Trung Tuyen Truong

Up-to-date publication list and talks (since I have started working at University of Oslo, and for journals covered of Level 1 and 2 in the Norwegian journal ranking system: note that the ranking is based on the sole suggestions of researchers working in Norway, and hence may not cover all or reflect correctly the relative qualities of different journals in the whole world) can be found here:

Publication list and talks (for journals covered by NVA)

https://nva.sikt.no/research-profile/898707

Publications in journals not covered by NVA:  

Selected preprints: 

Ji Li, Chun-Yen Shen, Tuyen Trung Truong and Liangchuan Wu, Polynomial corners in finite fields beyond the distinct-degree case, arXiv:2609.13891

Chun-Yen Shen, Tuyen Trung Truong and Wei-Hsuan Yu, On the structure and generic non-Cartesianity of polynomials in product spaces, arXiv:2605.22320.

My Thi Diem Phan, Tuyen Trung Truong, Hoai Phuong Ha and Dat Thanh Nguyen, Electricity price forecasting across Norway's five bidding zones in the post-crisis era, arXiv:2604.26634.

Tuyen Trung Truong, Standard conjecture D and some conjectures around Weil's Riemann hypothesis, arXiv:2508.13882.

Tuyen Trung Truong, Some iterative algorithms on Riemannian manifolds and Banach spaces with good global convergence guarantee, arXiv: 2505.22180. 

Viet-Anh Nguyen and Tuyen Trung Truong, Uniqueness of tangent currents for positive closed currents, arXiv:2502.06532. 

John Erik Fornæss, Mi Hu and Tuyen Trung Truong,  Backtracking New Q-Newton's method for finding roots of meromorphic functions in 1 complex variable: Global convergence, and local stable/unstable curves, arXiv:2412.02476. 

Thuan Quang Tran and Tuyen Trung Truong, The Riemann hypothesis and dynamics of Backtracking New Q-Newton's method, arXiv: 2405.05834. 

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]

• Hu, Fei; Truong, Trung Tuyen & Xie, Junyi (2026). Tate's question, Standard conjecture D, semisimplicity and Dynamical degree comparison conjecture. Acta Mathematica Sinica. English series. ISSN 1439-8516. doi: https:/arxiv.org/abs/2503.09432. Full text in Research Archive
• Fornæss, John Erik; Hu, Mi; Truong, Trung Tuyen & Watanabe, Takayuki (2026). Schröder’s theorem for backtracking new Q-Newton’s method. Complex Analysis and its Synergies. ISSN 2524-7581. 12(3). doi: 10.1007/s40627-026-00204-5. Full text in Research Archive Show summary

  Schröder’s theorem studied the convergence of Newton’s method for the complex quadratic function, showing that on either side of the perpendicular bisector of the roots, Newton’s method converges to the root on that particular side. This paper rigorously proves that Schröder’s theorem also holds for a new variant of Newton’s method—named Backtracking New Q-Newton’s method (BNQN). However, the orbit behavior of the BNQN method differs from Newton’s method on the perpendicular bisector of the roots. The motivation for our rigorous proof comes from a remarkable experimental discovery that the basins of attraction of the BNQN method of polynomials of any degree seem to have piecewise smooth boundaries, while for Newton’s method of polynomials of degrees larger than two are usually fractal.

• Truong, Trung Tuyen (2026). On the properness of polynomial selfmaps. Vietnam Journal of Mathematics. ISSN 2305-221X. doi: 10.1007/s10013-026-00804-y. Full text in Research Archive
• Charles, Favre; Truong, Trung Tuyen & Junyi, Xie (2026). Topological entropy of a rational map over a complete metrized field. Annales Scientifiques de l'Ecole Normale Supérieure. ISSN 0012-9593. 59(1), p. 67–124. doi: 10.24033/asens.2636. Full text in Research Archive Show summary

  We prove that the topological entropy of any dominant rational self-map of a projective variety defined over a complete non-Archimedean field is bounded from above by the maximum of its dynamical degrees. This extends a theorem of Gromov and Dinh-Sibony from the complex to the non-Archimedean setting. We proceed by proving that any regular self-map which admits a regular extension to a projective model defined over the valuation ring has necessarily zero entropy. To this end we introduce the ϵ-reduction of a Berkovich analytic space, a notion of independent interest.

