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University of Cambridge > Talks.cam > Geometric Group Theory (GGT) Seminar > On l^2-Betti numbers and their analogues in positive characteristic

## On l^2-Betti numbers and their analogues in positive characteristicAdd to your list(s) Download to your calendar using vCal - Andre Jaikin (Madrid)
- Friday 17 February 2017, 13:45-15:00
- CMS, MR13.
If you have a question about this talk, please contact Maurice Chiodo. Let G be a group, K a field and A an nxm matrix over the group ring K[G]. Let G=G1>G2>G3… be a chain of normal subgroups of G of finite index with trivial intersection. The multiplication on the right side by A induces linear maps
Φ_i : K[G/Gi] We are interested in properties of the sequence $\{\frac{\dim_K \ker \phi_i}{|G:G_i|}\}$. In particular, we would like to answer the following questions: 1. Is there the limit $ \lim_{i\to \infty}\frac{\dim_K \ker \phi_i}{|G:G_i|}$? 2. If the limit exists, how does it depend on the chain {G_i}? 3. What is the range of possible values for $ \lim_{i\to \infty}\frac{\dim_K \ker \phi_i}{|G:G_i|}$ for a given group G? It turns out that the answers on these questions are known for many groups G if K is a number field, less known if K is an arbitrary field of characteristic 0 and almost unknown if K is a field of positive characteristic. In my talk I will give several motivations to consider these questions, describe the known results and present recent advances in the case where K has characteristic 0. This talk is part of the Geometric Group Theory (GGT) Seminar series. ## This talk is included in these lists:- All CMS events
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