Geometry and Topology

Speaker: Benoit Charbonneau (Waterloo)

"Deformations of nearly Kahler instantons"

Time: 15:30

Room: MC 107

In joint work with Derek Harland, we have developed the deformations theory for instantons on nearly Kahler six-manifolds using spinors and Dirac operators. Using this framework we identify the space of deformations of an irreducible instanton with semisimple structure group with the kernel of an elliptic operator. As an application, we show that the canonical connection on three of the four homogeneous nearly Kahler six-manifolds G/H is a rigid instanton with structure group H. In contrast, these connections admit large spaces of deformations when regarded as instantons on the tangent bundle with structure group SU(3).

Noncommutative Geometry

Speaker: (Western)

"Learning Seminar"

Time: 11:30

Room: MC 107

This week we are covering: ---The index problem for elliptic PDE's, characteristic classes via Chern-Weil theory, ---Miraculous cancellations, Getzler's supersymmetric proof of the Atiyah-Singer index theorem, special cases: Gauss-Bonnet-Chern, Hirzebruch signature theorem, and Riemann-Roch, --- Approach via path integrals and quantum mechanics.

Analysis Seminar

Speaker: Fatemeh Sharifi (Western)

"Zero-free approximation"

Time: 15:30

Room: MC 107

Let $E$ be a closed subset in the complex plane with connected complement. We define $A(E)$ to be the class of all complex continuous functions on $E$ that are holomorphic in the interior $E^0$ of $E$. The remarkable theorem of Mergelyan shows that every $f\in A(E)$ is uniformly approximable by polynomials on $E$, but is it possible to realize such an approximation by polynomials that are zero-free on $E$? This question was first proposed by J.Anderson and P.Gauthier. Recently Arthur Danielyan described a class of functions for which zero-free approximation is possible on an arbitrary $E$. I am intending to talk about the generalization of his work on Riemann surfaces.

Noncommutative Geometry

Speaker: Yanli Song (U of Toronto)

"K-homological index for proper actions"

Time: 15:30

Room: MC 108