Tue, 12 May 2026
15:30
L4

A generalization of elliptic curves to higher dimensions

Valery Alexeev
(University of Georgia)
Abstract
Of course, there are many generalizations of elliptic curves. The one we consider here is a certain class of n-dimensional Calabi-Yau hypersurfaces in a weighted projective space, naturally associated with the Sylvester sequence $2,3,7,43,...,s_n$. The moduli space of such hypersurfaces is a weighted projective space itself. The case of $n=1$ for the Sylvester numbers 2,3 is the familiar case of elliptic curves in the Weierstrass form, and its compactified moduli space is the weighted projective line $P(4,6)$. 
 
For any n, we prove that the moduli space of pairs $(X,D)$ of such Calabi-Yau hypersurfaces $X$ augmented with a hyperplane $D$ at infinity is a connected component of the KSBA moduli space of stable pairs. A side result is a generalization of the theory of elliptic surfaces to higher dimensions. Based on https://arxiv.org/abs/2511.16562.
Mon, 15 Jun 2026
14:15
L4

Mass in almost Kähler geometry

Partha Ghosh
(IMJ-PRG/Sorbonne Université)
Abstract

In this talk, I present an explicit formula for the ADM mass of asymptotically locally Euclidean (ALE) almost Kähler manifolds. The formula expresses the mass in terms of the total Hermitian scalar curvature and topological data associated with the underlying almost complex structure, extending a result of Hein and LeBrun in the Kähler ALE case. The proof is based on a spin-c adaptation of Witten's proof of the positive mass conjecture in the spin case and is therefore distinct from previous complex-geometric methods. In dimension 4, I show that one can prove a positive mass theorem and a Penrose-type inequality for asymptotically Euclidean (AE) almost Kähler manifolds using this formula.

Thu, 26 Mar 2026

11:00 - 13:00
L3

Mathematics behind perturbative quantisation of gauge theories on curved spacetimes

Kasia Rejzner
(University of York)
Abstract
In this talk I will briefly introduce the framework of perturbative algebraic quantum field theory (pAQFT), which is a mathematically rigorous formulation of perturbative QFT that works on a large class of Lorentzian manifolds (globally hyperbolic ones). Then I will focus on the problem of quantisation of gauge theories, which is performed using the Batalin-Vilkovisky (BV) framework. I will also discuss the connection to the factorization algebras framework of Costello and Gwilliam.
 


 

Hilary Term 2026 Student Feedback - You Said, We Did!

We're always looking to improve the way things work in the Maths Institute for our students. This term, we've received some very useful student feedback, and have managed to implement some changes to be made going forward, to make your experience here as worthwhile and enjoyable as possible. 

We'll be sending round an end-of-term email with a full list of changes implemented as a result of your feedback, but for now, here's just one example below of a change we've made!

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Data Science Summer Internship Opportunity

Mercuria

 

Mercuria - a leading global commodities trading firm - is offering a highly selective Data Science Summer Internship for STEM students across all years (undergraduate and postgraduate).

PhD Studentship opportunity at the University of Manchester

A PhD studentship opportunity has arisen in the Department of Mathematics at the University of Manchester. The successful candidate will pursue a PhD in Solution Landscapes and Inverse Problems in the Landau-de Gennes theory for Liquid Crystals.

Café π news - Spring & Summer Menu Refresh

The seasonal hot food menu has arrived, bringing fresh new flavours for the months ahead. 

Enjoy a variety of options including Lamb kofta, BBQ pulled pork bap, black sesame chicken skewer, roast corn, pepper & feta tacos, fish burger with mushy peas, Kung Pao chicken with egg fried rice and more. Only £6.50

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