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# DuongNotes

#### Latest News

• 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. Its main content is a description of the CR umbilical locus of the ellipsoid in $$\mathbb{C}^2$$ given by the equation $|z|^2 + |w|^2 + \Re(a z^2 +b w^2) -1 = 0.$ In the case $$b=0$$ (resp. $$b=a$$), the locus is completely and explicitly determined: It consists of 3 curves (resp. 4 curves), among them, two curves are newly discovered and the others have been known previously.

• Vienna, 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/.

#### Recent Activities

• 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 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 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 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 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.

© 2021 – 2022 Duong Ngoc Son, Ph.D.