Welcome! This is my streamlined homepage. For a more detailed version, click here.
Tenure-track Assistant Professor
Auburn University
Department of Mathematics and Statistics
203 Parker Hall
Auburn, Alabama 36849
Email: le.chen AT auburn.edu
Zoom: 8141875411
- About Me
- Funding Supports
- Conferences or Seminars
- Teaching
- Publications
- Math Coauthors
- Some recent talks
- Supervision of Ph.D. Students and Postdocs
- Outreach
- Open source projects
- Miscs
I am a tenure-track assistant professor at Auburn University. Prior to this role, I held a position as a visiting assistant professor at Emory University from 2019-2021, spanning four semesters. From 2018-2019, I was a tenure-track assistant professor at the University of Nevada, Las Vegas, for three semesters. Earlier in my career, I held the Black-Babcock visiting assistant professorship at the University of Kansas working closely with David Nualart and Yaozhong Hu, a role I fulfilled from 2015-2017 over the course of five semesters.
My academic journey began at the Swiss Federal Institute of Technology, Lausanne -- École Polytechnique Fédérale de Lausanne, where I obtained my Ph.D. in April 2013 under the supervision of Robert Dalang. Following this, I received an SNSF (Swiss National Science Foundation) post-doctoral research fellowship in 2014, which allowed me to spend a year at the University of Utah working with Davar Khoshnevisan.
My research focus lies within the fields of analysis and probability,
specifically working on stochastic analysis and stochastic partial differential
equations.
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I am looking for Ph.D. students; please contact me if you are interested.
- Curriculum Vitae
- Another life on GitHub
- Previous life on Commputer Science
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Simons Foundation Collaboration Grant for Mathematicians
- 2022-2027
- Award Number: 959981
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NSF DMS-Probability
- 2023-2026
- Award Number: 2246850
- A convenient tool for searching NSF awards: NSF-Awards
- Past supports
- Seminar on Analysis and Stochastic Analysis (SASA) at Auburn.
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Others:
Conferences/Special Sessions Location Date Link Frontier Probability Days 2021 Las Vegas, NV, USA Dec. 3-5, 2021 http://webhome.auburn.edu/~lzc0090/FPD20/ Special Session on Stochastic Analysis and Application Virtual Nov. 20-21, 2021 AMS 2021 Fall Southeastern Sectional Meeting Special Session on Stochastic Processes and Related Topics Atlanta, GA, USA Mar. 18-19, 2023 AMS 2023 Spring Southeastern Sectional Meeting
| Course code | Course | Year | Term | University |
|---|---|---|---|---|
| Math 7800 | Probability I (Measure-based) | 2024 | Fall | Auburn |
| Math 7280 | Advanced ordinary differential equations I | |||
| Math 7830 | Stochastic processes II | Spring | ||
| Math 7820 | Stochastic processes I | 2023 | Fall | |
| Math 7810 | Probability II (Measure-based) | Spring | ||
| Math 7010 | Applied Mathematics II | |||
| Math 7800 | Probability I (Measure-based) | 2022 | Fall | |
| Math 7000 | Applied Mathematics I | |||
| Math 7210 | Real Analysis II | Spring | ||
| Math 5870/6870 | Mathematical Finance | 2021 | Fall | |
| STAT 3600 | Probability & Statistics - I | |||
| Summer Boost Camp | For Bioinformatics Ph.D. program | Summer | Emory | |
| Math 362 | Mathematical Statistics - II | Spring | ||
| Math 221 (two sessions) | Linear Algebra | |||
| Math 221 (three sessions) | 2020 | Fall | ||
| Math 362 (two sessions) | Mathematical Statistics - II | Spring | ||
| Math 361 (two sessions) | Mathematical Statistics - I | 2019 | Fall | |
| Math 463/663 | Advanced Matrix Theory | Spring | UNLV | |
| Math 283 | Calculus III | |||
| Math 432 | Elementary Complex Analysis | 2018 | Fall | |
| Math 181 | Calculus I | |||
| Math 365 | Computational Linear Algebra | Spring | ||
| Math 526 | Probability and Statistics | 2017 | KU | |
| Math 526 | 2016 | Fall | ||
| Math 526 | Spring | |||
| Math 526 | 2015 | Fall | ||
| Math 526 | Spring |
- Open slides for Linear Algebra (based on Math 221 taught at Emory)
- Open slides for Mathematical Statistics (based on Math 362 taught at Emory)
- Here are some teaching tools that I have been using.
- Download the .bib file of mine.
