Contact Info
Pure MathematicsUniversity of Waterloo
200 University Avenue West
Waterloo, Ontario, Canada
N2L 3G1
Departmental office: MC 5304
Phone: 519 888 4567 x43484
Fax: 519 725 0160
Email: puremath@uwaterloo.ca
Returning to inperson experiences in February: Visit the COVID19 website for more information.
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Mohammad Mahmoud, Department of Pure Mathematics, University of Waterloo
"Degrees of Categoricity, the Isomorphism Problem, and the Turing Ordinal"
Gregory Patchell, University of Waterloo
"Model Theory of Tracial von Neumann Algebras"
This talk is the latest in a series of seminars on the model theory of C*algebras. This week, we axiomatize tracial von Neumann algebras, tracial factors, and II\textsubscript{1} factors. We define local classes of algebras and determine whether several classes of finite factors are local and/or axiomatizable. We follow Farah, Hart, and Sherman's work in their series of papers titled “Model Theory of Operator Algebras.”
MC 5403
Samuel Harris, University of Waterloo
Jaspar Wiart, RICAM, Austrian Academy of Sciences
Mohammad Mahmoud, Department of Pure Mathematics, University of Waterloo
"Degrees of Categoricity and the Isomorphism Problem"
Mahmoud Filali, University of Oulu
"Arens irregularity in harmonic analysis"
Arens irregularity of a Banach algebra is due to elements in its Banach dual which are not weakly almost periodic.
Jeffrey Samuelson, Department of Pure Mathematics, University of Waterloo
"Introducing affine schemes"
We will introduce the notion of an affine scheme and describe the Zariski topology, after which we will discuss several examples.
MC 5479
Robert Xu Yang, Department of Pure Mathematics, University of Waterloo
"Sidon and Kroneckerlike sets in harmonic analysis"
Let $G$ be a compact abelian group and $\Gamma$ be its discrete dual group. In this thesis we study various types of interpolation sets.
Aasaimani Thamizhazhagan, Department of Pure Mathematics, University of Waterloo
"On the invertible elements of FourierStieltjes algebra"
Michael Hartz, FernUniversität in Hagen
"Dilations in finite dimensions and matrix convexity"
Pawel Sarkowicz, Department of Pure Mathematics, University of Waterloo
This week we will define elementary substructures and prove the Downward (and possibly Upward) LöwenheimSkolem Theorem(s). To that end, we will introduce the notion of separable languages.
MC 5403
Samuel Harris, University of Waterloo
Speaker 1: Christopher Lang, Department of Pure Mathematics, University of Waterloo
"Using Group Actions to Simplify Nahm Data"
The Nahm equations are a system of differential equations for $u(k)$valued functions on $(a,b)\subset\mathbb{R}$. Solutions of the Nahm equations are called Nahm data. By imposing certain conditions on the Nahm data, the ADHMNahm procedure gives rise to monopoles in $\mathbb{R}^3$. Elaborating on [1], we examine how the actions of $\mathbb{R}^3$, $u(k)$, and $\mathrm{SU}(2)$ simplify the Nahm data.
Ehsaan Hossain, Department of Pure Mathematics, University of Waterloo
"Zariski Topology 101"
We'll (at least partially) answer the following questions: when is Spec(R) compact? Hausdorff? connected? irreducible? noetherian? Also, the basic open sets that Jeff described last time can be interpreted as localisations  we will talk about that if time permits.
MC 5479
Mohammad Mahmoud, Department of Pure Mathematics, University of Waterloo
"Degrees of Categoricity of Trees"
Greg Patchell, Department of Pure Mathematics, University of Waterloo
"Model Theory of von Neumann Algebras II"
Sam Harris, Department of Pure Mathematics, University of Waterloo
"Quantum XOR games and Connes' embedding problem"
Speaker 1: Shubham Dwivedi, Department of Pure Mathematics, University of Waterloo
"Differential Harnack estimates"
We will discuss differential harnack estimates including Hamilton’s matrix harnack estimate for solutions of the heat equation and the LiYau inequality. If time permits, we will discuss harnack estimates for the Ricci flow.
Speaker 2: Spiro Kargiannis, Department of Pure Mathematics, University of Waterloo
"Bubble Tree Convergence for Harmonic Maps"
Ehsaan Hossain, Department of Pure Mathematics, University of Waterloo
"Localisation and the Nullstellensatz"
Jeff defined the basic open sets $D_f$. We'll see that in fact $D_f\simeq \mathrm{Spec}(R_f)$ where $R_f$ is a localisation. We might be able to finish the proof that $\mathrm{Spec}(R)$ is Hausdorff iff $\mathrm{Kdim}(R)=0$. Lastly, we can show that if $A$ is an affine algebra then the closed points are dense in $\mathrm{Spec}(A)$.
MC 5479
Pawel Sarkowicz, Department of Pure Mathematics, University of Waterloo
"A Fourier Series Approach to the Isoperimetric Problem"
We will discuss the isoperimetric problem, which is a question of relating the area of an enclosed space to its perimeter (at least in the plane). We will see how this inequality comes to fruition and what it’s optimal solution is using Fourier series. Time permitting, we will look at generalizations of the problem.
MC 5501
Michael Deveau, Department of Pure Mathematics, University of Waterloo
"Computability Theory and Some Applications"
Alessandro Portaluri, University of Turin
"Existence and Stability Results in Celestial Mechanics"
Is the solar system stable? This is maybe one of the oldest open questions in dynamical systems. It is still a lively and very active research field starting from Newton, Lagrange, Maxwell, Poincar\'e and Birkhoff (only to mention a few) who proved several astonishing results in this direction.
Departmental office: MC 5304
Phone: 519 888 4567 x43484
Fax: 519 725 0160
Email: puremath@uwaterloo.ca
The University of Waterloo acknowledges that much of our work takes place on the traditional territory of the Neutral, Anishinaabeg and Haudenosaunee peoples. Our main campus is situated on the Haldimand Tract, the land granted to the Six Nations that includes six miles on each side of the Grand River. Our active work toward reconciliation takes place across our campuses through research, learning, teaching, and community building, and is centralized within our Indigenous Initiatives Office.