Albachiara Cogo
I am a PhD student in the Research Group of Geometrische Analysis, Differentialgeometrie und Relativitätstheorie at the University of Tübingen under the supervision of Gerhard Huisken. As a Master's student, I took part in the Double Degree Program between the University of Trento and the University of Tübingen, writing my thesis under the supervision of Carla Cederbaum and Lorenzo Mazzieri.
Currently ( Oct-Dec 2023 ), I am on a research stay funded by the DAAD in the Group of Gravitational Physics at the University of Wien under the supervision of Piotr T. Chruściel.
My interests are Geometric Analysis and Nonlinear PDEs, in particular with regard to applications to General Relativity:
Maximal Surfaces in asymptotically flat spacetimes, Quasilinear Elliptic PDEs.
Ancient Solutions to Fully Nonlinear Geometric Flows, Parabolic PDEs.
Equipotential Photon Surfaces in static spacetimes, Potential Theory and Robinson's method.
Problems related to Metrics with Lower Regularity in Geometric Analysis and Causality Theory, Yamabe Problem and Lorentzian Length Spaces.
Gluing Problems for Initial Data Sets, Elliptic PDEs.
Preprints
Rotational symmetry of ancient solutions to fully nonlinear curvature flows (with Stephen Lynch and Olivia Vičánek Martínez), arXiv:2310.08301 (submitted)
Black Hole and Equipotential Photon Surface Uniqueness in 4-dimensional Asymptotically Flat Electrostatic Electro-Vacuum Spacetimes (with Stefano Borghini and Carla Cederbaum), arXiv:2401.05253 (submitted)
Uniqueness of static vacuum asymptotically flat black holes and equipotential photon surfaces in (n+1) dimensions à la Robinson (with Carla Cederbaum, Benedito Leandro and João Paulo dos Santos), arXiv:2403.14422
Uniqueness of equipotential photon surfaces in 4-dimensional static vacuum asymptotically flat spacetimes for positive, negative, and zero mass - and a new proof of the Willmore inequality (with Carla Cederbaum and Axel Fehrenbach), in preparation
Selected Talks
They are linked to the correspondent videos, when available.
"On ancient solutions to Fully Nonlinear Curvature Flows" at the Vienna Geometric Analysis Seminar (November 2023), Universität Wien, Vienna.
"Maximal Surfaces over exterior domains and approximation of Null Hypersurfaces" at the Geometric Analysis, Differential Geometry and Relativity Seminar (February 2023), Institut für Mathematik Universität Potsdam and Universität Tübingen and at the Workshop: Mass, the Einstein Constraint Equations and the Penrose inequality Conjecture (September 2023), Simons Center for Geometry and Physics, New York. | Video |
"Introduction to Mean Curvature Flow" at the BIGW: Geometric Flows and related topics (July 2023), Inverness (UK).
"Uniqueness of black holes and equipotential photon surfaces in (n+1)-dimensional static vacuum via Robinson’s approach" at the Interdisciplinary Jr Scientists Workshop: Mathematical General Relativity (February 2023), Wildberg (Germany) and at the 13th Central European Relativity Seminar (April 2023), KTH Stockholm, Stockholm. | Video |
"On Maximal Surfaces in Minkowski and asymptotically flat spacetimes", Minicourse (August 2022) at Universitade Federal de Goiàs, Goiania (Brasil).
"Uniqueness of Equipotential Photon Surfaces in Electrovacuum", at the 12th Central European Relativity Seminar (February 2022) Hungarian Academy of Science, Budapest and at the EWM-EMS Summer School “The Cauchy Problem in General Relativity” (June 2022) Mittag-Leffer Institut, Stockholm and at the UnB Geometry Seminar (August 2022) Universitade de Brasilia, Brasilia and at the UFC Geometric Analysis Seminar (September 2022) Universitade Federal do Cearà, Fortaleza (Brasil). | Video |
"Uniqueness of Photon Spheres in Geometrostatic Spacetimes via Potential Theory" at the 11th Central European Relativity Seminar (February 2021), online. | Video |
University of Tübingen
University of Trento
Teaching
Proseminar Kurven und Flächen (WS 22).
Exercise Classes of Nonlinear Elliptic PDEs in Minimal Surfaces Theory (SS 22).
Exercise Classes of Geometry in Physics (WS 21).
Tutor in Mathematical Relativity (SS 20).
Exercise Classes of Riemannian Geometry (SS 20).
Tutor in Mathematical Analysis (Calculus 1-2) for students with special needs in engineering (SS 19).
Tutor in Mathematical Analysis (Calculus 1-2) for Mathematics and Physics (WS 18 - SS 19).
Events
I am co-organizer of the workshop
BIGW V: "Mathematical General Relativity" (8th-12th July 2024).
The applications are open! Fill out the form HERE.
University Service
I have been elected as Eingeschriebene Doktorandin in the Fakultätsrats der Mathematisch-Naturwissenschaftliche Fakultät (Council of the Faculty of Mathematics and Natural sciences) at the University of Tübingen for the Academic Year 2023/2024.
I have been elected as a member (Vice President 23/24) of the Postgraduate Convention of the Faculty of Science at the University of Tübingen for the Academic Years 2022/2023 and 2023/2024.
I have been Member of ESN (Erasmus Student Network) at the University of Trento in 2019.
Contact me at
albachiara.cogo@uni-tuebingen.de
Auf der Morgenstelle 10, 72076, Tübingen (DE)