Schedule:

Mondays 17:00 – 19:00

For the room or zoom (depending on what’s going on) contact me.

We begin on September 13 and go on until the end of term.

About:

We will study the idea of Beyond Endoscopy [1], as proposed by Langlands in his original paper on the subject, and as was carried out by Altug in his first paper [2] of the three on the topic. The idea is to use this paper as a backbone to follow a sequence of otherwise maybe random topics and how they are needed for this to work and what might be needed for other situations in which the tools are not immediately available.

Bibliography and References:

The basic bibliography are the following two articles:

1. Langlands, Beyond Endoscopy, Shalika volume, Johns Hopkins University Press, 2004	Link
2. Ali Altug, Beyond endoscopy via the trace formula: 1. Poisson summation and isolation of special representations, Compositio Mathematica, 151 (10), 1791-1820, 2015	Link

The references will be changing as we move forwards in the seminar.

Reference	Link
3. Larsen, M., Pink, R. Determining representations from invariant dimensions. Invent Math 102, 377–398 (1990). https://doi.org/10.1007/BF01233432	Link
4. Song Wang, Dimension Data, Local and Global Conjugacy in Reductive Groups, arXiv:0707.0144	Link

Logbook and notes:

Date	Description	Notes
September 13	We discussed the plan we will follow during the seminar. I described how the paper [2] is structured and how many parts show a lot of directions to be further researched.	N/A
September 20	I tried to motivate why the approach in Beyond Endoscopy might work by discussing the basic theory of Invariant Dimensions of representations as shown in [3] and [4].	N/A
September 27
October 4
October 11
October 18
October 25
November 1
November 8
November 15
November 22
November 29
December 6
December 13

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