Past Talks

October 11th, 2024: Mahan Moazzeni (McMaster University)

• Title: An Invitation to Non-classical Knot Theories

• Abstract: A knot is a smooth embedding of the circle in 3-dimensional sphere and two knots are equivalence as long as they are ambient isotopic. In this talk we briefly discus the classical knots and try to generalize this theory to higher dimensions and different settings in the hope to get interesting knot theories. Then we focus on two theories, virtual and welded knot theories, which are related to the knots in thickened surfaces and ribbon knotted tori in 4-dimensional sphere. Although they are related and relatively close to the classical knot theory, they behave differently and there are a lot of properties that are quite unknown.

October 25th, 2024: Francisco Villacis (University of Waterloo)

• Title: Integrable Systems and Its Applications to Mirror Symmetry

• Abstract: Completely integrable systems and toric moment maps form an important set of tools for symplectic geometers. These give rise to Lagrangian fibrations, which in turn play an important role in quantization problems and are the main object of study in the SYZ formulation of mirror symmetry. In this talk I will give a brief overview of (completely) integrable systems, their relation to toric moment maps, and how these appear in the context of mirror symmetry.

November 1st, 2024: Jeffrey Marshall-Milne (McMaster University)

• Title: Projective Knot theory and an application of Dynikov's Algorithm

• Abstract: The basics of projective knot theory are laid out. The class of a link and its relation to spanning surfaces is discussed. Results on $S$-equivalence and $S^*$-equivalence of spanning surfaces are presented, and an algorithm for affine knot detection is outlined.