Events

Faisal Romshoo, University of Waterloo

Symmetry groups, moment maps and cohomogeneity one special Lagrangians in C^m

We will discuss the relationship between symmetries and moment maps as explained in arXiv:math/0008021 and how this allows us to construct cohomogeneity one special Lagrangians in C^m. Time permitting, we will discuss some examples of SL m-folds in C^m.

MC 5403

Alex Pawelko, University of Waterloo

The Formal Kaehler Structure of the G2 Knot Space

We will explore the usual suspects of the moduli space of knots embeddable in a G2 manifold, based upon the work of Brylinski for the analogous space corresponding to the 3-dimensional cross product. This gives an infinite-dimensional "formally Kaehler" manifold, which one can consider Kaehler reduction on. If time permits, we will gesture vaguely at considerations from gauge theory and geometric quantization that motivate many interesting questions in the case of G2 manifolds.

MC 5403

Cynthia Dai, University of Waterloo

Categories as Complex Numbers

Let T be the set of all binary trees. It is well-known that T = 1+T^$. This implies that T^2-T=-1, and solving for T over the complex numbers, we can conclude it must be a 6th primitive root of unity. Hence we have an isomorphism T = T^7. Come to this talk and learn why this nonsense works.

MC 5403

Andy Zucker, University of Waterloo

On Ramsey Degrees

We discuss some dynamical reformulations of the notion of Ramsey degree. This meeting also serves as an organizational meeting to plan the rest of the learning seminar.

MC 5417

Francisco Villacis, University of Waterloo

A Deep Dive into Mathematicians’ Questionable Outfits

Being able to prove the most impressive theorems and having a good sense of fashion need not be mutually exclusive - except it might be? This will be up to you to judge in this talk. Together, we’ll apply the most unscientific of methodologies to create a tier list of mathematicians based solely on their dressing style - from Euclid’s timeless toga to Grothendieck’s "I’ve been living in a forest for five years" aesthetic. Be sure to bring your best outfits, otherwise you might end up in a bored grad student's tier list one day.

MC 5479

(snacks from 4:00pm)

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