On May 9, Professor Dohoon Choi from Korea University visited KAIST to hold a seminar on the multiplicities of automorphic representations of general linear groups of degree n, one of his main areas of research relating to number theory.
Professor Choi works for the Department of Mathematics in Korea University and has received grants from the Samsung Science and Technology Foundation, National Research Foundation of Korea, and Korea Research Foundation throughout the years. Currently, he is also a member of the Young Korean Academy of Science and Technology. Before his current area of study, Professor Choi had published a multitude of papers concerning modular forms, automorphic, and Galois representations.
By using concepts and theorems that were introduced by other mathematicians such as Linnik, Dirichlet, Maeda, Buzzard, and more, Professor Choi introduced the topic at hand with pre-established theorems. To summarize, previously, under the multiplicity one theorem, studies by Carlos Moreno and Farrell Brumley established that the best bound for multiplicities was a polynomial bound. Under the assumption of the General Riemann Hypothesis, this can be improved into a logarithm-squared bound. However, a conjecture by Maeda and Buzzard stated that the bound can be improved even further into a constant number. This conjecture, if true, would provide a much stronger bound.
Professor Choi sought to prove such a claim. At the end of the given lecture, he showcased his discovery, claiming that the multiplicities are indeed bound by a constant number.
While the study is yet to be published, Professor Choi assured that a proof existed and stated that he plans to publish the paper very soon. Previous studies dating back to the 20th century have delved into this area of research. However, it hasn’t been until now that such a strong bound has been determined under certain conditions. While a logarithm-squared bound is small in itself, a constant number bound provides a more definitive description of the multiplicities.