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Publications and Preprints

  1. 3-Selmer groups, ideal class groups and cube sum problem -- Somnath Jha, Dipramit Majumdar, and Pratiksha Shingavekar (2022), under review. 

  2. Cube sum problem for integers having exactly two distinct prime factors -- Dipramit Majumdar and Pratiksha Shingavekar, Proceedings - Mathematical Sciences 133 (2023), no. 43, (journal version).

  3. An analogue of Kida's formula for elliptic curves with additive reduction -- Anwesh Ray and Pratiksha Shingavekar, The Ramanujan Journal (2024), (journal version).

  4. Statistics for 3-isogeny induced Selmer groups of elliptic curves -- Pratiksha Shingavekar, Journal of Number Theory (2024), (journal version).

  5. Rank distribution in cubic twist families of elliptic curves -- Anwesh Ray and Pratiksha Shingavekar (2024), under review.

  6. 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

  1. 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. 

  2. 3-Selmer groups, ideal class groups and cube sum problem -- Chennai-Tirupati intercity number theory conference at Chennai Mathematical Institute (CMI), Feb 2023.

  3. 3-Selmer groups, ideal class groups and cube sum problem -- Integers conference 2023 at University of Georgia Athens (UGA), May 2023. 

  4. 3-Selmer groups, ideal class groups and cube sum problem -- 35th Automorphic forms conference at Louisiana State University (LSU), May 2023. 

  5. 3-Selmer groups, ideal class groups and cube sum problem -- A festival remembering Victor Snaith at University of Bristol (UoB), July 2023. 

  6. 3-Selmer groups, ideal class groups and cube sum problem -- Number theory seminar at Institute of Mathematical Sciences (IMSc), Nov 2023. 

  7. 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.

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