptic affine Hecke algebra is isomorphic to the equivariant elliptic cohomology of Steinberg variety with some twist.

Sept 18 (O) 
Alistair Savage (Ottawa) 
Heisenberg categorification and wreath product algebras
Abstract:
The Heisenberg algebra plays a vital role in many areas of mathematics and physics. In this talk, we will discuss a general method for categorifying this algebra. That is, we introduce a family of categories, depending on a Frobenius superalgebra B, whose Grothendieck groups are isomorphic to the Heisenberg algebra. The categories are graphical in nature, consisting of planar diagrams modulo local relations, and they act naturally on the category of finitely generated projective modules over wreath product algebras corresponding to B. Appropriate specializations of B recover results of Khovanov and CautisLicata. This is joint work with Daniele Rosso.

Sept 25 (O) 
Tiago Macedo (Ottawa) 
Extensions For Current Algebras
Abstract:
For this talk, a current algebra will be an
infinitedimensional Lie algebra formed as a tensor product of a
finitedimensional, simple Lie algebra over the complex numbers and
the polynomial ring in one variable. Current algebras are closely
related to affine KacMoody algebras. During this talk we will survey
some recent results related to extensions between finitedimensional,
irreducible modules for current algebras and report on a work in
progress, joint with B. Boe, C. Drupieski and D. Nakano.

Oct 2 (O) 
Baptiste Calmes (Universié d'Artois) 
MilnorWitt Ktheory is the generalized motivic cohomology of a field
Abstract:
Together with Jean Fasel, we introduced generalized motivic cohomology
groups of a smooth quasiprojective scheme over a field, and then we
proved that in the simplest case, when this scheme is a field, its
generalized motivic cohomology groups coincide with its MilnorWitt
Ktheory groups (as defined by Morel).
I will explain the proof of this isomorphism.

Nov 9 (O) 
Andrei Minchenko (Weizmann Institute) 
This talk is on Monday at 11:30 a.m. in Room FTX 361
Simple Lie conformal algebras
Abstract:
The notion of a Lie conformal algebra (LCA) comes from physics, and is related to the operator product expansion. An LCA is a module over a ring of differential operators with constant coefficients, and with a bracket which may be seen as a deformation of a Lie bracket. LCA are related to linearly compact differential Lie algebras via the socalled annihilation functor. Using this observation and the Cartan's classification of linearly compact simple Lie algebras, Bakalov, D'Andrea and Kac classified finite simple LCA in 2000.
I will define the notion of LCA over a ring R of differential operators with not necessarily constant coefficients, extending the known one for R=K[x]. I will explain why it is natural to study such an object and will suggest an approach for the classification of finite simple LCA over arbitrary differential fields.

Nov 13 (O) 
Roberto Pirisi (Ottawa) 
Cohomological Invariants for stacks of algebraic curves
Abstract:
Cohomological invariants are arithmetic analogues of characteristic classes in topology, in which singular cohomology is replaced with Galois cohomology, and topological spaces with spectra of fields. Given an affine algebraic group G, a cohomological invariant for G is a way to functorially assign to each principal Gbundle over the spectrum a field k an element of the Galois cohomology of k. These invariants form a graded ring, which has been computed for many classes of algebraic groups by several authors, including Rost, Serre, Merkurjev and many others.
In my talk I will show how to extend the classical theory to a theory of cohomological invariants for DeligneMumford stacks and in particular for the stacks of smooth genus g curves. The concept of general cohomological invariants turns out to be closely tied to the theory of unramified cohomology, which was introduced by Saltman, Ojanguren and ColliotThélène and is widely used to study rationality problems.
I will also show how to compute the additive structure of the ring of cohomological invariants for the algebraic stacks of hyperelliptic curves of all even genera and genus three.

Nov 20 (C) 
Yuly Billig (Carleton) 
Optimal control on SO(3)
Abstract:
Euler proved in 1776 that every rotation of a 3dimensional body can be
realized as a sequence of three rotations around two given axes. If we
allow sequences of an arbitrary length, such a decomposition will not be
unique. It is then natural to ask a question about decompositions that
minimize the total angle of rotation. In the talk we present a solution
to this problem.
Orientation of Kepler space telescope is controlled with reaction wheels.
In 2013, two of these wheels failed, and as a result Kepler may now be
rotated only around two axes. Our theorem provides optimal algorithms for
Kepler's attitude control. Other possible applications arise in quantum
information theory, where transformations on a single qubit are described
by the group SU(2), which is closely related to SO(3).

Nov 27 (O) 
Gufang Zhao (UMass Amherst) 
Elliptic affine Hecke algebras and their representations
Abstract:
This is based on a joint work with Changlong Zhong. In my talk,
I will explain the basic notions of equivariant elliptic cohomology. I
will prove that the convolution algebra of equivariant elliptic
cohomology of Steinberg variety is isomorphic to the elliptic affine
Hecke algebra constructed by GinzburgKapranovVasserot. As an
application, we study the DeligneLanglands theory in the elliptic
setting, and classify irreducible representations of the elliptic affine
Hecke algebra. The irreducible representations are in one to one
correspondence with certain nilpotent Higgs bundles on the elliptic
curve. We also study representations at torsion points in typeA.

(O) = uOttawa, (C) = Carleton