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Aleksa Vujicic, University of Waterloo

Fourier Algebras of Semi-Direct Product Groups of Local Fields

We look at Fourier Algebras of Semi-Direct Product Groups of Local Fields.

MC 5403

Nicolas Banks, University of Waterloo

Non-Trivial Theorems with Trivial Proofs

One of the most fruitful things we can do as mathematicians is to think deeply about simple things. As students and researchers, perhaps we come across results with simple proofs and believe that not much can be learned from them. In this talk, I will challenge this misconception by diving into three important, non-trivial theorems with seemingly trivial proofs - Desargue's Theorem of planar geometry, the finite intersection property of compact sets, and Lagrange's Theorem from group theory. These will demonstrate three reasons that a profound truth need not be complicated.

MC 5501

(snacks at 17:00)

Francisco Villacis, University of Waterloo

Computing the Quantum Cohomology

In this talk, I will compute the quantum cohomology ring of projective space and of the Grassmannian. If time permits, I will outline the computation of the quantum cohomology of generic quintic threefolds and their connections to the count of rational curves of a given degree on these.

MC 2017

Kaleb D Ruscitti, University of Waterloo

Real Analytic Varieties and Singularities

Analytic varieties have the flavour of algebraic geometry, but are also foreign in many ways. Of course, over the complex numbers, Serre showed that analytic and algebraic varieties are strongly related. Over the real numbers however, things are more interesting.

In this talk I will review the definition of analytic completion, analytic spaces, and their relationship to algebraic varieties. Then I will focus on the real case, and talk about singularities of real analytic spaces and real normal crossings divisors.

MC 5479

Kuntal Banerjee, University of Waterloo

Very stable and wobbly loci for elliptic curves

We explore very stable and wobbly bundles, twisted in a particular sense by a line bundle, over complex algebraic curves of genus 1. We verify that twisted stable bundles on an elliptic curve are not very stable for any positive twist. We utilize semistability of trivially twisted very stable bundles to prove that the wobbly locus is always a divisor in the moduli space of semistable bundles on a genus 1 curve. We prove, by extension, a conjecture regarding the closedness and dimension of the wobbly locus in this setting. This conjecture was originally formulated by Drinfeld in higher genus.

MC 5501

Kain Dineen, University of Waterloo

Symplectic Capacities and Rigidity

As an application of Gromov's non-squeezing theorem, we'll prove that the symplectomorphisms (and anti-symplectomorphisms) of (ℝ^2m, 𝜔_0) are exactly the diffeomorphisms that additionally preserve the capacity of every compact ellipsoid. If time permits, then we will use this to prove that if a sequence of symplectomorphisms of any symplectic manifold (M, 𝜔) converges in the C^0-sense to a diffeomorphism 𝜓, then 𝜓*𝜔 = ± 𝜔.

MC 5479

Erik Séguin, University of Waterloo

A Selected Topic on Fourier-Stieltjes Algebras of Locally Compact Hausdorff Groups

We discuss a particular selected topic on Fourier-Stieltjes algebras of locally compact Hausdorff groups. Time permitting, we may complete the proof a lemma.

MC 5403

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

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