webnotice

Elan Roth, University of Waterloo

A Continuation of Random Binary Sequences

We'll return to ML- and 1-Randomness and prove their equivalence. First, we will define some necessary machinery such as information content measures and the KC theorem.

MC 5403

Siyuan Lu, McMaster University 

Interior C^2 estimate for Hessian quotient equation

In this talk, we will first review the history of interior C^2 estimates for fully nonlinear equations. As a matter of fact, very few equations admit this property, not even the Monge-Ampère equation in dimension three or above. We will then present our recent work on interior C^2 estimate for Hessian quotient equation. We will discuss the main idea behind the proof. If time permits, we will also discuss the Pogorelov-type interior C^2 estimate for Hessian quotient equation and its applications.

MC 5417

Patrick Naylor, McMaster University

Doubling Gluck twists

The Gluck twist of an embedded 2-sphere in the 4-sphere is a 4-manifold that is homeomorphic but not obviously diffeomorphic to the 4-sphere. Despite considerable study, these strange manifolds have remained a long-standing source of potential counterexamples to the only remaining case of the Poincaré conjecture. In this talk, I will give an overview of this conjecture, a visual introduction to 2-dimensional knot theory, and describe conditions that guarantee that (some) Gluck twists are standard, i.e., diffeomorphic to the 4-sphere. This is based on joint work with Dave Gabai and Hannah Schwartz.

MC 5501

It is with sadness that we announce our William Gilbert passed away, surrounded by the love of his family on Saturday, October 25th, 2025 at the age of 84 years.  Will was a faculty member in our department for many years, retiring in 2004, and has been a fixture at various department events since then.  Those of you who knew him will remember his wry sense of humour and his cheerful demeanour.

Born in Exeter, England in March 1941, Will's early years took him from the Devon countryside to Deep River, Ontario—where his father Charles Gilbert was the lead Nuclear Physicist at Canada's first nuclear reactor—before the family returned to England and settled in Manchester. Will completed his undergraduate and master's degrees in mathematics at Cambridge University, and to his father's disappointment, completed his PhD at Oxford University. A distinguished mathematician and dedicated educator, Will built a remarkable academic career spanning nearly four decades at the University of Waterloo. He joined the Department of Pure Mathematics as an Assistant Professor in 1968, rising to full Professor and serving as Department Chair from 1995 to 1999 before becoming Professor Emeritus in 2004.

Will’s scholarly contributions were significant and diverse, exploring the elegant interplay between algebra and geometry. His research encompassed fractal geometry, complex bases, dynamical systems, and algebraic topology. He authored several influential textbooks, including "An Introduction to Mathematical Thinking" and "Modern Algebra with Applications," shaping the minds of countless mathematics students. He has 54 publications to his name, and his research is cited over 800 times according to ResearchGate. Throughout his career, he contributed to the study of mathematics internationally through research and teaching sabbaticals in Australia, New Zealand, and China

Beyond the classroom and research lab, Will embraced life as a quiet, patient, and caring man. He was known for his gentle presence, warm smile, and wry sense of humour. Will had a lifelong love of British comedy, particularly Monty Python—several members of which were his contemporaries at Cambridge and Oxford. He was an avid sailor, enjoying his Laser and Albacore sailboats on Conestoga Lake. He was a dedicated skier, enjoyed camping adventures, travelled the world extensively, and cultivated a refined palate as a wine connoisseur and member of both the International Cellar Society and the Kitchener German Wine Society. He once owned an extensive wine collection that was the envy of many. A passionate film enthusiast with a particular love for world cinema, he contributed reviews to the Internet Movie Database and attended the Toronto International Film Festival faithfully for decades.

In later years, Will treasured time with his family, completing jigsaw puzzles and swimming. His grandchildren adored their Grandpa deeply and will forever hold close memories of his kindness, intelligence, patience, and the special bond they shared.

Husband of Ruth Gilbert (née Hornig) for over 57 years. Loving father of Mandy Jean Ramirez (Jesse) and Peter Jay Gilbert (Farida). Cherished grandfather of Zachary Ramirez, Ethan Gilbert, and Gavin Gilbert. Dear big brother of Harry Gilbert (Awn) of England and Eva Smart of Australia. Loving uncle of Holly Gilbert, Judith Smart, Jonathan Smart, and Jason Smart.

