Events

Ken Dykema, Texas A & M University

"Commuting operators in finite von Neumann algebras"

We find a joint spectral distribution measure for families
of commuting elements of a finite von Neumann algebra.  This
generalizes the Brown measure for single operators.  Furthermore, we
find a lattice (based on Borel sets) consisting of hyperinvariant
projections that decompose the spectral distribution measure.  This
leads to simultaneous upper triangularization results for commuting
operators.  

Yoav Len, Department of Combinatorics & Optimization, University of Waterloo

"Combinatorial Hodge Theory"

Ilya Shapirovsky

"Locally tabular modal logics"

Mohammad Mahmoud, Pure Mathematics, University of Waterloo

"Existentially Algebraic Structures"

This week we talk about existentially algebraic structures. We will prove that every existentially algebraic structure is in fact existentially atomic. We will also try to establish a necessary and sufficient condition for a structure \mathcal{A}=(A,<, Adj) (linear order with the adjacency relation) to be existentially atomic.

MC 5403

Anthony McCormick, Pure Mathematics, University of Waterloo

"Nuclearity of Spaces of Distributions"

We will discuss the nuclearity of various useful locally convex spaces such as the spaces of smooth functions, compactly supported smooth functions, distributions, polynomials and formal power series. The notion of a parametrix, interpreted using the formalism we develop here, will provide valuable intuition when we discuss operator product expansions and vertex algebras in later talks.

MC 5417

Nickolas Rollick, Department of Pure Mathematics, University of Waterloo

"Staying connected"

Asif Zaman, University of Toronto

"A variant of Brun-Titchmarsh for the Chebotarev density theorem"

Anthony McCormick, Department of Pure Mathematics, University of Waterloo

"Solvable Algebraic Groups"

After finishing our examples from last time, we will discuss some of the structure theory of solvable algebraic groups. This will be a useful stepping-stone towards the theory of reductive and semisimple algebraic groups, which we will study next.

MC 5413

Ali Aleyasin, Université du Québec à Montréal

"The Calabi problem on edge-cone manifolds"

Boyu Li, Department of Pure Mathematics, University of Waterloo

"Regular Dilation on Graph Products of $\mathbb{N}$"