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UID:node-3060819@mathematics.huji.ac.il
DTSTAMP:20211213T123000Z
DTSTART:20211213T123000Z
DTEND:20211213T140000Z
SUMMARY:HUJI NT Seminar - Daniele Garzoni
DESCRIPTION:Title: Hilbert's Irreducibility Theorem via random walks\n\nAbstract: Let G be a linear algebraic group over a number field K, and let f: V --> G be a cover of finite degree, at least two. We wish to show that "many" points of G(K) do not lift to points of V(K), and that "many" points of G(K) have K-irreducible fibre. This is analogous to Hilbert's Irreducibility Theorem and, of course, depends on the meaning of the word "many".\n\nWe will focus on the following model: Fix any finitely generated Zariski dense subgroup H of G(K), and perform a random walk on a Cayley graph of H. We will see that, under suitable necessary conditions on G and f, almost surely a long random walk hits elements having the above property. We will also see examples and variations of this result.\n\nJoint work with Lior Bary-Soroker.
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