Trung Tuyen Truong

Image of Trung Tuyen Truong
Norwegian version of this page
Phone +47 22855932
Room 711
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Visiting address Moltke Moes vei 35 Niels Henrik Abels hus 0851 Oslo
Postal address Postboks 1053 Blindern 0316 Oslo

 

(My name in native language is Trương Trung Tuyến.  Trương is the surname (usually has no meaning), while Trung Tuyến together has this meaning: https://en.wikipedia.org/wiki/Median_(geometry)  Informally, I am called "Tuyến", which sounds like "Twain" in Mark Twain.)

 

Since September 2023, I am a Professor of Mathematics at University of Oslo. From September 2017-September 2023, I was an Associate Professor of Mathematics at University of Oslo. 

I am very excited to work here at University of Oslo, with a long tradition of strong research and teaching, where Niels Henrik Abel used to be. My research is in Several Complex Variables, Dynamical Systems and related topics in Algebraic Geometry. I am also keen to applications of these fields. Originally from Vietnam, I traveled all around the world studying and working : Indiana University (USA) PhD, 2006-2012, under the supervision of Professor Eric Bedford; Syracuse University (USA), Postdoc, 2012 - 2014; Korea Institute for Advanced Study (South Korea), Postdoc, 2014-2015; and The University of Adelaide (Australia), Postdoc 2015 - 2017; before coming here to Oslo. My PhD dissertation was on pullback of positive closed currents by meromorphic maps.

Some main research themes and results

Some of my current research topics are: algebraic interpolation, embedding of algebraic curves in the complex plane, geometry and dynamics of Abelian varieties and their quotients, relations between Weil's Riemann hypothesis and standard conjectures and dynamical systems. A common theme is my enthusiasm in applying computers into solving problems, both in pure theory and in real life applications.

Recently, I also do research on  Gradient Descent methods and applications in Deep Learning, with help from (Random) Dynamical Systems and Geometry research. My joint work arXiv:1808.05160 demonstrated the feasibility and good performance of Backtracking Gradient Descent in Deep Neural Networks, and the results therein have been vindicated by subsequent work by other authors such as arXiv:1905.09997. 

In another recent paper arXiv:2006.01512, my collaborators and I proposed a new modification of Newton's method, roughly having the following property: if the sequence {x_n},  constructed by the new method from a random initial point x_0, converges, then the limit point is a local minimum, and the rate of convergence is quadratic. The complexity of the algorithm is O(m^3) at each step, where m is the dimension.  My paper after that arXiv:2209.05378 incorporated Backtracking line search into the method, which boosts its convergence guarantee. 

In the series of two papers arXiv:2102.04405 and arXiv:2104.12660, joint with Fei Hu, I propose a new approach towards the long standing open questions of generalised Weil's Riemann hypothesis and semisimplicity for polarised endomorphisms. Our approach is less demanding than the approach through Standard conjectures by Bombieri and Grothendieck. 

In a recent paper arXiv:2309.11475 I propose two new methods concerning the following question: Assume one uses an iterative method to solve a system of equations or an optimization problem on a space X. Let A be a closed subset of X. Is it possible to use the given iterative method avoiding converging to A? One method is to divide the cost function by d(.,A)^N, where d(.,.) is the distance function. Another method is to redefine F(x)=f(x) is x not in A, and F(x)=M if x in A, where M>0 is a big number. Iterative methods which has strong convergence guarantee and descent property, like Backtracking Gradient Descent or Backtracking New Q-Newon's method are suitable. Applications include: constrained optimization, finding roots in a given domain...Even application to Linear Programming (difficult for iterative methods using gradient and Hessian) is possible, with the help from stochastic dynamics caused by cut-off in calculations on computers!   

Since I am concerned about the correctness of the proofs of claims in mathematics (in many cases - most of cases, I think - people either do not have the competence or time to check, and hence just believe the claims, in particular if the claimants are famous), I am doing research also in Automated Proof Checking. It is interesting to know that there is growing interest of applying Machine Learning techniques into Automated Proof Checking. By Curry-Howard correspondence, roughly speaking, checking the correctness of mathematical proofs are equivalent to verifying  the correctness of computer programs. Therefore, if the mentioned idea works well, then it will influence enormously both whole mathematics and your daily life (given that computers and computer softwares are now universal).   

