Peter Koymans

Leiden University, Leiden, The Netherlands.



I am a PhD student under the supervision of Jan-Hendrik Evertse and Peter Stevenhagen. I am interested in number theory and surrounding areas, in particular the distribution of class groups and Diophantine equations in positive characteristic. Together with Carlo Pagano I am organizing a seminar on the work of Alexander Smith, see here.

Papers:

  1. On the distribution of Cl(K)[l^infty] for degree l cyclic fields (with C. Pagano), arXiv, submitted.
  2. Joint distribution of spins (with D. Milovic), arXiv, submitted.
  3. The 16-rank of Q(-p), arXiv, submitted.
  4. Unit equations and Fermat surfaces in positive characteristic (with C. Pagano), Acta Arithmetica, To Appear.
  5. Vinogradov's three primes theorem with primes having given primitive roots (with C. Frei and E. Sofos), arXiv, submitted.
  6. Spins of prime ideals and the negative Pell equation x^2 - 2py^2 = -1 (with D. Milovic), Compositio Mathematica, 155(2019), 100-125. [arXiv:1611.10337]
  7. On the 16-rank of class groups of Q(-2p) for primes p = 1 mod 4 (with D. Milovic), International Mathematics Research Notices, To Appear. [arXiv:1705.05505]
  8. On the equation x_1 + x_2 = 1 in finitely generated multiplicative groups in positive characteristic (with C. Pagano), The Quarterly Journal of Mathematics, 68(2017), 923-934. [arXiv:1610.08377]
  9. The generalized Catalan equation in positive characteristic, arXiv.
  10. The Catalan equation, Indagationes Mathematicae, 28(2017), 321-352. [arXiv:1610.06440]

Talks:

Conferences and symposia:

Teaching:

Diophantine approximation (Fall 2015)
MasterMath Elliptic curves (Fall 2015)
Algebra 1 (Spring 2016)
Lineaire Algebra 1 (Fall 2016)
MasterMath Elliptic curves (Spring 2017)
Diophantine approximation (Fall 2017)
Algebra 1 (Spring 2018)
Analytic Number Theory (Fall 2018)

Seminars:

Algebra, Geometry and Number Theory Seminar (continuously)
Intercity Number Theory Seminar (continuously)
General Mathematics Colloquium (continuously)
Knot Theory (Spring 2016)
Analytic Number Theory Seminar (Summer 2016 and Winter 2017)
Obstructions to local-global principles (Spring 2017)
Seminar on the work of Alexander Smith (Fall 2018)
Diophantine Seminar

Bachelor and master theses:

Irreducible polynomials (bachelor thesis, Dutch)
The Catalan equation (master thesis)

Contact details:

Peter Koymans
Snellius office 227A
PhD supervisors: Jan-Hendrik Evertse , Peter Stevenhagen
E-mail: p dot h dot koymans (at) math dot leidenuniv dot nl