题目：Free Algebras of Modular Forms on Type IV Symmetric Domains
摘要： It is a classical problem to determine the algebra of automorphic forms on symmetric domains. The first breakthrough was due to Igusa, who showed in 1962 that the algebra of genus 2 Siegel modular forms of even weight is freely generated by four forms of weights 4, 6, 10, 12.In this talk, we introduce a new approach to classify and construct free algebras of modular forms on symmetric domains of type IV. We first establish a sufficient and necessary condition for the graded algebra of orthogonal modular forms being free. We then prove an explicit classification result and present more than 70 such algebras which recover all known examples in the literature. This greatly expands Igusa's theorem.