The Singularity Theory Problem List
We collect a list of problems that involve singularity theory. We want to serve as an inspiration to work on new problems, build connections between areas as well as make them visible to other researchers.
Anyone is encouraged to contribute: PhD students, postdocs, and senior mathematicians. We welcome any topic related to Singularity Theory, including but not limited to:
- Singularities of maps (Thom-Mather theory, density problems, Thom polynomials, etc.),
- Singular varieties (normal surface singularities, resolution of singularities, combinatorial aspects, etc.),
- Low-dimensional topology,
- Symplectic and contact topology,
- Dynamical systems,
- Geometry of singularities (generic geometry),
- Other geometry categories (Lipschitz, tropical, O-Minimal, etc.),
- Characteristic classes,
- Computational aspects of singularities,
- Applications to physics and other sciences,
- Stratification theory.
How to contribute
Without the involvement of the community this project will die, so we invite you to contribute in two possible different ways: add problems to the list (several authors are allowed) and/or organise a brain-storming seminar. Feel free to send an email and ask any question you may have.
Write problems:
- Check if the problem has been posted already in the preliminary list. This list contains the title and the author(s) of the contribution, if you think your problem may be covered by someone you can ask the author(s) directly or send an email to roberto.gimenez@uv.es.
- Get inspiration in the seminars that are mentioned below.
- Use the available templates.
- Follow the style guidelines. Available in the comments of both templates (.tex files).
- Send the PDF, LaTeX and necessary files by email with subject "Problem to List" and your name to roberto.gimenez@uv.es
Organise a seminar:
- The goal is to have an itinerant seminar (if possible, online and in-person) running through the different groups in the world where one or more people introduce a topic or problem, and the attendees suggest more related problems.
- Round table discussions during conferences are a great chance to do them as well.
- Afterwards, the organizers are encouraged to write a small summary record of the problems that were suggested in a way that any expert can understand the problem (no need for details) and send it to roberto.gimenez@uv.es with subject "Seminar to List" and the city where it was held.
- Attendees, and also other people, can contribute to the problem list selecting any suggested problem(s) during the seminar. The selection can be made during the seminar, in which case the summary record has to include the (future) author(s) of the problem(s).