The paper, “Liouville-type results for infinity elliptic equations involving gradient and Hardy-Hénon nonlinearities,” was authored by Khuu Tan Dat, a recent graduate from the Faculty of Mathematics and Statistics at Ton Duc Thang University, and Huynh Trung Hieu, a senior in the Department of Mathematics at the Ho Chi Minh City University of Education. It was published in late March by Mathematische Zeitschrift.
Founded in 1918 and published by Springer Nature, the publication is widely recognized as a high-impact journal focused on pure and applied mathematics. Recent bibliometric analyses continue to identify it as a top-quartile (Q1) publication.
Khuu Tan Dat (L) and Huynh Trung Hieu in photos they provided. |
Dat and Hieu conducted their research under the supervision of Associate Professor Dr. Vo Hoang Hung from Saigon University.
This collaboration was part of the “Research Experience for Undergraduates” (REU) summer program, organized last year by the Vietnam Institute for Advanced Study in Mathematics (VIASM), whose Scientific Director, Professor Ngo Bao Chau, is the first Vietnamese national to receive the Fields Medal, the world’s top honor in mathematics.
During the VIASM summer program, students attended a week of lectures before registering to work with instructors whose research aligned with their own interests. Dat and Hieu, sharing a passion for mathematical analysis, were guided in developing logical reasoning, approaching complex problems directly, and presenting their results effectively.
The students’ research establishes a mathematical framework for analyzing systems dictated by extreme constraints rather than averages. This work has practical applications in optimal transport, material failure, and image processing.
It also utilizes Liouville results to ensure physical models remain stable and to set critical boundaries for simulations.
“This is such a great joy for our student years,” Dat shared.
Associate Professor Hung noted that the study is highly theoretical, significantly expanding mathematical knowledge while offering potential applications in physics. The research direction, which Hung initiated in 2022, builds directly upon his previous scholarly work.
Dat acknowledged the highly challenging nature of the research, especially since their prior mathematical knowledge from high school and university was primarily foundational.
To bridge this gap, the pair spent extensive time studying advanced materials. They worked intensively with Hung for over three months, frequently discussing the project until midnight to maintain their progress. Following the formal program, they continued to explore the topic independently.
Their dedication paid off: the project won first prize in the REU program and earned an “excellent” rating from VIASM.
Associate Professor Hung emphasized that programs like the REU provide vital opportunities for outstanding students to connect with domestic and international professors, exposing them to significant mathematical problems. He also highlighted that working with talented young students allows established mathematicians to help train the next generation.
“This is a special opportunity to learn, connect, and receive dedicated guidance from leading experts,” Dat reflected.
Hung hopes this milestone will serve as a solid foundation for both students to continue pursuing their passion and tackling even more challenging mathematical problems in the future.
Prior to this, Dat had published a paper in a Q3 journal, while Hieu secured first prize in analysis and second prize in algebra at the 2023 National Student Mathematics Olympiad.
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