About I am an applied mathematician with a great interest in interdisciplinary research. My main interests are information geometry, stochastic processes, optimal transport, partial differential equations, combinatorics, statistics and their applications in mathematical population genetics as well as mathematical finance. I am also interested in statistical analysis methods and machine learning algorithms in order to construct/refer mathematical models based on available big data.
Education I received my Bachelor degree in Mathematics in 2004 and my Master degree in Mathematics in 2006 from the VNU-Hanoi University of Sciences. Both these degrees are under the advisory of Prof. Dr. Nguyen Van Minh. In 2012, I received my Ph.D. degree in applied mathematics from Leipzig Univeristy under the advisory of Prof. Dr. Juergen Jost.

Below is a part of my mathematical genealography:
Experience

Work Experience

  • 01.10.2019-30.09.2020: W2 Vertretungsprofessor at Institute of Mathematics, Leipzig University.
  • 01.10.2019-30.09.2020: Guest researcher at Max Planck Institute for Mathematics in the Sciences.
  • 01.06.2019-31.07.2019: Visiting researcher at VIASM, Hanoi.
  • 20.05.2019-22.05.2019: Visiting researcher at Institute of Mathematics of ASCR, Zitna 25, Praha.
  • 20.11.2018-24.11.2018: Visiting researcher at Institute of Mathematics of ASCR, Zitna 25, Praha.
  • 15.05.2018-15.06.2018: Visiting professor at Institut Denis Poisson, Tours.
  • 01.03.2017-31.05.2017: Visiting researcher at VIASM, Hanoi.
  • 05.07.2012-30.09.2019: Postdoctoral researcher, Max Planck Institute for Mathematics in the Sciences, Leipzig.
  • 2011–2012: Research assistant, Max Planck Institute for Mathematics in the Sciences, Leipzig.
  • 2007–2011: PhD-student, Max Planck Institute for Mathematics in the Sciences, Leipzig.

Teaching and supervisor experience

Organization experience

Funded project experience

  • 2019-2020: Member, H2020-EU.1.2.2., ID: 732942, ODYCCEUS, Leipzig.
  • 01.06-31.07.2019: PI, 2 month research project, Stationary states for stochastic processes, VIASM, Hanoi.
  • 01.03-31.05.2017: PI, 3 month research project, Stationary measures for stochastic differential equations with Hoelder continuous coefficients, VIASM, Hanoi.
  • 2011-2016: Member, FP7-IDEAS-ERC, ERC Advanced Grant, ID: 267087, VARIOGEO, Leipzig.
  • 2007-2008: PI, University project, Some problems in differential equations with piecewise constant argument, Hanoi.
Research Topics

Mathematical Population Genetics



Mathematical Population Genetics is a very old subject (back to 1920s by Sewall Wright and Ronald Fisher) but it remains many interesting open problems and itself contains many beautiful mathematical structures.
In this project, we aim to systematically reconsider many particular results of this subject from the point of view of information geometry to gain a better understanding (geometric structures) of the whole behaviour of mathematical models considered.
For wonderful works of its probabilistic structures, I would refer you to Probabilistic Structures in Evolution - SPP1590.
For basic simulations written in R, I would refer you to learnPopGen.

References:

