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Explore the intricacies of modular forms in this comprehensive lecture by Mahesh Kakde at the International Centre for Theoretical Sciences. Delve into key concepts including Seegel and elliptic modular forms, congruence subgroups, cusps, Fourier expansions, and fundamental domains. Examine Gauss's Theorem, Eisenstein series, and dimension formulas. Investigate holomorphic modular forms, differential operators, and theta series. Learn about Hecker's trick and explore various examples and propositions throughout the lecture. Gain insights into extremal practices and their applications in modular form theory.
