Tran Vu Khanh's homepage

RESEARCH INTERESTS

Harmonic Analysis, Partial Differential Equations, Several Complex Variables, Inverse problems,  Financial Mathematics, Machine Learning, Artificial Intelligence.  

PUBLICATIONS 

Appeared and accepted papers (34)

1. (with Andrew Raich) Local regularity of the Bergman projection on a class of pseudoconvex domains of finite type, Journal of Funtional Analysis 288 (2025), 110855. pdf

2.  The Kohn-Laplace equation on abstract CR manifolds: Local regularity,  Journal of Fourier Analysis and Applications, 31 (2025), 31:10.  pdf

3.  (with Andrew Raich) A note on estimates of the Newtonian potential on bounded domains, Math. Inequalities Appl. 27 (2024), 679-689. pdf

4. A general estimate for the D-bar-Neumann problem. Acta. Math. Vietnam 48 (2023), 83–115. pdf 

5. (with  Cao Tien Dung, Truong Huu Tran,  Tran Duy Hien) A Federated Learning Framework for Privacy-preserving and Parallel Training, Journal of Systems Architecture 124 (2022), 102413. pdf

6. (with Pham Trong Tien) Bergman-Toeplitz operators between weighted $L^p$-spaces on weakly pseudoconvex domains, J. Geom. Anal. 31 (2021), 4612-4640. pdf

7. (with Andrew Raich) L^p-Estimates for the D-bar_b-equation on a class of infinite type domains, Math. Nachr.  294 (2021), 82-97. pdf

8.  (with Andrew Raich) The Kohn-Laplace equation on abstract CR manifolds: Global regularity, Trans. Amer. Math. Soc. 373 (2020), 5775–7606. pdf

9. (with Jiakun Liu, Phung Trong Thuc) Bergman–Toeplitz operators on weakly pseudoconvex domains, Math. Z. 291 (2019), 591–607. pdf

10. (with Jiakun Liu, Phung Trong Thuc) Bergman-Toeplitz operators on fat Hartogs triangles, Proc. Amer. Math. Soc,  147 (2019), 327–338. pdf 

11. (with Luca Baracco, Stefano Pinton) The complex Monge-Amp\`ere equation on weakly pseudoconvex domains, Comptes Rendus Math. 355 (2017), 411-414. pdf

12. (with Nhat-Tan Le, Duy-Minh Dang) A Fourier Sine transform decomposition approach for valuing American knock-out options with time-dependent rebates,  J. Comput. Appl. Math. 317 (2017), 652-671. pdf

13. (with Luca Baracco, Stefano Pinton and Giuseppe Zampieri) Holder regularity of the solution to the complex Monge-Amp`ere equation with L^p density, Calc. Val. Partial Differential Equations 55 (2016), 55:74 pdf

14. (with Ninh Van Thu) Iterates of holomorphic self-maps on pseudoconvex domains of finite and infinite type in $C^n$, Proc. Amer. Math. Soc.  144 (2016),  5197–5206. pdf

15. Equivalence of estimates on domain and its boundary, Vietnam J. Math . 44 (2016), 29-48. pdf

16. Lower bounds on the Kobayashi metric near a point of infinite type, J. Geom. Anal. 26 (2016), 616–629. pdf

17. (with Stefanno Pinton and Giuseppe Zampieri) Loss of derivatives in the infinite type, Pure Appl. Math. Q. 11 (2015) , 315–327. pdf

18. (with Ly Kim Ha) Boundary regularity for the Complex Monge-Amp`ere equation on peudoconvex domains of infinite type, Math. Res. Lett. 22 (2015), 467–484. pdf

19. (with Luca Baracco and Giuseppe Zampieri) Hypoellipticity of the D-bar-Neumann problem at exponentially degenerate points, Asian J. Math. 18 (2014), 623-632. pdf

20. (with Ly Kim Ha and Andrew Raich) L^p-Estimates for the D-bar-equation on a class of infinite type domains, Internat. J. Math. 25 (2014), 1450106 [15 pages]. pdf

21. (with Giuseppe Zampieri) Precise subelliptic estimates for a class of special domains,  J. Anal. Math. 123 (2014), 171–181. pdf

22. Lower bound for the geometric type from a generalized estimate in the D-bar-Neumann problem - a new approach by peak functions, Michigan Math. J. 63 (2014), 209–212. pdf

23. (with Giuseppe Zampieri) Regularity at the boundary and tangential regularity of solutions of the Cauchy-Riemann system, Pacific J. Math. 265 (2013), 491–498. pdf

24. Supnorm and f-H\"older estimates for D-bar on convex domains of general type in C^2, J. Math. Anal. Appl. 403 (2013), 522–531. pdf

25. (with Giuseppe Zampieri) Necessary geometric and analytic conditions for general estimates in the D-bar-Neumann problem, Invent. Math. 188 (2012), 729–750. pdf

26. (with Luca Baracco and Giuseppe Zampieri) Propagation of regularity for solutions of the Kohn-Laplacian in a flat point . Adv. Math. 230 (2012) 1972–1978. pdf

27. (with Stefanno Pinton and Giuseppe Zampieri) Compactness estimates for Box_b on CR manifolds, Proc. Amer. Math. Soc. 140 (2012), 32229–3236. pdf

28. (with Stefanno Pinton and Giuseppe Zampieri) Loss of derivatives for systems of complex vector fields and sums of squares, Proc. Amer. Math. Soc. 140 (2012), 519–530. pdf

