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) Quiescent Big Bang formation in 2+1 dimensions,
arXiv:2412.03396 (uploaded December 2024)
- (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,
February 2025, General Relativity Seminar, Harvard University (online)
- Quiescent Big Bang formation in polarized U(1)-symmetry,
January 2025, 15th Central European Relativity Seminar, Radboud University
- 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
Summer 2019, FAU Erlangen-Nürnberg, Tutor
- Analysis I
Winter 2018, FAU Erlangen-Nürnberg, Tutor
Awards and Scholarships