Below is a part of my mathematical genealography:
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
-
SS20: Link
- 2SWS Introduction to Combinatorics, Leipzig University.
- 2SWS Seminar on Combinatorics and its applications, Leipzig University.
- WS19/20:
Link
- 4SWS An introduction to Geometric and Algebraic Methods in Statistics, Leipzig University.
- 2SWS Practice course on Python and R, Leipzig University.
- 2SWS Machine learning practice, Leipzig University.
- 07.2019: Lecturer, A basic notion on Information Geometry, VIASM, Hanoi.
- WS18/19: Lecturer, Information Geometry and Mathematical Population Genetics, MPI-MiS, Leipzig.
- 04.2017: Lecturer, A mini-course on Stochastic differential equations with Hölder continuous coefficients - PDE vs Geometry, VIASM, Hanoi (April, 2017)
- 08–15.03.2017: Invited lecturer, SEAMS school Mathematical Modelling in Biology, VIASM, Hanoi (March 08-15, 2017)
- SS16: Tutor, IMPRS Ringvorlesung "Discrete Structures", MPI-MiS, Leipzig.
- 2004–2007: Teaching assistant/Lecturer, Calculus, ODEs, VNU University of Sciences, Hanoi.
- 2006: Co-supervisor, A bachelor thesis, VNU University of Sciences, Hanoi.
Organization experience
- 30.03–25.05.2017: Co-organizer, Seminar: Working group on applied probability, VIASM, Hanoi.
- 12–14.05.2017: Co-organizer, Workshop: Some selected problems in modern probability, Tuan Chau.
- 09.03.2017: Co-organizer, Mini-workshop: Stochastic processes and their applications, VIASM, Hanoi.
- 08-15.03.2017: Co-organizer, SEAMS school: Mathematical Modelling in Biology, VIASM, Hanoi.
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.
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:
- 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.
- 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
- Hofrichter J., Jost J., Tran T.D., The geometry of recombination, Information Geometry, 2:177-207, 2019. Link to Journal
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- Information Geometry and the Wright-Fisher model of mathematical
population genetics.
Ph. D. Thesis, University of Leipzig (2012).
Preprints:
- 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.
- 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:
- Yamakou M., Tran T.D., Lévy noise-induced self-induced stochastic resonance in a memristive neuron, Nonlinear Dynamics, 107:2847-2865, 2022 .
- 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:
- (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:
- 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
- Tal O., Tran T.D., New perspectives on multilocus ancestry informativeness, Mathematical Biosciences, 306:60-81, 2018. Link to Journal bioRxiv
- 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
Journals
- Yamakou M., Tran T.D., Lévy noise-induced self-induced stochastic resonance in a memristive neuron, Nonlinear Dynamics, 107:2847-2865, 2022 .
- 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.
- Jost J., Le H.V., Tran T.D., Probabilistic mappings and Bayesian nonparametrics, The European Physical Journal Plus, 136: 441, 2021.
- Tal O., Tran T.D., Adaptive Bet-Hedging Revisited: Considerations of Risk and Time Horizon, Bulletin of Mathematical Biology 82:50, 2020.
- Hofrichter J., Jost J., Tran T.D., The geometry of recombination, Information Geometry, 2:177-207, 2019.
- 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.
- 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.
- Tal O., Tran T.D., New perspectives on multilocus ancestry informativeness, Mathematical Biosciences, 306:60-81, 2018. bioRxiv
- 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
- Tal O., Tran T.D., Portegies J., From Typical Sequences to Typical Genotypes, Journal of Theoretical Biology 419(21):159-183, 2017. bioRxiv
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- Neutral dierential equations with piecewise constant arguments.
Diploma Thesis, Vietnam National University (2000). - On the almost automorphiy of bounded solutions to dierential equation with piecewise constant arguments.
M. Sc. Thesis, Vietnam National University (2004). - Information Geometry and the Wright-Fisher model of mathematical population genetics.
Ph. D. Thesis, University of Leipzig (2012).