- Open reference bank: SPDEs-Bib; Download the latest version of All.bib; View the bank in pdf.
- Search for the open reference bank at https://spdes-bib.readthedocs.io/en/latest/ where you can download pdf or epub files.
- Source codes of the reference bank at: SPDEs-Bib.
- Some symbolic tools for the Fox H-function.
| Co-authors | Title | Ref | Misc | |
|---|---|---|---|---|
| 36 | M. Foondun, J. Huang, and M. Salins | Global solution for superlinear stochastic heat equation on Rd under Osgood-type conditions | arXiv:2310.02153 | 22 pages |
| 35 | P. Xia | Asymptotic properties of stochastic partial differential equations in the sublinear regime | arXiv:2306.06761 | 50 pages |
| Co-authors | Title | Journal | Year | Status | |
|---|---|---|---|---|---|
| 34 | C. Ouyang and W. Vickery | Parabolic Anderson model with colored noise on torus | Bernoulli | 2024 | Accepted , pending revision |
| 33 | S. Kuzgun, C. Mueller, and P. Xia | On the radius of the self-repellent fractional Brownian motion | Journal of Statistical Physics | 2023 | Vol. 191, article No. 19 (2024). Open access |
| 32 | N. Eisenberg | Invariant measures for the nonlinear stochastic heat equation on Rd without any drift term | Journal of Theoretical Probability | To appear, Open access | |
| 31 | Y. Guo and J. Song | Moments and asymptotics for a class of SPDEs with space-time white noise | Transactions of the American Mathematical Society | To appear | |
| 30 | D. Candil and C.Y. Lee | Parabolic stochastic PDEs on bounded domains with rough initial conditions: moment and correlation bounds | Stochastic Partial Differential Equations: Analysis and Computations | To appear | |
| 29 | N. Eisenberg | Interpolating the stochastic heat and wave equations with time-independent noise: solvability and exact asymptotics | 11 (3):1203-1253 | ||
| 28 | J. Huang | Superlinear stochastic heat equation on Rd | Proceedings of American Mathematical Society | 151 (9):4063-4078 | |
| 27 | D. Khoshnevisan, D. Nualart, and F. Pu | Central limit theorems for spatial averages of the stochastic heat equation via Malliavin-Stein's method | Stochastic Partial Differential Equations: Analysis and Computations | 11 (1):122-176 | |
| 26 | R. Balan and Y. Ma | Parabolic Anderson model with rough noise in space and general initial conditions | Electronic Communication of Probability | 2022 | (2022) Paper No. 65, 12 pp. |
| 25 | G. Hu | Hölder regularity of the nonlinear stochastic time-fractional slow and fast diffusion equations on Rd | Fractional Calculus and Applied Analysis | 25 (2), 608-629. | |
| 24 | D. Khoshnevisan, D. Nualart, and F. Pu | Spatial ergodicity and central limit theorems for parabolic Anderson model with delta initial conditions. | Journal of Functional Analysis | 282 (2), Paper No. 109290, 35 pp. | |
| 23 | Spatial ergodicity for SPDEs via a Poincaré-inequalities | Electronic Journal of Probability | 2021 | 26, Paper No. 140, 37 pp. | |
| 22 | A CLT for dependent random variables, with applications to infinitely-many interacting diffusion processes. | Proceedings of American Mathematical Society | 149 (12), 5367–5384 | ||
| 21 | Central limit theorems for parabolic stochastic partial differential equations. | Annales de l'Institut Henri Poincaré, Probabilités et Statistiques | 58 (2), 1052-1077 | ||
| 20 | R. Balan and X. Chen | Exact asymptotics of the stochastic wave equation with time-independent noise. | 58 (2022), no. 3, 1590-1620 | ||
| 19 | Y. Hu and D. Nualart | Regularity and strict positivity of densities for the nonlinear stochastic heat equation. | Memoirs of American Mathematical Society | Vol. 273, no. 1340. | |
| 18 | K. Kim | Stochastic comparison for stochastic heat equation on Rd. | Electronic Journal of Probability | 2020 | 25, article No. 140, 1--38 |
| 17 | J. Huang, D. Khoshnevisan and K. Kim | Dense blowup for parabolic SPDEs. | 2019 | Vol. 24, paper no. 118, 1-33 | |
| 16 | Y. Hu and D. Nualart | Nonlinear stochastic time-fractional slow and fast diffusion equations on Rd. | Stochastic Processes and their Applications | 129, 5073-5112 | |
| 15 | J. Huang | Comparison principle for stochastic heat equation on Rd. | Annals of Probability | Vol. 47, No. 2, 989-1035 | |
| 14 | K. Kim | Nonlinear stochastic heat equation driven by spatially colored noise: moments and intermittency. | Acta Mathematica Scientia | 2018 | 39B (3): 645-668 |
