Postgraduate Seminars Summer 2025
These seminars (unless otherwise stated) will take place on Thursdays at 2pm-3pm on an almost weekly basis.
Talks are being given by 2nd and 3rd year Mathematics PhD students for PhD students.
01 May 2025 - 2pm in Maths Room 416
Speaker: Brad Wilson
TITLE: The braid group and monodromy
Abstract:
The braid group describes how several strands of string can be twisted together into a braid. I will explain how a braid determines a family of hyperelliptic curves. Assigning each braid to the monodromy of this family defines the symplectic representation of the braid group. If time permits, I will introduce the Burau representation and its probabilistic interpretation due to Jones. The symplectic representation is recovered as a special case.
08 May 2025
NO SEMINAR
15 May 2025
NO SEMINAR
22 May 2025 - 2pm in Maths Room 416
Speaker: Micheal Nguyen
TITLE: A two-basin model of the Arctic Ocean with low frequency waves
Abstract:
The Arctic Ocean’s dynamics are fundamentally different to midlatitude oceans, which is governed by Coriolis effect variations due to the Earth's rotation. Circulation in the Arctic is instead driven by wind forcing and the basin topography but predicting their evolution in a changing climate remains an open challenge. We present a minimal two-basin model that incorporates these factors to explore simplified Arctic flows. We find low frequency waves by solving the linearised, rigid-lid Shallow-water equation using complex variables and Fourier mode-matching techniques. We show possible extensions to multiple basins when looking at more realistic depictions of the Arctic Ocean.
29 May 2025
NO SEMINAR
05 June 2025
NO SEMINAR
12 June 2025 - 2pm in Maths Room 706
Speaker: Teymour Gray
TITLE: Special values of L-functions: how to find them and why they are oh so special
Abstract:
This will be an introductory (and very accessible!) talk to special values of Dirichlet L-functions. We will discuss two ways to compute these special values, with the second approach allowing us to make meaningful sense of the identity 1+2+3+4+...= - 1/12 without resorting to the functional equation. Then we will discuss what all this has to do with the arithmetic of number fields :)
19 June 2025
NO SEMINAR
26 June 2025 - 2pm in Maths Room 416
Speaker: Ling Chen
TITLE: Adapted optimal transport and its application in financial attack and defence
Abstract:
Financial attack and defence is an inf-sup problem, where the attacker wants to maximise the loss/misclassification probability within some range while the defender wants to minimise the worst-case probability. It is important to define the distance between the adversarial distribution and our model distribution as this determines which ambiguity set we consider. The traditional Wasserstein distance is not suitable as it does not contain any temporal information, i.e., it uses the future information which we should not know. We will start with the simple optimal transport and then move to the adapted optimal transport, in particular adapted Wasserstein distance.