Mon, 27 Apr 2026
15:30
15:30
L5
Nilpotent Deformation Theory
Sofia Marlasca Aparicio
((Mathematical Institute University of Oxford))
Abstract
Deformation theory studies how varieties and other algebro-geometric objects vary in families. A central part of the subject is formal deformation theory, where one deforms over an Artinian base; such deformation problems are governed by Lie algebraic models.
We pose the question of deforming varieties over nilpotent but not necessarily Artinian bases. These turn out to be classified by the same Lie algebraic models plus some topological structure. More precisely, we will consider partition Lie algebras in the category of ultrasolid modules, a variation of the solid modules of Clausen and Scholze that give a well-behaved category akin to topological modules.
To approach this result, we decompose deformation problems into n-nilpotent layers. Each of these layers is individually easier to understand, and is classified by simpler variants of partition Lie algebras.
Are you a UK-registered student with an interest in the future of pensions and long-term saving? If so, our Student Essay Competition for a prize of up to £3,000 is open for entries!
Find out more below, and apply here: https://aca.org.uk/aca-75th-anniversary-future-of-pensions-student-essay-competition-entry-form/
The 
Nightline is an independent listening, support, and information service run for students, by students.Would you be interested in some work teaching 12-14 year olds that that are interested in Science and Technology in Greater London in June and July?
We are looking for students to assist leading activities and answer questions about University at some of our events. Each day is a regional competition designed to raise enthusiasm for STEM subjects and encourage more young people to consider a career in them.
The Centre for Quantum Mathematics at the University of Southern Denmark is advertising a fully funded PhD position with targeted starting date September 1st, 2026 or soon thereafter. Candidates are expected to have obtained their MSc degree in mathematics or mathematical physics by the starting date, but not necessarily at the time of application.
Saïd Business School runs a portfolio of academic pre-university summer schools for students aged 15 to 18, covering a range of subjects including Future Climate Tech Innovators, AI and Machine Learning Pioneers, and Future Entrepreneurs.