Waterloo Differential Geometry Working Seminar

Speaker: Spiro Karigiannis

Title: Organizational Meeting

Abstract: We will plan the speakers for the rest of the semester.

Speaker: Viktor Majewski

Title: Non-Existence of Smooth Full-Holonomy Cayley Fibrations

Abstract: In this talk, I complete the proof that every Cayley fibration of a compact torsion-free \(\textrm{Spin(7)}\)-manifold with full holonomy must have singular fibers. This confirms a long-standing expectation in the study of calibrated fibrations with exceptional holonomy. Last semester, I showed that using the rigidity of the \(\textrm{Spin(7)}\)-structure to reduce any hypothetical nonsingular Cayley fibration to two possible topological configurations. This time, I exclude both by proving a new spinnability theorem for smooth fiber bundles over simply-connected \(4\)-manifolds with fiber homeomorphic to the elliptic surfaces \(E(2)\) or \(E(4)\). The \(E(4)\) case, which constitutes the main new difficulty, is established by combining families Seiberg–Witten theory with parametrized equivariant homotopy theory and equivariant \(K\)-theory.

Speaker: Paul Cusson

Title: TBA

Abstract: TBA

Speaker: Facundo Camano

Title: TBA

Abstract: TBA

Reading week

Speaker: Spencer Kelly

Title: TBA

Abstract: TBA

Speaker: Faisal Romshoo

Title: TBA

Abstract: TBA

Speaker: Benoit Charbonneau

Title: TBA

Abstract: TBA

Speaker: Francisco Villacis

Title: TBA

Abstract: TBA

Speaker: Jacques Van Wyk

Title: TBA

Abstract: TBA

Speaker: Faisal Romshoo

Title: TBA

Abstract: TBA

Speaker: Danial Ghamari

Title: TBA

Abstract: TBA

Speaker: Spencer Kelly

Title: TBA

Abstract: TBA

Speaker: Danial Ghamari

Title: TBA

Abstract: TBA