Jacobi-Like Forms, Pseudodifferential Operators, and Quasimodular Forms

YoungJu Choie, currently Professor of Mathematics at Pohang University of Science and Technology and was an Assistant Professor at the University of Colorado at Boulder, works in the area of number theory, in particular modular forms. She has over 100 publications including a monograph in the Memoirs of American mathematical Society. She served as Editor in Chief of the Bulletin of the Korean Mathematical Society and is currently an Editor of the International Journal of Number Theory. In 2013, she became inaugural Fellow of the American Mathematical Society and In 2018 she became a member of the Korean Academy of Science and Technology. She has received several awards such as  "The best woman Scientist of the year" award (2005) from the Ministry of Science and Technology of  Korea. She has been a visiting fellow at the Max-Planck Institute for Mathematics in Bonn, Stanford University, University of Cambridge. MinHo Lee,  currently Professor of Mathematics at the University of Northern Iowa, works in the area of number theory and algebraic geometry. He has over 100 publications including the monograph "Mixed Automorphic Forms, Torus Bundles, and Jacobi Forms" published by Springer-Verlag in the Lecture Notes in Mathematics series (No. 1845).

• Introduction.-  Formal power series and pseudodifferential operators.- Jacobi-like forms and pseudodifferential operators.- Hecke operators.- Lie algebras.- Heat operators.- Group cohomology.- Quasimodular forms.- Quasimodular and modular polynomials.- Liftings of quasimodular forms.- Quasimodular forms and vector-valued modular forms.- Differential operators on modular forms.- Half-integral weight forms.- Projective structures.-  Applications of quasimodular forms.

“The book does an outstanding job of curating and detailing a list of important and interconnected mathematical concepts surrounding quasimodular forms, while also building the useful languages for Jacobi-like forms, pseudodifferential operators, and the connections among these objects. … It comprehensively examines the chosen topics … and detailed proofs. At the same time, the book excels at maintaining its focus on the topics at hand, and not leading the reader astray by examining too many ancillary themes.” (Matthew Krauel, Mathematical Reviews, June, 2023)