I have moved to the University of Nevada, Las Vegas since January 2018.


Le Chen

Le Chen

Black-Babcock visiting assistant professor

University of Kansas
Department of Mathematics
405 Snow Hall, 1460 Jayhawk Blvd
Lawrence, Kansas, 66045-7594
USA
Email: chenle AT ku.edu (Internet)
Tel: +1 785 864 4452
FAX: +1 785 864 5255


About me

I have moved to the University of Nevada, Las Vegas, for the tenure-track position since Jan. 2018. Here is my new page. This appointment has been postponed for one semester from Aug. 2017. Prior to this, I was a visiting assistant professor at the University of Kansas, working with Professor David Nualart and Professor Yaozhong Hu. I obtained my Ph.D. in April 2013 from Swiss Federal Institute of Technology, Lausanne (or École Polytechnique Fédérale de Lausanne, EPFL, in french), under the guidance of Professor Robert C. Dalang. In 2014, I was an SNSF (Swiss National Science Foundation) post-doctoral research fellow working with Professor Davar Khoshnevisan and Dr. Kunwoo Kim. I am an analysist/probabilist, working on stochastic partial differential equations.

You may find more information in my Curriculum Vitae.

Teaching


Publications

Ph.D. thesis

Published (or to appear)

  1. (with R. Dalang), Moments and growth indices for the nonlinear stochastic heat equation with rough initial conditions
    Annals of Probability, Vol. 43, No. 6, 3006-3051, 2015.

  2. (with R. Dalang) Hölder-continuity for the nonlinear stochastic heat equation with rough initial conditions
    Stochastic Partial Differential Equations: Analysis and Computations, Volume 2, Issue 3, pp 316-352, 2014.

  3. (with R. Dalang) Moment bounds and asymptotics for the stochastic wave equation
    Stochastic Processes and their Applications, Volume 125, Issue 4, pp 1605-1628, 2015.
    (This paper corresponds mostly to Section 3 of the unpublished notes arXiv:1401.6506v1)

  4. (with R. Dalang) Moments, intermittency and growth indices for nonlinear stochastic fractional heat equation
    Stochastic Partial Differential Equations: Analysis and Computations, Volume 3, Issue 3, pp 360-397, 2015.

  5. (with M. Cranston, D. Khoshnevisan and K. Kim) Dissipation and high disorder
    Annals of Probability, Vol. 45, No. 1, 82-99, 2017 (arXiv:1411.6607)

  6. (with K. Kim) On comparison principle and strict positivity of solutions to the nonlinear stochastic fractional heat equations
    Annales de l'Institut Henri Poincaré, Probabilités et Statistiques, Vol. 53, No.1, 358-388, 2017. (arXiv:1410.0604)

  7. (with K. Kim and D. Khoshnevisan) Decorrelation of total mass via energy.
    Potential Analysis, Vol. 45, pp. 157-166, 2016.

  8. (with G. Hu, Y. Hu and J. Huang) Space-time fractional diffusions in Gaussian noisy environment.
    Stochastics, 89 (1), 171-206, 2016.

  9. Nonlinear stochastic time-fractional diffusion equations on R: moments, Hölder regularity and intermittency.
    Transactions of the American Mathematical Society, 2016. (to appear, arXiv:1410.1911)

  10. (with D. Khoshnevisan and K. Kim) A boundedness trichotomy for the stochastic heat equation.
    Annales de l'Institut Henri Poincaré, Probabilités et Statistiques, 2016. (to appear, arXiv:1510.04674)

  11. (with Y. Hu and D. Nualart) Two-point correlation function and Feynman-Kac formula for the stochastic heat equation.
    Potential Analysis, 2016. (arXiv:1509.01121v1)

  12. (with Y. Hu, K. Kalbasi and D. Nualart) Intermittency for the stochastic heat equation driven by a rough time fractional Gaussian noise.
    Probability Theory and Related Fields 171(1), 431-457, 2018, arXiv:1602.05617.

  13. (with R. Balan) Parabolic Anderson Model with space-time homogeneous Gaussian noise and rough initial condition.
    Journal of Theoretical Probability (to appear, arXiv:1606.08875)

  14. (with J. Huang) Comparison principle for stochastic heat equation on Rd.
    Annals of Probability (to appear, arXiv:1607.03998)

Submitted

  1. (with Y. Hu and D. Nualart) Nonlinear stochastic time-fractional slow and fast diffusion equations on Rd. arXiv:1509.07763 (43 pages).

  2. (with K. Kim) Nonlinear stochastic heat equation driven by spatially colored noise: moments and intermittency. arXiv:1510.06046 (26 pages).

