Contact Info
Pure MathematicsUniversity of Waterloo
200 University Avenue West
Waterloo, Ontario, Canada
N2L 3G1
Departmental office: MC 5304
Phone: 519 888 4567 x33484
Fax: 519 725 0160
Email: puremath@uwaterloo.ca
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PengJie Wong, University of Lethbridge
"Holomorphy of Lfunctions and its applications"
The analytic properties of Lfunctions have been one of the central topics in number theory as they have a deep connection with the distribution of primes. For example, the Riemann zeta function led to a proof of the celebrated prime number theorem. In general, for any number field, there are primes and Lfunctions of similar nature. In this talk, we shall discuss the holomorphy of such Lfunctions and its applications to the distributions of the associated primes.
Justin Laverdure, Department of Pure Mathematics, University of Waterloo
"The Hyperreals (Infinitesimals and the transfer principle)"
Nasir Sohail, Wilfrid Laurier University
"Ultraproducts and congruence distributive varieties  Part 1"
I shall go from (direct) product to ultraproduct using a particular congruence. The ultraproduct of a finite set of finite algebras will be considered as a special case.
MC 5479
Vern Paulsen, University of Waterloo
"Complexity and Capacity Bounds for Operator Systems and Quantum Channels"
Eli Shamovich, Department of Pure Mathematics, University of Waterloo
"Real Fibered Morphism and Definite Determinantal Representations"
John Sawatzky, Department of Pure Mathematics, University of Waterloo
"Ultraproducts and some loose ends"
We'll complete the metric ultraproduct construction, and show that a sofic group embeds in an ultraproduct of symmetric groups equipped with the Hamming distance. If possible we'll tie up some of the loose ends from last time, e.g. the dependence on that constant r, and residually finite groups.
MC 5403
Boris Khesin, University of Toronto
"Integrability and nonintegrability in pentagram maps"
Chris Schafhauser, Department of Pure Mathematics, University of Waterloo
"More on GLq(2) and SLq(2)"
Last week Hongdi constructed the Hopf algebra structure on GLq(2) and SLq(2). I will discuss the natural coaction of these objects on the quantum plane kq(2).
MC 5403
Jeffrey Shallit, David R. Cheriton School of Computer Science, University of Waterloo
"Waring's theorem for binary k'th powers and palindromes"
Diana Castaneda Santos, Department of Pure Mathematics, University of Waterloo
"Finite and integral morphisms"
We will continue studying properties of finite and integral morphisms. We will use properties of algebra homomorphisms to prove that finite morphisms have finite fibers and that they are affine local on the target. We will also prove that integral morphisms are closed and we will study some examples. Time permitting we will introduce morphisms (locally) of finite type.
MC 5417
Arthur Mehta, Department of Pure Mathematics, University of Waterloo
"An Introduction to Quantum Graphs, Chromatic Numbers and Lovász Inequalties"
Christopher Schafhauser, Department of Pure Mathematics, University of Waterloo
"An Embedding Theorem for C*algebras"
Nasir Sohail, Wilfrid Laurier University
"Ultraproducts and congruence distributive varieties  Part 2"
I shall prove that the class of subdirectly irreducible algebras in a congruence distributive variety V generated by a class K is contained in the class obtained by taking the closures under S (subalgebras) and H (homomorphisms) of the class of all ultraproducts over K.
MC 5479
Sam Kim, Department of Pure Mathematics, University of Waterloo
"On Synchronous Quantum Games"
Ehsaan Hossain, Department of Pure Mathematics, University of Waterloo
"Ultraproducts again"
We'll finish the proof for ordinary products and start the ultraproduct construction.
MC 5403
Matt Satriano, Department of Pure Mathematics, University of Waterloo
"Introduction to the work of Baker and DeMarco"
We give an overview of the following result of BakerDeMarco: if $\varphi, \psi \in\mathbb{C}(z)$ have infinitely many preperiodic points in common, then all of their preperiodic points are the same. We discuss the connection between this complex analytic statement and nonarchimedean Berkovich spaces.
MC 5403
Omer Tamuz, Caltech
"The Poisson boundary, strong amenability and the infinite conjugacy class property"
David Urbanik, Department of Pure Mathematics, University of Waterloo
"Chevalley's Theorem on Constructible Sets in the Language of Schemes"
Mizanur Rahaman, Department of Pure Mathematics, University of Waterloo
"Eventually Entanglement Breaking Maps"
Justin Laverdure, Department of Pure Mathematics, University of Waterloo
"Facts about finite algebras"
If an algebra A is finite, what can we say about the variety HSP(A)? We'll show that such varieties are locally finite, i.e. its members which are finitely generated are in fact finite. Further, if such a variety has any infinite subdirectly irreducible algebras, then in fact it has arbitrarily large finite ones as well.
MC 5479
Boyu Li, Department of Pure Mathematics, University of Waterloo
"Examples of Free Semigroupoid Algebras"
Ali Aleyasin, Department of Pure Mathematics, University of Waterloo
"Calabi problem on conifolds"
Sebastien Picard, Columbia University
"The Anomaly flow over Riemann surfaces"
Matt Satriano, Department of Pure Mathematics, University of Waterloo
"Short Ride in a Height Machine"
This talk is meant to be a quick introduction to the theory of height functions on projective varieties defined over number fields. After describing the fundamental case of heights on projective space, we go into the basics of Weil's height machine. For any projective variety, this gives a height function attached to each linear equivalence class of Cartier divisors (or each line bundle), satisfying a variety of pleasant functorial properties.
Francesco Cellarosi, Queen's University
"Statistical properties of Bfree numbers"
Bfree numbers were introduced by Erdős as a generalization of squarefree integers. I will present some results about the statistical properties of Bfree numbers and a dynamical systems naturally associated to them. In particular, I will discuss a central limit theorem resembling a result by J. Beck on irrational circle rotations. Joint work with M. Avdeeva and Ya.G. Sinai.
MC 5417
Sascha Troscheit, Pure Math Department, University of Waterloo
"Nonlinear fractals and Hausdorff measure"
Departmental office: MC 5304
Phone: 519 888 4567 x33484
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.