Events

Joey Lakerdas-Gayle, University of Waterloo

Sacks' Splitting Theorem on a tree

We will prove Sacks' Splitting Theorem following the method of Steffen Lempp which uses a dynamically constructed priority tree.

MC 5403

Julius Frizzell, University of Waterloo

Generic Measures and Unitary Transformations

We continue our discussion of generic measures and prove some facts about unitary transformations, which moves us toward a proof of Roth's theorem.

MC 5417

Kaleb Ruscitti, University of Waterloo

Extending Hitchin's connection across nodal curves

Hitchin gave a projectively flat connection on the 'Verlinde bundle' over the moduli space of complex structures on a compact genus \(g>=2\) surface (Flat connections and geometric quantization, 1990). Such a surface can be deformed to a stable curve with nodal singularities, and I will discuss the extension of the Verlinde bundle and Hitchin's connection across such deformations.

MC 4058

Facundo Camano, University of Waterloo

Equivalent Formulations of Monopole Asymptotics

I will go over three ways of defining monopole asymptotics and prove they are all equivalent for finite energy solutions.

MC 4058

Catherine St-Pierre, University of Waterloo

Group Actions in Non-Commutative Algebraic Geometry: a survey of homological property and invariants

We survey non-commutative analogues of classical regularity, Gorenstein, and Cohen-Macaulay properties in the framework of Artin-Schelter. After reviewing the foundational homological properties that govern this theory, we will focus on the structure of invariant rings under group and Hopf algebra actions and review some noncommutative analogues of classical results in invariant theory to characterize the invariant rings of noncommutative rings. The talk concludes with new results extending this invariant-theoretic framework.

MC 5403

Beining Mu, University of Waterloo

Thickness Lemma and Infinite Injury Priority Argument

In this talk, I will present Strong Thickness Lemma, which states that every piecewise computable c.e. set has a thick subset which lies outside of an upper cone of a non-computable c.e. set, as an example of infinite injury priority argument. In addition, I will discuss how thickness lemma implies the lack of least upper bound for infinite ascending c.e. degrees.

MC 5403

Michael Gregory, University of Waterloo

Basic Universal Algebra Aimed at Isomorphism Problems for c.e. Presentations

We begin with the notions of a universal algebra, homomorphism, congruence, and quotient algebra, and discuss the relationship between congruences and homomorphic images. We then introduce term algebras and varieties, culminating in a statement of Birkhoff's HSP Theorem. To prepare for later computability applications, we briefly review lattices and the congruence lattice of an algebra. Finally, we describe how finitely generated and computably enumerable algebras may be specified by presentations.

MC 5403

Julius Frizzell, University of Waterloo

Roth's Theorem

We will continue to discuss unitary transformations and generic measures and work towards a proof of Roth's theorem for arithmetic progressions.

MC 5417

Jules Ribolzi, University of Waterloo

Definable groups in the nonstandard model of CCM

We review the two main results about definable groups in the nonstandard model of CCM.

M3 4001

Faisal Romshoo, University of Waterloo

Anisotropic Calibrations

I aim to talk about some of the technical details in Tomasso Pacini and Kotaro Kawai’s paper ”Anisotropiccalibrations, adiabatic limits, and mirror symmetry” which Tomasso presented in the Geometry and Topology seminar last month. If time permits, I want to explore how we can generalize the notion of Smith maps using anisotropic calibrations.

MC 5417