• Hu, Fei & Truong, Trung Tuyen (2025). A dynamical approach to generalized Weil’s Riemann hypothesis and semisimplicity. Science China Mathematics. ISSN 1674-7283. doi: 10.1007/s11425-024-2363-9. Full text in Research Archive Show summary

  Let f be a dynamical correspondence of a smooth projective variety X over an algebraically closed field of arbitrary characteristic. In 2016, Truong conjectured that the dynamical degrees of f defined via the pullback actions on ℓ-adic étale cohomology groups and on numerical cycle class groups are equivalent, which we call the dynamical degree comparison (DDC) conjecture. It contains the generalized Weil’s Riemann hypothesis (for polarized endomorphisms) as a particular case. In this paper, we introduce a quantitative strengthening of the standard conjecture C, named as Conjecture Gr, and show that it holds on abelian varieties and Kummer surfaces. We prove that Conjecture Gr yields the generalized Weil’s Riemann hypothesis. Moreover, Conjecture Gr plus the standard conjecture D imply the norm comparison conjecture, whose consequences include the DDC conjecture and the generalized semisimplicity conjecture. As applications, we prove the DDC conjecture for algebraically stable dynamical correspondences of abelian varieties and Kummer surfaces, extending Hu’s previous work (2019, 2024) on endomorphisms of abelian varieties. We also obtain a similar comparison result for effective finite correspondences of abelian varieties and prove the generalized semisimplicity conjecture for Kummer surfaces.

• Truong, Trung Tuyen (2024). Relations between dynamical degrees, Weil’s Riemann hypothesis and the standard conjectures. Commentarii Mathematici Helvetici. ISSN 0010-2571. 100(1), p. 61–92. doi: 10.4171/CMH/580. Full text in Research Archive Show summary

  Let K be an algebraically closed field, X a smooth projective variety over K and f:X→X a dominant regular morphism. Let Ni(X) be the group of algebraic cycles, of codimension i, modulo numerical equivalence. Let χ(f) be the spectral radius of the pullback f∗: H∗(X,Ql)→H∗(X,Ql) on l-adic cohomology groups, and λ(f) the spectral radius of the pullback f∗:N∗(X)→N ∗(X). We prove in this paper, by using consequences of Deligne’s proof of Weil’s Riemann hypothesis, that χ(f)=λ(f). This answers affirmatively a question posed by Esnault and Srinivas. Consequently, the algebraic entropy logχ(f) of an endomorphism is both a birational invariant and étale invariant. More general results are proven if either K=Fˉp or the Standard Conjecture D holds (this applies specially to Abelian varieties). Among other results in the paper, we show that if some properties of dynamical degrees, known in the case K=C, hold in positive characteristics, then simple proofs of Weil’s Riemann hypothesis follow. More generally, the analogy in positive characteristic of Serre’s famous result on polarized endomorphisms of compact Kähler manifolds also follows.

• Fornæss, John Erik; Hu, Mi; Truong, Trung Tuyen & Watanabe, Takayuki (2024). Backtracking New Q-Newton’s Method, Newton’s Flow, Voronoi’s Diagram and Stochastic Root Finding. Complex Analysis and Operator Theory. ISSN 1661-8254. 18(5). doi: 10.1007/s11785-024-01558-6. Full text in Research Archive Show summary

  A new variant of Newton’s method - named Backtracking New Q-Newton’s method (BNQN) - which has strong theoretical guarantee, is easy to implement, and has good experimental performance, was recently introduced by the third author. Experiments performed previously showed some remarkable properties of the basins of attractions for finding roots of polynomials and meromorphic functions, with BNQN. In general, they look more smooth than that of Newton’s method. In this paper, we continue to experimentally explore in depth this remarkable phenomenon, and connect BNQN to Newton’s flow and Voronoi’s diagram. This link poses a couple of challenging puzzles to be explained. Experiments also indicate that BNQN is more robust against random perturbations than Newton’s method and Random Relaxed Newton’s method.

