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
Boyu Li, University of Victoria
"Amenable and Nonamenable Semigroups"
Since Nica introduced the notion of amenability of quasilattice ordered semigroups, the amenability for many classes of semigroups remain unanswered. We will give a brief overview of semigroup amenability, and show some recent developments on this topic using dilation theory. In particular, we shall show that Artin monoids are nonamenable except the class of rightangled. This is a joint work with Marcelo Laca.
MC 5417
Daniel Le, University of Toronto
"Congruences between modular forms"
Dino Rossegger, Department of Pure Mathematics, University of Waterloo
"Determinacy in second order arithmetic"
Arpita Kar, Queen's University
"Some reflections on the Riemann Hypothesis"
Wilson Poulter, Department of Pure Mathematics, University of Waterloo
"NIP VI"
We finish section 2.2.2 of Simon's Guide to NIP theories and move on to 2.2.3.
MC 5413
Alexandru Nica, Department of Pure Mathematics, University of Waterloo
"Free probabilistic aspects of meandric systems"
Andrej Vukovic, Department of Pure Mathematics, University of Waterloo
We continue where last week's discussion left off by discussing the classification of semivaluations in the valuative tree. Then we return to our study of plane polynomial dynamics.
M3 3103
Luke MacLean, Department of Pure Mathematics, University of Waterloo
"Reverse Mathematics"
We say that $S \subseteq \mathcal{P}(\omega)$ is an $\omega$model of a subsystem of second order arithmetic if the $L_2$ structure $(\omega, S, +, \cdot, 0, 1, <)$ correctly models the subsystem in question. The goal of this lecture will be to prove that there is an $\omega$model of $WKL_0$ consisting entirely of low sets.
This will involve learning about PA degrees and the low basis theorem.
All are welcome.
MC 5413
Hayley Reid, Department of Pure Mathematics, University of Waterloo
"Cutting a square into triangles of equal area"
Andrej Vukovic, Department of Pure Mathematics, University of Waterloo
We review aspects of the theory of Berkovich spaces, including quasimonomial valuations and invariants associated to a valuation. We then discuss birational geometry, introducing blowups and log resolutions of ideals. We discuss dual graphs and describe the classification of semivaluations in the valuative tree. We conclude by returning to our earlier study of plane polynomial dynamics.
M3 3103
Luke MacLean, Department of Pure Mathematics, University of Waterloo
"Reverse Mathematics (part 2)"
Having heard a brief overview of the basics of reverse mathematics, we will continue to learn about the system RCA_0 and the theorems provable therein.
Attendance of part 1 is not required, only an interest in logic and computability.
MC 5413
Alexander Yong, University of Illinois at UrbanaChampaign
"Complexity, combinatorial positivity, and Newton polytopes"
The Nonvanishing Problem asks if a coefficient of a polynomial is nonzero. Many families of polynomials in algebraic combinatorics admit combinatorial counting rules and simultaneously enjoy having saturated Newton polytopes (SNP). Thereby, in amenable cases, Nonvanishing is in the complexity class of problems with “good characterizations”. This suggests a new algebraic combinatorics viewpoint on complexity theory.
Dan Ursu, Department of Pure Mathematics, University of Waterloo
"Rulercompass constructions"
Don Hadwin, University of New Hampshire
"Tracial Stability for C*algebras (and Groups)"
Luke MacLean, Department of Pure Mathematics, University of Waterloo
"REVERSE MATHEMATICS"
While most of mathematics is concerned with using a set of axioms to prove theorems, reverse mathematics is a relatively new form of mathematical logic that seeks to determine which axioms are required to prove certain theorems. This gives a notion of the “strength” of a certain theorem by looking at which theorems imply it, and which are implied by it.
Zack Cramer, Department of Pure Mathematics, University of Waterloo
"Compressible Matrix Algebras and the Distance from Projections to Nilpotents"
Adian Diaconu, University of Minnesota
"Moments of Lfunctions"
I will begin by discussing some recent results (joint in part with Ian Whitehead) about moments of quadratic Dirichlet Lfunctions. While our understanding of these moments over number fields still remains largely elusive, their function field analogs are more tractable. The main focus will be to describe some partial results in the function field setting. (Joint work with Jonas Bergström, Dan Petersen and Craig Westerland.)
MC 5417
Gabriel Islambouli, Deaprtment of Pure Mathematics, University of Waterloo
"Smooth 4manifolds and the Pants Complex"
Marco Handa, Department of Pure Mathematics, University of Waterloo
"NIP IV"
We begin section 2.2.1 of Simon's Guide to NIP theories.
MC 5413
Kevin Hare, Department of Pure Mathematics, University of Waterloo
"Entropy of Selfsimilar Measures"
It is known that a selfsimilar measure is either purely singular or absolutely continuous. Despite this, for most measures we cannot say which case we are in. One technique that has proved promising is the study of the Garsia Entropy of the measure. In this talk I will discuss the history, properties and recent results for selfsimilar measures and Garsia Entropy.
MC 5417
Brett Nasserden, Department of Pure Mathematics, University of Waterloo
"Normal forms of dominant polynomial morphisms of the affine plane"
Ertan Elma, Department of Pure Mathematics, University of Waterloo
"Discrete Mean Values of Dirichlet Lfunctions"
Let χ be a Dirichlet character modulo a prime number p ⩾ 3 and let \mathfrak a_χ:=(1χ(1))/2. Define the mean value
\begin{align*}
\mathcal{M}_{p}(s,\chi):=\frac{2}{p1}\sum_{\substack{\psi \bmod p\\\psi(1)=1}}L(1,\psi)L(s,\chi\overline{\psi})
\end{align*}
for a complex number s such that s≠ 1 if \mathfrak a _χ=1.
Jeffrey Diller, University of Notre Dame
"A transcendental first dynamical degree"
Fenglong You, University of Alberta
"Structures of relative GromovWitten theory"
Steven Lazzaro, McMaster University
"NIP III"
We begin section 2.2 of Simon's Guide to NIP theories.
MC 5413
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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.