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PhD position in noncommutative geometry and singular foliations

University of Amsterdam Faculty of Science
Self-funded ⏰ Closing Soon 🎓 Mathematics mathematical physics noncommutative geometry singular foliations groupoids manifolds mathematics research algebra geometry

Explore the mathematical frontiers of singular foliations with noncommutative geometry techniques. Join a collaborative team to develop innovative invariants and shape your own research directions under expert supervision.

AI-generated overview

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Why This Research Matters

This research advances our fundamental understanding of singular foliations, which are pivotal in many areas of mathematics, including analysis and mathematical physics. Developing new invariants can lead to breakthroughs in how geometric structures are understood and applied, potentially influencing related scientific disciplines.

Wiskunde Lie groupoids Dubrovin-Zhang hierarchies Hopf algebroids Poisson pencils Deformation quantization Index theorems

Project Description

Project Overview

The PhD project focuses on developing novel invariants of singular foliations, structures that play an important role in contemporary mathematics. Employing methods from noncommutative geometry, groupoids, and analysis on manifolds, the research aims to explore these complex mathematical objects deeply.

What You Will Do

As a member of a research team under Dr. Hessel Posthuma, the candidate will initially work on defined subprojects to build expertise and research skills. They will collaborate closely with another PhD student and Dr. Peter Hochs at Radboud University Nijmegen. Responsibilities include conducting innovative research, publishing findings, presenting at international conferences, and participating in seminars.

Expected Outcomes

The study aims to provide new mathematical invariants that enrich the theory of singular foliations and contribute to broader areas such as noncommutative geometry. The candidate will complete and defend a PhD thesis based on original research over four years.

Why This Matters

Singular foliations are increasingly significant in many fundamental mathematical disciplines. Developing new invariants will advance mathematical knowledge and may impact related scientific fields where geometry and analysis are relevant.

Entry Requirements

Master’s degree in mathematics (to be completed before start) or a related degree with strong mathematical component. Creativity, motivation, and excellent English communication skills. Ability to work independently and in a team. Knowledge of noncommutative geometry is a plus.

How to Apply

Apply online via the application button before June 1, 2026. For questions, contact Dr. Hessel Posthuma via h.b.posthuma@uva.nl.

Eligibility

UK/Home
EU
International

Supervisor Profile

DH
Dr. Hessel Posthuma
University of Amsterdam, Faculty of Science

Dr. Hessel Posthuma is a mathematician specializing in noncommutative geometry and its applications to singular foliations and groupoids. His work often bridges algebra, geometry, and analysis, contributing to foundational areas in mathematics. He leads research projects within the Korteweg-de Vries Institute and collaborates internationally, fostering a dynamic research environment for PhD candidates.

Key Publications

2012 91 citations
A polynomial bracket for the Dubrovin-Zhang hierarchies
Introduces a polynomial bracket structure for the Dubrovin-Zhang integrable hierarchies enhancing the mathematical understanding of these systems.
2010 67 citations
Geometry of orbit spaces of proper Lie groupoids
Explores geometric properties of orbit spaces associated with proper Lie groupoids, advancing the field of differential geometry.
2012 55 citations
On deformations of quasi-Miura transformations and the Dubrovin–Zhang bracket
Studies deformations of quasi-Miura transformations and their effects on the Dubrovin-Zhang bracket, contributing key insights into integrable systems.
2011 48 citations
The cyclic theory of Hopf algebroids
Develops cyclic theory concepts for Hopf algebroids, enriching the theory of noncommutative geometry.
2004 44 citations
Homology of formal deformations of proper étale Lie groupoids
Investigates the homological properties of formal deformations of proper étale Lie groupoids, enhancing algebraic and differential geometric frameworks.

Research Contributions

Developed polynomial bracket structures for Dubrovin-Zhang hierarchies.
Provided a new mathematical framework that facilitates the study of integrable systems and their deformations.
Advanced the geometry of orbit spaces related to proper Lie groupoids.
Improved understanding of geometric and topological properties in differential geometry with applications to mathematical physics.
Analyzed cyclic theory for Hopf algebroids in noncommutative geometry.
Contributed to the foundation of algebraic structures used in quantum groups and noncommutative spaces.
Studied homology of formal deformations of proper étale Lie groupoids.
Enhanced theoretical tools for deformation theory in geometry and mathematical physics.

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