Events

Alex Pawelko, University of Waterloo

Riemannian Geometry of Knot Spaces

We will review the construction of knot spaces of manifolds, specifically over G2 and Spin(7) manifolds. We will then see an explicit construction of the Levi-Civita connection of the knot space, and see what this can tell us about the torsion of the induced special geometric structures on knot spaces of G2 and Spin(7) manifolds.

MC 5403

Joaco Prandi, University of Waterloo

When the weak separation condition implies the generalize finite type in R^d

Let S be an iterated function system with full support. Under some restrictions on the allowable rotations, we will show that S satisfies the weak separation condition if and only if it satisfies the generalized finite-type condition. To do this, we will extend the notion of net intervals from R to R^d. If time allows, we will also use net intervals to calculate the local dimension of a self-similar measure with the finite-type condition and full support.

QNC 1507 or Join on Zoom

Sergey Grigorian, University of Texas Rio Grande Valley

Geometric structures determined by the 7-sphere

The 7-sphere is remarkable not only for its rich topological and algebraic properties but also for the special geometric structures it encodes. In this talk, we explore how the symmetries and stabilizer subgroups of Spin(7) acting on the 7-sphere, regarded as the set of unit octonions, give rise to G2​-structures on 7-manifolds, SU(3)-structures on 6-manifolds, and SU(2)-structures on 5-manifolds. We will trace how these structures arise naturally via the inclusions of Lie groups and are reflected in the geometry of sphere fibrations. This perspective highlights the role of the 7-sphere as a unifying object in special geometry in dimensions from 5 to 8.

MC 5417