• Cinzia, Bisi; Jonathan, Hauenstein & Truong, Trung Tuyen (2024). Some interesting birational morphisms of smooth affine quadric 3-folds. Nonlinearity. ISSN 0951-7715. 37(7). doi: 10.1088/1361-6544/ad48f3. Full text in Research Archive
• Barth, Viktor Balch & Truong, Trung Tuyen (2024). Images of dominant endomorphisms of affine space. Communications in Algebra. ISSN 0092-7872. doi: 10.1080/00927872.2024.2418374. Full text in Research Archive
• Truong, Trung Tuyen; To, Tat Dat; Nguyen, Hang-Tuan; Nguyen, Thu Hang; Nguyen, Hoang Phuong & Helmy, Maged (2023). A fast and simple modification of Newton's method avoiding saddle points. Journal of Optimization Theory and Applications. ISSN 0022-3239. 199, p. 805–830. doi: 10.1007/s10957-023-02270-9. Full text in Research Archive Show summary

  We propose in this paper New Q-Newton’s method. The update rule is conceptually very simple, using the projections to the vector subspaces generated by eigenvectors of positive (correspondingly negative) eigenvalues of the Hessian. The main result of this paper roughly says that if a sequence {xn} constructed by the method from a random initial point x0 converges, then the limit point is a critical point and not a saddle point, and the convergence rate is the same as that of Newton’s method. A subsequent work has recently been successful incorporating Backtracking line search to New Q-Newton’s method, thus resolving the global convergence issue observed for some (non-smooth) functions. An application to quickly find zeros of a univariate meromorphic function is discussed, accompanied with an illustration on basins of attraction.

• Truong, Tuyen Trung & Nguyen, Hang-Tuan (2022). Backtracking gradient descent method and some applications in Large scale optimisation. Part 1: Theory. Minimax Theory and its Applications. ISSN 2199-1413. 7(1), p. 79–108. Full text in Research Archive Show summary

  Deep Neural Networks (DNN) are essential in many realistic applications, including Data Science. At the core of DNN is numerical optimisation, in particular gradient descent methods (GD). The purpose of this paper is twofold. First, we prove some new results on the backtracking variant of GD under very general situations. Second, we present a comprehensive comparison of our new results to the previously known results in the literature, providing pros and cons of these methods. To illustrate the efficiency of Backtracking line search, we will present some experimental results (on validation accuracy, training time and so on) on CIFAR10, based on implemetations developed in another paper by the authors. Source codes for the experiments are available on GitHub.

• Helmy, Maged; Truong, Trung Tuyen; Dykyy, Anastasiya; Ferreira, Paulo & Jul, Eric Bartley (2022). CapillaryNet: An automated system to quantify skin capillary density and red blood cell velocity from handheld vital microscopy. Artificial Intelligence in Medicine. ISSN 0933-3657. 127. doi: 10.1016/j.artmed.2022.102287. Full text in Research Archive Show summary

  Capillaries are the smallest vessels in the body which are responsible for delivering oxygen and nutrients to surrounding cells. Various life-threatening diseases are known to alter the density of healthy capillaries and the flow velocity of erythrocytes within the capillaries. In previous studies, capillary density and flow velocity were manually assessed by trained specialists. However, manual analysis of a standard 20-s microvascular video requires 20 min on average and necessitates extensive training. Thus, manual analysis has been reported to hinder the application of microvascular microscopy in a clinical environment. To address this problem, this paper presents a fully automated state-of-the-art system to quantify skin nutritive capillary density and red blood cell velocity captured by handheld-based microscopy videos. The proposed method combines the speed of traditional computer vision algorithms with the accuracy of convolutional neural networks to enable clinical capillary analysis. The results show that the proposed system fully automates capillary detection with an accuracy exceeding that of trained analysts and measures several novel microvascular parameters that had eluded quantification thus far, namely, capillary hematocrit and intracapillary flow velocity heterogeneity. The proposed end-to-end system, named CapillaryNet, can detect capillaries at ~0.9 s per frame with ~93% accuracy. The system is currently used as a clinical research product in a larger e-health application to analyse capillary data captured from patients suffering from COVID-19, pancreatitis, and acute heart diseases. CapillaryNet narrows the gap between the analysis of microcirculation images in a clinical environment and state-of-the-art systems.

