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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**CANCELLED**
RagnarOlaf Buchweitz, University of Toronto
"The McKay Correspondence Then and Now"
Patrick Naylor, Department of Pure Mathematics, University of Waterloo
"The Review Continues"
We'll continue our review from last week. This week, we're actually defining a scheme, as well as giving a quick review of some of the associated topological properties.
MC 5413
Peter Sinclair, McMaster University
"Dpfinite fields"
Sascha Troscheit, Department of Pure Mathematics, University of Waterloo
"Branching Processes, Martingales, Kingman’s Subadditive Ergodic Theorem, and some applications"
Sam Kim, Department of Pure Mathematics, University of Waterloo
"I'll prove the Fundamental Theorem of Algebra"
Gauss proved that complex polynomials always admit a root. I'll explain how he came to that conclusion and present a proof that rigorizes his argument in a nice way. You will only need to know a little vector calculus and the intermediate value theorem. If we have time, I'll show you why a flat triangle has angles that add up to π and why a triangle on a sphere doesn't.
MC 5501
Ross Willard, Department of Pure Mathematics, University of Waterloo
"An introduction to finite basis problems"
To get us started this term, I will describe some known instances of the finite basis problem in universal algebra, and one unknown instance that is currently bugging me: “Murskii + L'vov.” This will be an elementary lecture, intended as a warmup for Justin’s lectures later this month.
MC 5413
Ajneet Dhillon, University of Western Ontario
"Tamagawa numbers and connected components of stacks"
Let X be a smooth projective curve over a finite field and $G$ a semisimple algebraic group over its function field. Let $\mathcal{G}$ be a smooth group scheme over X with generic fiber $G$. The Tamagawa number of $G$ is an arithmetic invariant obtained from a Haar measure on the adelic points of $G$. A conjecture of Harder relates this number to the number of components of the moduli stack of $\mathcal{G}$bundles.
Ping Zhong, Department of Pure Mathematics, University of Waterloo
"Estimates for compression norms and additivity violation in quantum information"
Rekha Biswal, Université Laval
"Demazure flags, Chebyshev polynomials and mock theta functions"
Sascha Troscheit, Department of Pure Mathematics, University of Waterloo
"Branching Processes, Martingales, Kingman’s Subadditive Ergodic Theorem, and some applications, Part II: The almost sure number of descendants and finer information, such as expected deviations from the average behaviour and `immigration'"
Andrei Krokhin, Durham University
"The complexity of valued constraint satisfaction problems"
Karen Yeats, Department of Combinatorics & Optimization, University of Waterloo
"Chord diagram expansions in quantum field theory"
Over the last few years we have been able to reexpand certain series in perturbative quantum field theory using chord diagrams. These new expansions have nice mathematical structure. I will give an overview on them and how they can be useful.
MC 5501
Diana Castaneda Santos, Department of Pure Mathematics, University of Waterloo
"Review (Episode 3)"
We will continue our review of schemes. We will mention some examples of schemes that are not affine schemes. We will review the proj construction, and more topological properties of schemes. If time permits we'll define morphisms of schemes.
MC 5413
Levon Haykazyan, Department of Pure Mathematics, University of Waterloo
"Introduction to Positive Logic"
Sascha Troscheit, Department of Pure Mathematics, University of Waterloo
"Branching Processes, Martingales, Kingman’s Subadditive Ergodic Theorem, and some applications, Part III: The probability of deviating from the mean behaviour"
John Friedlander, University of Toronto
"Exceptional characters and their consequences"
We review some history about the possible existence of certain Dirichlet characters which might possess a zero very close to the line $Re s = 1$ and the remarkably strong consequences which could be derived under the assumption of their existence.
MC 5501
Adam Dor On, Technion
"CuntzNicaPimsner algebras over $\mathbb{N}^d$"
An effective model for encoding multivariable dynamical systems via C*algebras is given by ToeplitzNicaPimsner algebras introduced by Fowler. In the work of Carlsen, Larsen, Sims and Vitadello, the right notion of a "boundary quotient" CuntzNicaPimsner algebra is established, but the precise relations between minimal generators are sometimes very difficult to ascertain.
