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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Michael Deveau, Department of Pure Mathematics, University of Waterloo
"Games, Determinacy and Martin's Theorem"
We first define the notion of a game and then discuss the Axiom of Determinacy (AD), which is inconsistent with ZFC. We work instead in ZF + AD, and explore the consequences of AD as it relates to Turing degrees. In particular, we prove Martin's Theorem: assuming AD, every set of Turing degrees contains or omits a cone of degrees.
MC 5403
Janez Bernik, University of Ljubljana
"Quasifiliform Lie algebras of maximum length revisited"
Ross Willard, Department of Pure Mathematics, University of Waterloo
"Uncountable SIs in residually small varieties in a countable signature, part III"
Continuing the proof of "the theorem" of McKenzie and Shelah, I will prove a technical theorem about the automorphism groups of maximal special subdirectly irreducible members in the relevant varieties. Then I will assemble the pieces to show that the types realized in a maximal special subdirectly irreducible algebra form a compact second countable topological space.
MC 5479
Mohammad Mahmoud, Department of Pure Mathematics, University of Waterloo
"Degree invariant functions and Martin's Conjectures"
We will go through a theorem which proves a special case of one of Martin's conjectures about degree (Turing) invariant functions. The theorem says: Assuming the Axiom of Determinacy, a uniformly degree invariant function that is not increasing on a cone must be constant on a cone. The theorem is about a uniformly degree invariant function while the conjecture is about any degree invariant function, not necessarily uniformly.
Ross Willard, Department of Pure Mathematics, University of Waterloo
"Uncountable SIs in residually small varieties in a countable signature, part IV"
Continuing the proof of "the theorem" of McKenzie and Shelah, I will define how the types realized over a countable set in a maximal special subdirectly irreducible algebra form a compact T1 second countable topological space.
MC 5479
Mohammad Mahmoud, Department of Pure Mathematics, University of Waterloo
"Degree invariant functions and Martin's Conjectures"
We will continue the proof we started for the special case of Martin's conjecture. That special case result says: Assuming the Axiom of Determinacy, a uniformly degree invariant function that is not increasing on a cone must be constant on a cone.
MC 5403
Jacob Campbell, Department of Pure Mathematics, University of Waterloo
We will study a class of compact quantum groups whose structure and representation theory depend on the combinatorics of set partitions, and we will also study some "noncommutative spaces" on which these quantum groups act. The emphasis of the presentations will be placed on the illustrative examples provided by the quantum permutation group and by the free orthogonal quantum group.
Josh Hews, Department of Pure Mathematics, University of Waterloo
"Algorithms for 3Manifolds"
Ross Willard, Department of Pure Mathematics, University of Waterloo
"Uncountable SIs in residually small varieties in a countable signature, Part V"
Having assembled the pieces, I will attempt to put them together to prove the theorem of McKenzie and Shelah.
MC 5479
Yifan Yang, National Taiwan University
"Equations of Shimura curves"
Shimura curves are generalizations of classical modular curves. Because of the lack of cusps on Shimura curves, there are very few explicit methods for Shimura curves. In this talk, we will introduce Borcherds forms and use them to determine the equations of Shimura curves. The construction of Borcherds forms is done by solving certain integer programming problems. This is a joint work with JiaWei Guo.
MC 5403
Mohammad Mahmoud, Department of Pure Mathematics, University of Waterloo
"Degree Invariant Functions and Martin's Conjecture"
This week we prove the Delay Lemma which is the essential part of proving that if our degree invariant function is strictly decreasing on a cone then it is constant on a cone.
MC 5417
Jonathan Herman, Department of Pure Mathematics, University of Waterloo
"Weak Moment Maps in Multisymplectic Geometry"
We introduce the notion of a `weak (homotopy) moment map' associated to a Lie algebra action on a multisymplectic manifold.
We use weak moment maps to extend Noether's theorem from Hamiltonian mechanics by exhibiting a correspondence between multisymplectic conserved quantities and continuous symmetries on a multiHamiltonian system.
Andrew Swann, Aarhus University
"Toric geometry of G2 metrics"
Jorge Galindo, Universitat Jaume I
"\ell_1sequences and Arens regularity of the Fourier algebra"
The Fourier algebra A(G) of a locally compact Abelian group G is the algebra of functions on G whose Fourier transforms are integrable on the dual group \widehat{G}. When G is not commutative, the definition of A(G) is more sophisticated and produces an often intriguing Banach Algebra that has interest from the perspectives of Harmonic Analysis and Operator Theory.
Malabika Pramanik, University of British Columbia
"Configurations in sets big and small"
Daniel Pepper, Department of Pure Mathematics, University of Waterloo
In this learning seminar we will study some basic facts about the free probability analogue of the Brownian motion, and about how one can do stochastic integration against the free Brownian motion. The framework used will be the one of a C*probability space. The main reference followed will be a paper by P. Biane and R. Speicher titled "Stochastic calculus with respect to free Brownian motion and analysis on Wigner space" (in Probability Theory and Related Fields, 1998).
M3 3103
Hongdi Huang, Department of Pure Mathematics, & William Dugan, Department of Combinatorics & Optimization, University of Waterloo
"An introduction to Kreimer's Hopf algebra and GrossmanLarson Hopf algebra"
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 promised 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.