AI in Practical Life: Understanding and appreciating the power of Deep Learning techniques to solve many difficult practical questions in real life and science/education, One product which we is developing, Hi-Math Essentials, with the goal of combining AI and human experts to help high school students improve their knowledge and scores in multiple choice and short response questions in mathematics, can be found here: himathessentials dot com. 

Another project, which I am collaborating with AI companies and medical doctors, is to use AI to help doctors with diagnosing from lung data measurement (like spirometry data...)

Page on teaching, supervising, conferences/seminar organised, other activities

https://www.mn.uio.no/math/english/research/projects/granddrm/events/conferences/index.html

Research grants

Seed grant from UiO Growth House for the project "Harnessing AI to assist human experts in creating mathematical questions in elementary schools", Spring 2023 -. 

Member of MSCA-Cofund-DP, #945371, ERC, 5 year grants funding for PhD positions, 2020-. 

PI of Young Research Talents grant, #300814, Research Council of Norway, 2020 -- 2024

Supported (indirectly) by the Australian Research Council grants DP120104110 and DP150103442, 2015 --  2017. 

PI of "Young and pioneering scientist development",  Ministry of Education, Science and Technology (Republic of Korea), 2014--2015.  

 

Some favourite quotes

Who hopes for what he already has? But if we hope for what we do not yet have, we wait for it patiently. (The Bible)

For what shall it profit a man, if he shall gain the whole world, and lose his own soul? (The Bible)

There is no way to happiness. Happiness is the way. (The Buddha)

Now, Kalamas, don't go by reports, by legends, by traditions, by scripture, by logical conjecture, by inference, by analogies, by agreement through pondering views, by probability, or by the thought "This contemplative is our teacher." When you know for yourselves that "These qualities are skilful; these qualities are blameless; these qualities are praised by the wise; these qualities, when adopted and carried out, lead to welfare and to happiness"- then you should enter and remain in them. (The Buddha)

A foolish faith in authority is the worst enemy of truth. (Albert Einstein)

All truths are easy to understand once they are discovered; the point is to discover them. (Galileo Galilei)

Live as if you were to die tomorrow. Learn as if you were to live forever. (Mahatma Gandhi)

Your time is limited, don't waste it living someone else's life. Don't be trapped by dogma, which is living the result of other people's thinking. Don't let the noise of other opinions drown you own inner voice. And most important, have the courage to follow your heart and intuition, they somehow know what you truly want to become. Everything else is secondary. (Steve Jobs)

That's been one of my mantras - focus and simplicity. Simple can be harder than complex; you have to work hard to get your thinking clean to make it simple. But it's worth it in the end because once you get there, you can move mountains. (Steve Jobs)

A lot of companies have chosen to downsize, and may be that was the right thing for them. We chose a different path. Our belief was that if we kept putting great products in front of customers, they would continue to open their wallets. (Steve Jobs)

 

Others

 

My hobbies include: reading, swimming and diving, listening to music, hanging out with friends, travelling, playing the game of Go, and solving mazes. 

Here is my (not updated) personal webpage: 

https://sites.google.com/site/tuyentruongswebpage/home

I also have accounts  on Wikipedia, Quora and Reddit on optimisation there. Nowadays, I mostly write on my LinkedIn page. 

 

 

 

Tags: Mathematics, Several Complex Variables, (Complex), Dynamical Systems, (Dynamical), Algebraic Geometry, Root finding, Optimization, (Optimal), Deep learning, (Deep)

Publications

 

Selected preprints

 

John Erik Fornæss, Mi Hu, Tuyen Trung Truong and Takayuki Watanabe, Backtracking New Q-Newton's method, Newton's flow, Voronoi's diagram, and Stochastic root finding. arXiv:2401.01393

John Erik Fornæss, Mi Hu, Tuyen Trung Truong and Takayuki Watanabe, Backtracking New Q-Newton's method, Schroder's theorem, and Linear conjugacy, arXiv:2312.12126  

Viktor Balch Barth and Tuyen Trung Truong, Images of dominant endomorphisms of affine space, arXiv: 2311.08238.  

