Junhwi Lim receives Provost Pathbreaking Discovery Award and Vanderbilt Award for Doctoral Discovery
Junhwi Lim, a PhD student in the Vanderbilt Mathematics Department, has received the Provost Pathbreaking Discovery Award, as well as Vanderbilt Award for Doctoral Discovery. Junhwi is a fifth-year graduate student who has been working under the direction of Prof. Dietmar Bisch since 2021. He has proved several first-rate results in the theory of subfactors and their planar algebras, an area of study introduced by Vaughan Jones, a Fields medalist and former faculty member at Vanderbilt.
The Provost Pathbreaking Discovery Award is the premier award from the Provost and Vice Chancellor for Academic Affairs, as well as the Vice Provost for Graduate Education and Dean of the Graduate School. The award celebrates doctoral students who demonstrate truly exceptional research and scholarship.
The College of Arts and Science’s Vanderbilt Award for Doctoral Discovery (VADD), previously named the Summer Research Award (SRA) program, is designed to help graduate students with outstanding potential to accelerate progress on their research. VADDs are also granted on a competitive basis.
Jones, in collaboration with Bisch, showed that the fundamental quantum symmetries of a subfactor, when a single intermediate subfactor is present, are given by what they called the Fuss-Catalan algebras. These are generalizations of the Temperley-Lieb algebras, that are prevalent in mathematics and physics. So, what happens when two intermediate subfactors are present? Junhwi managed to resolve this difficult problem. The resulting symmetries are related to quantum groups, another important area of mathematics.
In a separate collaboration with Corey Jones (former Vanderbilt PhD student and current professor at NCSU) Junhwi used the Jones index for a subfactor to completely classify quantum cellular automata. This marvelous result was published in Annales Henri Poincaré, a prestigious theoretical and mathematical physics journal.
Junhwi’s contributions have already been recognized by the international mathematical community. In 2024, he has delivered nine talks at seminars and conferences outside Vanderbilt. In Summer 2025, he will attend a workshop at Oberwolfach, and he will use the VADD to visit Saarland University in Saarbruecken, Germany to work on problems related to quantum groups with the operator algebras researchers based there.
Congratulations, Junhwi!