Wed, 21 May 2025
16:00
L6

(Seminar cancelled) Generalized Tate-Shafarevich groups over function fields

Tamás Szamuely
(Università degli studi di Pisa)
Abstract

Given a smooth geometrically connected curve C over a perfect field k and a smooth commutative group scheme G defined over the function field K of C, one can consider isomorphism classes of G-torsors locally trivial at completions of K coming from closed points of C. They form a generalized Tate-Shafarevich group which specializes to the classical one in the case when k is finite. Recently, these groups have been studied over other base fields k as well, for instance p-adic or number fields. Surprisingly, finiteness can be proven in some cases but there are also quite a few open questions which I plan to discuss  in my talk.

Mon, 09 Jun 2025
15:30
L3

Well-Posedness and Regularity of SDEs in the Plane with Non-Smooth Drift

Prof. Olivier Menoukeu Pamen
(University of Liverpool)
Abstract

Keywords: SDE on the plane, Brownian sheet, path by path uniqueness, space time local time integral, Malliavin calculus

 

In this talk, we discuss the existence, uniqueness, and regularisation by noise for stochastic differential equations (SDEs) on the plane. These equations can also be interpreted as quasi-linear hyperbolic stochastic partial differential equations (HSPDEs). More specifically, we address path-by-path uniqueness for multidimensional SDEs on the plane, under the assumption that the drift coefficient satisfies a spatial linear growth condition and is componentwise non-decreasing. In the case where the drift is only measurable and uniformly bounded, we show that the corresponding additive HSPDE on the plane admits a unique strong solution that is Malliavin differentiable. Our approach combines tools from Malliavin calculus with variational techniques originally introduced by Davie (2007), which we non-trivially extend to the setting of SDEs on the plane.


This talk is based on a joint works with A. M. Bogso, M. Dieye and F. Proske.

Flat-space limit of defect correlators and stringy AdS form factors
Alday, L Zhou, X Journal of High Energy Physics volume 2025 issue 3 (25 Mar 2025)
Exploring the relationship between vascular remodelling and tumour growth using agent-based modelling
Fan, N Bull, J Byrne, H
Ringel’s tree packing conjecture in quasirandom graphs
Keevash, P Staden, K Journal of the European Mathematical Society (21 Feb 2025)

A film of the Hyndman exhibition by Evan. If you haven't had a look at the exhibition yet, please do. It will add some colour to your life.

Apologies for not updating new starters recently. 

November new starters:

James Harris,  Industry Engagement Officer: S0.16

Sadok Jerad,  PDRA in Mathematical Foundations of Data Science, TopologyS2.29

Torkel Loman, PDRA in Data-Driven Modelling of Collective Cell Behaviour, Mathematical Biology: S4.04

December new starters:

Tessa Bonilha:  Project Manager: S0.19

Mon, 19 May 2025

14:00 - 15:00
Lecture Room 3

Bridging Classical and Modern Computer Vision: PerceptiveNet for Tree Crown Semantic Segmentation

Dr Georgios Voulgaris
(Department of Biology, Oxford University)
Abstract

The accurate semantic segmentation of individual tree crowns within remotely sensed data is crucial for scientific endeavours such as forest management, biodiversity studies, and carbon sequestration quantification. However, precise segmentation remains challenging due to complexities in the forest canopy, including shadows, intricate backgrounds, scale variations, and subtle spectral differences among tree species. While deep learning models improve accuracy by learning hierarchical features, they often fail to effectively capture fine-grained details and long-range dependencies within complex forest canopies.

 

This seminar introduces PerceptiveNet, a novel model that incorporates a Logarithmic Gabor-implemented convolutional layer alongside a backbone designed to extract salient features while capturing extensive context and spatial information through a wider receptive field. The presentation will explore the impact of Log-Gabor, Gabor, and standard convolutional layers on semantic segmentation performance, providing a comprehensive analysis of experimental findings. An ablation study will assess the contributions of individual layers and their interactions to overall model effectiveness. Furthermore, PerceptiveNet will be evaluated as a backbone within a hybrid CNN-Transformer model, demonstrating how improved feature representation and long-range dependency modelling enhance segmentation accuracy.

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