Word maps: properties, applications, open problems
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Tue, 03/05/2011 17:00 |
Prof. Aner Shalev (Jerusalem) |
Algebra Seminar  |
L2 |
| Word maps on groups were studied extensively in the past few years, in connection to various conjectures on profinite groups, finite groups, finite simple groups, etc. I will provide background, as well as very recent works (joint with Larsen, Larsen-Tiep, Liebeck-O'Brien-Tiep) on word maps with relations to representations (e.g. Gowers' method and character ratios), geometry and probability. Recent applications, e.g. to subgroup growth and representation varieties, will also be described. I will conclude with a list of problems and conjectures which are still very much open. The talk should be accessible to a wide audience. | |||