(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.
In recent joint work, https://arxiv.org/abs/2405.05834, we explore using Backtracking New Q-Newton's method (BNQN) for Riemann xi function. We show in particular that the Riemann hypothesis is equivalent to that all attractors of BNQN lie on the critical line. BNQN works well and stably for the very transcendental function xi, and we present some concrete steps to using BNQN for the Riemann hypothesis.
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.
I and my team are developing softwares: 1. to help high school students learn mathematics and 2. to provide efficient computing tools.
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.