-
2021
- Zoom Talk at Franz Baumdicker's group, Universität Tübingen (January 20, 2020)
- Zoom Talk at Matteo Smerlak's group, MPI-MiS, Leipzig (December 22, 2020)
- Zoom Talk at Max Renesse's group, Leipzig University (June 08, 2020)
- Special session Talk at Vietnam-USA joint mathematical meeting, Quy Nhon (June 10–13, 2019)
- Invited Talk at Berlin-Leipzig workshop in analysis and stochastics, Leipzig (January 16–18, 2019)
- Invited Talk at Institute of Mathematics of ASCR, Zitna 25, Praha 1 (20-24 November, 2018)
- Contributed talk at ECMTB 2018, Lisbon, Portugal (July 23-27, 2018)
- Invited Talk at Math Bio working group in Institut Denis Poisson, Tours (June 7, 2018)
- Invited Talk at Math Bio Day, Leipzig (April 09, 2018)
- Contributed Talk at 7th International Conference on Modeling, Simulation and Optimization of Complex Processes, Hanoi (March 19-March 23, 2018)
- Invited Talk at Mini-workshop on recent developments in stochastic dynamics and stochastic analysis, Hanoi (15-16 March, 2018)
- Invited Talk at Department of Probability and Statistics, Faculty of Mathematics, Mechanics, and Informatics, VNU University of Science, Hanoi (May 27, 2017)
- Invited Talk at workshop Some selected problems in modern probability, Tuan Chau (May 12-14, 2017)
- Invited Talk at Department of Analysis, Faculty of Mathematics, Mechanics, and Informatics, VNU University of Science, Hanoi (April 14, 2017)
- Invited Talk at workshop Stochastic processes and their applications, VIASM, Hanoi (March 09, 2017)
- Invited Talk at 3rd Dresden-Leipzig Dynamics Day, TU Dresden, Germany (November 11, 2016)
- Invited Talk at International Workshop on Statistical Mechanics and Information in Evolution, Ludwig Maximillians University, Munich, Germany (July 4-6, 2016)
- Poster section at Information Geometry and its Applications IV, Liblice, Czech Republic (June 12-17, 2016)
- Invited Talk at Berlin-Leipzig workshop in analysis and stochastics (April 13-15, 2016)
- Invited Talk: Review colloquium SPP 1590: Probabilistic structures in Evolution, Bielefeld (September 3-4, 2015)
- Contributed Talk at Workshop on Mathematical Trends in Reaction Network Theory, July 1-3, 2015 in Copenhagen
- Invited Talk at Arne Traulsen's group, Max Planck Institute for Evolutionary Biology, Ploen (June 3-5, 2015)
- Contributed Talk at International conference: Modelling Biological Evolution 2015: Linking Mathematical Theories with Empirical Realities, combined with the LMS workshop: Mathematical and Computational Models in Evolutionary Biology: Shifting the Existing Paradigms (University of Leicester (UK), April 28 - May 1, 2015)
- Contributed Talk at The 9th European Conference on Mathematical and Theoretical Biology, Gothenburg, Sweden (June 15-19, 2014).
- Contributed Talk at The 8th Vietnamese Mathematical Conference, Nha Trang, Vietnam (August 10-14, 2013).
- Seminar Talk at Central European Seminar, Brno, Czech (May 24, 2013).
- Invited Talk at WIAS, Berlin, Germany (February 05, 2013).
- Invited Talk at WIAS, Berlin, Germany (September 13, 2012).
- Invited Talk: Minisymposium "Computational Biology with Medical Applications", Helmholtz Centre for Infection Research, Braunschweig, Germany (June 21, 2011).
- Contributed Talk at 5th Annual PhD Student Conference in Probability, Leipzig, Germany (September 10-12, 2009).
- Contributed Talk at VNU and CNU Workshop on Analysis, Differential Equations, and Dynamical Systems, Hanoi, Vietnam (February 2-5, 2007).
- Contributed Talk at International Conference on Differential Equations and Applications, HoChiMinh City, Vietnam (August 22-25, 2004).
2020
2019
2018
2017
2016
2015
2014
2013
2012
2011
2009
2007
2004
Journal Editor
Funding Referee
Journal Referee
- Numerical Methods for Partial Differential Equations (NMPDE)
- Journal of Theoretical Biology (JTB)
- SIAM Journal on Applied Mathematics (SIAP)
- Mathematical Reviews (MR)
- Theory in Biosicences (TIBI)
- Acta Biotheoretica (ACBI)
- Asian-European Journal of Mathematics (AEJM)
- MDPI-Energies
- MDPI-Computation
- MDPI-Data
- Journal of Mathematical Biology (JOMB)
- Information Geometry (INGE)
- Bulletin of the Malaysian Mathematical Sciences Society (BMMS)
- Stochastics: An International Journal of Probability and Stochastic Processes
- Frontiers in Genetics, section Evolutionary and Population Genetics
-
01.2023-02.2023: Deep Learning Specialization, from coursera.org
- Sequence Models
- Improving Deep Neural Networks: Hyperparameter Tuning, Regularizationand Optimization
- Structuring Machine Learning Projects
- Convolutional Neural Networks
- Neural Networks and Deep Learning
- 09.2021-02.2022: Data Science course, from alfatraining.de