Tuyen Trung Truong, Creating walls to avoid unwanted points in root finding and optimization, arXiv:2309.11475. 

Tuyen Trung Truong, Backtracking New Q-Newton's method: a good algorithm for optimization and solving systems of equations, arXiv:2209.05378. This paper supersedes the 3 previous ones: arXiv:2108.10249, arXiv: 2109.11395, and arXiv:2110.07403. Source code is available at GitHub's link: [Link]

 

Cinzia Bisi, Jonathan D. Hauenstein and Tuyen Trung Truong, Some interesting birational morphisms of smooth affine quadric 3-folds, arXiv:2208.14327 

 

Charles Favre, Tuyen Trung Truong and Junyi Xie, Topological entropy of a rational map over a complete metrized field, arXiv:2208.00668 

 

 

 

Fei Hu and Tuyen Trung Truong, A dynamical approach to generalized Weil's Riemann hypothesis and semisimplicity, arXiv:2102.04405 (The older version contains also other results which will be developed in another paper later)

 

Tuyen Trung Truong, Unconstrained optimisation on Riemannian manifolds, arXiv:2008.11091.

 

Tuyen Trung Truong, Some observations on the properness of Identity plus linear powers: part 2, arXiv:2005.02260.

 
Tuyen Trung Truong, Some observations on the properness of Identity plus linear powers, arXiv:2004.03309.
 
Tuyen Trung Truong, Coordinate-wise Armijo's condition: General case, arXiv: 2003.05252 (the preprint arXiv: 1911.07820 is incorporated as a special case).
 
Tuyen Trung Truong, Some convergent results for Backtracking Gradient Descent method on Banach spaces, arXiv:2001.05768.
 
Tuyen Trung Truong, Convergence to minima for the continuous version of Backtracking Gradient Descent, arXiv: 1911.04221.

Tuyen Trung Truong, Strong submeasures and applications to non-compact dynamical systems, arXiv:1910.06394. This is extracted and developed from the more dynamical part of arXiv: 1712.02490.

 

 

 

 

Selected published papers:

 

Tuyen Trung Truong, Relations between dynamical degrees, Weil's Riemann hypothesis and the standard conjectures, 20 pages. Preprint arXiv: 1611.01124. Accepted in Commentarii Mathematici Helvetici. 

Tuyen Trung Truong, Tat Dat To, (Tuan Hang) Hang-Tuan Nguyen, Thu Hang Nguyen, Hoang Phuong Nguyen and Maged Helmy, A modification of quasi-Newton's methods helping to avoid saddle points, arXiv:2006.01512. Source code is available on GitHub (Link)  Accepted in Journal of Optimization Theory and Applications. 

Tuyen Trung Truong, Bounded birationality problem is computable, arXiv: 1801.00901.  Accepted in Beitrage zur Algebra und Geometrie (Contributions to Algebra and Geometry). 

Maged Helmy, Tuyen Trung Truong, Eric Jul and Paulo Ferreira, Deep Learning and Computer vision techniques for microcirculation analysis: a review, arXiv:2205.05493. Accepted in Patterns (Cell Press, Elsevier). 

Fei Hu and Tuyen Trung Truong, An inequality for polarized endomorphisms, arXiv:2104.12660. Accepted in Archiv der Mathematik. 

Maged Helmy, Anastasiya Dykyy, Tuyen Trung Truong, Paulo Ferreira, Eric Jul, CapillaryNet: An automated system to analyze microcirculation videos from handheld vital microscopy, arXiv:2104.11574. Accepted in Artificial Intelligence in Medicine. 

