Dichotomy and Howe Duality for Exceptional Theta Correspondences

Explore a comprehensive lecture on exceptional theta correspondences, focusing on the Dichotomy and Howe duality theorems. Delve into Wee Teck Gan's joint work with Gordan Savin, examining their proof of the Howe duality theorem for exceptional dual pairs of the form G_2 x H. Investigate the dichotomy theorem in the style of Kudla and Rallis' conservation relation. Cover key topics such as local data correspondence, doubling seesaw, period pingpong, reductive periods, and chain of containments. Gain insights into the main ingredients, constraints, and general principles underlying these theorems. Engage with thought-provoking questions and learn about an ongoing book project related to this research area.