Events

Jeremy Champagne, University of Waterloo 

On the generalisation of a theorem of Watson

This talk is a continuation of the one I gave in March. In essence, we are discussing the set of real valued functions f(n) such that gcd(n,[f(n)])=1 happens with probability 1/zeta(2) (in the sense of natural densities), and related problems. I will give a general gameplan to establishing such results, and I will prove that gcd(n, [alpha_1n], [alpha_2n^2],...,[alpha_kn^k])=1 happens with probability 1/zeta(k+1) foralpha_1,...,alpha_k irrational.

MC 5403

Larissa Kroell, University of Waterloo

Partial C*-Dynamical Systems: Injective Envelopes and the Ideal Intersection Property

Partial C*-dynamical systems are a generalization of ordinary C*-dynamical systems and were first introduced by Ruy Exel (1994) to express certain C*-algebras as crossed products by a single partial automorphism. In this talk, we will show the existence of an equivariant injective envelope for partial C*-dynamical systems — a concept which has been a driving force in many recent results regarding the ideal structure of ordinary C*-dynamical systems. We will motivate our construction by highlighting its connection to ordinary C*-dynamical systems via enveloping actions. Furthermore, we provide a characterization of the ideal intersection property for partial C*-dynamical systems as an application of equivariant injective envelopes in this setting. This is based on joint work with Matthew Kennedy and Camila Sehnem.

This seminar is held jointly with the Canadian Operator Symposium.

M3 1006

Kain Dineen, University of Waterloo

Linear maps preserving powers of the symplectic form

Let Ω denote the standard symplectic form on ℝ^{2m} For k = 1,..., m, we will describe the subgroup of GL(2m, ℝ) which fixes Ω^k.

STC 0010

Dashen Yan, Stony Brook University

Non-degenerate Z_2 harmonic 1-forms on R^n and their geometric applications

The Z_2 harmonic 1-form arises in various compactification problems in gauge theory, including those involving PSL(2,C) connections and Fueter sections. In this talk, we will describe a recent construction of non-degenerate Z_2 harmonic 1-forms on R^n for n >(=) 3 , and explore their relation to Lawlor’s necks—a family of special Lagrangian submanifolds in C^n.

We will also discuss a gluing construction in which these examples are glued to a regular zero of a harmonic 1-form on a compact manifold. This yields a sequence of non-degenerate Z_2 harmonic 1-forms whose branching sets shrink to points. As a result, we obtain many new examples of non-degenerate Z_2 harmonic 1-forms on compact manifolds.

STC 0010

Jashan Bal, University of Waterloo

More on Ramsey degrees

We continue discussing various dynamical reformulations of having finite Ramsey degree.

MC 5417

Dashen Yan, Stony Brook University

Non-degenerate Z_2 harmonic 1-forms with shrinking branching sets

In this talk, we will explain the technical aspects of the gluing construction presented in Thursday’s talk. Specifically, we adapt Donaldson’s framework for deforming multivalued harmonic functions to our gluing setting and establish a weighted version of the Hamilton–Nash–Moser–Zehnder implicit function theorem to prove the gluing result.

MC 5417

Paul Pollack, University of Georgia

How nonunique is your factorization?

Number theorists learn early on not to take unique factorization for granted. In 1980, R.J. Valenza introduced the "elasticity” of an integral domain as a means of measuring how far away the domain is from possessing unique factorization. I will survey what is known about elasticity of rings of number theoretic interest. Particular attention will be paid to recent work of the speaker on elasticity of orders in quadratic fields. Much of this is joint with Steve Fan (UGA) and Enrique Trevino (Lake Forest).

MC 5417

Joey Lakerdas-Gayle, University of Waterloo

Effective Algebra 2

We will continue learning about recursively presented groups.

MC 5417

Francisco Villacis, University of Waterloo

Algebraic Geometry Working Seminar

In this talk, we will explore the "marriage of matroid theory and convex set theory" initiated by I.M. Gelfand and R. MacPherson back in the 80s. In their seminal work, they construct a bijection between projective configurations of n points in P^(k-1) and C*^n-orbits of the Grassmannian of n-k-planes in C^n. This gives a one-to-one correspondence between representable matroids over C and certain convex polyhedra, which in turn gives two equivalent decompositions of the Grassmannian into strata. This decomposition is also equivalent to the decomposition of the Grassmannian into intersections of translates of certain Shubert cells, as shown by Gelfand, Goresky, MacPherson and Serganova a few years later. We will explore these three decompositions and talk about related results.

MC 5403

Eason Li, University of Waterloo

The Hales-Jewett Theorem

We discuss the Hales-Jewett theorem, time permitting giving a full proof.

MC 5417