|COOKIES: By using this website you agree that we can place Google Analytics Cookies on your device for performance monitoring.|
Free subgroups of linear groups and diophantine heights
If you have a question about this talk, please contact Ben Green.
I will first discuss the statement and some ideas of the proof of Tits’ alternative for groups generated by finitely many matrices over an arbitrary field. Then I will present a strengthening of Tits’ theorem which can be described as a uniform effective version of it. This strong Tits alternative has various consequences regarding the growth, co-growth and uniform spectral gap of finitely generated linear groups. Reducing mod p it also yield some new results about the girth of finite subgroups of GL_d(Z/pZ). Underlying the proofs are some number theoretical results about points of small height in algebraic varieties and an unexpected connection with the Lehmer Conjecture
This talk is part of the Discrete Analysis Seminar series.
This talk is included in these lists:
Note that ex-directory lists are not shown.
Other listsWolfson College Lunchtime Seminar Series - Wednesdays of Full Term Frank King University of Cambridge Conservation Research Institute (UCCRI)
Other talksTracing potential energy surfaces of electronic excitations via their transition origins: application to oxirane Succulents in South Africa Probabilistic Models of Human Behaviour Inferno XXV, Purgatorio XXV, Paradiso XXV Stability and breakup of liquid threads Structure and Dynamics of Mutlilayer Networks