Theta Correspondence and Relative Langlands

Watch this advanced mathematics lecture from the Arithmetic Quantum Field Theory Conference where MIT professor Zhiwei Yun explores the geometric aspects of theta correspondence and its connection to relative Langlands duality. Examine how reductive dual pairs act on tensor products of standard representations as hyperspherical varieties, serving as geometric avatars for theta correspondence. Learn about two key geometric results: the behavior of principal series representations under theta correspondence using Springer correspondence, and the definition of character sheaves in theta correspondence contexts. Delve into the relationship between these geometric constructions and relative Langlands duality, with particular focus on applications over finite fields. The presentation includes collaborative research findings with Jiajun Ma, Congling Qiu, Jialiang Zou, and Shamgar Gurevich.