DuongNotes

Welcome to my page!

I currently work as a lecturer at Phenikaa University in Hanoi, Vietnam. Prior to this, I held the position of a postdoctoral researcher in the Complex Analysis Group at the Faculty of Mathematics, University of Vienna. During that time, I received support from FWF-projects led by Bernhard Lamel and Friedrich Haslinger. I was a Principal Investigator of the Lise Meitner FWF-Projekt M2472-N35, a postdoctoral researcher at University of Vienna under the FWF-project I01776 by Bernhard Lamel (09/2017-08/2018), and a postdoctoral research associate at Texas A&M University at Qatar (2015-17) under the NPRP project 7-511-1-098 by Nordine Mir. Furthermore, I had the privilege of being a Visiting Assistant Professor at the Department of Mathematics, University of California at Irvine where I was supervised by Song-Ying Li.

In 2012, I earned my Ph.D. degree at the University of California at San Diego, where I had the privilege of being mentored by Professor Peter Ebenfelt. My Ph.D thesis has the title  "Transversality of CR mappings between CR submanifolds of complex spaces" and can be downloaded from eScholarship.

In 2020, I earned my Habilitation at the University of Vienna, with the dissertation title "Some aspects of CR manifolds."

My research interest are Several Complex Variables and CR geometry. For more details, see Research page or my Curriculum Vitae.

Contact me at contact@duongnotes.com

Blogs / News

• 30 October, 2025, My book "Linear Algebra", ISBN: 978-604-43-3989-4, which I co-authored with Dr. Bui Xuan Quang, Dr. Phan Quang Sang, and A. Prof. Dr. Do Quoc Tuan has now been published by the Hanoi National University Press.

• 30 August 2025 - On September 11, 2025, Phenikaa University will host the Phenikaa Math Autumn Meeting 2025, an academic workshop aimed at fostering exchange and collaboration among mathematicians in Vietnam. The program features three invited talks by distinguished researchers: Associate Professor Ninh Van Thu (Hanoi University of Science and Technology) will present on "Asymptotic behavior of the Bergman kernel and associated invariants in weakly pseudoconvex domains". Associate Professor Le Duc Ninh (Phenikaa University) will speak on "Feynman integrals".  Dr. Pham Ba Duc (Phenikaa University) will give a talk on "Rank metric cryptosystems and decoding sums of Gabidulin codes".

  By covering topics from complex analysis and mathematical physics to modern cryptography, the meeting underlines the breadth of contemporary mathematical research and provides a platform for connecting scholars across different fields.

  The event is open to faculty members, researchers, and students interested in mathematics and its applications.

  For more details about this event, see the announcement in the website of Faculty of Fundamental Sciences of Phenikaa University.

• 30 June 2025 – I am pleased to participate in the 2025 International Conference on Several Complex Variables, which takes place from June 30 to July 3, 2025, at Wuhan University, Hubei, China.

  The conference brings together researchers from around the world to discuss recent advances in several complex variables, CR geometry, and related fields. It features 21 invited talks by leading experts, including colleagues from North America, Europe, and Asia.

  As part of the scientific program, I will be giving a talk on: June 30 at 2:00pm. Further details about the conference can be found on the official website.

• 22 May 2025 – The Phenikaa Math Summer Meeting took place on Thursday, May 22, 2025. The invited speakers included Assoc. Prof. Dr. Trinh Viet Duoc from VNU University of Science, along with Dr. Nguyen Thi Ngoc Anh and Dr. Tran Manh Hung from PHENIKAA University. Their presentations covered a diverse range of topics, including the Navier-Stokes-Oseen equations, Vines and MAT-labeled graphs, and Tropical Geometry.

• 09 October 2024 – 2024 Phenikaa Autumn Math-Workshop is going to be held on Friday, October 11, 2024. The venue for the workshop is A9 Building, 24th floor, Phenikaa University Campus | Program and Book of Abstract.

• 25 August 2024 – The Conference on Complex Analysis and Geometry is going to be held on August 26 - 29, 2024 at VIAMS, Hanoi, Vietnam. I am going to contribute a talk in the conference on Wednesday, 28 August 2024.

• 21 May 2024 – The second Phenikaa Math Seminar of the year is going to be on Thursday, 23/5/2024, at A9 building, Phenikaa University main campus. The invited speakers are from Hanoi National University of Education.

• 19 January 2024 – The first Phenikaa Math Seminar of the year is going to be on Tuesday, 23/1/2024, at A9 building, Phenikaa University main campus. The invited speakers are from Hanoi University of Science and Technology.

• 13 September 2023 – The Phenikaa Autumn Math-Workshop is going to be tomorrow, 14 September 2023, 13:45, at the A9 building, Phenikaa University main campus. The invited speakers are from Institute of Mathematics, VAST, and the Hanoi National University of Education.

• 11 August 2023 – At University of Science and Education, The University of Da Nang, I give a talk on the classification of the CR maps from the sphere into the tube over the future light cone. This talk is based on my joint work with Michael Reiter, published in Adv. Math. Vol. 410, Part A, 3 December 2022, 108743.

