’On the derived category of the Iwahori-Hecke algebra’ Eugen Hellmann (University of Muenster) Monday 6 July 5:00pm - 6:30pm (AEST) Online via Zoom Abstract: In this talk I will state a conjecture which predicts that the derived category of smooth representations of a p-adic split reductive group admits a fully faithful embedding into the derived category of (quasi-)coherent sheaves on a stack of L-parameters. We will make the conjecture precise in the case of the principal block of GL_n and relate it to the construction of a family of representations on the stack of L-parameters that interpolates a modified version of the local Langlands correspondence. The existence of this family is suggested by the work of Helm and Emerton-Helm. I will explain why the derived tensor product with this "Emerton-Helm family" should realize the expected embedding of derived categories and discuss some explicit examples. Register here: https://uni-sydney.zoom.us/meeting/register/tJAuc-ChpzMuG9b6uEaR_xsJudgB1POwNKkN You will be sent a confirmation email with the Zoom details prior to the event. (Please email smri.admin@sydney.edu.au if you do not receive the email with the link ~72 hours before the event)