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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John Dykes, Department of Pure Mathematics, University of Waterloo
"Propositional Logic"
In this week's meeting of the homotopy type theory seminar, we begin by discussing how homotopy equivalence behaves with certain common types. We talk about the difference between classical and intuitionistic logic and introduce propositional truncation. We then prove that univalence implies function extensionality.
MC 5413
Yin Zhi, Harbin Institute of Technology
"Random and free observables saturate the Tsirelson bound for CHSH inequality"
Michael Coons, University of Newcastle
"Mahler’s methods: theorems, speculations and variations"
Ertan Elma, Department of Pure Mathematics, University of Waterloo
"The PólyaVinogradov Inequality"
Eli Shamovich, Department of Pure Mathematics, University of Waterloo
"The isomorphism problem"
We will continue the discussion of the isomorphism problem for subvarieties of the free ball. We will prove that the algebras of bounded nc functions on two subvarieties are completely isometrically isomorphic if and only if the varieties are ballbiholomorphic. We will then discuss the homogeneous case and talk a bit about other isomorphism types.
MC 5479
Justin Laverdure, Department of Pure Mathematics, University of Waterloo
"Duality Compactness Theorem"
One more building block on the way to establishing some nice theorems: if a finite structure of finite signature dualizes every finite member of ISP(M), then it dualizes the entirety of the class. If we have time, we'll also see that brute force does dualize the finite members! Unfortunately, these two facts don't mesh yet.
MC 5403
Daniel Perales, Department of Pure Mathematics, University of Waterloo
"Random matrices, interlacing families of polynomials, and the expected characteristic polynomial"
Christopher Hawthorne, Department of Pure Mathematics, University of Waterloo
"Stable Regularity Lemma"
Artour Tomberg, Western University
"Metrics on twistor spaces of hypercomplex manifolds"
Chelsea Walton, University of Illinois at UrbanaChampaign
"On the quadratic dual of the FominKirillov algebras"
This talk will be based on recent joint work with James Zhang on the quadratic dual (aka Koszul dual) of the FominKirillov algebras. It will include a brief review of nice ringtheoretic and homological properties of noncommutative graded algebras. No prior knowledge is assumed and open questions will be provided at the end.
MC 5479
Laurent Marcoux, Department of Pure Mathematics, University of Waterloo
"Hilbert space operators with compatible offdiagonal 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 $\mathcal{H}$.
Jerry Wang, Department of Pure Mathematics, University of Waterloo
"The number of elliptic curves ordered by conductor"
Travis Scrimshaw, University of Queensland
"Stable Grothendieck polynomials and crystals"
Justin Laverdure, Pure Math Department
"Duality Compactness Part 2"
We'll prove the DCT itself, after having seen several supporting lemmas.
MC 5403
Daniel Perales Anaya, Pure Math Department, University of Waterloo
"Random matrices, interlacing families of polynomials, and the expected characteristic polynomial"
Remi Jaoui, Pure Math Department, University of Waterloo
"Pseudofinite sets and dimension, Part 5"
In this second talk on probability logic, I will discuss stability for terms (or realvalued formulas) in probability logic.
MC 5403Jesse Madnick, McMaster University
"NearlyKahler 6Manifolds of CohomogeneityTwo"
Brian Forrest, Department of Pure Mathematics, University of Waterloo
"Exotic Ideals in the FourierStieltjes Algebra of a Locally Compact Group"
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 quasivariety 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
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 BorsukUlam Theorem implies Kneser’s Conjecture), and a combinatorial proof of a topological result (Sperner’s Lemma implies the Brouwer fixed point theorem).
MC 5501
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 GaussLucas 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.
Ruizhang Jin, Department of Pure Mathematics, University of Waterloo
"Modeltheoretic Analysability in Differentially Closed Fields"
Hanci Chi, McMaster University
"Invariant Einstein Metrics of Cohomogeneity One with Principal Orbits as Wallach Spaces"
Andrea Vaccaro, University of Pisa/York University
"Trace spaces of Counterexamples to Naimark's Problem"
Ananth Shankar, MIT
"Exceptional splitting of abelian surfaces over global function fields"
Owen Biesel, Carleton College
"Gclosures and discriminant algebras"
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 metatheorem in harmonic analysis that can be summed up as follows:
"A nonzero function and its Fourier transform cannot both be sharply localized." G. B. Folland
MC 5501
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
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
Rahim Moosa, Department of Pure Mathematics, University of Waterloo
"Pseudofinite sets and dimension, Part 6"
I will discuss the pseudofinite LarsenPink inequality, which compares pseudofinite dimension to algebraic dimension in simple algebraic groups.
MC 5403
Sascha Troscheit, Department of Pure Mathematics, University of Waterloo
"Quasi selfsimilarity and the dimension drop conjecture for selfconformal sets"
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.