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
Dmitry Zakharov, Central Michigan University
"Maps to trees and loci in the moduli space of tropical curves"
Sven Raum, Stockholm University
"Superrigidity for group operator algebras"
Sascha Troscheit, Department of Pure Mathematics, University of Waterloo
"Quasi self-similarity and the dimension drop conjecture for self-conformal sets"
Rahim Moosa, Department of Pure Mathematics, University of Waterloo
"Pseudo-finite sets and dimension, Part 6"
I will discuss the pseudo-finite Larsen-Pink inequality, which compares pseudo-finite dimension to algebraic dimension in simple algebraic groups.
MC 5403
Andrej Vukovic, Department of Pure Mathematics, University of Waterloo
"Fundamental Group of the Circle and Other Highlights"
Today we construct the circle type and show that its fundamental group is Z, using synthetic homotopy theory. As requested at the last meeting, we also show that function extensionality implies weak function extensionality.
MC 5413
Ross Willard, Department of Pure Mathematics, University of Waterloo
"Examples of dualizable and nondualizable algebras"
Having established useful criteria, I will illustrate their use in proving finite algebras are, or are not, dualizable.
MC 5403
Aasaimani Thamizhazhagan, Department of Pure Mathematics, University of Waterloo
"Uncertainty Principles and Fourier Analysis"
The uncertainty principle is partly a description of a characteristic feature of quantum mechanical systems, partly a statement about the limitations of one's ability to perform measurements on a system without disturbing, and partly a meta-theorem in harmonic analysis that can be summed up as follows:
"A non-zero function and its Fourier transform cannot both be sharply localized."- G. B. Folland
MC 5501
Owen Biesel, Carleton College
"G-closures and discriminant algebras"
Ananth Shankar, MIT
"Exceptional splitting of abelian surfaces over global function fields"
Andrea Vaccaro, University of Pisa/York University
"Trace spaces of Counterexamples to Naimark's Problem"
Hanci Chi, McMaster University
"Invariant Einstein Metrics of Cohomogeneity One with Principal Orbits as Wallach Spaces"
Ruizhang Jin, Department of Pure Mathematics, University of Waterloo
"Model-theoretic Analysability in Differentially Closed Fields"
Daniel Perales, Department of Pure Mathematics, University of Waterloo
"Random matrices, interlacing families of polynomials, and the expected characteristic polynomial"
In this session we will begin by ;reviewing the notion of real stability and some of its basic properties. Then we continue with the study of operators that preserve real stability. For this, we will look into the proof of the Gauss-Lucas Theorem, which asserts that for any complex polynomial f, the roots of its derivative, f', are contained in the convex hull of the roots of f.
Maxwell Levit, Department of Combinatorics & Optimization, University of Waterloo
"Topological Combinatorics and Combinatorial Topology"
I’ll tell you about a topological proof of a combinatorial result (The Borsuk-Ulam Theorem implies Kneser’s Conjecture), and a combinatorial proof of a topological result (Sperner’s Lemma implies the Brouwer fixed point theorem).
MC 5501
Ross Willard, Department of Pure Mathematics, University of Waterloo
"Dualizing the finite level"
Last week, Justin proved the Duality Compactness Theorem, which reduces the task of proving a duality to proving it “at the finite level,” that is, for the finite algebras in the quasi-variety ISP(M), at least for alter egos with a finite signature. This week I will present a characterization of when an alter ego dualizes the finite algebras in ISP(M). The characterization is especially useful when the term operations of M are understood.
MC 5403
Brian Forrest, Department of Pure Mathematics, University of Waterloo
"Exotic Ideals in the Fourier-Stieltjes Algebra of a Locally Compact Group"
Jesse Madnick, McMaster University
"Nearly-Kahler 6-Manifolds of Cohomogeneity-Two"
Remi Jaoui, Pure Math Department, University of Waterloo
"Pseudo-finite sets and dimension, Part 5"
In this second talk on probability logic, I will discuss stability for terms (or real-valued formulas) in probability logic.
Daniel Perales Anaya, Pure Math Department, University of Waterloo
"Random matrices, interlacing families of polynomials, and the expected characteristic polynomial"
Justin Laverdure, Pure Math Department
"Duality Compactness Part 2"
We'll prove the DCT itself, after having seen several supporting lemmas.
MC 5403
Travis Scrimshaw, University of Queensland
"Stable Grothendieck polynomials and crystals"
Jerry Wang, Department of Pure Mathematics, University of Waterloo
"The number of elliptic curves ordered by conductor"
Laurent Marcoux, Department of Pure Mathematics, University of Waterloo
"Hilbert space operators with compatible off-diagonal corners"
Given a complex, separable Hilbert space $\mathcal{H}$, we characterize those operators for which $\| P T (I − P ) \| = \| (I − P )T P \|$ for all orthogonal projections $P$ on $\mathcal{H}$.
Chelsea Walton, University of Illinois at Urbana-Champaign
"On the quadratic dual of the Fomin-Kirillov algebras"
This talk will be based on recent joint work with James Zhang on the quadratic dual (aka Koszul dual) of the Fomin-Kirillov algebras. It will include a brief review of nice ring-theoretic and homological properties of noncommutative graded algebras. No prior knowledge is assumed and open questions will be provided at the end.
MC 5479
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 Office of Indigenous Relations.