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My Research interests primarily lie in the fields of Low-Dimensional topology and Quantum topology, with an emphasis on Knot Theory. Recently I have been interested in Quantum Invariants and completed my senior thesis under Constantin Teleman, titled Quantum Invariants For Knots, 3-Manifolds and 3D-TQFTS, where I detail some wonderful constructions and examples. I hope to make a version of this available pending some revisions.
In 2023 I participated in the CUBE Reu at Georgia Tech, under professors Ryan Dickmann and Dan Margalit where we studied geodesic preserving bijections in the 8 Thurston geometries. Along with my research Partner Akash Narayanan, we formed versions of the fundamental theorem of affine geometry for 3 of the other 8 Thurston geometries. We hope to submit our research for publication soon. Our research Poster can be seen below
LiderosNaranayanPoster.pdf
In 2022 I participated in the TXST Math Reu in Algebra Combinatorics and Statistics. Under the supervision of Professors Yong Yang and Nguyen Ngoc Hung our group studied conjugacy classes of varying P-Regularity Level. Along with my research partners Kawika O'Connor and Neelam Akula we studied bounds on the number of conjugacy classes with certain properties. We hope to publish our research soon. The Research Poster for this project can be seen below
On_conjugacy_classes_of_varying_p_regularity_level__Poster_.pdfPage updated
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