• Helmy, Maged; Truong, Trung Tuyen; Jul, Eric Bartley & Ferreira, Paulo (2022). Deep Learning and Computer Vision Techniques for Microcirculation Analysis: A Review. Patterns. 4(1). doi: 10.1016/j.patter.2022.100641. Full text in Research Archive Show summary

  The analysis of microcirculation images has the potential to reveal early signs of life-threatening diseases such as sepsis. Quantifying the capillary density and the capillary distribution in microcirculation images can be used as a biological marker to assist critically ill patients. The quantification of these biological markers is labor intensive, time consuming, and subject to interobserver variability. Several computer vision techniques with varying performance can be used to automate the analysis of these microcirculation images in light of the stated challenges. In this paper, we present a survey of over 50 research papers and present the most relevant and promising computer vision algorithms to automate the analysis of microcirculation images. Furthermore, we present a survey of the methods currently used by other researchers to automate the analysis of microcirculation images. This survey is of high clinical relevance because it acts as a guidebook of techniques for other researchers to develop their microcirculation analysis systems and algorithms.

• Truong, Trung Tuyen (2022). Bounded birationality and isomorphism problems are computable. Beitraege zur Algebra und Geometrie. ISSN 0138-4821. doi: 10.1007/s13366-022-00679-3. Full text in Research Archive Show summary

  Let X, Y be two irreducible subvarieties of the projective space Pn, and d≥1 an integer number. The main result of this paper is an algorithm to construct explicitly, in terms of d and the ideals defining X and Y, a quasi-affine algebraic variety parametrising the set of all birational maps f from X onto Y which can be extended to a self-rational map of Pn of algebraic degree ≤d. We also prove similar results for the case f is a dominant rational map, regular morphism, isomorphism or regular embedding. Similar results are valid for varieties over an arbitrary algebraically closed field, and also for maps on non-projective varieties.

• Hu, Fei & Truong, Trung Tuyen (2022). An inequality on polarized endomorphisms. Archiv der Mathematik. ISSN 0003-889X. 120, p. 27–34. doi: 10.1007/s00013-022-01802-5. Full text in Research Archive
• Truong, Tuyen Trung (2020). Etale dynamical systems and topological entropy. Proceedings of the American Mathematical Society. ISSN 0002-9939. doi: 10.1090/proc/14100. Full text in Research Archive
• Truong, Tuyen Trung (2020). Some new theoretical and computational results around the Jacobian conjecture. International Journal of Mathematics. ISSN 0129-167X. 31(7). doi: 10.1142/S0129167X20500500. Full text in Research Archive Show summary

  In this paper, we study a so-called Condition C1 on square matrices with complex coefficients and a weaker Condition C2. For Druzkowski maps Condition C2 is equivalent to the Jacobian conjecture. We show that these conditions satisfy many good properties and in particular are satisfied by a dense subset of the set of square matrices of a given rank [Formula: see text]. Based on this, we propose a heuristic argument for the truth of the Jacobian conjecture. We propose some new equivalent formulations and some generalizations of the Jacobian conjecture, and some approaches (including computer algebra and numerical methods) toward resolving it. We show that some of these equivalent formulations are automatically satisfied by generic Druzkowski matrices. Applications and experimental results are included.

• Truong, Tuyen Trung (2020). Strong submeasures and applications to non-compact dynamical systems. Ergodic Theory and Dynamical Systems. ISSN 0143-3857. doi: 10.1017/etds.2020.132. Full text in Research Archive
• Truong, Tuyen Trung & Nguyen, Hang-Tuan (2020). Backtracking Gradient Descent Method and Some Applications in Large Scale Optimisation. Part 2: Algorithms and Experiments. Applied Mathematics and Optimization. ISSN 0095-4616. doi: 10.1007/s00245-020-09718-8. Full text in Research Archive Show summary

  In this paper, we provide new results and algorithms (including backtracking versions of Nesterov accelerated gradient and Momentum) which are more applicable to large scale optimisation as in Deep Neural Networks. We also demonstrate that Backtracking Gradient Descent (Backtracking GD) can obtain good upper bound estimates for local Lipschitz constants for the gradient, and that the convergence rate of Backtracking GD is similar to that in classical work of Armijo. Experiments with datasets CIFAR10 and CIFAR100 on various popular architectures verify a heuristic argument that Backtracking GD stabilises to a finite union of sequences constructed from Standard GD for the mini-batch practice, and show that our new algorithms (while automatically fine tuning learning rates) perform better than current state-of-the-art methods such as Adam, Adagrad, Adadelta, RMSProp, Momentum and Nesterov accelerated gradient. To help readers avoiding the confusion between heuristics and more rigorously justified algorithms, we also provide a review of the current state of convergence results for gradient descent methods. Accompanying source codes are available on GitHub.

