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.
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Mon, 15 Jun 2026
14:15
L4

TBA

Partha Ghosh
(IMJ-PRG/Sorbonne Université)
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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!

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Data Science Summer Internship Opportunity

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PhD Studentship opportunity at the University of Manchester

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