Time: 13:30
Speaker: Ali Fathi (Western)
Title: "On certain spectral invariants of noncommutative tori and curvature of Quillen's determinant line bundle for noncommutative two-torus"
Room: MC 108

Abstract: By extending the canonical trace of Kontsevich-Vishik to Connes' pseudodifferential operators on noncommutative tori, we study various spectral invariants associated to elliptic operators in this setting. We also consider a family of Cauchy-Riemann operators over noncommutative 2-torus and using the machinery of canonical trace, we compute the curvature form of the associated Quillen determinant line bundle.

Time: 14:00
Speaker: Martin Frankland (Western)
Title: "The Moss convergence theorem"
Room: MC 107

Abstract: We will present a theorem due to R.M.F. Moss which says, roughly, that 3-fold Massey products of permanent cycles in the Adams spectral sequence converge to the corresponding 3-fold Toda brackets in stable homotopy.

Time: 15:30
Speaker: Tom Hales (Pittsburg)
Title: "The formal proof of the Kepler conjecture"
Room: MC 107

Abstract: The Kepler conjecture asserts that no packing of congruent balls in space can have density greater than the familiar cannonball arrangement. If every logical inference of proof has been checked all the way to the fundamental axioms of mathematics, then we say that the proof has been formally verified. The Kepler conjecture has now been formally verified by computer, in a massive cloud computation. This talk will report on this and other massive formal verification projects.