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Vandita Patel

Having completed my PhD studies at the University of Warwick, this page will no longer be updated. Please visit my new website here for up-to-date information.

Welcome to my homepage! I am currently a fourth (and final!) year PhD student in Number Theory working under the supervision of Professor Samir Siksek.

Personal: sdc11372c_2.jpg
Hometown: Leicester, UK.
Current town: Leamington Spa, UK.
Nationality: British Citizen.
Email: Vandita<dot>Patel<at>warwick<dot>ac<dot>uk

Research Interests: Number Theory, Modular Forms, Diophantine Equations, Enumerating Number Fields.

Publications and Preprints:

  • F. Luca, V. Patel. On perfect powers that are sums of two Fibonacci numbers, (preprint).
  • N. Anbar, A. Ozdak, V. Patel, L. Quoos, A. Somoza, A. Topuzoğlu. On the difference of permutation polynomials, submitted to Finite Fields and their Applications (preprint).
  • N. Anbar, A. Ozdak, V. Patel, L. Quoos, A. Somoza, A. Topuzoğlu. On permutation polynomials over finite fields: differences and iterations, submitted to Proceedings of Women in Numbers Europe 2.
  • V. Patel, S. Siksek. On powers that are sums of consecutive like powers. Research in Number Theory (to appear) (preprint).
  • M. A. Bennett, V. Patel, S. Siksek. Perfect Powers that are sums of Consecutive Cubes. Mathematika, 63 (2016), no. 1, 230 -- 249, (preprint).
  • M. A. Bennett, V. Patel, S. Siksek. Superelliptic Equations Arising from Sums of Consecutive Powers. Acta Arithmetica, 172 (2016), no. 4, 377 -- 393, (preprint).
  • V. Patel. Irrationality of some p-Adic Integers. MMath Dissertation, University of Warwick, 2012.

Work in Progress:

  • V. Patel. Perfect Powers that are Sums of Consecutive Squares, in preparation.
  • M. A. Bennett, V. Patel, S. Siksek. On the Diophantine Equation $F_n + 2 = y^p$, in preparation.

First Year Report: A report from my first year as a PhD student.
We look at some potential links between totally real number fields and some theta expansions (these being modular
forms). The literature related to modular forms is rich, and any links made to totally real number fields could help us to
understand the number field better.

Teaching:

  • 2016 Term 2: Teaching Assistant for MA426 Elliptic Curves.
  • 2014 Term 1: Teaching Assistant for MA3D5 Galois Theory.
  • 2013-2014: Supervised a group of five first year undergraduate mathematics students, mark their work and provide feedback.
  • 2011-2012: Supervised a group of four first year undergraduate MORSE students, mark their work and provide feedback.

Talks / Posters:

Conferences: