# Vandita Patel

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:
**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:**

- Fermat's Last Theorem and Beyond (poster), LMS Women in Maths Day, University of Warwick, 27/06/2017.
- Perfect Powers that are Sums of Consecutive like Powers, Number Theory Seminar, University of Warwick, 12/06/2017.

- Sums of consecutive perfect powers is seldom a perfect power, Journées Algophantiennes Bordelaises 2017, 07/06/2017.

- Perfect Powers that are Sums of Consecutive like Powers, Number Theory Lunch Seminar, Max Planck Institute for Mathematics, 10/05/2017.

- Perfect powers that are sums of consecutive k-th powers, Postgraduate Seminar - University of Warwick, 02/11/16.

- Perfect powers that are sums of consecutive k-th powers, Linfoot Seminar - University of Bristol, 26/10/2016.

- Descent of a Sum of Consecutive Cubes ... Twice!!, Junior Number Theory Seminar - University of Oxford, 09/05/2016.
- Graphing Congruences of Newforms (Poster), British Mathematical Colloquium (BMC) - University of Bristol, 21/03/2016.
- Bunnies, Stars and SuperForms, Postgraduate Seminar (Open Day) - University of Warwick, 10/02/2016.
- Bunnies, Stars and SuperForms, Ada Lovelace Day - University of Warwick, 14/10/2015.
- Graphing Congruences of Newforms, Young Women in Algebraic Geometry (YWiAG) - University of Bonn, 05/10/2015.

- The Hunt for Totally Real Number Fields, Young Researchers in Mathematics (YRM) - University of Oxford, 18/08/2015.
- The Hunt for Totally Real Number Fields, Postgraduate Seminar - University of Warwick, 03/06/2015.
- On the equation $F_n+2=y^p$, Postgraduate Seminar (Open Day) - University of Warwick, 26/11/2014.

**Conferences:
**

- LMS Women in Maths Day, University of Warwick, 27th June 2017.
- Journées Algophantiennes Bordelaises 2017, Université de Bordeaux - France, 7th - 9th June 2017.

- Modular Forms Are Everywhere, Max Planck Institute for Mathematics - Bonn, Germany, 15th - 26th May 2017.
- WIN-E2: Women in Numbers Europe-2, Lorentz Center - Leiden, Netherlands, 25th - 30th September 2016.

- Building Bridges: 3rd EU/US Summer School, University of Sarajevo, Bosnia, 11th - 16th July 2016.

- Arithmetic statistics and the Cohen-Lenstra heuristics, University of Warwick, UK, 27th June - 1st July 2016.

- Explicit Methods in Number Theory: Conference in Honour of John Cremona's 60th Birthday, University of Warwick, UK, 4th - 8th April 2016.

- British Mathematical Colloquium (BMC), University of Bristol, UK, 21st - 24th March 2016.
- Barcelona Fall Workshop on Number Theory, Universitat de Barcelona, Spain, 25th - 27th November 2015.
- Young Women in Algebraic Geometry, University of Bonn, Germany, 5th - 7th October 2015.

- LMS-CMI Summer School on Diophantine Equations, Baskerville Hall - Hay-on-Wye, Wales, 15th - 19th September 2015.
- Young Researchers in Mathematics 2015, University of Oxford, UK, 17th - 20th August 2015.
- French-German Summer School on Galois Theory and Number Theory, University of Konstanz, Germany, 18th - 24th July 2015.
- The 4th Joint British Mathematical Colloquium & British Applied Mathematics Colloquium, University of Cambridge, UK, 30th March - 2nd April 2015.

- Elliptic Curves, Modular Forms and Iwasawa Theory, University of Cambridge, UK, 25th - 27th March 2015.
- Seminari de Teoria de Nombres de Barcelona, Universitat de Barcelona, Spain, 26th - 30th January 2015.

- Introductory Workshop on Modular Methods in Diophantine Equations, Bilecik Şeyh Edebali University - Turkey, 8th-11th September 2014.
- Arithmetic of Hyperelliptic Curves and Cryptography , UIST "St. Paul the Apostle" - Ohrid, Macedonia, 25th August - 5th September 2014.
- Building Bridges: Workshop on Automorphic Forms and Related Topics, University of Bristol, UK, 7th - 11th July 2014.
- Young Researchers in Mathematics 2014, University of Warwick, UK, 30th June - 3rd July 2014.