Today's colloquium talk was interrupted by technical problems. We are planning to postpone it to next Monday (May 17th) *_Time_: **Monday, **May 10th**- 16:00 h s.t.* (canceled) *_Colloquium_: Aniket Shah (Ohio State University)* *_Title_: A q-analogue of Brion's identity* *_Abstract_:*Rogers-Szegő polynomials are a family of orthogonal polynomials on the circle. We introduce a generalization of these polynomials which depend on the data of a polytope and prove a vertex sum formula for them when the polytope is smooth. This formula recovers Brion's formula when the parameter q is set to 0.