 

Tuyen Trung Truong and (Tuan Hang) Hang-Tuan Nguyen, Backtracking gradient descent method and some applications in Large scale optimisation. Part 1: Theory, accepted in Minimax Theory and its Applications. This is the more theoretical part of arXiv: 1808.05160, with some additional experiments. Accompanying source codes are available on GitHub: [Link] 

Tuyen Trung Truong. Strong sub measures and applications to non-compact dynamical systems, (this is the more dynamical part of arXiv: 1712.02490), accepted in Ergodic Theory and Dynamical Systems. The paper is Open Access. doi.org/10.1017/etds.2020.132  

Tuyen Trung Truong, When will a sequence of points in a Riemannian submanifold converge? (Mostly a survey paper, invited submission.) Special issue "Riemannian geometry of submanifolds", journal: Mathematics (MDPI), 2020, 8 (11), 1934. This is open access [Link to the paper] .

Tuyen Trung Truong and (Tuan Hang) Hang-Tuan Nguyen, Backtracking Gradient Descent method and some applications in Large scale optimisation. Part 2: algorithms and experiments. The main part of the paper is based on the more experimental part of arXiv:1808.05160, together with arXiv:2001.02005 and arXiv:2007.03618. Accompanying source codes are available on GitHub: [Link] Published online in Applied Mathematics and Optimization. The paper is Open Access. doi:10.1007/s00245-020-09718-8. [Link to PDF]

Tuyen Trung Truong, Some new theoretical and computational results around the Jacobian conjecture, developed and revised from preprint arXiv: 1503.08733. Accepted in International Journal of Mathematics. 

Finnur Larusson and Tuyen Trung Truong, Approximation and interpolation of regular maps from affine varieties to algebraic manifolds, 9 pages. Preprint: arXiv: 1706.00519. Accepted in Mathematica Scandinavia. 

Tuyen Trung Truong, Etale dynamical systems and topological entropy, 13 pages. Preprint arXiv: 1607.07412. Accepted in Proceedings of the American Mathematical Society. 

Shalom Kaliman, Frank Kutzschebauch and Tuyen Trung Truong, On subelliptic manifolds, 12 pages. Preprint arXiv: 1611.01311v3. Accepted in Israel Journal of Mathematics.

Tuyen Trung Truong, Relative dynamical degrees of correspondences over a field of arbitrary characteristic, 41 pages. Preprint arXiv: 1605.05049. Accepted in Journal fur die Reine und Agnewandte Mathematik (Crelle's journal). DOI: 10.1515/crelle-2017-0052.  

Tien-Cuong Dinh, Viet-Anh Nguyen and Tuyen Trung Truong, Growth of the number of periodic points of meromorphic maps, 18 pages. Preprint arXiv: 1601.03910. Accepted in Bulletin of the London Mathematical Society. 

Finnur Larusson and Tuyen Trung Truong, Algebraic subellipticity and dominability of blowups of affine spaces, 10 pages. Preprint: arXiv: 1606.08115. Accepted in Documenta Mathematica. 

Tuyen Trung Truong, Comments on Sampson's approach toward Hodge conjecture on Abelian varieties, accepted in Annali di Matematica Pura ed Applicata. Preprint arXiv: 1409.0495.

Tuyen Trung Truong, Automorphisms of blowups of threefolds being Fano or having Picard number 1, accepted in Ergodic Theory and Dynamical Systems. Preprint arXiv: 1501.01515.

Tuyen Trung Truong, Some dynamical properties of pseudo-automorphisms in dimension 3. Transactions of the American Mathematical Society 368 (2016), no 1, 727--753.

Keiji Oguiso and Tuyen Trung Truong,  Explicit examples of rational and Calabi-Yau threefolds with primitive automorphisms of positive entropy. Kodaira Centennial Volume, J. Math. Sci. Univ. Tokyo 22 (2015), no 1, 361--385.

Tien-Cuong Dinh,  Viet-Anh Nguyen and Tuyen Trung Truong,  Equidistribution for meromorphic maps with dominant topological degree. Indiana University Journal of Mathematics 64, No 6 (2015), 1805--1828.  

