Tuyen Trung Truong
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. Recently, I also do research on Gradient Descent methods and applications in Deep Learning. 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. Since August 2019, I am co-ordinating an informal meeting on Automated Proof Checking.
Warning: Many people, including experts, are confused about the following 2 statements about optimisation methods, and think that they are the same. Given f a C^1 function, and {x_n} a sequence of points. Let \nabla f be the gradient of f. Statement 1: the sequence {\nabla f(x_n)} converges to 0. Statement 2: the sequence {x_n} converges to a point z, and \nabla f(z)=0.
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:
https://sites.google.com/site/tuyentruongswebpage/home
I also have an account (username: Tuyen) on Data Science Stack Exchange (https://datascience.stackexchange.com/?tab=active) and answered some questions about the gradient descent method (the most popular method used in practice, in particular machine learning), there.
Publications
Selected preprints:
Tuyen Trung Truong, Coordinate-wise Armijo's condition, arXiv: 1911.07820.
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.
Tuyen Trung Truong and Tuan Hang Nguyen, Backtracking gradient descent method for general C^1 functions with applications in Deep Learning, 37 pages. Preprint: arXiv: 1808.05160v2. Accompanying source codes are available on GitHub: [Link]
Tuyen Trung Truong, Bounded birationality problem is computable, 17 pages. Preprint: arXiv: 1801.00901. (An extended version, 20 pages, which contains additional results compared to the arXiv version, is available on my personal webpage.)
Tuyen Trung Truong, Sub-measures and applications to wedge intersection of positive closed currents and complex dynamics, 29 pages. Preprint: arXiv: 1712.02490.
Tuyen Trung Truong, Relations between dynamical degrees, Weil's Riemann hypothesis and the standard conjectures, 20 pages. Preprint arXiv: 1611.01124.
Tuyen Trung Truong, Some approaches toward the Jacobian conjecture, 29 pages. Preprint arXiv: 1503.08733.
Selected published papers:
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.
- Truong, Tuyen Trung (2019). Etale dynamical systems and topological entropy. Proceedings of the American Mathematical Society. ISSN 0002-9939. . doi: 10.1090/proc/14100
- Kaliman, Shulim; Kutzschebauch, Frank & Truong, Tuyen Trung (2018). On subelliptic manifolds. Israel Journal of Mathematics. ISSN 0021-2172. 228(1), s 229- 247 . doi: 10.1007/s11856-018-1760-7
- Truong, Tuyen Trung (2018). Bounded birationality problem is computable. arXiv.org. ISSN 2331-8422. Show summary
- Truong, Tuyen Trung (2018). Relative dynamical degrees of correspondences over a field of arbitrary characteristic. Journal für die Reine und Angewandte Mathematik. ISSN 0075-4102. . doi: 10.1515/crelle-2017-0052
- Dinh, Tien Cuong; Nguyen, Viet Anh & Truong, Tuyen Trung (2017). Growth of the number of periodic points for meromorphic maps. Bulletin of the London Mathematical Society. ISSN 0024-6093. . doi: 10.1112/blms.12082