Khoa Dang Nguyen
Department of Mathematics and The Pacific Institute for the Mathematical Sciences The University of British Columbia Vancouver, BC V6T 1Z4
1st email address: abc at xyz (where abc=khoanguyen2511 and xyz=gmail.com) 2nd email address: abc at xyz (where abc=dknguyen and xyz=math.ubc.ca)
About me: CV and Publication List (arXiv links given below)
Research interests: algebraic dynamics, diophantine geometry, and related problems in algebra and number theory.
5/2014: PhD in math at UC Berkeley. Coadvisors: Professors Thomas Scanlon and Paul Vojta (I was also mentored by Professor Thomas Tucker during a 3month visit at ICERM.)
Teaching at UBC: Spring 2015: MATH 101 (Integral Calculus with Applications) Fall 2014: MATH 200 (Multivariable Calculus)
Publications: (Warning: papers provided here may be different from the published versions) 1. (with B. Schmidt) Fast computation of Gauss sums and resolution of the root of unity ambiguity. Acta Arith. 140 (2009), 205232. pdf 2. (with C. Gratton and T. Tucker) ABC implies primitive prime divisors in arithmetic dynamics. Bull. London Math. Soc. 45 (2013), 11941208 3. Some arithmetic dynamics of diagonally split polynomial maps. Int. Math. Res. Not. IMRN. 2015 (2015), 11591199. Errata. 4. Algebraic independence of local conjugacies and related questions in polynomial dynamics. Proceedings AMS, 143 (2015), 14911499 5. (with D. Ghioca and T. Tucker) Portraits of preperiodic points for rational maps. Math. Proc. Cambridge Philos. Soc., 159 (2015), 165186. 6. (with D. Ghioca and H. Krieger) A case of the dynamical AndréOort conjecture. Accepted to Int. Math. Res. Not. IMRN., 2015. 7. (with E. Amerik, P. Kurlberg, A. Towsley, B. Viray and F. Voloch) Evidence for the dynamical BrauerManin criterion. Accepted to Experimental Math., 2015. 8. On modules of integral elements over finitely generated domains. Accepted to Trans. Amer. Math. Soc., 2015. 9. (with D. Ghioca) Dynamical anomalous subvarieties: structure and bounded height theorems. Accepted to Advances in Math., 11/2015.
Preprints and Work in Progress: 1. (with D. Ghioca, H. Krieger, and H. Ye) The dynamical AndréOort conjecture: unicritical polynomials. Submitted, 2015. 2. (with J. Bell) Some finiteness results on monogenic orders in positive characteristic. Submitted, 2015. 3. (with D. Ghioca) Dynamics of split polynomial maps: uniform bounds for periods and application. Submitted, 2015. 4. (with D. Ghioca and H. Ye) The dynamical ManinMumford conjecture and the dynamical Bogomolov conjecture for split rational maps. Submitted, 2015. 5. (with A. Kulkarni and N. M. Mavraki) Algebraic approximations to linear combinations of powers: an extension of results by Mahler and CorvajaZannier. Submitted, 12/2015.
Collaborators: Bernhard Schmidt, Chad Gratton, Tom Tucker, Katia Amerik, Pär Kurlberg, Adam Towsley, Bianca Viray, Felipe Voloch, Dragos Ghioca, Holly Krieger, Hexi Ye, Jason Bell, Avi Kulkarni, Myrto Mavraki.
Some slides: (for very short talks) 1. 5minute talk at UNCG Summer School In Computational Number Theory 2013. 2. 25minute talk at Pacific Northwest Number Theory Conference 2015.
Previous Teaching at Berkeley: Spring 2013: GSI for MATH 54 (lecturer: Zvezdelina Stankova) Fall 2013: GSI for MATH 16B (lecturer: James Demmel) Spring 2014: GSI for MATH 16B (lecturer: Alexander Coward)
