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Wednesday, September 16, 2026 2:30 pm - 3:30 pm EDT (GMT -04:00)

Pure Mathematics Colloquium | Yasuyuki Kawahigashi | Operator algebras, conformal field theory and condensed matter physics

Yasuyuki Kawahigashi (University of Tokyo)

Operator algebras, conformal field theory and condensed matter physics

We present an operator algebraic approach to conformal field theory in connection to other topics such as vertex operator algebras, quantum groups and quantum invariants in low-dimensional topology, which started with subfactor theory of Jones. We then present recent advances on similar mathematical structures that appear in two-dimensional condenses matter physics such as quantum spin systems, tensor networks and topological quantum computation. No knowledge on operator algebras are assumed.
MC 5479
Thursday, September 17, 2026 1:30 pm - 3:00 pm EDT (GMT -04:00)

Computability Learning Seminar | Joey Lakerdas-Gayle | The Game Metatheorem

Joey Lakerdas-Gayle (University of Waterloo)
The Game Metatheorem
The Game Metatheorem is a framework for constructing computable structures as a game between players using noncomputable \(\Delta^0_\eta\) information for a transfinite ordinal \(\eta\). We will introduce the Game Metatheorem following Montalbán's second computable structure theory book, and use it to prove the pairs of structures theorem.
MC 5301
Thursday, September 17, 2026 3:00 pm - 4:00 pm EDT (GMT -04:00)

Model Theory Seminar | Yutong Duan | Strongly Minimal Sets in DCF_0

Yutong Duan (University of Waterloo)

Strongly Minimal Sets in DCF_0

We introduce the theory of differentially closed fields of characteristic zero (DCF_0) and the pregeometry associated with minimal types, and explain how strong minimality connects questions about ordinary differential equations with model theory.

MC 5403

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