# Dang-Khoa Nguyen

**Mailing address:**

University of Calgary

Mathematical Sciences Building MS 542

2500 University Drive NW

Calgary, AB T2N 4T4, Canada

**1st email address**: abc at xyz, where

abc=dangkhoa.nguyen and xyz=ucalgary.ca

**2nd email address**: abc at xyz, where

abc=khoanguyen2511 and xyz=gmail.com

**Office**: MS 542, (403) 220-3959

**About me**: CV

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

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

Research interests: algebraic dynamics, diophantine geometry, and related problems in algebra and number theory.

**Teaching (most recent course at UBC):**

Fall 2016: MATH 200 (Section 103 and Section 104)

**Papers (warning: these might differ from the published versions): **

- (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 - (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*, accepted to**J. Eur. Math. Soc., 9/2016** - (with J. Bell)
*Some finiteness results on monogenic orders in positive characteristic*, accepted to**Int. Math. Res. Not. IMRN, 11/2016** - (with D. Ghioca)
*The orbit intersection problem for linear spaces and semiabelian varieties*, accepted to**Math. Res. Letters, 2017** - (with D. Ghioca and L.-C. Hsia)
*Simultaneously preperiodic points for families of polynomials in normal form*, accepted to**Proc. Amer. Math. Soc., 2017** - (with A. Kulkarni and N. M. Mavraki)
*Algebraic approximations to linear combinations of powers: an extension of results by Mahler and Corvaja-Zannier*, accepted to**Trans. Amer. Math. Soc., 2017** - (with D. Ghioca and T. Tucker)
*Squarefree doubly primitive divisors in dynamical sequences*, accepted to**Math. Proc. Cambridge Philos. Soc., 2017** - (with L. DeMarco, D. Ghioca, H. Krieger, T. Tucker, and H. Ye)
*Bounded height in families of dynamical systems*, accepted to**Int. Math. Res. Not. IMRN, 2017** - (with D. Ghioca and H. Ye)
*The dynamical Manin-Mumford conjecture and the dynamical Bogomolov conjecture for endomorphisms of (P^1)^n*, submitted *The Hermite-Joubert problem and a conjecture of Brassil-Reichstein*, submitted- (with D. Ghioca)
*A dynamical variant of the Pink-Zilber conjecture*, in preparation, first draft available *A new mean ergodic theorem for tori and recurrences*, in preparation, first draft available- (with A. Medvedev and T. Scanlon)
*Algebraic independence of Mahler functions of non-exceptional polynomial type*, in preparation *On certain diophantine equations and the dynamical Mordell-Lang problem*, in preparation

**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