Noncommutative Geometry

Speaker: Travis Ens (Western)

"NCG Learning Seminar: Feynman's diagrams and Feynman's theorem (4)"

Time: 14:30

Room: MC 107

Geometry and Topology

Speaker: Steven Rayan (University of Toronto)

"Generalized holomorphic bundles on ordinary complex surfaces"

Time: 15:30

Room: MC 108

Generalized holomorphic bundles are a feature of Hitchin's generalized geometry. On an ordinary complex manifold, a generalized holomorphic bundle is not necessarily a holomorphic bundle. More generally, it is a kind of Higgs bundle -- sometimes called a co-Higgs bundle. I will discuss issues regarding stability and integrability for generalized holomorphic bundles over ordinary complex surfaces. In particular, I will construct a sequence of families of stable, integrable rank-2 generalized holomorphic bundles on CP^2, using the classical Schwarzenberger construction of ordinary holomorphic bundles.

Dept Oral Exam

Speaker: Claudio Quadrelli (Western)

"p-rigid fileds - a high cliff on the p-Galois see"

Time: 11:00

Room: MC 106

I plan to discuss my recent joint work with S. Chebolu and J. Minac. Let p be an odd prime and assume that a primitive p-th root of unity is in a field F. Then F is said to be p-rigid if only those cyclic algebras are split which are split for trivial reasons. I will present new characterizations of such fields and their Galois groups, which come from a more group-theoretical and cohomological approach. Our work extends, illustrates and simplifies some previous results and provides a new direct foundation of rigid fields which does not rely on valuation techniques. This work shows in fact how this new cohomological approach on maximal p-extensions of fields can be powerful, especially after the proof of the Milnor-Bloch-Kato conjecture.

Analysis Seminar

Speaker: Blagovest Sendov (Bulgarian Academy of Sciences)

"Hausdorff Approximations"

Time: 15:30

Room: MC 108

Let $A$ be a functional space of high or infinite dimension, $r(f,g);\; f,g\in A$ be a metric defined on $A$ and $\PP_n\subset A$ be an $n$-dimensional subset of $A$. The main goal of Approximation Theory, which is a theoretical basis for Numerical analysis and Numerical methods, is for given $f\in A$ to find a $p\in \PP_n$, such that $r(f,p)$ is as small as possible. Hausdorff Approximation (see \cite{BS}) is a part of Approximation Theory, in which to every function $f\in A$ corresponds a closed and bounded point set $\bar{f}$, and the distance between two functions $f,g\in A$ is defined as the Hausdorff distance between $\bar{f}$ and $\bar{g}$. An important fact is that the Hausdorff distance is not derived from a norm.

In this lecture, we underline the specifics of Hausdorff Approximation and formulate the most interesting results.

Noncommutative Geometry

Speaker: Masoud Khalkhali (Western)

"Applications of the Atiyah-Singer index theorem 2: Hirzebruch signature theorem (continued)"

Time: 14:30

Room: MC 107

After giving the final details of the heat equation proof, I shall give some applications. Most notably Hirzebruch's Signature theorem and the Riemann-Roch theorem for compact complex manifolds.