Liam Urban

I am a doctoral student in the Vienna School of Mathematics at the University of Vienna, supervised by David Fajman and co-supervised by Michael Eichmair. My doctoral research is funded by a DOC-scholarship from the Austrian Academy of Sciences and by the FWF START-Project Y963.

Contact Information

Faculty of Mathematics
University of Vienna
Oskar-Morgenstern-Platz 1
1090 Vienna, Austria

Email: liam.urban@univie.ac.at
ORCID: 0000-0001-9185-9627
University webpage: here
Pronouns: he/they

Research

Preprints and Publications

(Preprint) On the past maximal development of near-FLRW data for the Einstein scalar-field Vlasov system (with David Fajman),
arxiv:2402.08544 (uploaded February 2024)
(Preprint) Cosmic Censorship near FLRW spacetimes with negative spatial curvature (with David Fajman),
arXiv:2211.08052 (first uploaded November 2022, revised version uploaded July 2023). Accepted for publication in Analysis & PDE
Blow-up of waves on singular spacetimes with generic spatial metrics (with David Fajman),
Letters in Mathematical Physics 112, 42 (2022)
Space versus energy oscillations of Prufer phases for matrix Sturm-Liouville and Jacobi operators (with Hermann Schulz-Baldes),
Electronic Journal of Differential Equations, Vol. 2020 (2020), No. 76, pp. 1-23

Presentations

On the past maximal development of near-FLRW data for the Einstein scalar-field Vlasov system,
October 2024, Seminar on Mathematical General Relativity, Sorbonne University
On the past maximal development of near-FLRW data for the Einstein scalar-field Vlasov system,
May 2024, Thematic Program Nonlinear Waves and Relativity, Erwin Schrödinger International Institute for Mathematics and Physics
On stable Big Bang formation,
May 2024, Vienna Geometric Analysis Seminar, University of Vienna
On the past maximal development of near-FLRW data for the Einstein scalar-field Vlasov system,
March 2024, Seminar Differential geometry and general relativity, Stockholm Mathematics Centre
Stable Big Bang formation for the Einstein scalar-field Vlasov system,
February 2024, 14th Central European Relativity Seminar, University of Tübingen
Strong Cosmic Censorship near FLRW spacetimes with negative spatial curvature,
May 2023, 13th Central European Relativity Seminar, Stockholm University
Strong Cosmic Censorship near FLRW spacetimes with negative spatial curvature,
November 2022, Vienna Relativity seminar, University of Vienna
Nonlinear stability of Big Bang formation for FLRW solutions with hyperbolic spatial geometry within the Einstein scalar-field system,
EWM-EMS Summer School: The Cauchy Problem in General Relativity, Mittag-Leffer Institut Djursholm
Nonlinear stability of Big Bang formation for FLRW solutions with hyperbolic spatial geometry within the Einstein scalar field system,
April 2022, Young PDEs Symposium, University of Vienna
Blow-up of geometric waves towards Big Bang singularities,
March 2022, Mini-Lecture Series on Waves, Masterclass Mathematical Physics, University of Vienna
Blow-up of waves on Friedmann-Lemaitre-Robertson-Walker spacetimes with arbitrary Riemannian spatial metric,
February 2021, 11th Central European Relativity Seminar, online

Education

since October 2021: Doctoral student in the Vienna School of Mathematics at the University of Vienna
October 2019 to July 2021: Master of Science in Mathematics at the University of Vienna, thesis supervised by David Fajman
October 2016 to July 2019: Bachelor of Science in Mathematics at the FAU Erlangen-Nürnberg, thesis supervised by Hermann Schulz-Baldes

Teaching

Tutorial: School mathematics arithmetics and algebra
Winter 2023, Tutor
School mathematics: applied mathematics
Summer 2023, Tutor
Mathematics for civil and environmental engineers II
Summer 2021, TU Vienna, Tutor
Mathematics for civil and environmental engineers I
Winter 2019, Summer 2020 and Winter 2020, TU Vienna, Tutor
Analysis II
Analysis I

Awards and Scholarships

since 2022: Doctoral scholarship (DOC-Stipendium) from the Austrian Academy of Sciences
2021: Winner of the Alfred-Wehrl-Prize in Theoretical and Mathematical Physics
since 2021: Doctoral scholarship from the Studienstiftung des deutschen Volkes (German Academic Scholarship Foundation)
2018 to 2021: Member of the Max-Weber-Program