  3. (with Y. Hu and D. Nualart) Regularity and strict positivity of densities for the nonlinear stochastic heat equation. arXiv:1611.03909 (90 pages)

  4. (with J. Huang, D. Khoshnevisan and K. Kim) Dense blowup for parabolic SPDEs arXiv:1702.08374 (39 pages)

Some unpublished preprints


Conferences delivered and to be delivered

    2016

  1. Stochastic Partial Differential Equations and Related Fields (Universität Bielefeld, Germany, Oct. 10 - 14, 2016)
    Title: Regularity and positivity of densities for the stochastic (fractional) heat equation

  2. Topics in Stochastic Partial Differential Equations, (the AMS Sectional Meeting) (University of Utah, Salt Lake City, April 9 - 10, 2016)
    Title: Regularity and strict positivity of densities for the stochastic heat equation.

  3. SUSTech Global Scientists Forum (South University of Science and Technology of China, Shenzhen, March 18 - 19, 2016)
    Title: Intermittency front for various SPDE's. (talk)
  4. 2015

  5. The 38th Conference on Stochastic Processes and their Applications (University of Oxford, UK. July 13 - 17, 2015)
    Title: Intermittency front for various SPDE's (talk, thanks to the Elsevier Travel Grant for young researchers)

  6. Random Dynamical Systems and Ergodicity (University of Loughborough, Loughborough, UK. July 7 - 10, 2015)
    Title: Nonlinear stochastic slow and fast diffusion equations on R. (talk).

  7. AMS Special Session on Stochastic Analysis and Rough Paths (University of Nevada, Las Vegas, USA. April 18 - 19, 2015)
    Title: On comparison principle and strict positivity of solutions to the nonlinear stochastic fractional heat equation (talk).
  8. 2014

  9. Rocky Mountain Mathematics Consortium (RMMC) (University of Wyoming, USA. May 27 - June 6, 2014)
    Title: Hölder continuity for the nonlinear stochastic heat equation with rough initial conditions (talk)

  10. Frontier Probability Days 2014 (Tucson, Arizona, USA. May 18-20, 2014)
    Title: Hölder continuity for the nonlinear stochastic heat equation with rough initial conditions (talk)
  11. 2013

  12. NSF/CBMS Conference: Analysis of Stochastic Partial Differential Equations (Michigan State University, East Lansing, U.S. Aug. 19-23, 2013)
    Title: Moments, intermittency and growth Indices for nonlinear stochastic space-fractional heat equation (talk)

  13. Stochastic Partial Differential Equations (SPDEs) (Isaac Newton Institute for Mathematical Sciences, Cambridge, UK. Sept. 10-14, 2012)
    Title: Some properties of the parabolic Anderson model (poster)
  14. 2012

  15. Stochastic Analysis and Applications (Centre Interfacultaire Bernoulli, Lausanne, Switzerland. June 4-8, 2012)
    Title: Intermittency for some parabolic and hyperbolic Anderson models (poster)

  16. Stochastic Analysis and Stochastic Partial Differential Equations (Banff International Research Station, Banff, Canada. Apr. 1-6, 2012)
    Title: Intermittency and exponential growth indices for some parabolic and hyperbolic Anderson models (talk)

    2010--2011

  17. Evolution Equations: Randomness and Asymptotics (The Karlsruhe Institute of Technology, Bad Herrenalb, Germany. Oct. 10-14, 2011)
    Title: Growth indices in a parabolic Anderson model (talk)

  18. Sixth Ph.D. Student Conference in Stochastics (Zurich, Switzerland. Sept. 30 -- Oct. 2, 2010)
    Title: A Feynman-Kac type formula for the deterministic wave equations on a domain with boundary conditions (talk)

Seminars delivered and to be delivered

    2017

  1. University of Virginia, Probability Seminar (Dec. 06, 2017)

  2. University of Berkeley, Probability Seminar (Nov. 29, 2017)

  3. University of California, Davis, Mathematical Physics & Probability Seminar (Oct. 11, 2017)

  4. Stevens Institute of Technology Math Colloquium (Feb. 15, 2017)

  5. University of Maryland at Baltimore County Math Colloquium (Feb. 10, 2017)

  6. University of Nevada, Las Vegas Math Colloquium (Feb. 6, 2017)

  7. University of Rochester Math Colloquium (Jan. 23, 2017)

  8. 2016

  9. Binghamton University Math Colloquium (Dec. 7, 2016)
    Title: Stochastic heat equation: intermittency and densities.

  10. McGill University Probability Seminar (Nov. 29, 2016)
    Title: Stochastic heat equation: intermittency, densities and beyond.

