Trung Tuyen Truong

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


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).   


Note: Don't believe in a blog if they don't allow you to post comments in opposite to their stand. Using this criterion, I don't have much truth in such blogs. Those blogs may serve some hidden agenda.  It's only a personal opinion though. 



2020-: I am a supporter/member of CLAIRE (Confederation of laboratories for Artificial intelligent research in Europe).




Spring 2021: supervisor for research undergraduate student (MAT2000) Erling Pettersen Vollan on the topic: Backtracking gradient descent and large scale applications. 

Fall 2020 -- current: Fei Hu, Postdoc, working in pure mathematics. This position is funded from Research Council of Norway grant 300814.  

Fall 2020 -- current: Viktor Balch Barth, PhD student, working in pure mathematics. I am the main advisor, co-supervising with . This position is funded from Research Council of Norway grant 300814.  

Fall 2019--current: Maged Abdalla Helmy Abdou (Industrial PhD student, Informatics Department), working in Deep Learning in medical imaging. I am a co-supervisor, together with Eric Jul and Paulo Ferreira. 

Fall 2018 - current: Giovanni Domenico Di Salvo (PhD student, Mathematics Department), working in Several Complex Variables. I am the main advisor, co-supervising with Erlend Fornaess Wold. 

Spring semester 2019: Supervisor for 4 research undergraduate students (course MAT2000): Besmira Amiti and Max Magnus Nils Rafstedt (gradient descent methods and applications in Deep Learning), Jon Elstad Maage and Christian Schive (Grobner Basis). 

Research grants

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.  


Editorial work


2021 -- current: Reviewer board for the journal Axioms (MDPI). This is an open journal. 

2020 -- current: The journal Experimental Results (Cambridge University Press) (link). I am Reviewing Editor (for Control systems and Optimisation in the Engineering section) and an Editor (for the section Mathematics, Statistics and Probability). Some special features of this journal: It publishes standalone experimental results (whether positive or negative). The journal is open for almost all fields in science, computer and mathematics. Its referee process is open: authors know who refereed their papers, and if a paper is accepted then referees reports for the paper is also published simultaneously - this is in harmony with my publishing philosophy, please see my more personal website (link below) for more detail. It is Open Access, you need to pay a fee, but then all people can read the paper for free. (You can check the journal webpage to see if you can get partial or total fee waiver. You can also check if your institution has some agreements with Cambridge University Press concerning the fee.)



Conferences and meetings organising

Organise informal meetings on Deep Neural Networks, University of Oslo, August 2019 -- current
Co-organise the informal meetings on Automated Proof Checking, University of Oslo, August 2019 -- current
Co-organise the SCV seminar, University of Oslo, 2018 -- current
Co-organised the conference "Mapping problems and complex manifolds in projective spaces", University of Oslo, December 2018.  (Link)
Co-organised the Differential and Complex Geometry Seminar, Korea Institute for Advanced Study, January to April 2015.  
Helped to organise and attended the Graduate Student Seminar in Several Complex Variables, Syracuse University, Fall 2012 and Spring 2013.    
Co-organised the Mathematical Summer Meeting, HCM University of Science, Vietnam, 2008.
Organised the Algebra Graduate Student Seminar, Indiana University Bloomington, Summer 2007.



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 personal webpage:

I also have accounts  on Wikipedia, Quora and Reddit on optimisation there. 




Tags: Mathematics, Several Complex Variables, Dynamical Systems, Algebraic Geometry, Gradient Descent, Newton's method, Optimisation, Deep Learning, Automated Proof Checking
Published Sep. 4, 2017 9:08 AM - Last modified Sep. 25, 2021 12:16 AM