  1. Peigné M., Tran T.D., On the asymptotic behavior of the Diaconis and Freedman's chain in a multidimensional simplex, Journal of Applied Probability, 59(2): 505-526, 2022. arXiv.
  2. Hofrichter J., Jost J., Tran T.D., Information geometry and population genetics: The Mathematical Structure of the Wright-Fisher model, Springer Series: Understanding Complex Systems, 2017. Link to Book
  3. Hofrichter J., Jost J., Tran T.D., The geometry of recombination, Information Geometry, 2:177-207, 2019. Link to Journal
  4. Tran T.D., Hofrichter J., Jost J., A general solution of the Wright-Fisher model of random genetic drift, Differential Equations and Dynamical Systems, 27:467–492, 2019. Link to Journal  arXiv
  5. Luu H.D., Tran T.D., Jost J., Ergodicity of scalar stochastic differential equations with Hölder continuous coefficients, Stochastic Processes and their Applications, 128(10):3253-3272, 2018. Link to Journal  arXiv
  6. Hofrichter J., Tran T.D., Jost J., The uniqueness of hierarchically extended backward solutions of the Wright-Fisher model, Communications in Partial Differential Equations 41(3):447-483, 2016. Link to Journal  arXiv
  7. Hofrichter J., Tran T.D., Jost J., A hierarchical extension scheme for solutions of the Wright-Fisher model, Communications in Mathematical Sciences 14(4):1093-1110, 2016. Link to Journal  arXiv
  8. Tran T.D., Hofrichter J., Jost J., The free energy method and the Wright-Fisher model with 2 alleles, Theory in Biosciences 134(3):83-92, 2015. Link to Journal  MIS-Preprint 28/2015
  9. Tran T.D., Hofrichter J., Jost J., The evolution of moment generating functions for the Wright-Fisher model of population genetics, Mathematical Biosciences 256:10-17, 2014. Link to Journal  arXiv
  10. Tran T.D., Hofrichter J., Jost J., The mathematical structure of the Wright-Fisher model of population genetics, Theory in Biosciences 132:73-82, 2013. Link to Journal MIS-Preprint 39/2014
  11. Information Geometry and the Wright-Fisher model of mathematical population genetics.
    Ph. D. Thesis, University of Leipzig (2012).

Preprints:

  1. Tran T.D., Hofrichter J., Jost J., The free energy method for the Fokker-Planck of the Wright-Fisher model, submitted, MIS-Preprint 29/2015.
  2. Hofrichter J., Tran T.D., Jost J., A hierarchical extension scheme for backward solutions of the Wright-Fisher model, submitted, arXiv1406.5146.

Neuroscience



Noise is ubiquitous in neural systems and it may arise from many different sources. In this project, we aim to understand affection of various noises on some mathematical models in neuroscience.

References:

  1. Yamakou M., Tran T.D., Lévy noise-induced self-induced stochastic resonance in a memristive neuron, Nonlinear Dynamics, 107:2847-2865, 2022 .
  2. Yamakou M., Tran T.D., Luu H.D., Jost J., The stochastic FitzHugh-Nagumo model embeds a leaky integrate-and-fire model, Journal of Mathematical Biology, 79(2):509-532, 2019. Link to Journal  arXiv

Opinion Dynamics



This is a joint work in ODYCCEUS project (funded by the European Union’s Horizon 2020 research and innovation programme) where many mathematical models in opinion dynamics are similar to those in Mathematical Population Genetics.

References:

  1. (with Banisch S., Olbrich E.) Opinion dynamics with polarization and coherence along multiple issues. In preparation.

Information theory and statistical inference



In this project, we use some core concepts in information theory to analysis of population genetic data.

References:

  1. Tal O., Tran T.D., Adaptive Bet-Hedging Revisited: Considerations of Risk and Time Horizon, Bulletin of Mathematical Biology 82:50, 2020. Link to Journal   MIS-Preprint 36/2019   arXiv
  2. Tal O., Tran T.D., New perspectives on multilocus ancestry informativeness, Mathematical Biosciences, 306:60-81, 2018. Link to Journal bioRxiv
  3. Tal O., Tran T.D., Portegies J., From Typical Sequences to Typical Genotypes, Journal of Theoretical Biology 419(21):159-183, 2017. Link to Journal  bioRxiv
Publications

Book

  1. Hofrichter J., Jost J., Tran T.D., Information geometry and population genetics: The Mathematical Structure of the Wright-Fisher model, Springer Series: Understanding Complex Systems, 2017.

