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

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


Since 7/2014: UBC-PIMS Distinguished Postdoctoral Fellow mentored by Professor Dragos Ghioca.

 

5/2014: PhD in math at UC Berkeley. Co-advisors: Professors Thomas Scanlon and Paul Vojta (I was also mentored by Professor Thomas Tucker during a 3-month 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)

 

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.
Acta Arith. 140 (2009), 205-232. pdf

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

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

4. Algebraic independence of local conjugacies and related questions in polynomial dynamics.
Proceedings AMS, 143 (2015), 1491-1499

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

6. (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

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.
Accepted to
Trans. Amer. Math. Soc., 2015.

10. (with D. Ghioca) Dynamics of split polynomial maps: uniform bounds for periods and application.
Accepted to
Int. Math. Res. Not. IMRN., 2016.

11. (with D. Ghioca, H. Krieger, and H. Ye) The dynamical André-Oort conjecture: unicritical polynomials.
Accepted to
Duke Math Journal, 2016.

 

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 Manin-Mumford 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 Corvaja-Zannier. Submitted.

4. (with D. Ghioca) The orbit intersection problem for linear spaces and semiabelian varieties. Submitted.

5. (with D. Ghioca and T. Tucker) Squarefree doubly primitive divisors in dynamical sequences. 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. 5-minute talk at UNCG Summer School In Computational Number Theory, May 2013.

2. 25-minute talk at Pacific Northwest Number Theory Conference, May 2015.

3. 45-mintute talk UBC Number Theory Seminar, March 2016.

4. 15-minute talk at CNTA XIV, June 2016.

5. 45-minute talk at the workshop “Interactions between Model Theory and Arithmetic Dynamics”, Fields Institute, Toronto, July 2016.

 

Previous Teaching at Berkeley:
Fall 2012: GSI for MATH 1A (lecturer: Paul Vojta)

Spring 2013: GSI for MATH 54 (lecturer: Zvezdelina Stankova)
Summer 2013: Full instructor for MATH 54.

Fall 2013: GSI for MATH 16B (lecturer: James Demmel)

Spring 2014: GSI for MATH 16B (lecturer: Alexander Coward)