Mailing address:
University of Calgary. MS 542
2500 University Drive NW
Calgary, AB T2N 4T4, Canada
Email address: abc at xyz where:
1st option: abc=dangkhoa.nguyen and xyz=ucalgary.ca
2nd option: abc=khoanguyen2511 and xyz=gmail.com
Office: MS 542, (403) 220-3959
About me:
2009-2014: PhD, UC Berkeley.
2014-2017: UBC-PIMS Distinguished Postdoctoral Fellow, UBC.
2017-2021: Assistant Professor, Department of Mathematics and Statistics, UCalgary
Starting from 5/2019: Canada Research Chair Tier 2. Renewed for the second term 2024-2029.
2021-2025: Associate Professor, UCalgary
Starting from 7/2025: Professor, UCalgary
Research interests: number theory, dynamical systems, combinatorics, and related problems.
Calgary Algebra & Number Theory Seminar 2022-2023
For talks in previous years, click here.
Current students and postdocs: Xiao Guo, Samprit Ghosh, Zheng Zhu, Amaury De Burgos
Teaching in Fall 2025:
Office hours: Monday 10:45am-11:45am, Wednesday 3pm-4pm, Thursday 11:15am-12:15pm (no office hours on Thursday September 4) or by appointment
Math 431: Algebra 2
Math 511/607: Algebra 3
Papers (warning: these might differ from the published version):
(with B. Schmidt) Fast computation of Gauss sums and resolution of the root of unity ambiguity, Acta Arith. 140 (2009), 205-232
(with C. Gratton and T. Tucker) ABC implies primitive prime divisors in arithmetic dynamics, Bull. London Math. Soc. 45 (2013), 1194-1208
(with E. Amerik, P. Kurlberg, A. Towsley, B. Viray, and F. Voloch) Evidence for the dynamical Brauer-Manin criterion, Experimental Math. 25 (2016), 54-65
Algebraic independence of local conjugacies and related questions in polynomial dynamics, Proc. Amer. Math. Soc. 143 (2015), 1491-1499
Some arithmetic dynamics of diagonally split polynomial maps, Int. Math. Res. Not. IMRN 2015 (2015), 1159-1199. Errata
(with D. Ghioca and T. Tucker) Portraits of preperiodic points for rational maps, Math. Proc. Cambridge Philos. Soc. 159 (2015), 165-186
(with D. Ghioca) Dynamical anomalous subvarieties: structure and bounded height theorems, Advances in Math. 288 (2016), 1433-1462
(with D. Ghioca and H. Krieger) A case of the dynamical André-Oort conjecture, Int. Math. Res. Not. IMRN 2016 (2016), 738-758
On modules of integral elements over finitely generated domains, Trans. Amer. Math. Soc. 369 (2017), 3047-3066
(with D. Ghioca) Dynamics of split polynomial maps: uniform bounds for periods and application, Int. Math. Res. Not. IMRN 2017 (2017), 213-231. Errata
(with D. Ghioca, H. Krieger, and H. Ye) The dynamical André-Oort conjecture: unicritical polynomials, Duke Math. J. 166 (2017), 1-25
(with D. Ghioca and H. Ye) The dynamical Manin-Mumford conjecture and the dynamical Bogomolov conjecture for split rational maps, J. Eur. Math. Soc. 21 (2019), 1571-1594
(with J. Bell) Some finiteness results on monogenic orders in positive characteristic, Int. Math. Res. Not. IMRN 2018 (2018), 1601-1637
(with D. Ghioca) The orbit intersection problem for linear spaces and semiabelian varieties, Math. Res. Letters 24 (2017), 1263-1283
(with D. Ghioca and L.-C. Hsia) Simultaneously preperiodic points for families of polynomials in normal form, Proc. Amer. Math. Soc. 146 (2018), 733-741
(with A. Kulkarni and N. M. Mavraki) Algebraic approximations to linear combinations of powers: an extension of results by Mahler and Corvaja-Zannier, Trans. Amer. Math. Soc. 371 (2019), 3787-3804
