About me:

5/2014: PhD, UC Berkeley. 7/2014-6/2017: UBC-PIMS Distinguished Postdoctoral Fellow, University of British Columbia.

7/2017: Assistant Professor,  Department of Mathematics and Statistics, University of Calgary 

Starting from 5/2019: Canada Research Chair Tier 2. Renewed for the second term 2024-2029.

Starting from 7/2021: Associate Professor, Department of Mathematics and Statistics, University of Calgary 

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: Keira Gunn, Seda Albayrak, Greg Knapp, Samprit Ghosh   

Teaching in Winter 2025: Math 641 Algebraic Number Theory 

Papers (warning: these might differ from the published version): 

1. (with B. Schmidt) Fast computation of Gauss sums and resolution of the root of unity ambiguity, Acta Arith. 140 (2009), 205-232

2. (with C. Gratton and T. Tucker) ABC implies primitive prime divisors in arithmetic dynamics, Bull. London Math. Soc. 45 (2013), 1194-1208

3. (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

4. Algebraic independence of local conjugacies and related questions in polynomial dynamics, Proc. Amer. Math. Soc. 143 (2015), 1491-1499

5. Some arithmetic dynamics of diagonally split polynomial maps, Int. Math. Res. Not. IMRN 2015 (2015), 1159-1199. Errata

6. (with D. Ghioca and T. Tucker) Portraits of preperiodic points for rational maps, Math. Proc. Cambridge Philos. Soc. 159 (2015), 165-186

7. (with D. Ghioca) Dynamical anomalous subvarieties: structure and bounded height theorems, Advances in Math. 288 (2016), 1433-1462

8. (with D. Ghioca and H. Krieger) A case of the dynamical André-Oort conjecture, Int. Math. Res. Not. IMRN 2016 (2016), 738-758 

9. On modules of integral elements over finitely generated domains, Trans. Amer. Math. Soc. 369 (2017), 3047-3066

10. (with D. Ghioca) Dynamics of split polynomial maps: uniform bounds for periods and application, Int. Math. Res. Not. IMRN 2017 (2017), 213-231. Errata

11. (with D. Ghioca, H. Krieger, and H. Ye) The dynamical André-Oort conjecture: unicritical polynomials, Duke Math. J. 166 (2017), 1-25

12. (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

13. (with J. Bell) Some finiteness results on monogenic orders in positive characteristic, Int. Math. Res. Not. IMRN 2018 (2018), 1601-1637

14. (with D. Ghioca) The orbit intersection problem for linear spaces and semiabelian varieties, Math. Res. Letters 24 (2017), 1263-1283

15. (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 

16. (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

17. (with D. Ghioca and T. Tucker) Squarefree doubly primitive divisors in dynamical sequences, Math. Proc. Cambridge Philos. Soc. 164 (2018), 551-572

18. (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

19. (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

20. The Hermite-Joubert problem and a conjecture of Brassil-Reichstein, Canadian Math. Bulletin 62 (2019), 169-177

21. On certain diophantine equations and the dynamical Mordell-Lang problem, CMS Notes 50 No. 2 (2018), 14-15

22. (with D. Ghioca) A dynamical variant of the Pink-Zilber conjecture, Algebra & Number Theory 12 (2018), 1749-1771

23. A new mean ergodic theorem for tori and recurrences, Ergodic Theory and Dynamical Systems 41 (2021), 570-577

24. (with J. Bell and U. Zannier) D-finiteness, rationality, and height, Trans. Amer. Math. Soc. 373 (2020), 4889-4906

25. (with J. Bell) An analogue of Ruzsa's conjecture for polynomials over finite fields, J. Combinatorial Theory Ser. A 178 (2021), Article 105337

26. (with Z. S. Aygin) Monogenic pure cubics, J. Number Theory 219 (2021), 356-367

27. Transcendental series of reciprocals of Fibonacci and Lucas numbers, Algebra & Number Theory 16 (2022), 1627-1654

28. (with Z. S. Aygin) N-colored generalized Frobenius partitions: generalized Kolitsch identities, Canadian J. Math. 75 (2023), 447-469

29. (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. 

30. Transcendence of polynomial canonical heights, Math. Annalen 387 (2023), 1-15

31. (with A. Medvedev and T. Scanlon) Skew-invariant curves and the algebraic independence of Mahler functions, under revision

32. (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

33. (with Y. Bugeaud) Some arithmetical properties of convergents to algebraic numbers, accepted to Pacific J. Math., 2023

34. (with J. Bell, S. Chen, and U. Zannier) D-finiteness, rationality, and height III: multivariate Pólya-Carlson dichotomy, accepted to Math. Zeit., 2024

35. (with J. Guo,  C.-L. Sun and J. Wang) Vojta's ABC Conjecture for algebraic tori and applications over function fields, submitted

36. (with F. Baril Boudreau and E. Holmes) Adelic perturbation of rational functions and applications, 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 

Slides for some talks:

• CRG Abelian Varieties Multi-site seminar series (10/2017)

• Alberta Number Theory Days X (5/2018)

• PRIMA 2022, Vancouver