Hello! I hope this website finds you well!
about me
My name is Rupadarshi Ray. I am from Balurghat, a town in the northern part of Bengal, India 🇮🇳. I speak Bengali, English and Hindi.
I am a masters in mathematics and am interested in mathematics research. My CV is at https://rupadarshiray.github.io/CV/RayCV.pdf.
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now
I graduated from IISER Mohali with a Masters in Mathematics in June ‘26 after completing my MS thesis in April.
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About this site
This website is an academic curation and journaling; where I document my experience and experiments with mathematics and the theoretical sciences.
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(My) academia
(My) math interests
My primary interests lie in the topics related to the analysis of manifolds: be it geometric, topological, dynamical or analytical. I have invested a lot of time on Riemann surfaces, hyperbolic manifolds and discrete subgroups of during my thesis.
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- my-blackboards
- my-masters-at-iiserm
- my-wiki
- seminars, workshops I attended
- talks that I have given
The highlight of my past year has been my MS thesis.
My MS thesis
path towards rigidity of discrete groups
I started my path towards the rigidity of discrete groups after I attended Summer School on Rigidity of Discrete Groups, June 30 – July 4, 2025 at IISER Mohali.
I started by looking at globally symmetric spaces and the necessary properties of CAT(0) spaces, specially smooth ones which are simply connected Riemannian manifolds of non-positive sectional curvature. These spaces have a well-defined boundary.
The slides for my PRJ501 presentation (after half of my MS thesis) is here.
Afterwards, I started specializing towards topics related to Patterson-Sullivan measures.
Finally I narrowed down my thesis to a narrative that is as follows.
We look at two proofs of Mostow’s rigidity theorem. First one uses the theory of quasiconformal mappings on the sphere following Tukia’s proof of Sullivan’s quasiconformal rigidity theorem. This general result is about quasiconformal rigidity of certain hyperbolic manifolds. If applied to the case of closed or finite volume hyperbolic manifolds, it implies Mostow and Prasad’s rigidity theorem.
Second one considers conformal density on the boundary of hyperbolic, constructed by Patterson and Sullivan, and follows Sullivan’s proof of preservation of cross-ratios almost everywhere with respect to the Patterson-Sullivan measures supported on the limit sets. This result gives us a measurable rigidity of these limit sets: it says that if we have a measurable map between the limit sets of two hyperbolic manifolds, which takes measure zero sets of the Patterson-Sullivan measure to measure zero sets in both directions, then the map preserves the cross-ratios almost everywhere. This quickly produces a conformal between these limit sets. Thus, in short if these limit sets are measurably conjugate then they has be to be conformally conjugate. Again, because in the case of closed or finite volume hyperbolic manifolds, the limit sets are the whole sphere, and this implies that the map is a conformal map of the sphere, which extends to an isometry of the hyperbolic space. This gives us Mostow and Prasad’s rigidity theorem.
I also presented a poster on Mostow rigidity.
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More stuff on this site includes the following.