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 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: Fall 2016: MATH 200 (Multivariable calculus), 2 sections. Fall 2015: MATH 200 (Multivariable calculus), 2 sections. Spring 2015: MATH 101 (Integral Calculus with Applications). Fall 2014: MATH 200 (Multivariable Calculus).
Accepted Papers: (Warning: these might differ from the published versions) 1. (with B. Schmidt) Fast computation of Gauss sums and resolution of the root of unity ambiguity. 2. (with C. Gratton and T. Tucker) ABC implies primitive prime divisors in arithmetic dynamics. 3. (with E. Amerik, P. Kurlberg, A. Towsley, B. Viray and F. Voloch) Evidence for the dynamical BrauerManin criterion. 4. Algebraic independence of local conjugacies and related questions in polynomial dynamics. 5. Some arithmetic dynamics of diagonally split polynomial maps. 6. (with D. Ghioca and T. Tucker) Portraits of preperiodic points for rational maps. 7. (with D. Ghioca) Dynamical anomalous subvarieties: structure and bounded height theorems. 8. (with D. Ghioca and H. Krieger) A case of the dynamical AndréOort conjecture. 9. On modules of integral elements over finitely generated domains. 10. (with D. Ghioca) Dynamics of split polynomial maps: uniform bounds for periods and application. 11. (with D. Ghioca, H. Krieger, and H. Ye) The dynamical AndréOort conjecture: unicritical polynomials. 12. (with D. Ghioca and H. Ye) The dynamical ManinMumford conjecture and the dynamical Bogomolov conjecture for split rational maps. 13. (with J. P. Bell) Some finiteness results on monogenic orders in positive characteristic. 14. (with D. Ghioca) The orbit intersection problem for linear spaces and semiabelian varieties. 15. (with D. Ghioca and L.C. Hsia) Simultaneously preperiodic points for families of polynomials in normal form.
Preprints and Work in Progress: 1. (with A. Kulkarni and N. M. Mavraki) Algebraic approximations to linear combinations of powers: an extension of results by Mahler and CorvajaZannier. Submitted. 2. (with D. Ghioca and T. Tucker) Squarefree doubly primitive divisors in dynamical sequences. Submitted. 3. The HermiteJoubert problem and a conjecture of BrassilReichstein. Submitted. 4. (with L. DeMarco, D. Ghioca, H. Krieger, T. Tucker, and H. Ye) Bounded height in families of dynamical systems. First draft available.
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, LiangChung Hsia, Laura DeMarco.
Some slides: (usually short talks) 1. 5minute talk at UNCG Summer School In Computational Number Theory, May 2013. 2. 25minute talk at Pacific Northwest Number Theory Conference, May 2015. 3. 45mintute talk UBC Number Theory Seminar, March 2016. 4. 15minute talk at CNTA XIV, June 2016. 5. 45minute talk at the workshop “Interactions between Model Theory and Arithmetic Dynamics”, Fields Institute, Toronto, July 2016. 6. Slides used for various talks in 2016
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)
