Studying Need advice for research subjects in both topological and general relativity

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A theoretical physics master's student in China is seeking to study abroad in France, specifically looking for a thesis topic that aligns with their interest in topological aspects of general relativity (GR). Despite a background in GR and mathematical skills related to wave equations, the student finds limited resources that combine topology with GR, as most topological research focuses on quantum materials. Mentors suggest consulting professors familiar with GR and topology, and recommend broadening the search to include institutions that may not specialize exclusively in GR but have relevant research. Notable French institutions mentioned include the Laboratoire d’Annecy-le-Vieux de Physique Theorique, Laboratoire Univers et Theories, Ecole Normale Superieure, Institut des Hautes Etudes Scientifiques, and the Astroparticle and Cosmology Laboratory, all of which explore intersections between GR and topology.
Atlantis_33399
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I'm a theoretical physics student working on my master's degree in China and trying to seize the opportunity to study abroad, especially in France. It's so frustrating that I still cannot find a subject or thesis that satisfies both my interests and learning goals.

Here's the thing. I major in GR, and studying with my tutor taught me some mathematical skills related to wave equations. However, as time went by, I found my true interest is definitely NOT in analytic or numerical relativity, but in the topological aspects related to my master's project.

I mean, the topological invariants. However, as far as my retrieval capability can reach, I can barely find something that is both topological and generally relativistic. Most topological studies focus on quantum materials.

Appreciate your generous advice!

MENTOR NOTE: minor edits to improve post clarity.
 
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Have you consulted with your profs especially those tuned to GR and/or Topology?

You may have to relax your desire to be schools that focus on GR or schools that focus in using topology in an applied manner. Its more likely that schools that have a GR department will have someone who is focused on GR and Topology.

Going at it from the Topology side may not be as fruitful a search.

What French schools have you identified that specialize in GR?

Have you considered schools in other countries?
 
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Here’s a list of French institutions studying General Relativity (GR) and topology. I don't know how useful it will be in your search. It seems you may have to read between the lines based on the research done to find the right fit for your interests.

Laboratoire d’Annecy-le-Vieux de Physique Theorique (LAPTh)
Focuses on integrability in gauge theories, field theory, and topology. Research includes Chern-Simons theories, Deligne-Beilinson cohomologies, and geometric quantization, exploring the interplay between GR and topology.

Laboratoire Univers et Theories (LUTH)
Part of the Observatoire de Paris, this lab conducts research in numerical relativity, including the 3+1 formalism and topological considerations in GR equations.

Ecole Normale Superieure (ENS) Department of Physics
Offers advanced courses and research opportunities in GR, often involving topological aspects of gravitational theories. ENS combines strong traditions in mathematics and physics.

Institut des Hautes Etudes Scientifiques (IHES)
Home to notable researchers like Thibault Damour. IHES supports theoretical physics and mathematics research, including topological facets of GR.

Astroparticle and Cosmology Laboratory (APC)
Researches high-energy astrophysics, cosmology, and gravitation, with work touching on the intersection of GR and topology.
 
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Hey, I am Andreas from Germany. I am currently 35 years old and I want to relearn math and physics. This is not one of these regular questions when it comes to this matter. So... I am very realistic about it. I know that there are severe contraints when it comes to selfstudy compared to a regular school and/or university (structure, peers, teachers, learning groups, tests, access to papers and so on) . I will never get a job in this field and I will never be taken serious by "real"...
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