Contact

Dr. Thomas Rot

Assistant professor

Center for topology and applications Amsterdam
Department of Mathematics
Vrije Universiteit Amsterdam

De Boelelaan 1111
1081 HV, Amsterdam

Room: 9A-59 (NU BUILDING)
Phone: (+31) 20 59 84436
email: spam@vu.nl (change spam to t.o.rot)
Office hours: By appointment

News

• (1-09-2024) The website of the Center of Topology and Applications Amsterdam (CTA2) has been launched
• (1-06-2024) My expository article "Ropes have an even number of ends" has appeared in the Nieuw Archief voor Wiskunde .
• (02-04-2024) I have been appointed treasurer of the KWG (Royal Dutch Mathematical Society)
• (26-03-2024) My Phd student Michael Jung and I just uploaded a revised version of our first joint paper A geometric computation of cohomotopy groups in co-degree one to the arxiv. It streamlines the argument about framings over surfaces.
• (14-03-2024) New preprint. Construction of invariant features for time-domain EEG/MEG 2 signals using Grassmann manifolds, Joint work with Rikkert Hindriks , Michel J.A.M. van Putten , Prejaas Tewarie
• (18-07-2023) My postdoc Lauran Toussaint and I just uploaded our first joint paper Non-linear proper Fredholm maps and the stable homotopy groups of spheres to the arxiv.

The DDT&G seminar

Together with Alvaro del Pino Gomez , Federica Pasquotto , I organize the Dutch Differential Topology & Geometry seminar (DDT&G). More information about the seminar can be found here . I strongly encourage master students with an interest in topology and/or geometry to attend!

Arbeitsgemeinschaft differential topology

This is a German style seminar series. Sometimes we will read papers/books together, and sometimes participants will present their work. The topic is broadly in (infinite dimensional) differential topology. Send me an email if you want to participate! This offer extends to advanced bachelor students and master students.

My group

Postdoc

• Lauran Toussaint

PhD

• Michael Jung

Publications

Preprints

• Construction of invariant features for time-domain EEG/MEG 2 signals using Grassmann manifolds, Joint work with Rikkert Hindriks , Michel J.A.M. van Putten , Prejaas Tewarie
• Non-linear proper Fredholm maps and the stable homotopy groups of spheres
Joint work with Lauran Toussaint

• A geometric computation of cohomotopy groups in co-degree one
Joint work with Michael Jung

• The relative cup-length in local Morse cohomology.
Joint work with Maciej Starostka and Nils Waterstraat

Papers

• The homotopy classification of proper Fredholm maps of index one.
Joint work with Alberto Abbondandolo
In: Topological Methods in Nonlinear Analysis (online). 30-01-2022, s. 1-37. DOI 10.12775/TMNA.2020.068.
(Preprint link)
• On the transitivity of the group of orbifold diffeomorphisms.
Joint work with Federica Pasquotto
In: Transformation Groups, Volume 28, pages 973–985, (2023).
(Preprint link)
• Degree theory for orbifolds.
Joint work with Federica Pasquotto
In: Topology Appl. 282 (2020), 107326.
(Preprint link)

• Homotopy classes of proper maps out of vector bundles.
In: Arxiv der Mathematik 114(1), 107-117.
(Preprint link)
• On the homotopy classification of proper Fredholm maps into a Hilbert space
Joint work with Alberto Abbondandolo
In: J. Reine Angew. Math. (ahead of print)
(Preprint link)

• Homotopy invariance of the Conley index and local Morse homology in Hilbert spaces
Joint work with Marek Izydorek , Maciej Starostka, Marcin Styborski , and Rob Vandervorst .
In: Journal of Differential Equations Volume 263, Issue 11.
(Preprint link)
• On periodic orbits in cotangent bundles of non-compact manifolds.
Joint work with Jan Bouwe van den Berg , Federica Pasquotto , and Rob Vandervorst .
In : Journal of Symplectic Geometry vol 14 number 4 pp 1145-1173 (2016).
(Preprint link)
• The Morse-Bott inequalities, orientations, and the Thom isomorphism in Morse homology.
In: Comptes Rendus Mathematique (2015-08-31). doi
(Preprint link)
• Functoriality and duality in Morse-Conley-Floer homology
Joint work with Rob Vandervorst .
In: Journal of Fixed Point Theory and Applications (2015-04-04). DOI: 10.1007/S1178401502236
(Preprint link)

• Morse-Conley-Floer Homology.
Joint work with Rob Vandervorst
in: J. Topol. Anal. 06, 305 (2014). DOI: 10.1142/S1793525314500174.
(Preprint link)

• Statistical modelling of pre-impact velocities in car crashes .
Joint work with Kager, W. , Kryven, I., Myerscough, K.W. , Van Opstal, T.
in: Proceedings of the Seventy-ninth European Study Group Mathematics with Industry (pp. 133-148)

Books

• Proceedings of the Seventy-ninth European Study Group Mathematics with Industry
Editors: Planqué, R., Bhulai, S., Hulshof, J., Kager, W., Rot, T.O.

Thesis

• Morse-Conley-Floer Homology
T.O. Rot, PhD thesis
A short presentation ("het lekenpraatje") for my defense is on youtube

Popular Science.

• Ropes have an even number of ends, in: Nieuw Archief voor Wiskunde 01-06-2024.
• Chaos en Dynamica
Joint with Sophia de Jong Pythagoras 59-2

Teaching

All courses are accessible through canvas . I am happy to supervise bachelor and master thesis projects and feel free to contact me. I am willing to supervise on most topics in algebraic or differential topology. You can get inspiration from the theses I have supervised in the past, or go through recordings of the DDT&G seminar .

Master students

Current

• Kfir Fleet (Leiden

Graduated

• Oscar Koster (Groningen): An exploration of sub-Riemannian orbifolds , joint supervision with Marcello Seri .
• Harold Nieuwboer: The differential topology of symplectic toric manifolds .

Bachelor students

Current

• Iris Ran.

Graduated

• Ábel Juhász, "Construction of Eilenberg-Maclane spaces", joint supervision with Lauran Toussaint
• Madeleine Gignoux: "Algorithms for Computing Fourier Transforms on Finite Groups " and Matlab code
• Ingrid Karnik Hinks: Geodesics in SL2(R).
• Carmen Oliver Huidobro: Discussion of the Square Peg Problem.
• Ramon Leiser: "Subriemannian geometry of the p,q Hopf actions"
• Orin Habich: "De Pontryagin-Thom constructie". The thesis (in Dutch) and the final presentation

Slides

Here are some of my recent slides. Other ones are available on request.

• Differential topology in infinite dimensions at the GQT colloquium.
• Een touw heeft een even aantal uiteinden
A popular science talk for the KWG wintersymposium .

• Proper Fredholm mappings and the stable homotopy groups of spheres
A 50 minute talk on non-linear Fredholm mappings at the conference "Prospects in Geometry and Global Analysis".

• Most ropes have two ends
A 60 minute colloquium talk on degree theory, in the classical setting as well as on orbifolds.

• Homotopy classes of proper maps
a 60 minute talk on proper homotopy classes of maps at the conference "Floer Theory and Hamiltonian Dynamics of Non-Compact Hypersurfaces".

• Proper homotopy classes of Fredholm mappings
A 30 minute talk at the conference on manifolds, groups and homotopy on skye

• Proper homotopy classes of Fredholm mappings
A 45 minute talk at the NDNS+ yearly workshop

• Morse-Conley-Floer homology
A 20 minute talk at the rigidity and flexibility conference in Leiden 2014