Notes & Videos
Notes
Below are some notes I've written in connection with talks given in the Farb and Friends Student Seminar (FFSS) and other seminars and workshops. These notes are also available on my Activities page.The FFSS notes are intended to be accessible to graduate students in geometric group theory, low-dimensional topology, and related fields.
Review of manifolds
WOMP First-year-graduate orientation program, 20 Sep 2012.
A gentle introduction to spectral sequences: The Leray-Serre spectral sequence
FFSS, 24 Feb 2011.
A gentle introduction to spectral sequences: Constructing spectral sequences
FFSS, 21 Apr 2011.
An introduction to representation stability and FI--modules (slides only)
Topology Student Workshop, Georgia Tech, 14 Jun 2012.
Polynomial invariants of finite reflection groups
FFSS, 14 Feb 2013.
Cohomology of braid groups and configuration spaces
FFSS, 16 May 2013.
An introduction to Outer space and homological properties of Out(Fn)
Reading group, 3 Jul 2013.
The topology of hyperplane complements
FFSS, 14 Nov 2013.
The cohomology of the braid group and polynomials over finite fields
FFSS, 30 Jan 2014.
A brief introduction to representation stability
Oberwolfach, 15 Jan 2018.
The geometry and topology of braid groups
Geometry–Topology Summer Workshop "Roots of Topology", Chicago, 12–15 Jun 2018.
Stability in the homology of the Torelli group
International Conference on Manifolds, Groups, and Homotopy, Skye, 19 Jun 2018.
An introduction to FI-modules and their generalizations
Michigan Representation Stability Week 2018, University of Michigan, 13–18 Aug 2018.
Representation stability for configuration spaces of open manifolds
Graduate Summer School on Representation Stability, MSRI, 24 Jun – 5 Jul 2019.
Quillen's approach to homological stability
Representation stability seminar, Michigan, 17 & 24 Apr 2020.
High-degree rational cohomology of special linear groups (2 talks)
Background notes & exercises: group (co)homology and virtual duality groups
Lecture 1: Cohomology in the top degree (video)
Lecture 2: Generators of the Steinberg modules (video)
Exercises on the lectures
High dimensional cohomology of moduli spaces, Copenhagen, 28 & 29 Jun 2021.
COGENT Summer School on cohomology of arithmetic groups,
(4 Patzt talks + 3 Wilson talks)
COGENT Patzt/Wilson lecture series notes + exercises
Background on cohomology of groups
Patzt Lecture 1: Borel-Serre duality (video)
Wilson Lecture 1: The top-degree cohomology of SL_n(R) for R Euclidean (video)
Wilson Lecture 2: The Steinberg module and (integral) apartment classes (video)
Wilson Lecture 3: The complex of partial bases is Cohen-Macaulay (video)
Patzt Lecture 2: The codimension-1 cohomology of SL_n(Z) (video)
Patzt Lecture 3: The top-degree cohomology of congruent subgroups of SL_n(Z) (video)
Patzt Lecture 4: Open problems and future directions (video)
COGENT Summer School, Institut Fourier, Grenoble, 13 – 24 June 2022.
Videos
Stability in the homology of configuration spacesUIUC Geometry, Groups, and Dynamics / GEAR Seminar, 13 Nov 2017.
FI–Modules and representations of the classical Weyl groups
Banff International Research Station Workshop, 28 Nov 2012.
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