Peter Koymans

Max Planck Institute for Mathematics, Bonn, Germany.



I am a postdoctoral student at the Max Planck Institute for Mathematics in Bonn. You can find me at the MPIM until August 2020, after which I will move to Ann Arbor, Michigan. I completed my PhD in Leiden under the supervision of Jan-Hendrik Evertse and Peter Stevenhagen. The PhD thesis is freely available here. I am interested in number theory and surrounding areas, in particular the distribution of class groups, the circle method and Diophantine equations.

Papers:

  1. Higher Rédei reciprocity and integral points on conics (with C. Pagano), arXiv.
  2. Effective convergence of coranks of random Rédei matrices (with C. Pagano), arXiv.
  3. On the 4-rank of class groups of Dirichlet biquadratic fields (with E. Fouvry and C. Pagano), arXiv, submitted.
  4. On Dirichlet biquadratic fields (with E. Fouvry), arXiv, submitted.
  5. Higher genus theory (with C. Pagano), arXiv, submitted.
  6. On the negative Pell equation (with S. Chan, D. Milovic and C. Pagano), arXiv.
  7. On the distribution of Cl(K)[l^infty] for degree l cyclic fields (with C. Pagano), arXiv, submitted.
  8. Joint distribution of spins (with D. Milovic), arXiv, submitted.
  9. The 16-rank of Q(-p), Algebra and Number Theory, 14(2020), 37-65. [arXiv:1809.07167]
  10. Unit equations and Fermat surfaces in positive characteristic (with C. Pagano), Acta Arithmetica, 193(2020), 133-156. [arXiv:1806.01614]
  11. Vinogradov's three primes theorem with primes having given primitive roots (with C. Frei and E. Sofos), Mathematical Proceedings of the Cambridge Philosophical Society, To Appear. [arXiv:1804.00573]
  12. 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]
  13. On the 16-rank of class groups of Q(-2p) for primes p = 1 mod 4 (with D. Milovic), International Mathematics Research Notices, 23(2019), 7406-7427. [arXiv:1705.05505]
  14. 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]
  15. The generalized Catalan equation in positive characteristic, arXiv.
  16. The Catalan equation, Indagationes Mathematicae, 28(2017), 321-352. [arXiv:1610.06440]
Coauthors: Stephanie Chan, Etienne Fouvry, Christopher Frei, Djordjo Milovic, Adam Morgan, Carlo Pagano, Mark Shusterman, Efthymios Sofos.

Talks:

Conferences and symposia:

Seminars organized:

In Leiden Carlo Pagano and I organized a seminar on the work of Alexander Smith, see here.

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
PLEASANT Seminar (Summer 2019 and Winter 2020)

Bachelor and master theses:

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

Contact details:

Peter Koymans
MPIM Office 221
E-mail: koymans (at) mpim-bonn dot mpg dot de