Events

Veronika Shelestunova, RBC Capital Markets

Teaching Stream

The Career Talks seminar series invites professionals from various fields to share their personal career journeys and insights on how they achieved success. Each session offers valuable advice and guidance for current graduate students. By hearing firsthand experiences, attendees gain a deeper understanding of the challenges and opportunities that lie ahead in their professional lives.

MC 5501

Refreshments will be available during the talk

Amanda Maria Petcu, University of Waterloo

A hypersymplectic structure on R^4 with an SO(4) action

Given a hypersymplectic manifold X^4, one can give a flow of hypersymplectic structures that evolve according to the equation

d_t w = d(Q d^*(Q^{-1} w), where w is the triple that gives the hypersymplectic structure and Q is a 3x3 symmetric matrix. In this talk we let X^4 be R^4 with an SO(4) action  The flow of the hypersymplectic triple then descends to a single flow of a function h. We will examine this flow, as well as solitons of the hypersymplectic flow in this set up. Furthermore, the triple w gives rise to a Riemannian metric g . We will conclude with a discussion about the Riemann and Ricci curvature tensors that are derived from this metric.

MC 5479

Erik Séguin, University of Waterloo

Selected Topics on Fourier-Stieltjes Algebras of Locally Compact Hausdorff Groups.

We discuss some selected topics on Fourier-Stieltjes algebras of locally compact Hausdorff groups.

MC 5403

Meenakshi McNamara, Perimeter Institute for Theoretical Physics

Exact quantum chromatic numbers of Hadamard graphs and products

Quantum chromatic numbers are defined in terms of non-local games on graphs. This talk gives a proof of the exact quantum chromatic number of Hadamard graphs using a conjugacy class graphs approach. This further allows us to consider graph products, and we compute the exact quantum chromatic number of the categorical product of Hadamard graphs. This work makes use of several results for the quantum chromatic numbers of quantum graphs, an operator algebraic generalizations of graphs. In particular, we also discuss results on products of quantum graphs from joint work with Rolando de Santiago.

MC 5417

Christine Eagles, University of Waterloo

Curve excluding fields IV

We continue to read Omar Leon Sanchez' paper.

MC 5403

Xinle Dai, Harvard University

Sectorial Decompositions of Symmetric Products and Homological Mirror Symmetry

Symmetric products of Riemann surfaces play a crucial role in symplectic geometry and low-dimensional topology. They are essential ingredients for defining Heegaard Floer homology and serve as important examples of Liouville manifolds when the surfaces are open. In this talk, I will discuss ongoing work on the symplectic topology of these spaces through Liouville sectorial methods, along with examples as applications of this decomposition construction to homological mirror symmetry.

MC 5417

Adrian Dawid, University of Cambridge

A promenade along the A-side

In this talk we will take a closer look at some of the structures that live on the A-side of mirror symmetry. In particular, the Fukaya category and symplectic cohomology. Along the way we will look at concrete examples of homological mirror symmetry. After a reminder about the Fukaya category, we will introduce symplectic cohomology. We will then discuss the relationship between these two given by open-closed and closed-open string maps. We will look at some examples with an emphasis on the mirror symmetry perspective. If time permits, we will also take a look at some structures that do not (yet?) have an obvious analogue under mirror symmetry, such as the action filtration of the Fukaya category and related invariants.

MC 2017 

Adam Logan, CSE & Kevin Hare, University of Waterloo

Research Stream

The Career Talks seminar series invites professionals from various fields to share their personal career journeys and insights on how they achieved success. Each session offers valuable advice and guidance for current graduate students. By hearing firsthand experiences, attendees gain a deeper understanding of the challenges and opportunities that lie ahead in their professional lives.

MC 5501

Sourabhashis Das, University of Waterloo

On the distributions of divisor counting functions: From Hardy-Ramanujan to Erdős-Kac

In 1917, Hardy and Ramanujan established that w(n), the number of distinct prime factors of a natural number n, and Omega(n), the total number of prime factors of n have normal order log log n. In 1940, Erdős and Kac refined this understanding by proving that w(n) follows a Gaussian distribution over the natural numbers.

In this talk, we extend these classical results to the subsets of h-free and h-full numbers. We show that w_1(n), the number of distinct prime factors of n with multiplicity exactly 1, has normal order log log n over h-free numbers. Similarly, w_h(n), the number of distinct prime factors with multiplicity exactly h, has normal order log log n over h-full numbers. However, for 1 < k < h, we prove that w_k(n) does not have a normal order over h-free numbers, and for k > h, w_k(n) does not have a normal order over h-full numbers.

Furthermore, we establish that w_1(n) satisfies the Erdős-Kac theorem over h-free numbers, while w_h(n) does so over h-full numbers. These results provide a deeper insight into the distribution of prime factors within structured subsets of natural numbers, revealing intriguing asymptotic behavior in these settings.

MC 5479

Jack Jia, University of Waterloo

Group Schemes: a Functor of Points Perspective

A group scheme is a group object in a category of schemes. This definition, much like other category theory mantras, is a great way to organize knowledge but falls short when one tries to work with it in a hands-on way. I will introduce a more hands-on classification for group schemes, which is aligned with how people work with them in practice. Time permitting, I will illustrate the advantage of this definition in the case of elliptic curves.

MC 5479