• Truong, Tuyen Trung (2020). When will a sequence of points in a Riemannian submanifold converge? Mathematics. 8(11). doi: 10.3390/math8111934. Full text in Research Archive Show summary

  Let X be a Riemannian manifold and xn a sequence of points in X. Assume that we know a priori some properties of the set A of cluster points of xn. The question is under what conditions that xn will converge. An answer to this question serves to understand the convergence behaviour for iterative algorithms for (constrained) optimisation problems, with many applications such as in Deep Learning. We will explore this question, and show by some examples that having X a submanifold (more generally, a metric subspace) of a good Riemannian manifold (even in infinite dimensions) can greatly help.

• Larusson, Finnur & Truong, Tuyen Trung (2019). Approximation and interpolation of regular maps from affine varieties to algebraic manifolds. Mathematica Scandinavica. ISSN 0025-5521. 125(2), p. 199–209. doi: 10.7146/math.scand.a-114893. Full text in Research Archive
• 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. Full text in Research Archive
• Kaliman, Shulim; Kutzschebauch, Frank & Truong, Tuyen Trung (2018). On subelliptic manifolds. Israel Journal of Mathematics. ISSN 0021-2172. 228(1), p. 229–247. doi: 10.1007/s11856-018-1760-7. Full text in Research Archive
• 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. Full text in Research Archive

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• Truong, Trung Tuyen (2026). Some new results on embedding of open Riemann surfaces. Full text in Research Archive
• Truong, Trung Tuyen (2026). Some facts about quantum computing. Full text in Research Archive
• Truong, Trung Tuyen (2026). Images and preimages of polynomial selfmaps. Full text in Research Archive
• Truong, Trung Tuyen (2026). BNQN: Interactions with (nonsmooth) Real and Complex Dynamical Systems, and Applications in Equations Solving and Number Theory. Full text in Research Archive
• Truong, Trung Tuyen (2026). The mathematical foundation in artificial intelligence. Full text in Research Archive
• Truong, Trung Tuyen (2026). non-Cartesian polynomials and applications. Full text in Research Archive Show summary

  A polynomial F(x,y,z,t) \in C^2 \times C^2 is Cartesian if it has the form: F(x,y,z,t)=F_1(x,y)G_1(x,y,z,t)+F_2(z,t)G_2(x,y,z,t), Where F_1,G_1,F_2,G_2 are polynomials, and F_1 and F_2 are non-constant. Otherwise, we say that F is non-Cartesian. In this talk I will show that: There is an algorithm, based on Groebner bases, to detect if a given polynomial F is Cartesian or not. There is an effective sufficient condition which guarantees that F is non-Cartesian. For each given degree d\geq 2, the set of non-Cartesian polynomials of degree at most d is a constructible and dense subset. The application of non-Cartesian polynomials in Discrete combinatorics lies in the fact (proven by Mojarrad, Pham, Valculescu and de Zeeuw in 2017) that the set {F=0}\cap (P_1xP_2), where P_1, P_2 are finite sets of C^2, is of much smaller size than that of P_1xP_2. This is a type of Schwartz-Zippel bounds, and is related to Erdos' unit distance problem in the complex variable setting (which recently has been disproven by the aid of AI). Generalisations to higher dimensions are also given. This is joint work with Chun-Yen Shen and Wei-Hsuan Yu.

