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: 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 2015: MATH 200 (Multivariable Calculus), 2 sections. 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. 2. (with C. Gratton and T. Tucker) ABC implies primitive prime divisors in arithmetic dynamics. 3. Some arithmetic dynamics of diagonally split polynomial maps. 4. Algebraic independence of local conjugacies and related questions in polynomial dynamics. 5. (with D. Ghioca and T. Tucker) Portraits of preperiodic points for rational maps. 6. (with E. Amerik, P. Kurlberg, A. Towsley, B. Viray and F. Voloch) Evidence for the dynamical BrauerManin criterion. 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.
Preprints and Work in Progress: 1. (with J. Bell) Some finiteness results on monogenic orders in positive characteristic. Submitted. 2. (with D. Ghioca and H. Ye) The dynamical ManinMumford conjecture and the dynamical Bogomolov conjecture for split rational maps. Submitted. 3. (with A. Kulkarni and N. M. Mavraki) Algebraic approximations to linear combinations of powers: an extension of results by Mahler and CorvajaZannier. Submitted. 4. (with D. Ghioca) The orbit intersection problem for linear spaces and semiabelian varieties. Submitted.
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: (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.
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)
