사범대학 | 교수소개 | 전임교수

부교수 대수학
임수봉

02-760-0537
subong@skku.edu
호암관 12층 51205호실

관심분야

보형 형식은 복소 함수 중에서 특정한 대칭 구조를 갖는 함수로서 정수론 분야에서 중요한 연구 주제 중 하나입니다. 보형 형식의 프리에 계수는 수학의 여러 분야와 관련이 있고, 와일즈는 보형 형식의 프리에 계수와 타원 곡선과의 관계를 이용하여 페르마의 마지막 정리를 증명하기도 하였습니다. 최근에는 보다 많은 대상을 보형 형식의 관점에서 이해하기 위해 막 보형 형식, 조화 보형 형식, 양자 보형 형식 등이 소개 되어 이와 관련된 연구들이 활발히 진행되고 있습니다. 저의 연구에서는 아이클러-시무라 코호몰로지 이론을 이용하여 여러 보형 형식들을 통합적으로 이해할 수 있는 방법을 찾고 그 구조를 연구하며 산술적 성질들을 얻고자 합니다.

학력

(Ph.D.) POSTECH 수학과 (2012.2)

약력/경력

고등과학원, 연구원 (2012.3 - 2015.2)
성균관대학교 수학교육과, 조교수 (2015.3 - 2019.2)
성균관대학교 수학교육과, 부교수 (2019.3 - 현재)

학술지 논문

(2021) Density of modular forms with transcendental zeros. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS. 500, 2
(2020) Congruences involving the Ul\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$U_{\ell }$$\end{document} operator for weakly holomorphic modular forms. RAMANUJAN JOURNAL. 51, 3
(2020) LIMITS OF TRACES OF SINGULAR MODULI. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY. 373, 1
(2020) Schneider-Siegel theorem for a family of values of a harmonic weak Maass form at Hecke orbits. FORUM MATHEMATICUM. 32, 1
(2019) Pairs of eta-quotients with dual weights and their applications. ADVANCES IN MATHEMATICS. 355,
(2019) On sign changes of Jacobi forms. JOURNAL OF NUMBER THEORY. 203,
(2019) Values of harmonic weak Maass forms on Hecke orbits. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS. 477, 2
(2019) Independence between coefficients of two modular forms. JOURNAL OF NUMBER THEORY. 202,
(2018) Arithmetic of generalized Dedekind sums and their modularity. OPEN MATHEMATICS. 16,
(2017) Hecke Bound of Vector-valued Modular Forms and its Relationship with Cuspidality. TAIWANESE JOURNAL OF MATHEMATICS. 22, 2
(2017) Hecke structures of weakly holomorphic modular forms and their algebraic properties. JOURNAL OF NUMBER THEORY. 184,
(2017) The Eichler-Shimura cohomology theorem for Jacobi forms. MONATSHEFTE FUR MATHEMATIK. 182, 2
(2016) Finite-dimensional period spaces for the spaces of cusp forms. ISRAEL JOURNAL OF MATHEMATICS. 216, 2
(2016) Series expansion of the period function and representations of Hecke operators. JOURNAL OF NUMBER THEORY. 171,
(2016) L-series for Vector-valued Modular Forms. TAIWANESE JOURNAL OF MATHEMATICS. 20, 4
(2016) ODD-BALANCED UNIMODAL SEQUENCES AND RELATED FUNCTIONS: PARITY, MOCK MODULARITY AND QUANTUM MODULARITY. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY. 144, 9
(2016) MOCK MODULAR FORMS AND QUANTUM MODULAR FORMS. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY. 144, 6
(2016) Shimura lifting on weak Maass forms. ACTA ARITHMETICA. 173, 1
(2015) Pairings of harmonic Maass-Jacobi forms involving special values of partial L-functions. JOURNAL OF NUMBER THEORY. 157, 1
(2015) Period functions of half-integral weight modular forms. JOURNAL DE THEORIE DES NOMBRES DE BORDEAUX. 27, 1

학술회의논문

(2021) Independence between coefficients of two modular forms. The 9th East Asia Number Theory Conference. 일본
(2021) Congruences for weakly holomorphic modular forms of half-integral weight. KIAS Number Theory Seminar. 대한민국
(2021) Schneider-Siegel theorem for harmonic weak Maass forms. UNIST 수리과학과 Colloquium. 대한민국
(2020) On sign changes of Jacobi forms. 2020년도 대한수학회 봄 연구발표회. 대한민국
(2019) Paris of Eta-quotients with dual weights. The 9th East Asia Number Theory Conference. 대한민국
(2019) Quantum modular forms and mock modular forms. 2019 2nd q-Day: q-series and related topics. 대한민국
(2017) Hecke structures of weakly holomorphic modular forms and their algebraic properties. Trends in modular forms. 대한민국
(2017) Limits of traces of singular moduli. Arithmetics on Automorphic Forms. 중국
(2017) Limits of traces of singular moduli. Number Theory Festival. 대한민국
(2016) Limits of traces of singular moduli. 2016 Seoul-Tokyo Conference on Number Theory. 대한민국

교수소개

교수소개 - 수학교육과

관심분야

학력

약력/경력

학술지 논문

학술회의논문