Embedded Files
A crash course on isoperimetry
A crash course on isoperimetry
Slides for the first lecture.
Slides for the second lecture.
Slides for the third lecture.
Exercises for all three lectures.
Martin Bridson's notes on the geometry of the word problem: https://people.maths.ox.ac.uk/bridson/papers/bfs/bfs.pdf
Bridson's ICM paper (section 4): https://people.maths.ox.ac.uk/bridson/papers/bridsonicm.pdf
Steve Gersten's Banff notes (section 7).
Tim Riley's CRM notes: http://pi.math.cornell.edu/~riley/papers/CRM%20Notes/CRM_Notes.pdf
Gersten's survey: http://math.uchicago.edu/~shmuel/lg-readings/Gersten,%20Isoperimetric.pdf
Hamish Short's CRM notes: https://www.i2m.univ-amu.fr/~short/Papers/barcelona.pdf
Cubulated groups and virtual specialness
Cubulated groups and virtual specialness
Slides for the first lecture.
Slides for the second lecture.
Slides for the third lecture.
Exercises for the first two lectures.
Exercises for the third lecture.
Sageev's notes: http://www.math.utah.edu/pcmi12/lecture_notes/sageev.pdf
Agol's ICM paper: https://math.berkeley.edu/sites/default/files/faculty/files/virtualspecialICM.pdf
Sam Shepherd's notes on Agol's theorem: https://arxiv.org/pdf/1905.06199.pdf
Haglund-Wise's special cube complexes paper (section 6 for canonical completion/retraction): https://docs.google.com/open?id=0B45cNx80t5-2LV9BRVJyek5CMjQ
The Poisson boundary and bounded harmonic functions on groups
The Poisson boundary and bounded harmonic functions on groups
Slides for the first lecture.
Slides for the second lecture.
Slides for the third lecture.
Exercises for the first two lectures.
Exercises for the third lecture.
Furstenberg's paper where he introduces the Poisson boundary.
Kaimanovich–Vershik's paper where they introduce a lot of the core material.
Kaimanovich's paper where he computes many Poisson boundaries.
Frisch–Hartman–Tamuz–Ferdowsi's paper where they classify which groups have a measure with non-trivial Poisson boundary.
Anosov representations of hyperbolic groups
Anosov representations of hyperbolic groups
Slides for the first lecture.
Slides for the second lecture.
Slides for the third lecture.
Exercises for the first two lectures.
Exercises for the third lecture.
Labourie's paper introducing Anosov representations: https://link.springer.com/article/10.1007/s00222-005-0487-3
Guichard-Wienhard paper on the general dynamical definition (part 1): https://link.springer.com/article/10.1007/s00222-012-0382-7)
Canary's Lecture notes on Anosov representations: http://www.math.lsa.umich.edu/~canary/Anosovlecnotes.pdf
Bochi-Potrie-Sambarino paper on dominated splittings: https://www.ems-ph.org/journals/of_article.php?jrn=jems&doi=905)
Gueritaud-Guichard-Kassel-Wienhard paper on characterizations of Anosov representations: https://msp.org/gt/2017/21-1/p11.xhtml
Kapovich-Leeb-Porti papers on characterizations of Anosov representations (https://link.springer.com/article/10.1007/s40879-017-0192-y and https://mathscinet.ams.org/mathscinet-getitem?mr=3890767)
Acylindrically and relatively hyperbolic groups
Acylindrically and relatively hyperbolic groups
F. Dahmani, V. Guirardel, D. Osin; Hyperbolically embedded subgroups and rotating families in groups acting on hyperbolic spaces, Mem. Amer. Math. Soc. 245 (2017), no.1156, v+152 pp.
S. Balasubramanya; Acilindrical actions on quasi-trees, Algebraic & Geometric Topology 17 (2017) pg 2145 - 2176.
M. Bestvina, K. Fujiwara, Bounded cohomology of subgroups of mapping class groups, Geom. Topol. 6 (2002), 6989.
B.H. Bowditch; Tight geodesics in the curve complex; Invent. Math. 171 (2008), no. 2, 281300.
M. Bridson, A. Haefliger; Metric spaces of nonpositive curvature; Springer, 1999.
J. Manning; Geometry of pseudocharacters, Geometry and Topology 9 (2005) 1147-1185.
M. Gromov, Hyperbolic groups, in: Essays in Group Theory, Math. Sci. Res. Inst. Publ. 8, Springer, New York (1987), 75–263.
M. Hull; Small cancellation in acylindrically hyperbolic groups; Groups Geom. Dyn. 109(2016), no. 4, 10771119.
M. Hull, D. Osin; Induced quasicocycles on groups with hyperbolically embedded subgroups; Alg. & Geom. Topol., 13 (2013) 26352665.
Sang-hyun Kim, T. Koberda; The geometry of the curve graph of a right angled Artin group; Int. J. Algebra Comput. 24 (2014), no. 2, 121169.
D. Osin; Acylindrically hyperbolic groups, Trans. Amer. Math. Soc. 368 (2016), no. 2, 851-888.
D. Osin; Groups acting acylindrically on hyperbolic spaces - https://arxiv.org/pdf/1712.00814.pdf
Artin groups: algebraic and geometric techniques
Artin groups: algebraic and geometric techniques
Exercises for the first two lectures.
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