Predeceased by his parents, nuclear physicist Charles Walton Gilbert and Irene Gilbert (née Gunn)

Cremation has taken place. A Celebration of Life open house will be held Sunday November 16th in the afternoon. Please email willcelebrationoflife@gmail.com for more information and to RSVP.

In lieu of flowers, donations may be made to Heart and Stroke Foundation of Canada as expressions of sympathy. Messages and condolences may be left at www.tricitycremations.com or 519.772.1237

Siyuan Yu, Western University

Symplectic embeddings of balls in ℂP² and the generalized configuration space

Let IEmb(B⁴(c),ℂP²) denote the space of unparameterized symplectic embeddings of k balls of capacities (c₁,...,cₖ), where 1 ≤ k ≤ 8. It is known from the work of S. Anjos, J. Li, T.-J. Li, and M. Pinsonnault that the space of capacities decomposes into convex polygons called stability chambers, and that the homotopy type of IEmb(B⁴(c),ℂP²) depends solely on the stability chambers. Based on recent results of M. Entov and M. Verbitsky on Kähler-type embeddings, we show that for 1 ≤ k ≤ 8, IEmb(B⁴(c),ℂP²) is homotopy equivalent to a union of strata F_I of the configuration space of the complex projective plane F(ℂP²,k). The proof relies on constructing an explicit map from the space of Kähler type embeddings to a generalized version of the configuration space that incorporates both configurations of points and compatible complex structures on ℂP².

MC 5417

Rahim Moosa, University of Waterloo

The binding group theorem in stable theories, as a bitorsor.

Recently,  Anand Pillay and I developed the theory of binding groups in the setting of CCM — the first order theory of compact complex manifolds. But this talk will not be about that. Rather, I will talk about a somewhat streamlined and simplified presentation of the binding group theorem for stable theories (that appears in the paper with Pillay mentioned above). There is little novelty here, except maybe the bitorsorial presentation that we give (and like).

MC 5403

Jérémy Champagne, University of Waterloo

Small fractional parts of polynomials (aka 11J54)

In the eary 1900's, Hardy and Littlewood asked the following question: given a real number α and integer k>1, what is the smallest distance obtained between αn^k and the nearest integer as n runs over the set {1,...,N}? More specifically, does there exist an exponent theta_k>0 such that the smallest distance is at most N^-theta_k for sufficiently large N? This question was answered positively by Vinogradov a couple decades later, but the question of finding the largest possible theta_k with this property is still open.

In this talk, I will discuss some historical results around this problem and present some typical methods used in the literature.

MC 5479

Facundo Camano, University of Waterloo

Dimensional Reduction of S^1-Invariant Instantons on the Multi-Taub-NUT

In this talk I will discuss the dimensional reduction of S^1-invariant instantons on the multi-Taub-NUT space to singular monopoloes on \mathbb{R}^3. I will first introduce the multi-Taub-NUT space, followed up by a discussion on S^1-equivariant principal bundles. Next, I will go over the natural decomposition of S^1-invariant connections into horizontal and vertical pieces, and then show how the self-duality equation reduces to the Bogomolny equation under said decomposition. I will then show how the smoothness of the instanton over the NUT points determines the asymptotic conditions for the singular monopole. Finally, I will go over the reverse construction: starting with a singular monopole on \mathbb{R}^3 and building up to an S^1-invariant instanton on the multi-Taub-NUT space.

MC 5403

Elan Roth, University of Waterloo

A Continuation of Random Binary Sequences 2.0

Inspired by probability theory, we can define a new notion of randomness using betting strategies. We'll discuss some properties of this notion of randomness and, you guessed it, prove its equivalence to ML-randomness and 1-randomness.

MC 5403

Liam Orovec, University of Waterloo

Greedy and Lazy Parry Numbers

We say a real number \beta is a Parry number provided the greedy \beta-expansion for 1 is eventually periodic or finite. We show conditions for when \beta is a Parry number and provide a family of real numbers which are always Parry numbers, the PV-numbers. The related Salem numbers, constructed from PV-numbers are then considered. We split this into four cases, the first of which was shown by Hare and Tweedle, we give criteria for finding Salem numbers which are Parry numbers. Time permitting we will explore the case where we look at lazy expansions instead of greedy expansions, we call these numbers lazy Parry numbers.

MC 5417