Publications

(34) Towards autonomous math research (with T. Feng, T.Trinh, G. Bingham, D. Hwang, Y. Chervonyi, J. Jung, J. Lee, S. Kim, F. Pasqualotto, S. Gukov, J. Lee, J. Kim, K. Hou, G. Ghiasi, Y. Tay, Y. Li, C. Juank, Y. Liu, H. Lin, E. Liu, N. Nayakanti, X. Yang, H. Cheng, D. Hassabis, K. Kavukcuoglu, Q. Le, T. Luong) ([ArXiv]), (Featured on DeepMind blog).

(33) Hilbert's tenth problem for finitely generated rings (with P. Koymans) ([ArXiv]), Notices of the American Mathematical Society (to appear).

(32) Semi-autonomous Mathematics  Discovery with Gemini: A case study on the Erdös problems (with T. Feng, T. Trinh, G. Bingham, J. Kang, S. Zhang, S. Kim, K. Barreto, C. Schildkraut, J. Jung, J. Seo, Y. Chervonyi, D. Hwang, K. Hou, S. Gukov, C. Tsai, H. Choi, Y. Jin, W. Li, H. Wu, R. Shiu, Y. Shih, Q.V. Le, T. Luong) ([ArXiv]). 

(31) Strongly Polynomial Time Complexity of Policy Iteration for L_infty Robust MDPS  (with A. Asadi, K. Chatterjee, E. Goharshady, M. Karrabi, A. Montaseri) ([ArXiv]).

(30) A heuristic for ray class groups of quadratic fields (with A. Bartel) ([ArXiv]).

(29) Elliptic curves of rank one over number fields (with P. Koymans) ([ArXiv]).

(28) Hilbert's tenth problem via additive combinatorics (with P. Koymans) ([ArXiv]) (Featured on Quanta Magazine).

(27) Diophantine stability and second order terms (with E. Sofos) ([ArXiv]), International Mathematics Research Notices (to appear). 

(26) Elliptic fibrations and 3x2^k (with P. Koymans and E. Sofos) ([ArXiv]).  

(25) 6-torsion and integral points on quartic surfaces (with S. Chan, P. Koymans and E. Sofos) ([ArXiv]), Annali della Scuola Normale Superiore (to appear). 

(24) Averages of multiplicative functions along equidistributed sequences (with S. Chan, P. Koymans and E. Sofos) ([ArXiv]), Journal of Number Theory (to appear). 

(23) Brauer--Manin obstructions requiring arbitrarily many classes (with J. Berg, B. Poonen, M. Stoll, N. Triantafillou, B. Viray, I. Vogt) ([ArXiv]), Bullettin of the London Mathematical Society (to appear). 

(22) Malle's conjecture for fair counting functions (with P. Koymans) ([ArXiv]), Algebra and Number Theory (to appear). 

(21) Frieze patterns over algebraic numbers (with M. Cuntz and T. Holm) ([ArXiv]), Bullettin of the London Mathematical Society (to appear). 

(20)  Abelian dynamical Galois groups for unicritical polynomials (with A. Ferraguti) ([ArXiv]).

(19) Two step nilpotent extensions are not anabelian (with P. Koymans) ([ArXiv]),  Mathematische Zeitschrift (to appear). 

(18) On Stevenhagen's conjecture (with P. Koymans) ([ArXiv]) (Featured on Quanta Magazine),  Acta Mathematica (to appear). 

(17) The size of arboreal images, I: exponential lower bounds for PCF and unicritical polynomials  ([ArXiv]), Proceedings of the American Mathematical Society (to appear). 

(16) On Malle's conjecture for nilpotent groups, I (with P. Koymans) ([ArXiv]), Transactions of the American Mathematical Society, Series B, 10(2023), 310-354.  

(15)  A sharp upper bound for the 2-torsion of class groups of multi-quadratic fields (with P. Koymans) ([ArXiv]),  Mathematika, Volume 68 Issue 1, January 2022.

(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]), Acta Arithmetica (to appear).  

(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, Volume 10, 21 June 2022. 

(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, Vol. 24 N. 4, Pages 1189-1283, 21 July 2021. 

(5) Jump sets in local fields, ([ArXiv]),  Journal of Algebra, Volume 593, Pages 398-476, 1 March 2022.

(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.