1. Full name:     Nguyen Duy Phuong                             2. Sex: Male

3. Date of birth: 12/05/1979                                            4. Place of birth: Hanoi

5. Admission decision number: No 696/ QĐ-ĐHKHTN on 19/03/2014 by Rector of VNU University of Science, Vietnam National University.

6. Changes in academic process:

- Extension decision number 3209/QĐ-ĐHKHTN dated on 20/09/2017 and 597/QĐ-ĐHKHTN dated on 06/03/2018 by Rector of VNU University of Science.

7. Official thesis title: The spectral of graph and incidence problems in finite fields.

8. Major: Mathematical basis for informatics                   9. Code: 9460117.02

10. Supervisors: Assoc.Prof.Dr. Le Anh Vinh

11. Summary of the new findings of the thesis

-  Construct and compute the spectrum of graphs on finite fields. Beside of proving some known results for determining the graph of sum-product, Cayley graph from diagonal polynomial, PhD student has some new results for the graph of incidence between planes.

- Present some new result on incidence bound between the set of points and the set of parabolas; incidence bound between the set of points and the set of general spheres (extend the results of Alex Iosevich), incidence bound between planes (extend the results of Vinh, B.Lund and S.Saraf). From that, PhD student gives new proofs for Beck’s kind theorem on spheres and planes, and Beck’s kind theorem on parabolas.

- Generalize the results for incidence bound between points and manifolds of Vinh, and from that PhD student gives some new results on incidence bound between the set of points and the set of lines, between the set of points and the set of manifolds.

12. Practical applicability, if any: One of the most important application of the incidence problem is the sum – product problem on finite field, which in turn is used to construct random extractors. The random extractors are widely used in many applications, especially in communication networks, expander grasp, error correcting codes, cryptographic protocols, data structures and samples.

13. Further research directions, if any.

- The future research of thesis may be the similar problems on small sets and their applications.

14. Thesis-related publications:

[1]. N. D. Phương, P. V. Thắng, L. A. Vinh (2017), "Incidences between points and generalized spheres over finite fields", Forum Mathematicum 29(2), pp. 449-456(SCI).

[2]. T. Pham, N. D. Phương, N. M. Sang, C. Valculescu, L. A. Vinh (2018), "Distinct distances between points and lines in F^2_q", Forum Mathematicum, 30(4), pp. 799-808 (SCI).

[3]. N. D. Phương, P. V. Thắng, L. A. Vinh (2019), "Incidences between planes over finite fields", Proceedings of American Mathematics Society, 147(5), pp. 2185-2196 (SCI).

 [4]. N. D. Phương, L. A. Vinh, "An incidences theorem for points and parabols in finite fields", Ars Combinatorica (SCIE) (accepted)