Publications and Preprints
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3-Selmer groups, ideal class groups and cube sum problem -- Somnath Jha, Dipramit Majumdar, and Pratiksha Shingavekar (2022), under review.
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Cube sum problem for integers having exactly two distinct prime factors -- Dipramit Majumdar and Pratiksha Shingavekar, Proc. Indian Acad. Sci. Math. Sci. 133 (2023), no. 2, article no. 43, pp. 22 (journal version).
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An analogue of Kida's formula for elliptic curves with additive reduction -- Anwesh Ray and Pratiksha Shingavekar, The Ramanujan Journal (2024) (journal version).
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Statistics for 3-isogeny induced Selmer groups of elliptic curves -- Pratiksha Shingavekar (2024), under review.
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Rank distribution in cubic twist families of elliptic curves -- Anwesh Ray and Pratiksha Shingavekar (2024), under review.
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A positive density of elliptic curves are diophantine stable in certain Galois extensions -- Anwesh Ray and Pratiksha Shingavekar (2024), under review.
Pratiksha Shingavekar
I am a postdoctoral fellow at Chennai Mathematical Institute (Jan 2024 - present) working in number theory.
I earned my PhD from Indian Institute of Technology, Madras (2017-2023) under the joint supervision of Dr. Dipramit Majumdar and Dr. Somnath Jha.
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My research focuses on elliptic curves and related objects. Recently, I am also drawn towards some aspects of Machine learning.
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Talks
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3-Selmer groups, ideal class groups and cube sum problem -- Elliptic curves and special values of L-functions at International Centre for Theoretical Sciences (ICTS), Aug 2022.
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3-Selmer groups, ideal class groups and cube sum problem -- Chennai-Tirupati intercity number theory conference at Chennai Mathematical Institute (CMI), Feb 2023.
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3-Selmer groups, ideal class groups and cube sum problem -- Integers conference 2023 at University of Georgia Athens (UGA), May 2023.
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3-Selmer groups, ideal class groups and cube sum problem -- 35th Automorphic forms conference at Louisiana State University (LSU), May 2023.
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3-Selmer groups, ideal class groups and cube sum problem -- A festival remembering Victor Snaith at University of Bristol (UoB), July 2023.
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3-Selmer groups, ideal class groups and cube sum problem -- Number theory seminar at Institute of Mathematical Sciences (IMSc), Nov 2023.
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A positive density of elliptic curves are diophantine stable in certain Galois extensions -- The Mordell conjecture: 100 years later at Massachusetts Institute of Technology (MIT), July 2024.