Clifton will make a small correction to the geometric multiplicity matrix for the admissible representations of G(2) with “subregular unipotent” infinitesimal parameter.
Qing will explain that he’s found all the admissible representations and standard modules of G(2) with “subregular unipotent” infinitesimal parameter and that the multiplicity matrix matches the geometric calculation. This concludes the proof of the Kazhdan-Lusztig conjecture (as it appears in the Voganish book) for the subregular unipotent infinitesimal parameter of G(2).

Presentation at the MATRIX conference on Geometric and Categorical Representation Theory

Title: Toward a geometrisation of functions on the integral points of p-adic varieties

Abstract: In this talk we will see how to define a topology on the category of formal schemes over the p-adic integers whose fundamental group coincides with the {\'e}tale fundamental group of Fp-schemes.

Speaker: Geoff Vooys

Presentation at the MATRIX conference on Geometric and Categorical Representation Theory

Title: The geometry of local Arthur packets

Speaker: Clifton Cunningham

Abstract: This talk explains how an Arthur parameter determines a category of perverse sheaves and how the microlocal perspective on this category reveals an Arthur packet.

There is a conference in Singapore IMS on the Langlands program. Here is a link of that conference
https://ims.nus.edu.sg/events/2018/lang/index.php

Hiraku Atobe gave a talk on the voganish projects in Singapore IMS.

Here is the link of the notes of his talk
https://ims.nus.edu.sg/events/2018/lang/files/atobe2.pdf

The following are videos of his talk
https://www.youtube.com/watch?v=Daj067Lsy18&feature=youtu.be
https://www.youtube.com/watch?v=npKhGJhBd98&feature=youtu.be

Conference on Geometric and Categorical Representation Theory at MATRIX, Creswick Campus, University of Melbourne and Monash University

Program Description: Geometric and categorical representation theory are advancing rapidly, with a growing number of connections to the wider mathematical universe. The goal of this program is to bring international experts in these areas together to facilitate exchange and development of ideas. During the first week, there will be a lecture series by Prof. Luca Migliorini on the arithmetic theory of Higgs bundles.

Organisers: Clifton Cunningham (University of Calgary), Masoud Kamgarpour (University of Queensland), Anthony Licata (Australian National University), Peter McNamara (University of Queensland), Sarah Scherotzke (Bonn University), Oded Yacobi (University of Sydney)

https://www.matrix-inst.org.au/events/geometric-and-categorical-represen...

Speaker: Clifton Cunningham
Room: MS 337
This is a continuation of the talk from last week on admissible representations of $p$-adic G(2) associated to cubic unipotent Arthur parameters.

We have seen how the subregular unipotent orbit in the L-group for split G(2) determines a unipotent Arthur parameter and thus an unramified infinitesimal parameter $\lambda : W_F \to \,^LG(2)$.
Using the Voganish conjectures (\texttt{https://arxiv.org/abs/1705.01885v4}) we find that there are exactly 8 admissible representations with infinitesimal parameter $\lambda$.
Last week Qing Zhang interpreted $\lambda$ as a Langlands parameter for the split torus in $p$-adic G(2) and worked out the corresponding quasi-character $\chi : T(F) \to \mathbb{C}^*$ using the local Langlands correspondence.
We expect that all admissible representations in the composition series of $\mathop{Ind}_{B(F)}^{G(2,F)} \chi$ have infinitesimal parameter $\lambda$; we wonder if not all 8 admissible representations arise in this way.

In this talk I will calculate the multiplicity matrix that describes how these 8 admissible representations are related to 8 standard modules with infinitesimal parameter $\lambda$, assuming the Kazhdan-Lusztig conjecture as in appears in Section 10.2.3 of the preprint above.
To make this calculation I will use the Decomposition Theorem to calculate the stalks of all simple $H_\lambda$-equivariant perverse sheaves on the mini-Vogan variety $V_\lambda$, following the strategy explained in Section 10.3.3 of the preprint.

Speaker: Clifton Cunningham and Qing Zhang,

We consider the Voganish project for the cubic unipotent Arthur parameter for the split exceptional group $G_2$ over a p-adic field, which was first considered by Gan-Gurevich-Jiang. After introducing this parameter $\lambda$, we consider the Vogan variety and its orbits under the action of the natural group $H_\lambda$. We then determine a smooth cover of each orbits which will help to compute the $H_\lambda$-equivariant local systems on each orbit. We also determine the principle series representation of $G_2(F)$ associated with the unramified Langlands parameter.

Location: MS 337, University of Calgary