| 13 | 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 | |
| 12 | R. Balan | Parabolic Anderson Model with space-time homogeneous Gaussian noise and rough initial condition. | Journal of Theoretical Probability | 31 (4), 2216-2265 | |
| 11 | Y. Hu and D. Nualart | Two-point correlation function and Feynman-Kac formula for the stochastic heat equation | Potential Analysis | 2017 | 46 (4), 779-797 |
| 10 | 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 | 53 (1), 358-388 | |
| 9 | M. Cranston, D. Khoshnevisan and K. Kim | Dissipation and high disorder | Annals of Probability | 45 (1), 82-99 | |
| 8 | D. Khoshnevisan and K. Kim | A boundedness trichotomy for the stochastic heat equation | Annales de l'Institut Henri Poincaré, Probabilités et Statistiques | 53 (4), 1991-2004 | |
| 7 | Nonlinear stochastic time-fractional diffusion equations on R: moments, Hölder regularity and intermittency | Transactions of the American Mathematical Society | 369 (12), 8497-8535 | ||
| 6 | G. Hu, Y. Hu and J. Huang | Space-time fractional diffusions in Gaussian noisy environment | Stochastics | 89 (1), 171-206 | |
| 5 | D. Khoshnevisan and K. Kim | Decorrelation of total mass via energy. | Potential Analysis | 2016 | 45 (1), 157-166 |
| 4 \(^*\) | R. Dalang | Moment bounds and asymptotics for the stochastic wave equation | Stochastic Processes and their Applications | 2015 | 125 (4), 1605-1628 |
| 3 | Moments, intermittency and growth indices for nonlinear stochastic fractional heat equation | Stochastic Partial Differential Equations: Analysis and Computations | 3 (3), 360-397 | ||
| 2 | Moments and growth indices for the nonlinear stochastic heat equation with rough initial conditions | Annals of Probability | 43 (6), 3006-3051 | ||
| 1 | Hölder-continuity for the nonlinear stochastic heat equation with rough initial conditions | Stochastic Partial Differential Equations: Analysis and Computations | 2014 | 2 (3), 316-352 |
\(^*\) This paper corresponds mostly to Section 3 of the unpublished notes [-2] arXiv:1401.6506v1
| Adviser | Title | Year | Misc | |
|---|---|---|---|---|
| 0 | Robert C. Dalang | Moments, intermittencey, and growth indices for nonlinear stochastic PDE's with rough initial conditions. | 2013 | The École polytechnique fédérale de Lausanne, Thesis No. 5712 |
| Co-authors | Title | Year | Misc | |
|---|---|---|---|---|
| -1 | R. Dalang | The nonlinear stochastic heat equation with rough initial data: a summary of some new results | 2012 | arXiv:120.1690 |
| -2 | Moment bounds in spde's with application to the stochastic wave equation | 2014 | arXiv:1401.6506 | |
| -3 | The third moment for the parabolic Anderson model | 2016 | arXiv:1609.01005 | |
| -4 | J. Huang | Regularity and strict positivity of densities for the stochastic heat equation on Rd | 2019 | arXiv:1902.02382 |
| Journal | Counts |
|---|---|
| Stochastic Partial Differential Equations: Analysis and Computations | 5 |
| Annales de l'Institut Henri Poincaré, Probabilités et Statistiques | 4 |
| Annals of Probability | 3 |
| Electronic Journal of Probability | 3 |
| Journal of Theoretical Probability | 2 |
| Potential Analysis | 2 |
| Proceedings of American Mathematical Society | 2 |
| Stochastic Processes and their Applications | 2 |
| Transactions of the American Mathematical Society | 2 |
| Acta Mathematica Scientia | 1 |
| Bernoulli | 1 |
| Electronic Communication of Probability | 1 |
| Fractional Calculus and Applied Analysis | 1 |
| Journal of Functional Analysis | 1 |
| Journal of Statistical Physics | 1 |
| Memoirs of American Mathematical Society | 1 |
| Probability Theory and Related Fields | 1 |
| Stochastics | 1 |
| Total | 34 |
| Name | University | Counts |
|---|---|---|
| Balan, Raluca | University of Ottawa, CA | 3 |
| Chen, Xia | University of Tennessee | 1 |
| Candil, David | École Polytechnique Fédérale de Lausanne, Switzerland | 1 |
| Cranston, Michael | University of California, Irvine | 1 |
| Dalang, Robert | École Polytechnique Fédérale de Lausanne, Switzerland | 4 |
| Eisenberg, Nicholas | University of Nevada, Las Vegas/Auburn University | 2 |
| Foondun, Mohammud | University of Strathclyde, Glasgow, UK | 1 |
| Guo, Yuhui | Shandong University, CN | 1 |
| Hu, Guannan | Washburn University | 2 |
| Hu, Yaozhong | University of Alberta, CA | 5 |