(with D. Ghioca and T. Tucker) Squarefree doubly primitive divisors in dynamical sequences, Math. Proc. Cambridge Philos. Soc. 164 (2018), 551-572
(with L. DeMarco, D. Ghioca, H. Krieger, T. Tucker, and H. Ye) Bounded height in families of dynamical systems, Int. Math. Res. Not. IMRN 2019 (2019), 2453-2482
(with D. Ghioca and H. Ye) The dynamical Manin-Mumford conjecture and the dynamical Bogomolov conjecture for endomorphisms of (P^1)^n, Compositio Math. 154 (2018), 1441-1472
The Hermite-Joubert problem and a conjecture of Brassil-Reichstein, Canadian Math. Bulletin 62 (2019), 169-177
On certain diophantine equations and the dynamical Mordell-Lang problem, CMS Notes 50 No. 2 (2018), 14-15
(with D. Ghioca) A dynamical variant of the Pink-Zilber conjecture, Algebra & Number Theory 12 (2018), 1749-1771
A new mean ergodic theorem for tori and recurrences, Ergodic Theory and Dynamical Systems 41 (2021), 570-577
(with J. Bell and U. Zannier) D-finiteness, rationality, and height, Trans. Amer. Math. Soc. 373 (2020), 4889-4906
(with J. Bell) An analogue of Ruzsa's conjecture for polynomials over finite fields, J. Combinatorial Theory Ser. A 178 (2021), Article 105337
(with Z. S. Aygin) Monogenic pure cubics, J. Number Theory 219 (2021), 356-367
Transcendental series of reciprocals of Fibonacci and Lucas numbers, Algebra & Number Theory 16 (2022), 1627-1654
(with Z. S. Aygin) N-colored generalized Frobenius partitions: generalized Kolitsch identities, Canadian J. Math. 75 (2023), 447-469
(with J. Bell, K. Gunn and J. C. Saunders) A general criterion for the Pólya-Carlson dichotomy and application, Trans. Amer. Math. Soc. 376 (2023), 4361-4382
This paper replaces the earlier paper Endomorphisms of positive characteristic tori: entropy and zeta function which is no longer intended for publication.
Transcendence of polynomial canonical heights, Math. Annalen 387 (2023), 1-15
(with A. Medvedev and T. Scanlon) Skew-invariant curves and the algebraic independence of Mahler functions, under revision
(with J. Bell and U. Zannier) D-finiteness, rationality, and height II: lower bounds over a set of positive density, Advances in Math. 414 (2023), Article 108859
(with Y. Bugeaud) Some arithmetical properties of convergents to algebraic numbers, Pacific J. Math. 326 (2023), 17-36
(with J. Bell, S. Chen, and U. Zannier) D-finiteness, rationality, and height III: multivariate Pólya-Carlson dichotomy, Math. Zeit. 306 (2024), Article 70
(with J. Guo, C.-L. Sun and J. Wang) Vojta's ABC Conjecture for algebraic tori and applications over function fields, accepted to Advances in Math., 2025
(with F. Baril Boudreau and E. Holmes) Adelic perturbation of rational functions and applications, accepted to Math. Annalen, 2025
(with S. Albayrak, S. Ghosh, and G. Knapp) On certain polytopes associated to products of algebraic integer conjugates, accepted to Proceedings AMS, 2024
(with Anwesh Ray) Counting rational maps on P^1 with prescribed local conditions, submitted
Collaborators: Bernhard Schmidt, Chad Gratton, Tom Tucker, Katia Amerik, Pär Kulrberg, Adam Towsley, Bianca Viray, Felipe Voloch, Dragos Ghioca, Holly Krieger, Hexi Ye, Jason Bell, Avi Kulkarni, Myrto Mavraki, Liang-Chung Hsia, Laura DeMarco, Alice Medvedev, Tom Scanlon, Umberto Zannier, Zafer Selcuk Aygin, Keira Gunn, J. C. Saunders, Yann Bugeaud, Shaoshi Chen, Félix Baril Boudreau, Erik Holmes, Ji Guo, Chia-Liang Sun, Julie Wang, Seda Albayrak, Samprit Ghosh, Greg Knapp, Anwesh Ray