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Tariq Syed (Heinrich-Heine-Universität Düsseldorf)

Vector bundles over topologically contractible smooth affine complex varieties

A smooth complex variety X is called topologically contractible if its set of complex points, viewed as a complex manifold with analytic topology, is a contractible topological space. The primordial examples of topologically contractible smooth affine complex varieties are given by affine spaces. The generalized Serre question on algebraic vector bundles asks whether algebraic vector bundles over topologically contractible smooth affine complex varieties are always trivial. In this talk, we survey classical results and highlight the most recent developments on this problem.

MC 5479

Viktor Majewski (University of Waterloo)

Non-Existence of Smooth Full-Holonomy Cayley Fibrations

In this talk, I complete the proof that every Cayley fibration of a compact torsion-free 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 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.

MC 5417

Wednesday, September 23, 2026 2:00 pm - 3:00 pm EDT (GMT -04:00)

Logic in Analysis Working Seminar | Andy Zucker | Brief introduction to forcing

Andy Zucker (University of Waterloo)

Brief introduction to forcing

With an eye towards working through the recent preprint by Arulseelan and Hanson on AW*-algebras, I will give a brief introduction to set-theoretic forcing, with a focus on Boolean-valued models.

MC 5301

Joey Lakerdas-Gayle (University of Waterloo)

The Pairs of Structures Theorem

We will finish the proof of the Pairs of Structures theorem using the Game Metatheorem.

MC 5301

Friday, September 25, 2026 12:00 pm - 1:00 pm EDT (GMT -04:00)