Dan Coman and Tuyen Trung Truong, Geometric properties of upper level sets of Lelong numbers on projective spaces. Mathematische Annalen 361 (2015), no 3--4, 981--994.  

Fabrizio Catanese, Keiji Oguiso and Tuyen Trung Truong, Unirationality of the Ueno-Campana's threefold. Manuscripta Mathematica 145 (2014), no 3--4, 399--406.

Kenji Oguiso and Tuyen Trung Truong, Salem numbers in dynamics of Kahler 3-folds and complex tori.  Mathematische Zeitschrift 278 (2014), no 1--2, 93--117.

Tuyen Trung Truong,  The simplicity of the first spectral radius of a meromorphic map. Michigan Mathematics Journal  63 (2014), no 3, 623--633.

Dang Duc Trong, Cao Xuan Phuong, Dinh Ngoc Thanh and Tuyen Trung Truong,  Tikhonov's regularization to deconvolution problem, Communications in Statistics: Theory and Methods, vol 43, issue 20, 2014, pp. 4384-4400. 

Tuyen Trung Truong, Pullback of currents by meromorphic maps,  Bulletin de la Societe Mathematique de France 141 (2013), no 4, 517--555.

Tien-Cuong Dinh, Viet-Anh Nguyen and Tuyen Trung Truong, On the dynamical degrees of meromorphic maps preserving a fibration, Communications in Contemporary Mathematics 14, 1250042, 2012. 

Tuyen Trung Truong,  Degree complexities of birational maps related to matrix inversions: Symmetric case, Mathematische Zeitschrift 270 (2012), no 3--4, 725--738. 

Eric Bedford and Tuyen Trung Truong, Degree complexities of birational maps related to matrix inversion, Communications in Mathematical Physics 298 (2010), no. 2, 357--368.

 

View all works in Cristin

  • Truong, Trung Tuyen (2023). Hvordan finner vi løsninger til polynomer i 1 kompleks variabel?
  • Truong, Trung Tuyen (2023). Backtracking New Q-Newton's method with applications in stochastic root finding.
  • Truong, Trung Tuyen (2023). Some interesting research topics relevant to Machine Learning/Deep Learning.
  • Truong, Trung Tuyen (2023). Stochastic dynamical systems coming from root finding: phenomena and questions.
  • Truong, Trung Tuyen (2023). Periodic points, dynamical degrees and root finding.
  • Truong, Trung Tuyen (2023). New Q-Newton's method and Backtracking line search.
  • Truong, Trung Tuyen (2023). Optimization algorithms: Theory and large scale applications, intensive course.
  • Truong, Trung Tuyen (2023). How good can AI do simple logical reasoning and mathematics now? - An update.
  • Truong, Trung Tuyen (2023). A better algorithm to solve equations than Newton's method.
  • Truong, Trung Tuyen (2022). Some interesting birational morphisms of smooth affine quadric 3-folds.
  • Truong, Trung Tuyen (2022). Entropy of maps on non-Archimedean fields.
  • Truong, Trung Tuyen (2022). Entropy of maps on non-Archimedean fields.
  • Truong, Trung Tuyen (2022). Optimization, Lojasiewicz inequalities, Dynamical Systems and Deep Neural Networks (Or: Is there a cat or not a cat?).
  • Truong, Trung Tuyen (2021). A quick method to find roots of univariate meromorphic functions.
  • Truong, Trung Tuyen (2021). Implementation of Backtracking line search in Deep Neural Networks: theory and practice.
  • Truong, Trung Tuyen (2021). A 10-line proof of a generalisation of Weil’s RH for Abelian varieties.
  • Truong, Trung Tuyen (2020). Rationality of quotients of Abelian varieties and computer algebra.
  • Truong, Trung Tuyen (2020). Rationality of quotients of Abelian varieties and computer algebra.
  • Truong, Trung Tuyen (2020). Deep Learning and Automated Proof Checking.

View all works in Cristin

Published Sep. 4, 2017 9:08 AM - Last modified Feb. 9, 2024 12:57 PM