Events

Alex Pawelko, University of Waterloo

Gerbes of Coassociative Submanifolds and the first Chern class

We will define (bundle) gerbes, a generalization of principal S^1-bundles, and define connections on gerbes, whose corresponding forms over a trivialization are 2-forms and whose curvatures are 3-forms. Then, we will build a gerbe from coassociative submanifolds of a G_2 manifold, and study its analogue of the first Chern class, an integral cohomology class in degree 3.

MC 5403

Xuemiao Chen, University of Waterloo

Space of lines-II

I will continue to talk about some related constructions on the space of oriented lines in the three dimensional Euclidean space.

MC 5403

Noah Slavitch, University of Waterloo

Generic Absoluteness in Set Theory

We give an overview of the study of generic absoluteness for V in set theory, including a discussion of projective absoluteness and Sealing.

MC 5403

Beatrice-Helen Vritsiou, University of Alberta

On the Hadwiger-Boltyanski illumination conjecture for convex bodies with many symmetries

Let us think of a convex body in R^n (convex, compact set, with non-empty interior) as an opaque object, and let us place point light sources around it, wherever we want, to illuminate its entire surface. What is the minimum number of light sources that we need? The Hadwiger-Boltyanski illumination conjecture from 1960 states that we need at most as many light sources as for the n-dimensional hypercube, and more generally, as for n-dimensional parallelotopes. For the latter their illumination number is exactly 2^n, and they are conjectured to be the only equality cases.

The conjecture is still open in dimension 3 and above, and has only been fully settled for certain classes of convex bodies (e.g. zonoids, bodies of constant width, etc.). In this talk I will briefly discuss some of its history, and then focus on recent progress towards verifying the conjecture for all 1-symmetric convex bodies and certain cases of 1-unconditional bodies.

MC 5501

Spiro Karigiannis, University of Waterloo

Organizational Meeting

The Differential Geometry Working Seminar is an opportunity for all participants (students, postdocs, and faculty) to learn new things, to teach each other new things, and to get more practice in giving talks. It is very informal and confusion is common/encouraged. That's how we learn.

As usual, we'll start the term by attempting to decide on as much of the schedule as we can for the coming term. We'll have one speaker per week (most weeks) on Thursdays at 2:30pm.

MC 5403

Aareyan Manzoor, University of Waterloo

There is a non-Connes embeddable equivalence relation

Connes embeddability of a group is a finite dimensional approximation property. It turns out this property depends only on the so-called group von Neumann algebra. The property can be extended to all von Neumann algebras. The fact that there is a von Neumann algebra without this property was proved in 2020 using the quantum complexity result MIP*=RE. It is still open for group von Neumann algebras. I will discuss the best-known partial result, which is that there is a group action without this property. In particular, this implies the negation to the Aldous-Lyons conjecture, a big problem in probability theory

QNC 1507 or Join on Zoom

Joey Lakerdas-Gayle, University of Waterloo

Algorithmic Randomness Organizational Meeting

Organizational meeting to plan the rest of the learning seminar. We might also discuss some computability theory and algorithmic randomness.

MC 5403

Marina Logares, Universidad Complutense de Madrid

From Higgs Bundles to Integrable Systems: Examples from Geometry and Physics

Hitchin systems are a central class of algebraically completely integrable systems, arising from moduli of Higgs bundles and their spectral curves. I will describe their structure as Lagrangian fibrations and illustrate these ideas through examples connecting geometry and mathematical physics.

MC 5403

Aleksandar Milivojevic, University of Waterloo

Realizing topological data by closed almost complex manifolds

I will talk about the topological obstructions to placing an almost complex structure on a smooth manifold. I will then discuss how the vanishing of these obstructions is in many cases sufficient to realize a given rational homotopy type (with a choice of cohomology classes) by an almost complex manifold (with those cohomology classes as its rational Chern classes).

MC 5403

Andy Zucker, University of Waterloo

Tameness, forcing, and the revised Newelski conjecture

The revised Newelski conjecture asserts that for any group definable in an NIP structure, the automorphism group of its definable universal minimal flow is Hausdorff in the so-called "tau-topology." Recently, the countable case of the conjecture was proven by Chernikov, Gannon, and Krupinski using a deep result of Glasner, which provides a structure theorem for minimal metrizable tame flows. With this result, they prove that the Ellis group of a minimal metrizable tame flow (the automorphism group of a related flow) has Hausdorff tau-topology, and the conjecture for groups definable in countable NIP structures follows. We prove the revised Newelski conjecture in full by showing that the Ellis group of any minimal tame flow has Hausdorff tau-topology. To do this, we introduce new set-theoretic methods in topological dynamics which allow us to apply forcing and absoluteness arguments. As a consequence, we obtain a partial version of Glasner's structure theorem for general minimal tame flows. Joint work with Gianluca Basso.

MC 5403