Justin Laverdure, Department of Pure Mathematics, University of Waterloo
"A finite pointed group with no finite basis, Part 1"
We'll go over a construction of Roger Bryant, by building a finite pointed group (P,p) with no finite basis for its laws, as far as we can go. We'll recap basic equational theory stuff, then wade kneedeep into semidirect products and counting arguments.
MC 5413
Esther CabezasRivas, Universität Frankfurt
"Ricci flow beyond nonnegative curvature conditions"
We generalize most of the known Ricci flow invariant nonnegative curvature conditions to less restrictive negative bounds that remain sufficiently controlled for a short time.
YiuTung Poon, Iowa State University
"(p,q) Matricial Range and Quantum Information Science"
Damien Roy, University of Ottawa
"Diophantine curiosities"
Michael Viscardi, University of California, Berkeley
"Quantum cohomology and 3D mirror symmetry"
Levon Haykazyan, Department of Pure Mathematics, University of Waterloo
"Introduction to Positive Logic II"
We continue our investigation of positive logic. I will define a new notion of the space of types and I will convince you that it is the right notion.
MC 5403
Sascha Troscheit, Department of Pure Mathematics, University of Waterloo
"Branching Processes, Martingales, Kingman’s Subadditive Ergodic Theorem, and some applications, Part IV: Kingman’s Subadditive Ergodic Theorem"
And now for something completely different. We leave GaltonWatson processes behind and talk a bit about Birkhoff’s Ergodic Theorem and Fekete’s Lemma. The latter states that an/n converges if an is a subadditive sequence and Kingman’s subadditive ergodic theorem provides a dynamical / random analogue.
Leah Duffett, Department of Pure Mathematics, University of Waterloo
"Horned spheres and Schoenflies Theorem"
Shaoming Guo, Indiana University Bloomington
"ParsellVinogradov systems in higher dimensions"
I will present a few results on counting the numbers of integer solutions of ParsellVinogradov systems in higher dimensions. A few techniques from harmonic analysis are crucial in our approach. They are BrascampLieb inequalities, multilinear Kakeya inequalities, induction on scales, etc.
MC 5501
Justin Laverdure, Department of Pure Mathematics, University of Waterloo
"A finite pointed group with no finite basis (part 2)"
We'll continue to go over the construction of Roger Bryant. Hopefully, we'll finally see the group P, and argue that every (n1)generated subalgebra of Q_n is in HSP(P).
MC 5413
Mykola Matviichuk, University of Toronto
"Deformation of Dirac structures via L infinity algebras"
Henna Koivusalo, University of Vienna
"Dimensions of sets arising from iterated function systems  with a special emphasis on selfaffine sets"
In this colloquium style talk I will review the history of calculating dimensions of sets that arise as invariant sets of iterated function systems. I will, in particular, compare the theory of selfsimilar sets to the theory of selfaffine sets.
Laurent Bienvenu, Montpelier, CNRS
"Randomized algorithms in computability theory"
Justin Laverdure, Department of Pure Mathematics, University of Waterloo
"Rational maps from reduced schemes"
I'll outline the definition of rational, dominant rational, and birational maps, and use these notions to outline the equivalence of the categories of finitely generated extensions of a field k and that of integral kvarieties. I'll also go over the classical example of rational points on the circle, in the light of rational maps.
MC 5413
Michael Deveau, Department of Pure Mathematics, University of Waterloo
"Isomorphisms that cannot be coded by computable relations"
When we wish to show that two structures have an isomorphism of a certain degree between them, a standard technique is to carefully choose some computable set $U$ and then show that under a natural isomorphism $f$, the image $f(U)$ has the degree we are interested in. We show a case of two structures isomorphic to $(\omega, <)$ where this method of establishing the degree of the isomorphism between them will not work.
Rahim Moosa, Department of Pure Mathematics, University of Waterloo
"Isolated types of finite rank"
Departmental office: MC 5304
Phone: 519 888 4567 x33484
Fax: 519 725 0160
Email: puremath@uwaterloo.ca