At the moment I am supervising Xenia Flamm and Anna Ribelles as Masters students.
I am not accepting additional students this semester.
My past Masters students are Guo Sheng Ho and Jose Pedro Quintanilha.
Class on Gromov's Polynomial Growth Theorem
I will teach a course
on Gromov's polynomial growth theorem, offered as Selected Topics
in Geometry (V5D4)
. This will be an (informal) continuation of my
course in geometric group theory. This means that the course will
deal with a more advanced topic in geometric group theory, but the
topics covered during my V5D3 are not required prerequites.
- On Amenability and Growth: "An introduction to amenable groups" by Alejandra Garrido, available here
- On Shaloms theorem and Property T: Chapter 3 of "Kazhdan's property (T)" by Becca, de la Harpe, Valette, available here
- Ozawa's theorem: "A functional analysis proof of Gromov's polynomial growth theorem", available here
- Using Ozawas theorem to get a finite dimensional representation: proof of Theorem 6.7.2 in "Harmonic analysis, cohomology and the large-scale geometry of amenable groups" by Y. Shalom
- Showing that the kernel of the map to the integers is finitely generated: "Growth of finitely generated solvable groups" by J. Milnor
- Using polynomial growth and unipotence to finish the induction: the last section of Terry Tao's blog entry here
- On Grigorchuk's group of intermediate growth: "Groups of intermediate growth, an introduction", available here
Seminar on Property (T)
Joint with Bram Petri
I will be running a seminar on Kazhdan's property (T), offered as
Graduate Seminar on Advanced Geometry (S4D3)
for an annoucement with summary and talk details.
Assigned Talks (dates might not be final)
- October 17: Talk 1 (Latifi)
- October 24: Talk 2 (Baker)
- October 31: No Talk
- November 7: Talk 3 (Caceres)
- November 14: Talk 4, part 1 (Ardryansyah)
- November 21: Talk 4, part 2 (Kabashaj)
- November 28: Talk 5 (Selimi)
- December 5: Talk 6 (Amontova)
- December 12: Talk 7 (Flamm)
- December 19: Talk 8 (Gajda)
- January 9: Talk 9 (Rumi)
- January 16: Talk 10 (Azemar)
teaching a course on Geometric Group Theory (V5D3). Here is a
brief course announcement
During the first half, we were (roughly) following the book "Trees" by Serre. In the second half, one useful source are the notes by Brian Bowditch
on geometric group theory.
There are no problem sessions, but there will be (irregular)
problem sets here. Please try to solve them -- they are excellent preparation
for the exam!
- Problem set 3. Hyperbolic spaces and groups. PDF
- Problem set 2. Translation length, axes of hyperbolic elements. PDF
- Problem set 1. Trees, Amalgams, early Bass-Serre theory. PDF
Warning: The original version had a mistake, which made 1.2 and 1.3 unsolvable as stated (May 16). There also was a typo in 1.4 (May 29).
I try to be very careful typesetting these, but there may always be typos. If you feel that an exercise contains a mistake, please email me.
In Wintersemester 2016/2017, I am
organizing a Graduate Seminar on Advanced Geometry (S4D3) on Heegaard splittings
and the Curve Graph. See the announcement and talk details here
. The preliminary meeting took
place Tuesday, July 19, 14:00-15:00 (N0.003). The seminar will
take place on Wednesdays, 16:00-18:00 (N.008).
Assigned Talks (dates should be final)
- October 26: Talk 1 (Lay)
- November 2: Talk 2 (Foniqi)
- November 9: Talk 3 (Quintanilha)
- November 16: Talk 4 (Rehn)
- November 23: Talk 5 (Atza)
- November 30: Talk 6 (Shi)
- December 7: No Talk.
- December 14: No Talk.
- December 21: Talk 7 (Bertozzi)
- January 11: Talk 8 (Wang)
- January 18: Talk 9 (Ho)
- January 25: No Talk.
- February 1: No Talk.
- February 8: Talk 10 (Zhicheng)
During Sommersemester 2016, I am teaching a
course on Teichmüller theory. See here
for the announcement.
In the Wintersemester 2015, I am
co-organizing (with Ursula Hamenstädt) the Graduate Seminar on
Advanced Topology (S4D4) on group cohomology and bounded
cohomology. See here
for a summary of topics.
Assigned Talks (dates should be stable)
- October 30 (te Winkel)
- November 6 (Cabezuelo)
- November 13 (Bellumat and Han)
- November 20 (Karlhofer)
- November 27 (Pedrotti)
- December 4: NO TALK
- December 11 (Spirano)
- December 18 (Fluhr)
- January 8 (Lenzen)
- January 15: NO TALK
- January 22 (Koch)