• 25 May 2023 – At PHENIKAA University, I have the privilege of instructing three classes in Analysis. As part of my role, I am currently crafting a series of comprehensive lecture notes to aid my students' learning experiences. Among these resources, I am diligently working on a concise set of notes (in Vietnamese) specifically focused on Differential Equations.

• 19 May 2023 – I will be delivering a seminar presentation at VIASM, located at 157 Chua Lang Street, Hanoi, Vietnam. The seminar will take place in room C101 from 14:30 to 16:00, 22 May 2023. During the presentation, I will be discussing the eigenvalues of the Kohn Laplacian.

• 17 March 2023 – It is honored to speak at The 10th National Congress of Mathematics 2023. The conference is going to be held from 8-12/8/2023 at The University of Science and Education, University of Danang. I am very thankful to the organizers for a kind invitation to speak at the Analysis Section of this conference.

• 19 February 2023 – I am going to speak at Summer Meeting 2023. It is very honored to speak at this meeting. I am very thankful to the organizers for a kind invitation.

• 2 March 2023 – I am going to speak at Workshop on Differential Equations and Related Topics. The conference is going to be held on March 9 at VIASM. It is very honored to speak at this meeting. I am very thankful to the organizers of this meeting for an invitation.

• 10 February 2023 – I am honored to accept an invitation to speak at the Seminar on Algebra and Number Theory at Instute of Mathematics, VAST, Hanoi. The talk is going to be in the morning of February 15, 2023. Detailed information about the talk is here.

• 18 August 2022 – Faculty of Fundamental Sciences, Phenikaa University organized a joint mathematics seminar. Speakers were from the Hanoi Institute of Mathematics, VAST, and Phenikaa University. The detail of the event is here.

• 23 July 2022 – I am honored to join Faculty of Fundamental Sciences, Phenikaa University.

• 09 May 2022 – My preprint The CR umbilical locus of a real ellipsoid in \(\mathbb{C}^2\) has been announced on the preprint server arXiv: 2205.03342.

• 28 Mar 2022 – I am honored to accept an invitation to speak at the Several Complex Variables Seminar of the IBS Center for Complex Geometry, one of the research centers in the Institute for Basic Science of Korea. I sincerely thank the organizers for the invitation. For more details of the event, see https://ccg.ibs.re.kr/event/2022-04-27/.

• 10 Feb 2022 – Colloquium Mathematicum, a journal of the Institute of Mathematics, Polish Academy of Sciences, has finally published my paper on a new notion of "convexity" for pseudohermitian manifolds that are semi-isometrically embedded in a Kähler manifold. An online first copy of the paper can be downloaded here.

• 16 Dec 2021 – My paper with Prof. Bernhard Lamel about the CR Ahlfors derivative has been published as an "Online first" article in Annales de l'Institut Fourier (Grenoble). It can be accessed here DOI: 10.5802/aif.3438.

• 20 Nov 2021 – I was honored to accept an invitation to speak (via Internet) at the conference Một số vấn đề chọn lọc trong Giải tích phức và Hình học phức [Some selected Topics in Complex Analysis and Complex Geometry] on the occasion of the 70th birthday of Professor Le Mau Hai and of the 60th birthday of Professor Do Duc Thai. The conference will be held on 9-10/12/2021 at the VIASM, Hanoi, Vietnam.

• 29 Sep 2021 – Today, I gave a talk at the conference DMV-ÖMG Jahrestagung 2021, §8 Funktionalanalysis, Reelle, Komplexe Analysis, Passau, Germany, via Zoom. The talk was about my recent joint work with Dr. Gian Maria Dall’Ara regarding a sharp upper bound for the first positive eigenvalue of the Kohn Laplacian on Reinhard real hypersurfaces in two dimensional complex space. The details have been written up and made public at arXiv: 2110.06704.

• 24 Jun 2021 – Today, I gave a talk based on a joint work with Prof. Bernhard Lamel about the CR Ahlfors derivative and its applications to the study of sphere maps at the Minisymposium “Complex Analysis and Geometry,” 8th European Congress of Mathematics, Portorož, Slovenia, June 20–26, 2021 (rescheduled from July 2020). The details have been written up in a paper which is going to appear in Annales de l’Institut Fourier.

• 15 Jun 2021 – A preprint by Dr. Michael Reiter and I, which provides a complete classification of proper holomorphic maps from the unit ball in a two dimensional complex space into the Cartan’s symmetric domain of type IV in a three dimensional complex space, has been posted on the arXiv, see arXiv:2106.07002. The result was first announced by Dr. Reiter in the joint Reseach Seminar Nice-Brno-Vienna-Doha on April 1, 2021.

• I like to read books, both in Vietnamese and English. I particularly like to read ancient books. Recently, I spent time reading Buddhist texts, starting with "The Long Discourses of the Buddha" (A Translation of the Dīgha Nikāya).