Events

Shintaro Fushida-Hardy, University of Waterloo

Constructing Lagrangians in S2xS2

We investigate the existence of non-orientable Lagrangian surfaces in symplectic S^2xS^2s. On one hand, it is known that a Klein bottle embedded in S^2xS^2 cannot be Lagrangian in almost half of the possible symplectic structures on S^2xS^2. On the other hand, we use trisection-inspired methods to describe a general construction of Lagrangian surfaces, and ask "what is the minimal genus such that a non-orientable Lagrangian surface of said genus exists in every symplectic S^2xS^2?". This is joint work with Laura Wakelin.

MC 5417

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

Yunqing Tang, Berkeley

Irrationality of periods

Periods are interesting numbers arising from algebraic geometry. Grothendieck’s period conjecture provides predictions on irrationality and transcendence of periods. There have been some systematic studies on certain periods, such as Baker’s theory on linear forms of logarithms of algebraic numbers. However, beyond special cases, we do not know the irrationality of simple-looking periods such as the product of two logs. In this talk, I will discuss the joint work with Calegari and Dimitrov on an irrationality result of certain product of two logs and some other periods. A classical prototype of the method was first used by Apéry to prove the irrationality of zeta(3). The key ingredient is an arithmetic holonomy theorem built upon earlier work by André, Bost, Charles (and others) on arithmetic algebraization theorems via Arakelov theory.

MC 5501

Yunqing Tang, Berkeley

The arithmetic of power series and applications to irrationality

We will discuss a new approach to prove irrationality of certain periods, including the value at 2 of the Dirichlet L-function associated to the primitive quadratic character with conductor -3. Our method uses rational approximations from the literature and we develop a new framework to make use of these approximations. The key ingredient is an arithmetic holonomy theorem built upon earlier work by André, Bost, Charles (and others) on arithmetic algebraization theorems via Arakelov theory. This is joint work with Frank Calegari and Vesselin Dimitrov.

MC 5417

Elan Roth, University of Waterloo

A Continuation of Random Binary Sequences

Filling some gaps left by last week's presenter, we'll show the K is a minimal information content measure and finally conclude that 1-Randomness and ML-Randomness are equivalent.

MC 5403

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 monopolos on 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 R^3 and building up to an S^1-invariant instanton on the multi-Taub-NUT space.

MC 5403

Jennifer Zhu, University of Waterloo

Limits of Quantum Graphs

Quantum graphs were originally introduced as confusability graphs of quantum channels by Duan, Severini, and Winter. Weaver generalized a quantum graph to any weak-* closed operator system $\mathcal V \subseteq B(\mathcal H)$ that is bimodule over the commutant of some von Neumann algebra $\mathcal M \subseteq B(\mathcal H)$. To date, there seem to be two notions of quantum graph morphism. Weaver introduced and Daws extended a notion of CP morphism of quantum graphs. Musto, Reutter, and Verdon have also defined classical morphisms of quantum graphs in finite dimensions which agrees with CP morphisms in finite dimensions. Notably, however, these morphisms are not UCP maps between operator systems of the respective quantum graphs.

      Using a characterization of quantum relations as left ideals in the extended Haagerup tensor product, we will obtain a notion of quantum graph morphism (and hence limit) using the categories of von Neumann algebras and operator spaces. Time permitting, we will show that this limit recovers profinite classical graphs.

QNC 1507

Laindon Burnett, University of Waterloo

A definable criterion for definability

In 2001, A.A. Muchnik proved the surprising result that for any n, there is a formula within Presburger arithmetic which takes in a predicate A and is true if and only if A is definable in Presburger arithmetic; that is, within this setting, the property of being definable is itself definable. We will go over the proof of this result and, time permitting, discuss its applications to automata theory.

MC 5403

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

Mateusz Wasilewski, Polish Academy of Sciences

Quantum graphs and their symmetries

I will present an overview of the theory of quantum graphs, which form a natural generalization of graphs from the point of view of operator algebras/quantum information. I will discuss several approaches to the theory, each coming with its own motivation. Just like in the classical case, studying symmetries is extremely important and this naturally leads to quantum groups. It turns out that to some extent one can go back: for a rich class of quantum groups one can construct quantum graphs, whose symmetries are given by the original quantum group. It is the quantum analogue of Frucht's theorem.

MC 5501