University of California, San Diego
Organizers: Dan Rogalski, Alireza Salehi Golsefidy, Efim Zelmanov.
|Saturday,||January 19||Sunday,||January 20|
|9:30-10:30||Light breakfast||9:00-10:00||Light breakfast|
|10:30-11:30||Nolan Wallach||Ricci flow on Wallach flag varieties||10:00-11:00||Misha Kapovich||Noncoherence of arithmetic groups|
|13:00-14:00||Bert Kostant||On the algebraic set of singular elements in a complex simple Lie algebra||13:00-14:00||Amir Mohammadi||Unipotent flows and infinite measures|
|14:30-15:30||Vera Serganova||On the Kostant theorem for Lie superalgebras||14:00-14:30||Tea time|
|15:30-16:30||Tea time||14:30-15:30||Alex Lubotzky||Arithmetic groups, Ramanujan graphs and error correcting codes|
|16:30-17:30||Terry Tao||Hilbert's fifth problem and approximate groups|
|19:00-||Conference dinner||Sammy's pizza (Del Mar highlands town center)|
Abstracts (and related PDF files)
Title: Noncoherence of arithmetic groups (Here is the related PDF file.)
Abstract: It follows from the work of Borel and Serre on bordification of locally-symmetric spaces that all arithmetic groups have finite type. This, of course, does not extend to subgroups of arithmetic lattices in semisimple Lie groups, since these lattices always contain free subgroups of infinite rank. A group is called coherent if all its finitely-generated subgroups are also finitely-presented. In the talk I will discuss coherence and non-coherence of arithmetic lattices in semisimple Lie groups.
Hilbert's fifth problem asked for a topological description of Lie groups, and in particular whether any topological group that was a continuous (but not necessarily smooth) manifold was automatically a Lie group. This problem was famously solved in the affirmative by Montgomery-Zippin and Gleason in the 1950s.
These two mathematical topics initially seem unrelated, but there is a remarkable correspondence principle (first implicitly used by Gromov, and later developed by Hrushovski and Breuillard, Green, and myself) that connects the combinatorics of approximate groups to problems in topological group theory such as Hilbert's fifth problem. This correspondence has led to recent advances both in the understanding of approximate groups and in Hilbert's fifth problem, leading in particular to a classification theorem for approximate groups, which in turn has led to refinements of Gromov's theorem on groups of polynomial growth that have applications to the study of the topology of manifolds. We will survey these interconnected topics in this talk.Nolan Wallach
All talks will be held in Mathematics Department Room 6402 on the UCSD campus.
The refreshments will be served in the same building Room 7356 .
Click on campus map to locate mathematics department (the AP&M building is the red building on the map.)
Here are directions to the UCSD campus and mathematics department (AP&M building).
Parking on the UCSD campus is free during the weekend. You may park in any of the parking lots next to the AP&M building.
Please do not park in the "reserved" or "A parking only" spaces.
You can find Hotel information here. Residence Inn and Sheraton La Jolla are in walking distance. Also, the shuttle to UCSD from the Del Mar Inn does not run during weekends. So anyone staying there should either have a car, arrange to get picked up by someone, or else it is possible to take the 101 bus. This runs every half hour in the mornings on Sat/Sun, but becomes every hour after about 6pm and ends early (the last bus north from campus is about 9:30pm).
Registration and funding
There is no registration fee. However, if you are interested in participating, please fill in the blank fields below and click on the "Submit" button in order to register for the conference.
Please indicate on the form below if you would like to be considered for funding to reimburse your travel costs. Since the amount of funding available is limited, priority will be given to graduate students, recent PhD graduates, or members of underrepresented groups.
If you are applying for funding, would you please write in the comments section an estimate of your travel costs and arrange for a recommendation letter to be sent to gem at cats.ucsc.edu .
This will help us make proper funding managment, catering arrangements and dinner reservations.