Tran Vu Khanh's homepage

CONTACT INFORMATION
  • Name: Tran Vu Khanh (Trần Vũ Khanh in Vietnamese, T.V. Khanh in publications)
  • Address: School of Mathematics & Applied Statistics, University of Wollongong, NSW, Australia,  2522
  • Office: Building 39C Room 165
  • Email: tkhanh (at) uow.edu.au
  • Website: https://sites.google.com/site/tranvukhanhmath

EDUCATION

  • Ph.D. in Mathematics: University of Padova, Padova, Italy; 2007 - 2010.
  • Undergraduate student: University of Science, Hochiminh city, Vietnam; 2001 - 2005.
PUBLICATIONS 

Appeared and accepted papers (24)

  1. (with Luca Baracco, Stefano Pinton) The complex Monge-Amp\`ere equation on weakly pseudoconvex domainsComptes Rendus Math. 355 (2017), 411-414. pdf
  2. (with Nhat-Tan Le, Duy-Minh DangA Fourier Sine transform decomposition approach for valuing American knock-out options with time-dependent rebates,  J. Comput. Appl. Math. 

    317 (2017), 652-671. pdf

  3. (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
  4. (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
  5. Equivalence of estimates on domain and its boundary, Vietnam J. Math . 44 (2016), 29-48. pdf
  6. Lower bounds on the Kobayashi metric near a point of infinite type, J. Geom. Anal. 26 (2016), 616–629pdf
  7. (with Stefanno Pinton and Giuseppe Zampieri) Loss of derivatives in the infinite type, Pure Appl. Math. Q. 11 (2015) , 315–327pdf
  8. (with Ly Kim Ha) Boundary regularity for the Complex Monge-Amp`ere equation on peudoconvex domains of infinite typeMath. Res. Lett. 22, (2015), 467–484. pdf
  9. (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
  10. (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
  11. (with Giuseppe Zampieri) Precise subelliptic estimates for a class of special domains,  J. Anal. Math. 123 (2014), 171–181. pdf
  12. 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
  13. (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
  14. 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
  15. (with Giuseppe Zampieri) Necessary geometric and analytic conditions for general estimates in the D-bar-Neumann problem, Invent. Math. 188 (2012), 729–750. pdf
  16. (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
  17. (with Stefanno Pinton and Giuseppe Zampieri) Compactness estimates for Box_b on CR manifoldsProc. Amer. Math. Soc. 140 (2012), 32229–3236. pdf
  18. (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
  19. (with Giuseppe Zampieri) Compactness of the D-bar-Neumann operator on q-pseudoconvex domain, Complex Var. Elliptic Equ. 57 (2012) 1325–1337. pdf
  20. (with Giuseppe Zampieri) Estimates for regularity of the tangential D-bar system, Math. Nachr. 284 (2011), 2212 – 2224. pdf
  21. (with Giuseppe Zampieri) Subellipticity of the D-bar-Neumann problem on a weakly Q-pseudoconvex/concave domain, Adv. Math. 228 (2011), 1938–1965. pdf
  22. (with Giuseppe Zampieri) Regularity of the D-bar-Neumannn problem at infinity typeJ. Funct. Anal. 259 (2010), 2760–2775. pdf
  23. (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
  24. (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
Preprints (4)
  1. The Kohn-Laplace equation on abstract CR manifolds: Local regularity, submitted. arXiv
  2.  (with Andrew Raich)The Kohn-Laplace equation on abstract CR manifolds: Global regularity arXiv 
  3. (with Andrew Raich) Zero sets of functions in the Nevanlinna class and the $\bar\partial_b$-equation on convex domains of general type in $\mathbb{C}^2$. submitted. arxiv
  4. (with Andrew Raich) Local regularity properties for the Bergman projection on a class of pseudoconvex domains of finite type, submitted. arxiv

ACADEMIC APPOINTMENTS

  • ARC DECRA 2016 and Vice-Chancellor’s Research Fellow: University of Wollongong, Australia; April 2015–current.
  • Visiting Fellow: National Univeristy of Singapore, Singapore; August 2013–January 2015.
  • Postdoctoral Fellow: University of Padova, Italy; August 2011–July 2013.
  • Lecturer: University of Sciences, Vietnam National University of Ho Chi Minh City and  Tan Tao University, Viet Nam; March 2010–July 2011.
  • High school teacher: High school for the Gifted, Vietnam National University of Ho Chi Minh City, Vietnam; 2005–2006.

INVITED VISITS

  • Korea Institute for Advanced Study (KIAS), South Korea; April 2015.
  • Department of Mathematics, POSTECH, South Korea; February−March, 2013.
  • Vietnam institute for Advanced Study in Mathematics (VIASM), Vietnam; July−September, 2012; April-June, 2016.
  • University of Padova, Italy; June −August, 2010.

RESEARCH INTERESTS

      Harmonic analysis, Partial differential equations, Several complex variables, Cauchy-Riemann geometry, Geometric analysis, Inverse problems, Real/Complex Monge-Ampepre equation. 


PROFESSIONAL SERVICES

  • . Editorial board member of Vietnam Journal of Mathematics.
  • . Review for Mathematical Reviews.

ACADEMIC HONORS, AWARDS AND GRANTS

  • ARC DECRA grant, principal investigator; Australia; 2016-
  • 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. 
  • NAFOSTED grant, Principal Investigator; Vietnam; 2012–2014.
  • 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.