Noncommutative Geometry

Speaker: Ali Moatadelro (Western)

"Representation theory of compact quantum groups with examples, lecture 5. Irreducible representations of SU(3), continued."

Time: 09:30

Room: MC 107

In this series of lectures, we will discuss basic examples of compact quantum groups and their (finite dimensional) representations. We will start with reviewing the classical theory. We shall classify all finite dimensional irreducible representations of compact Lie groups SU(2) and SU(3). Then we will proceed to the general theory of representation of compact Lie groups and will discuss several important results including the highest weight theory, the Peter-Weyl decomposition theorem, and also the Borel-Weil-Bott construction of representations. Finally, we will see how much of the theory holds in the quantum case.

Geometry and Topology

Speaker: Bert Guillou (University of Illinois)

"G-spectra are spectral Mackey functors "

Time: 15:30

Room: MC 107

Equivariant spectra have received a good deal of attention lately due to their central role in the Hill-Hopklins-Ravenel proof of the Kervaire invariant one problem. I will describe joint work with Peter May that provides an alternative model for equivariant spectra (indexed on a complete G-universe).

Analysis Seminar

Speaker: Ilya Kossovskiy (Western)

"Envelopes of holomorphy for real submanifolds in a complex space"

Time: 15:30

Room: MC 107

One of the most impressive phenomena in several complex variables is the phenomenon of forced analytic continuation for holomorphic functions. The biggest domain, to which the family of all holomorphic functions extends, is called the envelope of holomorphy of a domain or of a real submanifold in a complex space. Envelopes of holomorphy have some nice geometric description, making them in a sense similar to convex hulls of domains and submanifolds in a Euclidian space. In the present talk we discuss some classical theorems for domains of holomorphy as well as some new results for real submanifolds in a complex space.

Noncommutative Geometry

Speaker: Ali Moatadelro (Western)

"Holomorphic structures on the quantum projective space"

Time: 14:30

Room: MC 107

We review the notion of holomorphic vector bundles in noncommutative geometry and then define holomorphic structures on canonical line bundles on the quantum projective space. The space of holomorphic sections of these line bundles will determine the quantum homogeneous coordinate ring of the quantum projective space. We also show that the holomorphic structure is naturally represented by a twisted positive Hochschild cocycle.

Symplectic Learning Seminar

Speaker: M. VanHoof (Western)

"Connectedness of Symp groups, part II"

Time: 13:00

Room: MC 105C

This is a continuation of our discussion of the connectedness of $Symp(CP^2)$ an other symplectomorphism groups.

Colloquium

Speaker: Rahim Moosa (Waterloo)

"A Hasse-Schmidt approach to expansions of algebraic geometry"

Time: 15:30

Room: MC 107

Differential-algebraic geometry is the expansion of algebraic geometry where in addition to polynomial equations one considers (partial) algebraic differential equations. Similarly, using automorphisms instead of derivations, we have difference-algebraic geometry. In this talk I will give an introduction to these subjects and to describe recent work with Tom Scanlon in which we develop a new foundation that unifies and generalises them. Our approach is informed by the theory of iterative Hasse-Schmidt derivations and is based upon an abstract notion of "prolongation" for an algebraic variety.

Algebra Seminar

Speaker: Andrey Minchenko (Western)

"Differential representations of $SL(2)$"

Time: 14:30

Room: MC 107

In order to describe linear representations of a group, it is sufficient to find all its indecomposable representations. It is known that indecomposable algebraic representations of G=SL(2) correspond to irreducible subrepresentations of G in the ring R of polynomials in two variables x and y. Given a derivation ' on the ground field, R extends to a G-representation R' by adding variables x', y', x", y", etc. We will investigate indecomposable subrepresentations of R' and discuss their relation to description of all differential representations of G. If time permits, I will describe the category of differential representations of tori.