Events

Ross Willard, Pure Mathematics, University of Waterloo

"Larose's theorem"

Putting together some of the machinery developed this term, I will prove Larose’s Theorem: if X is a ﬁnite, connected reﬂexive digraph and X admits a Taylor operation, then for every k ≥ 1, the k-th homotopy group of X is trivial.

Stanley Yao Xiao, Pure Mathematics, University of Waterloo

"Introduction to Bhargavaology"

In this introductory talk I aim to give a sampling of the vast web of important theorems related to Manjul Bhargava, one of the four Fields Medalists of 2014, and describe their importance in the context of modern number theory. There are no technical details in the talk, making it very accessible.

Ehsaan Hossain, Pure Mathematics, University of Waterloo

"Hilbert's Syzygy Theorem"

Last semester we studied the group $K_0$, whose elements are stable equivalence classes of projective modules. Tangent to this, I want to discuss the Quillen--Suslin Theorem, which states that every finitely-generated projective module over a polynomial ring $k[x_1,\ldots,x_n]$ is free. On the topological side, this says every algebraic vector bundle over affine $n$-space is free.

Michael Baker, Pure Mathematics, University of Waterloo

"Global theory of algebraic number fields"

In this talk, I will embark on an informal review of the global theory of algebraic number fields: integrality, discriminants and integral bases, Dedekind domains, fractional ideals and the ideal class group, Minkowski theory, Dirichlet's unit theorem, splitting of primes, as time permits. Motivation for class field theory will be discussed.

Rahim Moosa, Department of Pure Mathematics, University of Waterloo

"Introduction"

We intend in this seminar to read Lou van den Dries’ Seminaire Bourbaki article entitled ”Approx- imate Groups [after Hrushovski, and Breuillard, Green, Tao]”.

Vern Paulsen, University of Houston

“The Conjectures of Connes, Kirchberg and Tsirelson”

Connes Embedding Conjecture has recently been shown to be equivalent to a problem of Tsirelson about sets of quantum correlation matrices. In this talk we will outline this material and its proof, including a few simplifications from our joint work with Todorov.

Raymond Cheng, University of Waterloo

"Local theory of algebraic number fields"

Having reviewed the global aspects of algebraic number theory, I will begin to develop the local aspects of the theory. The goal here will be to define and hopefully get to grips with objects known as local fields. To that end, I will speak about absolute values on fields, completions of fields and properties of local fields.

Stanley Yao Xiao, Department of Pure Mathematics, University of Waterloo

“Binary quartic forms and average ranks of elliptic curves”

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Eric Sawyer, McMaster University

“Corona problems - still open on the ball a half century after Carleson’s corona theorem in the unit disk.”

In 1962 Lennart Carleson showed that the maximal ideal space of the algebra of bounded analytic functions on the unit di

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Learning Seminar on Finite Relational Structures

"Larose's theorem"

Bhargavaology learning seminar

Stanley Yao Xiao, Pure Mathematics, University of Waterloo

"Introduction to Bhargavaology"

Algebra seminar

Ehsaan Hossain, Pure Mathematics, University of Waterloo

"Hilbert's Syzygy Theorem"

Class Field Theory seminar

Michael Baker, Pure Mathematics, University of Waterloo

"Global theory of algebraic number fields"

Working seminar on Approximate Groups

Rahim Moosa, Department of Pure Mathematics, University of Waterloo

"Introduction"

Analysis seminar

Vern Paulsen, University of Houston

“The Conjectures of Connes, Kirchberg and Tsirelson”

Class Field Theory seminar

Raymond Cheng, University of Waterloo

"Local theory of algebraic number fields"

Bhargavology Learning seminar

Stanley Yao Xiao, Department of Pure Mathematics, University of Waterloo

“Binary quartic forms and average ranks of elliptic curves”

Pure Math colloquium

Eric Sawyer, McMaster University

“Corona problems - still open on the ball a half century after Carleson’s corona theorem in the unit disk.”

Algebra seminar

Blake Madill, Department of Pure Mathematics, University of Waterloo

“On the Jacobson radical of differential polynomial rings.

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