Differential Geometry Working Seminar

Talk #1 (9:30-10:30): Spiro Karigiannis, Department of Pure Mathematics, University of Waterloo 

Title: Calibrated subbundles of R^7, part II
Abstract: I will continue, and hopefully conclude, the discussion of calibrated subbundles in R^7. We will quickly review the previous talk and then focus on the coassociative case, which corresponds to negative superminimal surfaces.

Talk #2 (10:45-11:00): Spencer Whitehead, Department of Pure Mathematics, University of Waterloo 

Title: Generalized Pythagorean Lutes
Abstract: The lute of Pythagoras is a well-known self-similar pattern filling the plane with regular pentagons and pentagrams. This talk describes a generalization to higher dimensions and classification of such objects, yielding lutes corresponding to the dodecahedron in three dimensions and the 120-cell in four dimensions. A semi-formal discussion of these results is presented, together with Zome models and computer images of the new lutes.

Talk #3 (11:15-12:30): Anton Iliashenko, Department of Pure Mathematics, University of Waterloo 

Title: Instantons on Flat Spaces

Abstract: This talk is based on the paper by Jason D. Lotay and Thomas Bruun Madsen "Instantons on Flat Space: Explicit Constructions". Currently, the idea of generalisation of the (anti-)self-duality conditions to higher dimensions is getting a lot of attention. In this talk, we take the basic (or BPST) instanton on R^4 with its flat hyperkähler structure and show that it has natural generalisations to R^7 and R^8 viewed as flat G2- and Spin7-manifolds, respectively.

MC 5403