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Tuesday, September 22, 2026 1:30 pm - 2:30 pm EDT (GMT -04:00)

Algebra Seminar | Tariq Syed | Vector bundles over topologically contractible smooth affine complex varieties

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

Tuesday, September 22, 2026 2:30 pm - 4:00 pm EDT (GMT -04:00)

Differential Geometry Working Seminar | Viktor Majewski | Non-Existence of Smooth Full-Holonomy Cayley Fibrations

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
Thursday, September 24, 2026 3:00 pm - 4:00 pm EDT (GMT -04:00)

Model Theory Seminar | Yutong Duan | Strong minimality of Lotka-Volterra system

Yutong Duan (University of Waterloo)

Strong minimality of Lotka-Volterra system
We will begin with the notion of irreducibility for differential equations, introduced by Painlevé in his search for new transcendental functions, and explain its relationship with strong minimality. We will then introduce the Lotka–Volterra system and try to show that, under certain conditions on the parameters, its degree of non-minimality is zero; by convention, this means that its generic type is minimal. Finally, we will show that the resulting strongly minimal set has trivial geometry; moreover, it is strictly disintegrated.
MC 5403
Thursday, September 24, 2026 3:30 pm - 4:30 pm EDT (GMT -04:00)

Geometry & Topology Seminar | Dominik Gutwein | The moduli space of conically singular SU(3)-instantons

Dominik Gutwein (Universität Hamburg)
The moduli space of conically singular SU(3)-instantons
Instantons over manifolds with special holonomy are a distinguished class of connections on principal bundles. In their seminal paper from 1998 Donaldson and Thomas envisioned invariants of special holonomy manifolds based on the moduli space of such instantons. However, a rigorous construction of these invariants faces formidable challenges arising from the possible non-compactness of this moduli space. One source of non-compactness comes from the formation of non-removable singularities, that is, a sequence of instantons might converge to an instanton that is singular along a subset of the underlying manifold. In this talk, I will focus on instantons over 6-manifolds with SU(3)-structures that have isolated singularities of conical type. In particular, I will discuss their moduli space, its structure, and its virtual dimension. This talk is based on joint work with Yuanqi Wang.
MC 5417
Friday, September 25, 2026 10:00 am - 11:00 am EDT (GMT -04:00)

Algebraic Geometry Working Seminar | Francisco Villacis | Principal Minors and Absolute Values

Francisco Villacis (University of Waterloo)
Principal Minors and Absolute Values
The classification of matrices by their principal minors has been an area of interest to many since at least the 1980s. In this talk we expand on this work by outlining a proof that, if two orthogonal projection matrices have the same principal minors, then the coordinatewise absolute value of their images coincide. Generalizing the ideas of the proof gives rise to a stratification of the Grassmannian which is coarser than the well-known matroid stratification of Gelfand-Goresky-MacPherson-Serganova. We conclude this talk with some applications of this theorem to geometry.
MC 5403
Friday, September 25, 2026 12:00 pm - 1:00 pm EDT (GMT -04:00)

Intro to My Research | Michael Rubinstein

Michael Rubinstein (University of Waterloo)

Intro to My Research

This is a series of talks by faculty members explaining their research at a level aimed at master's students. All other department members are welcome as well.

MC 5417

Thursday, October 1, 2026 2:30 pm - 3:30 pm EDT (GMT -04:00)

Intro to My Research | Spiro Karigiannis

Spiro Karigiannis (University of Waterloo)

Intro to My Research

This is a series of talks by faculty members explaining their research at a level aimed at master's students. All other department members are welcome as well.

MC 5501