# Publications

## Papers:

(19) Two step nilpotent extensions are not anabelian (with P. Koymans) ([ArXiv] ).

(18) On Stevenhagen's conjecture (with P. Koymans) ([ArXiv] ) (Featured on Quanta Magazine) .

(17) The size of arboreal images, I: exponential lower bounds for PCF and unicritical polynomials ([ArXiv]).

(16) On Malle's conjecture for nilpotent groups, I (with P. Koymans) ([ArXiv]), *Transactions of the American Mathematical Society (to appear). *

(15) A sharp upper bound for the 2-torsion of class groups of multi-quadratic fields (with P. Koymans) ([ArXiv]), *Mathematika (to appear).*

(14) Higher Redei reciprocity and integral points on conics (with P. Koymans) ([ArXiv]).

(13) Effective convergence of coranks of random Redei matrices (with P. Koymans) ([ArXiv]).

(12) Constraining images of quadratic arboreal representations (with A. Ferraguti) ([ArXiv]), ([Journal]), *International Mathematics Research Notices, *Volume 2020, Issue 22, November 2020, Pages 8486-8510.

(11) On the 4-rank of class group of Dirichlet biquadratic fields (with E. Fouvry and P. Koymans) ([ArXiv]), ([Journal]), *Journal of the Institute of Mathematics of Jussieau, *22 December 2020.

(10) Diameters of random Cayley graphs of finite nilpotent groups (with D. El-Baz) ([ArXiv]), ([Journal]), *Journal of Group Theory, *2 February 2021.

(9) Higher genus theory (with P. Koymans) ([ArXiv]), ([Journal]), *International Mathematics Research Notices*, 24 August 2020.

(8) On the Negative Pell equation (with S. Chan, P. Koymans and D. Milovic), ([ArXiv]), *Forum of Mathematics , Sigma (to appear). *

(7) The inverse problem for Arboreal Galois representation of index two (with A. Ferraguti and D. Casazza), ([ArXiv]).

(6) On the distribution of the l-Sylow of Cl(K) for degree l cyclic fields (with P. Koymans), ([ArXiv]), *J. Europ. Math. Society (to appear). *

(5) Jump sets in local fields, ([ArXiv]), *J**ournal of Algebra** (to appear).*

(4) Unit equation and Fermat surfaces in positive characteristic (with P. Koymans), ([ArXiv]), ([Journal]), *Acta Arithmetica*, 193 (2020), 133-156.

(3) 4-ranks and the general model for statistics of ray class groups of imaginary quadratic fields (with E. Sofos), ([ArXiv]).

(2) Calculating the power residue symbols and Ibeta (with K. de Boer), ([Journal]), *Proceedings of the International Symposium on Symbolic and Algebraic Computation*, (2017).

(1) On the equation x+y=1 in finitely generated groups in positive characteristic (with P. Koymans), ([ArXiv]), ([Journal]) , *The Quarterly Journal of Mathematics, *Volume 68, Issue 3, September 2017, Pages 924-943.

## Notes:

(1) A characterization of free abelian pro-p groups of finite rank (with M. Stajnokovski, 2015), [PDF].

(2) Pro-nilpotent Galois groups (with bounded ramification) and random profinite groups *(Upcoming). *