29. (with Giuseppe Zampieri) Compactness of the D-bar-Neumann operator on q-pseudoconvex domain, Complex Var. Elliptic Equ. 57 (2012) 1325–1337. pdf

30. (with Giuseppe Zampieri) Estimates for regularity of the tangential D-bar system, Math. Nachr. 284 (2011), 2212 – 2224. pdf

31. (with Giuseppe Zampieri) Subellipticity of the D-bar-Neumann problem on a weakly Q-pseudoconvex/concave domain, Adv. Math. 228 (2011), 1938–1965. pdf

32. (with Giuseppe Zampieri) Regularity of the D-bar-Neumannn problem at infinity type, J. Funct. Anal. 259 (2010), 2760–2775. pdf

33. (with Luca Baracco and Stefanno Pinton) Uniform regularity in a wedge and regularity of traces of CR functions, J. Geom. Anal. 20 (2010), 996–1007. pdf

34. (with Dang Duc Trong, Pham Hoang Quan and Nguyen Huy Tuan) A nonlinear 1-D case backward heat problem: Regularization and error, Z. Anal. Anwendungen 26 (2007), 231-245. pdf

Miscellaneous 

1. (with Ngo Quoc Anh) Phan Thành Nam và giải thưởng Hội Toán Học Châu Âu năm 2020, Thông Tin Toán Học, tập 24 , số 4 (2020), 2-8. pdf  

Preprint

1. (with Andrew Raich) Global regularity for the D-bar-Neumann problem on pseudoconvex manifolds Arxiv

ACADEMIC APPOINTMENTS

• Associate Professor (December 2021 -  ): International University - Vietnam National University Ho Chi Minh City, Vietnam

• Associate Professor (January 2020– December 2021) and Lecturer (April 2019–December 2019): Tan Tao University, Vietnam

• ARC DECRA Research Fellow (April 2015–April 2016) and Vice-Chancellor’s Research Fellow (April 2016–April 2019): University of Wollongong, Australia

• Visiting Fellow (August 2013–March 2015): National Univeristy of Singapore, Singapore

• Lecturer (February 2011–July 2013 ): Tan Tao University, Vietnam 

• Lecturer (March 2010–January 2011): University of Sciences, Vietnam National University of Ho Chi Minh City, Vietnam

• High school teacher (August 2005 - December 2006): High school for the Gifted, Vietnam National University of Ho Chi Minh City, Vietnam

PROFESSIONAL SERVICES

• Member of VIASM Scientific Council (2025-2027) 

• Member of the NAFOSTED Scientific Committee in Mathematics (2020-2022; 2023-2025)

• Member of the VNU-HCM Scientific Committee in  Natural Sciences (2023 - )

• Editorial board member of the Vietnam Journal of Mathematics (2018 - )

• Editorial board member of the Hue University Journal of Science: Natural Science (2018- )

• Editorial board member of the Journal of the Korean Mathematical Society (2019-2021; 2022-2024)

ACADEMIC HONORS, AWARDS AND GRANTS

• NAFOSTED-SNSF grant, Chief Investigator; Vietnam-Swiss, 2024-2029

• NAFOSTED grant, Principal Investigator; Vietnam; 2012-2014, 2020–2022, 2024-2026

• VNU-HCM grant B, Principal Investigator, Vietnam National University - Ho Chi Minh City; 2023-2025

• ARC DECRA grant, Principal investigator; Australia; 2016-2019

• Vice-Chancellor’s Postdoctoral Research Fellowship award from the University of Wollongong; Australia; 2015-2016

• Plenary speaker in the 8th Vietnamese Mathematical Conference; Nha Trang, VietNam; 10-14 August  2013

•  Scientific Prize of the Institute of Mathematics; Hanoi, Vietnam; 2011

• Travel Grant  from the National Institute for Advanced Mathematics F. Severi; Italy, June-August 2010

• PhD Scholarship for international students at the University of Padova; Italy; 2007-2010

• Scholarship from the ICE-EM Australian Graduate School in Mathematics for advanced postgraduate researchers; Queensland,  Australia; July 2006

INVITED VISITS

• Korea Institute for Advanced Study (KIAS), South Korea; April 2015, April 2018

• Department of Mathematics, POSTECH, South Korea; February−March, 2013

• Vietnam Institute for Advanced Study in Mathematics (VIASM), Vietnam; July−September, 2012; April-June, 2016;  November-December 2018

• University of Padova, Italy; June −August, 2010

TEACHING

• VIASM Summer School for students 2024

Mathematical Foundations for Machine Learning

• 2022 - now : International University, VNU-HCM

Calculus 1, Calculus 2, Calculs 2-BT, Analysis 3, Linear Algebra, Applied Linear Algebra, Differential Equation for ISE, Introduction to Python, Introduction to Machine Learning

•  VIASM Winter School in Complex Analysis and Applications 2021

An introduction to Several Complex Variables

• VIASM Winter School 2020

Reinforcement Learning, Mathematics for Deep Learning

• 2019 - 2021: Tan Tao University

Pre-Calculus, Calculus 1, Calculus 2, Reinforcement Learning, Neural Networks and Deep Learning, Introduction to Machine Learning

• 2015 - 2018: University of Wollongong

Advanced Complex Analysis, Graduate PDEs and Complex Analysis

• 2013 - 2015: National University of Singapore

Complex Analysis II, Graduate Complex Analysis