16:30
Alexandrov immersed mean curvature flow
Abstract
Geometric Incarnations of (Shifted) Quantum Loop Algebras
Abstract
I'll briefly explain quantum groups and $R$-matrices and why they're the same thing. Then we'll see how to construct various $R$-matrices from Nakajima quiver varieties and some possible applications.
16:00
Sums of arithmetic functions over F_q[T] and non-unitary distributions (Joint junior/senior number theory seminar)
Abstract
In 2018, Keating, Rodgers, Roditty-Gershon and Rudnick conjectured that the variance of sums of the divisor
function in short intervals is described by a certain piecewise polynomial coming from a unitary matrix integral. That is
to say, this conjecture ties a straightforward arithmetic problem to random matrix theory. They supported their
conjecture by analogous results in the setting of polynomials over a finite field rather than in the integer setting. In this
talk, we'll discuss arithmetic problems over F_q[T] and their connections to matrix integrals, focusing on variations on
the divisor function problem with symplectic and orthogonal distributions. Joint work with Matilde Lalín.
The Estates Services Travel team are due to carry out removal of unused or unclaimed bicycles across the ROQ (excluding internal bicycle stores).
Over the coming weeks, all bicycles will have a removable tag placed on them. If your bicycle is tagged, please do not be concerned, simply remove the tag and dispose of appropriately. The bicycles that still have a tag on them by early February will be removed and taken away.
15:00
15:00
Applied Topology TBC
I am an applied mathematician working as an associate professor at American University. I am interested in signal processing, dynamics, and applications of topology.
16:00
Sums of arithmetic functions over F_q[T] and non-unitary distributions
Abstract
In 2018, Keating, Rodgers, Roditty-Gershon and Rudnick conjectured that the variance of sums of the divisor function in short intervals is described by a certain piecewise polynomial coming from a unitary matrix integral. That is to say, this conjecture ties a straightforward arithmetic problem to random matrix theory. They supported their conjecture by analogous results in the setting of polynomials over a finite field rather than in the integer setting. In this talk, we'll discuss arithmetic problems over F_q[T] and their connections to matrix integrals, focusing on variations on the divisor function problem with symplectic and orthogonal distributions. Joint work with Matilde Lalín.
16:00
Symmetric Tensor Products: An Operator Theory Approach
Abstract
Although tensor products and their symmetrisation have appeared in mathematical literature since at least the mid-nineteenth century, they rarely appear in the function-theoretic operator theory literature. In this talk, I will introduce the symmetric and antisymmetric tensor products from an operator theoretic point of view. I will present results concerning some of the most fundamental operator-theoretic questions in this area, such as finding the norm and spectrum of the symmetric tensor products of operators. I will then work through some examples of symmetric tensor products of familiar operators, such as the unilateral shift, the adjoint of the shift, and diagonal operators.