  11. University of Tennessee, Stochastic Seminar (Nov. 19, 2016)
    Title: Regularity of densities for the nonlinear stochastic heat equations.

  12. University of Kansas, (Oct. 5, 2016)
    Title: Regularity of densities for stochastic fractional heat equation with rough initial data.

  13. Chinese Academic of Science, four lectures (July 5-6, 2016)
    Title: A random field approach to stochastic partial differential equations.

  14. Stanford University, Applied Math Seminar (May 25, 2016)
    Title: Intermittency fronts for the stochastic heat equation and beyond.

  15. Chinese Academy of Science, Colloquium (March 21, 2016)
    Title: Moments and intermittent stochastic heat equation.

  16. University of Tennessee, Colloquium (Jan. 19, 2016)
    Title: Intermittent stochastic partial differential equations.

  17. 2015

  18. Ottawa University, Probability Seminar (Nov. 27, 2015)
    Title: Moments and intermittency fronts for various SPDE's.

  19. McGill/Concordia Universities, CRM-ISM Probability Seminar (Nov. 26, 2015)
    Title: Moments, rough initial data and intermittency for various SPDE's.

  20. University of Kansas, Kansas Stochastics Seminar (May 6, 2015)
    Title: On comparison principle and strict positivity of solutions to the nonlinear stochastic fractional heat equation

  21. University of Kansas, Kansas Stochastics Seminar (April 8, 2015)
    Title: Nonlinear stochastic time-fractional diffusion equations on R

  22. University of Kansas, Kansas Stochastics Seminar (Feb. 11, 2015)
    Title: Intermittency fronts for various SPDE's

    2014

  23. University of Utah, Utah Stochastics Seminar (Dec. 12, 2014)
    Title: Moments and intermittency fronts for the stochastic heat equation with spatially colored noise

  24. Lehigh University, (Math Colloquium) invited by Professor Daniel Conus (Oct. 29, 2014)
    Title: Intermittency fronts for the stochastic heat equation

  25. École Polytechnique Fédérale de Lausanne, invited by Professor Robert Dalang (Aug. 12, 2014)
    Title: A sample-path comparison principle for the nonlinear stochastic space-fractional heat equation with rough initial conditions

  26. University of York, invited by Professor Zdzislaw Brzezniak (Aug. 4, 2014)
    Title: Some studies on the nonlinear stochastic space-fractional heat equation

  27. Loughborough University, invited by Professor Mohammud Foondun (July 29, 2014)
    Title: Intermittence, growth indices and sample-path comparison principle for nonlinear stochastic space-fractional heat equation

  28. Beijing Normal University, invited by Professor Zenghu Li (June 16, 2014)
    Title: Some studies on the stochastic heat equation on R

  29. University of Utah, Utah Stochastics Seminar (Feb. 28, 2014)
    Title: Moment estimates for various SPDE's driven by space-time white noise

    2013

  30. National Center for Mathematics and Interdisciplinary Sciences, (Chinese Academy of Sciences) invited by Professor Tao Zhou (May 3, 2013)
    Title: Moments and growth indices for the nonlinear stochastic heat equation with rough initial conditions

Miscellaneous

My early work on computer science

Between my master and Ph.D., I worked (as a visiting scholar) for one year at Microsoft Research Asia in the Web Search and Mining group and for another year at IDIAP research institute (Switzerland). I was working on statistical machine learning, content-based image retrieval and computer vision. I have one US patent Here are some selected publications during that period:
  1. Le Chen, David Barber, Jean-Marc Odobe, Dynamical Dirichlet mixture model, in IDIAP-RR, 2007-02. (source codes here).

  2. Le Chen, Lei Zhang, Feng Jing, Kefeng Deng, Wei-Ying Ma, Ranking web objects from multiple communities, in ACM Fourteenth Conference on Information and Knowledge Management (CIKM), 2006. (conference presentation)

  3. Lei Zhang, Le Chen, Feng Jing, Kefeng Deng, Wei-Ying Ma, EnjoyPhoto: a vertical image search engine for enjoying high-quality photos, in ACM Multimedia, 2006. (conference presentation)

  4. Xirong Li, Le Chen, Lei Zhang, Fuzong Lin and Wei-Ying Ma, Image annotation by large-scale content-based image retrieval, in ACM Multimedia 2006.

  5. Le Chen, Dayong Ding, Dong Wang, Fuzong Lin and Bo Zhang, Ap-based borda voting method for feature extraction in trecvid-2004, in Advances in Information Retrieval, Lecture Notes in Computer Science Volume 3408, 2005.

Some useful links