Young Researchers’ Meeting

9th October, 5pm

Common Room

Introductory presentations from current PhD students.

16th October, 5pm

Common Room

23rd October, 5pm

Common Room

Introductory presentations from new first year PhD students.

30th October, 5pm

Common Room

Speaker: Ruairi GarrettLink opens in a new window

Title: Genealogy of large logistic branching processes

Abstract: Logistic branching processes have been introduced as a simplified model of a population competing for resources. Genetic drift in such populations was recently studied (Forien '25) and shown to converge to the family of so called Beta-Fleming Viot processes. In this talk we will give some background on (probabilistic) population genetics, and discuss an extension of the result of Forien to obtain the behaviour of the genealogy relating finite samples taken from the population at some fixed time horizon. These are shown to converge to Kingman, Beta(2-alpha, alpha) and Bolthausen-Sznitman coalescents. Based on joint work with Julio Ernesto Nava Trejo.

6th November, 5pm

Common Room

Speaker: Leonardo BaggianiLink opens in a new window

Title: Optimal Dynamic Fees in Automated Market Makers

Abstract: Automated Market Makers (AMMs) are emerging as the most popular decentralized trading platforms. In this study, we examine the problem of determining optimal dynamic fees in a Constant Function Market Maker (CFMM). We assume that order arrivals in the market depend on the distance between the oracle price and the exchange rate within the pool. We demonstrate that if the oracle price is close to its fundamental value, the model admits a closed-form solution. Furthermore, we highlight the key features of our model and compare the optimal strategy against different fee structures.

13th November, 5pm

Common Room

Speaker: Alexander KentLink opens in a new window

Title: Some practical advances in Local Differential Privacy

Abstract: Local Differential Privacy, which you either have heard a lot about already, or will hear a lot about in the future, is a popular framework for data anonymisation used in academia, in industry and by governments. Despite this, at times there are issues with implementing it, due to either shortcomings of the framework in certain contexts, or a more theoretical and less methodological focus on developed procedures. In this talk, I will cover two main topics I have researched so far as part of my PhD, User-Level Local Differential Privacy, and private permutation testing procedures. I will give high-level overviews of these topics, and motivate the techniques we have developed to help further the practical implementation of Local Differential Privacy.

20th November, 5pm

Common Room

Speaker: Usman LadanLink opens in a new window

Title: An introduction to branching processes and their approximations

Abstract: In this talk, we introduce branching processes and discuss the behaviour of both discrete and continuous time models. These objects have applications in a wide variety of areas such as biology and physics. We will also discuss how to efficiently approximate these objects via mutation/selection type schemes.

27th November, 5pm

Common Room

Speaker: Juan Pablo Chávez OchoaLink opens in a new window

Title: Descent from infinity of Reflected Brownian motion in unbounded, generalized parabolic domains

Abstract: We study the long-term behaviour of a continuous reflected diffusion on an unbounded, horn-shaped domain with asymptotically oblique reflection at the boundary. We establish a criterion for uniform ergodicity in terms of the geometry of the boundary and show that the diffusion has infinity as an entrance boundary whenever it is uniformly ergodic. We further determine the asymptotic speed of the diffusion and its local time as it descends from infinity. Quantitative upper and lower bounds are obtained for the tails of the invariant distribution, for the total variation distance to stationarity, and for the tails of the return times to compact subsets of the domain. These estimates reveal phase transitions in the ergodic behaviour of the process, depending on the geometry of the boundary: ergodicity passes from sub-exponential to exponential and ultimately becomes uniform.

4th December, 5pm

Common Room

Speaker 1: Yunus CobanogluLink opens in a new window

Title: Implicit Bias: How Gradient Dynamics Choose Solutions

Abstract: Training overparameterized machine learning models with gradient descent often yields many parameter settings that fit the data exactly. Yet optimization reliably converges to a particular one. This talk introduces implicit bias—the effective regularization induced by the parameterization—and explains how gradient-flow dynamics select among perfect-fit solutions, with implications for generalization and algorithm design. This fairly recent theory was developed to clarify why simplified deep-learning models work in practice.

Speaker 2: Edwin TangLink opens in a new window

Title: When the Sample Mean Fails: A Median-Based Approach to Change Point Detection in Noisy Data

Abstract: We’re all taught early on to use the sample mean to estimate the true mean of a distribution—but is that always the best choice? In this talk, we’ll explore situations where the sample mean works well, and where it starts to break down. Using the powerful toolkit of concentration inequalities (you may already know Markov’s inequality), we’ll discuss why the alternative estimators, such as the median and RUME estimator (Prasad et al 2020), can be more reliable. Finally, I will discuss how this is applicable in univariate change point detection and present our results so far on what is the optimal detection delay given some signal strength size when detecting change points under contaminated and/or heavy-tailed data.

11th December, 5pm

Common Room

(TBC) Small Talks