2020-2021 Colloquia
Title: Subordination Principle for the Fractional Diffusion-Wave Equation
Speaker: Yuri Luchko
Date: Wednesday, November 11, 2020Time: 12:30pm—1:30pm
Room: See Zoom web address below
Abstract
Title: Theory and numerics of some types of fractional differential equations
Speaker: Jeffrey Slepoi
Date: Wednesday, October 28, 2020Time: 1:00pm—2:00pm
Room: See Zoom web address below
Abstract
Title: Polyalgorithms, Number Fields, and Motives
Speaker: Ivan Horozov
Date: Wednesday, October 7, 2020Time: 12:00pm—1:00pm
Room: See Zoom web address below
Abstract
Title: Almost complex and complex structures on manifolds
Speaker: Luis Fernandez
Date: Wednesday, September 23, 2020Time: 12:30pm—1:30pm
Room: See Zoom web address below
Abstract
An almost complex structure on a manifold is a way to define an operation similar to multiplication by i (the imaginary unit) on the tangent space of the manifold; a manifold with an almost complex structure is called an almost complex manifold.
On the other hand, a complex manifold is a manifold modeled over complex vector spaces.
I will explain these concepts carefully and compare them, showing several examples, especially those based on algebra structures like the quaternions and the octonions. Then I will show examples of almost complex manifolds that cannot be complex manifolds, but can be as close as we want to complex manifolds in a certain sense. This work is in collaboration with Scott Wilson, from Queen's College and the GC.
If there is enough time, I will also talk about almost complex curves on the 6-sphere.
Title: Left Invariant Complex Structures on Double Lie Groups
Speaker: D. N. Pham
Date: Wednesday, September 23, 2020Time: 1:10pm—2pm
Room: See Zoom web address below
Abstract
Roughly speaking, a Lie bialgebra is a Lie algebra g such that its dual space g* is equipped with its own Lie algebra structure. The Lie algebras g and g* are compatible in the sense that they define a Lie algebra on g⨁g* which contain g and g* as subalgebras and for which the natural scalar product on g⨁g* is invariant. This Lie algebra structure on g⨁g* is denoted as D(g) and is called a double Lie algebra. A Lie group whose Lie algebra is D(g) is called a double Lie group. In this talk, I will discuss the problem of constructing left invariant complex structures on double Lie groups (which will in effect turn these objects into complex manifolds). The only prerequisites for this talk are basic differential geometry and familiarity with Lie groups and Lie algebras. No familiarity with complex manifolds is assumed. We will review the relevant background on complex manifolds as part of the talk. This project is joint work with Fei Ye.