| Huang, Jingyu | University of Birmingham, UK | 6 |
| Kalbasi, Kamran | University College Dublin | 1 |
| Khoshnevisan, Davar | University of Utah | 9 |
| Kim, Kunwoo | Pohang University of Science and Technology, Korea | 7 |
| Kuzgun, Sefika | University of Rochester | 1 |
| Lee, Cheuk Yin | Taiwan Tsing Hua University | 1 |
| Ma, Yiping | University of Ottawa, CA | 1 |
| Mueller, Carl | University of Rochester | 1 |
| Nualart, David | University of Kansas | 9 |
| Ouyang, Cheng | University of Illinois, Chicago | 1 |
| Pu, Fei | Beijing Normal University | 5 |
| Salins, Mickey | Boston University | 1 |
| Song, Jian | Shandong University, CN | 1 |
| Vickery, William | University of Illinois, Chicago | 1 |
| Xia, Panqiu | Auburn University | 2 |
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I am looking for Ph.D. students starting from Fall 2023; please contact me if you are interested.
Name Years Subsequenct position Eisenberg, Nicholas 2018 Fall -- 2022 Summer Postdoc at Department of Energy
| Name | Years | Subsequent position |
|---|---|---|
| Xia, Panqiu | 2022 Fall -- 2024 Summer | Lecture (Tenure-track) at University of Cardiff, UK |
- I have one postdoc position for one year, which can be potentially extended to two years, starting anytime from Summer 2024. Please contact me if you are interested.
- AMS Sectional meeting at FSU 2024 March 24 and 25
- Seminar on Analysis and Stochastic Analysis, at Auburn, 2024 March 13.
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Auburn University Summer Science Institute (AU-SSI)
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My AU-SSI course materials on github
- 2022: An Invitation to Probability
- 2023: Embracing the randomness: Intriguing Role of Chance in Science
- 2024: TBA
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My AU-SSI course materials on github
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Destination STEM (official website)
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My table of exhibition on github
- 2023: How Surface Grows, one media photo
- 2024: TBA
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My table of exhibition on github
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Graduate Student Seminars (Github)
- 2021-09-27: Introduction to stochastic partial differential equations
- 2023-01-18: Introduction to stochastic heat equation
- 2023-02-15: Sharpening your saw before cutting down the tree -- Personal development environment (PDE)
- 2023-11-01: Disorderly surface growth
| GitHub Projects | Descriptions | Teaching/Education | Research | Software | Citation/Documentations |
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| chenle02/SPDEs-Bib | SPDEs-Bib: A Comprehensive Bibliography of Stochastic Partial Differential Equations and Related Topics | X |
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| chenle02/Fox-H_Symbolic_Tools | Some symbolic tools for the Fox H-function | X | X |
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| chenle02/Open_Slides_for_Linear_Algebra | Open slides for linear algebra | X |
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| chenle02/Open_Slides_Statistics | Statistics: Open Slides | X |
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| chenle02/2022_SSI-AU_Probability_by_Le | Probability: Summer Science Institute at Auburn | X |
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| chenle02/NSF-Awards | Awards from National Science Foundation (NSF) with a Focus on Division of Mathematical Sciences (DMS) | X |
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| chenle02/Graduate_Student_Seminars_by_Le_Chen | Graduate Student Seminars by Le Chen | X |
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| chenle02/Open_Slides_Financial_Mathematics | Financial Mathematics: Open Slides | X |
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| chenle02/Simulations_on_Some_Surface_Growth_Models | This is a python package to simulate the surface growth using, e.g, Tetris pieces. | X | X | X | Documentations in html and pdf |
| Social Medias in Academia | Others | ||
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| Google Scholar | arXiv | Github | Huggingface |
| ORCID | Research Gate | Tereminal Cast | Twitwer/X |
| Mathscinet | My neovim 0.5+ setup | ||
| Web of Science (Publon) | |||