Event Date: Sunday, August 12, 2018 - 09:00 to Saturday, August 18, 2018 - 17:00 Event Type: Project: Voganish Project |

## Calculation of the characteristic cycles of the Kashiwara-Saito singularitySpeaker: Reggie Lybbert In their 1997 paper, _Geometric construction of crystal bases_ (Duke Math Journal, Vol 89, No. 1), Masaki Kashiwara and Yoshihisa Kashiwa Saito described a singularity in a quiver representation variety of type A_5 with the property that the characteristic cycles of the singularity is reducible, this providing a counterexample to a conjecture of Kazhdan and Lusztig. This singularity is now commonly know at the Kashiwara-Saito singularity. While the 1997 paper showed that the characteristic cycles of the Kashiwara-Saito singularity decomposes into at least two irreducible cycles, they promised, but did not prove, that it decomposes into exactly two irreducible cycles. Using techniques developed in the example part of the Voganish paper, augmented by some computational tools developed this summer, we believe we have a proof of this promise. In this seminar we'll give a sketch of the proof. Using this calculation and the local Langlands correspondence for GL(16), we should be able to exhibit an irreducible representation \pi of p-adic GL(16) with the property that its ABV-packet (as defined in the Voganish paper) contains exactly one other irreducible representation, \pi', and also describe that representation. We refer to this \pi as the Kashiwara-Saito representation of GL(16) and to \pi' as its coronal representation. This will provide the smallest known example of an irreducible representation of p-adic general linear group with one coronal representation. Locations: Zoom (https://zoom.us/j/238450154), Calgary, Lethbridge Event Date: Tuesday, July 24, 2018 - 10:00 to 11:30 Event Type: Project: Voganish Project |

## Updates and questions for Ahmed on his recent workLocations: Zoom, Calgary, Paris, Lethbridge Event Date: Thursday, July 19, 2018 - 10:00 to 11:30 Event Type: Project: Voganish Project |

## Overview of the proof of the conjectureAndrew, Bin and Clifton Event Date: Monday, May 28, 2018 - 19:00 to 20:00 Event Type: Project: Voganish Project |

## Voganish Seminar: Fourier transform and induction, continuedSpeaker: Andrew Fiori Location: Zoom, Paris, Calgary and Lethbridge Event Date: Thursday, May 10, 2018 - 09:00 to 10:30 Event Type: Project: Voganish Project |

## Voganish Seminar: Fourier transform and inductionTopic: Progress on the Fourier transform and induction for Vogan varieties! Speaker: Andrew Fiori Location: Zoom, Beijing, Calgary and Lethbridge Event Date: Monday, May 7, 2018 - 19:00 to 20:30 Event Type: Project: Voganish Project |

## Student research seminar: Classification of strata in Vogan varieties for GL(n)Topic: How to enumerate all stata in Vogan varieties for GL(n). Quivers perspective. Speaker: Reginald Lybbert Location: Calgary, MS337 Event Date: Friday, May 4, 2018 - 10:00 to 11:30 Event Type: Project: Voganish Project |

## Summer Student Research Seminar on the Kashiwara-Saito singularityOverview of the Voganish Project Statement of summer objectives: Microlocal vanishing cycles of the Kashiwara-Saito singularity Divide and conquer: Location: University of Calgary, MS 337 Event Date: Tuesday, May 1, 2018 - 10:00 to 11:30 Event Type: Project: Voganish Project |

## Fourier transform of equivariant perverse sheavesThe Fourier transform we're using is taken from Kashiwara and Shapira by way of Schurmann, and has the vanishing cycles functor built in. Today we're working on establishing and documenting the main properties of this functor. Andrew and Clifton, at the University of Lethbridge Event Date: Saturday, April 14, 2018 - 10:00 to 16:00 Event Type: Project: Voganish Seminar |

## Construction of supercuspidal representationsSpeaker: Kam-Fai Tam (Max-Planck-Institut für Mathematik, Bonn) Title: Construction of supercuspidal representations Location: Hilbert Seminar Room (MS 337) Time: Thursday, April 5, 14:00--15:00 Abstract: Given a supercuspidal representation of GL_2 over a p-adic field or the group U_2 of 2-by-2 unitary matrices relative to a quadratic p-adic field extension, we explain how to use the internal structure of its Langlands parameter to construct a underlying type of this representation. (If time permits, we will also cover a construction of discrete series representations.) Event Date: Thursday, April 5, 2018 - 14:00 to 15:00 Event Type: |