• Truong, Trung Tuyen (2025). Backtracking line search and applications. Full text in Research Archive
• Truong, Trung Tuyen (2025). A new equivalence and approach to the Riemann hypothesis, via root finding and optimization. Full text in Research Archive
• Truong, Trung Tuyen (2025). Introduction to NUV Optimization. Full text in Research Archive
• Truong, Trung Tuyen (2025). Some new results concerning Tate's questions and generalisations. Full text in Research Archive
• Truong, Trung Tuyen (2025). A new equivalence and approach to the Riemann Hypothesis, via root finding and optimization. Full text in Research Archive
• Truong, Trung Tuyen (2025). An introduction to university education in Norway, and a review of some optimization algorithms and software. Full text in Research Archive
• Truong, Trung Tuyen (2025). The role of mathematics and optimization in Machine Learning/Deep Learning. Full text in Research Archive
• Truong, Trung Tuyen (2024). Maths, Optimization and Deep Learning/Machine Learning. Full text in Research Archive
• Truong, Trung Tuyen (2024). Applications of mathematics in Machine Learning and Deep Learning. Full text in Research Archive
• Truong, Trung Tuyen (2024). A new equivalence and approach to the Riemann hypothesis, via dynamical systems. Full text in Research Archive
• Truong, Trung Tuyen (2024). The role of Mathematics and Optimization in Machine Learning/Deep Learning. Full text in Research Archive
• Truong, Trung Tuyen (2024). The Riemann hypothesis and the dynamics of Backtracking New Q-Newton's method. Full text in Research Archive
• Truong, Trung Tuyen (2024). A NEW NEWTON-TYPE METHOD AND CONNECTiONS TO SCHRODER THEOREM, VORONOi’S DiAGRAMS, NEWTON’S FLOWS AND THE RiEMANN HYPOTHESiS. Full text in Research Archive
• Truong, Trung Tuyen (2024). Backtracking New Q-Newton’s method and connection to the Riemann hypothesis. Full text in Research Archive
• Truong, Trung Tuyen (2024). The Riemann hypothesis and dynamics of a root finding method. Full text in Research Archive
• Truong, Trung Tuyen (2024). A new equivalence and a new approach to the Riemann hypothesis, via complex analysis and dynamical systems. Full text in Research Archive
• Truong, Trung Tuyen (2024). The Riemann hypothesis and dynamics of a root finding algorithm. Full text in Research Archive
• Truong, Trung Tuyen (2024). How is AI doing with mathematical arguments. Full text in Research Archive
• Truong, Trung Tuyen (2024). A new equivalence and approach to the Riemann hypothesis, via dynamical systems. Full text in Research Archive
• Truong, Trung Tuyen (2023). Backtracking New Q-Newton's method with applications in stochastic root finding. Full text in Research Archive
• Truong, Trung Tuyen (2023). Stochastic dynamical systems coming from root finding: phenomena and questions. Full text in Research Archive
• Truong, Trung Tuyen (2023). Some interesting research topics relevant to Machine Learning/Deep Learning. Full text in Research Archive
• Truong, Trung Tuyen (2023). Hvordan finner vi løsninger til polynomer i 1 kompleks variabel? Full text in Research Archive
• Truong, Trung Tuyen (2023). A better algorithm to solve equations than Newton's method. Full text in Research Archive
• Truong, Trung Tuyen (2023). Optimization algorithms: Theory and large scale applications, intensive course. Full text in Research Archive
• Truong, Trung Tuyen (2023). How good can AI do simple logical reasoning and mathematics now? - An update. Full text in Research Archive
• Truong, Trung Tuyen (2023). New Q-Newton's method and Backtracking line search. Full text in Research Archive
• Truong, Trung Tuyen (2023). Periodic points, dynamical degrees and root finding. Full text in Research Archive
• Truong, Trung Tuyen (2022). Some interesting birational morphisms of smooth affine quadric 3-folds. Full text in Research Archive
• Truong, Trung Tuyen (2022). Entropy of maps on non-Archimedean fields. Full text in Research Archive
• Truong, Trung Tuyen (2022). Entropy of maps on non-Archimedean fields. Full text in Research Archive
• Truong, Trung Tuyen (2022). Optimization, Lojasiewicz inequalities, Dynamical Systems and Deep Neural Networks (Or: Is there a cat or not a cat?). Full text in Research Archive
• Truong, Trung Tuyen (2021). A 10-line proof of a generalisation of Weil’s RH for Abelian varieties. Full text in Research Archive
• Truong, Trung Tuyen (2021). A quick method to find roots of univariate meromorphic functions. Full text in Research Archive
• Truong, Trung Tuyen (2021). Implementation of Backtracking line search in Deep Neural Networks: theory and practice. Full text in Research Archive
• Truong, Trung Tuyen (2020). Rationality of quotients of Abelian varieties and computer algebra. Full text in Research Archive
• Truong, Trung Tuyen (2020). Rationality of quotients of Abelian varieties and computer algebra. Full text in Research Archive
• Truong, Trung Tuyen (2020). Deep Learning and Automated Proof Checking. Full text in Research Archive

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