Noncommutative Geometry

Speaker: Masoud Khalkhali (Western)

"Habemus Higgs!"

Time: 14:30

Room: MC 107

On 4 July 2012 at a conference in CERN, Geneva, the latest findings of the LHC experiment were unveiled: ``We observe in our data clear signs of a new particle, at the level of 5 sigma, in the mass region around 126 GeV. The outstanding performance of the LHC and ATLAS and the huge efforts of many people have brought us to this exciting stage", said ATLAS experiment spokesperson Fabiola Gianotti.

It is now believed beyond any doubts that the long sought after Higgs particle, the last missing part of the Standard Model of elementary particles, has been detected. In this talk I shall sketch the so called Higgs mechanism (due independently to Englert-Brout; Kibble-Guralnik-Hagen; and Higgs) and will show how symmetry breaking creates the much needed massive gauge bosons of the standard model. In a follow up talk I shall explain what noncommutative geometry adds to this picture.

Note: The 2013 Nobel prizes in physics will be announced tomorrow, Oct. 8. The odds for a prize going to a Higgs related work is quite high. We shall see!

Analysis Seminar

Speaker: Rasul Shafikov (Western)

"Structure of the polynomially convex hulls of singular real manifolds in $\mathbb C^n$."

Time: 14:30

Room: MC 108

I will discuss possible descriptions of the structure of polynomially convex hulls of singular totally real and Lagrangian submanifolds of $\mathbb C^n$. This is joint work with A. Sukhov.

Homotopy Theory

Speaker: Mike Misamore (Western)

"Localization of spectra with respect to homology"

Time: 14:30

Room: MC 108

Algebra Seminar

Speaker: Sean Fitzpatrick (Western)

"Clifford algebras and Bott periodicity in K-theory"

Time: 15:30

Room: MC 108

I will review the classic paper "Clifford modules", by Atiyah, Bott, and Shapiro, which had its 50th birthday last month. This paper explores both Clifford algebras and K-theory, and the connections between them. In particular, we see that Bott periodicity arises as a purely algebraic phenomenon in the study of Clifford modules. Although this paper did not give a proof of Bott periodicity in K-theory via Clifford algebras, it certainly provided strong evidence in that direction. (This problem was tackled by other authors at the same time.) Time permitting, I will discuss some of the topological applications that arise from applying the algebraic machinery of Clifford modules to K-theory, such as the Thom isomorphism and vector fields on spheres.