Journals

  1. Yamakou M., Tran T.D., Lévy noise-induced self-induced stochastic resonance in a memristive neuron, Nonlinear Dynamics, 107:2847-2865, 2022 .
  2. Peigné M., Tran T.D., On the asymptotic behavior of the Diaconis and Freedman's chain in a multidimensional simplex, Journal of Applied Probability, 59(2): 505-526, 2022. arXiv.
  3. Jost J., Le H.V., Tran T.D., Probabilistic mappings and Bayesian nonparametrics, The European Physical Journal Plus, 136: 441, 2021.  
  4. Tal O., Tran T.D., Adaptive Bet-Hedging Revisited: Considerations of Risk and Time Horizon, Bulletin of Mathematical Biology 82:50, 2020.
  5. Hofrichter J., Jost J., Tran T.D., The geometry of recombination, Information Geometry, 2:177-207, 2019.
  6. Yamakou M., Tran T.D., Luu H.D., Jost J., The stochastic FitzHugh-Nagumo model embeds a leaky integrate-and-fire model, Journal of Mathematical Biology, 79(2):509-532, 2019.
  7. Tran T.D., Hofrichter J., Jost J., A general solution of the Wright-Fisher model of random genetic drift, Differential Equations and Dynamical Systems, 27:467–492, 2019.
  8. Tal O., Tran T.D., New perspectives on multilocus ancestry informativeness, Mathematical Biosciences, 306:60-81, 2018.  bioRxiv
  9. Luu H.D., Tran T.D., Jost J., Ergodicity of scalar stochastic differential equations with Hölder continuous coefficients, Stochastic Processes and their Applications, 128(10):3253-3272, 2018.  arXiv
  10. Tal O., Tran T.D., Portegies J., From Typical Sequences to Typical Genotypes, Journal of Theoretical Biology 419(21):159-183, 2017.  bioRxiv
  11. Hofrichter J., Tran T.D., Jost J., The uniqueness of hierarchically extended backward solutions of the Wright-Fisher model, Communications in Partial Differential Equations 41(3):447-483, 2016.  arXiv
  12. Hofrichter J., Tran T.D., Jost J., A hierarchical extension scheme for solutions of the Wright-Fisher model, Communications in Mathematical Sciences 14(4):1093-1110, 2016.  arXiv
  13. Tran T.D., Hofrichter J., Jost J., The free energy method and the Wright-Fisher model with 2 alleles, Theory in Biosciences 134(3):83-92, 2015.  MIS-Preprint 28/2015
  14. Tran T.D., Hofrichter J., Jost J., The evolution of moment generating functions for the Wright-Fisher model of population genetics, Mathematical Biosciences 256:10-17, 2014.  arXiv
  15. Tran T.D., Hofrichter J., Jost J., The mathematical structure of the Wright-Fisher model of population genetics, Theory in Biosciences 132:73-82, 2013.  MIS-Preprint 39/2014
  16. Nguyen V.M., Tran, T.D., On the almost automorphy of bounded solutions of differential equations with piecewise constant argument, J. Math. Anal. Appl. 326:165-178, 2007.  pdf-file
  17. Ngo Q.A., Du D.T., Tran T.D., Dang A.T., Notes on an Integral Inequality, JIPAM 7(4) Article 120, 2006. pdf-file
  18. Tran T.D., On the existence of almost periodic, periodic and quasi-periodic solutions of neutral differential equations with piecewise constant argument, Intern. J. of Evolution Equations 1(2):121-135, 2005. pdf-file

Theses

  1. Neutral dierential equations with piecewise constant arguments.
    Diploma Thesis, Vietnam National University (2000).
  2. On the almost automorphiy of bounded solutions to dierential equation with piecewise constant arguments.
    M. Sc. Thesis, Vietnam National University (2004).
  3. Information Geometry and the Wright-Fisher model of mathematical population genetics.
    Ph. D. Thesis, University of Leipzig (2012).
Talks

Services

Funding Referee

  • NSF-Mathematical Biology
    • Skills

    IT skills

  • Word, Excel, Powerpoint, Latex
  • Mathematica, Matlab, Python, R, Fortran, C++
  • Power BI, Tableau
  • SQL
  • html, css, js
  • ChatGPT prompt

    • Language skills

    • Vietnamese: mother tongue
    • English: fluent
    • German: basic (B2-C1)
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