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Events happening on October 11, 2016

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Oct. 11, 2016 10am (MATH 220)	Number Theory Xin Zhang (University of Illinois Urbana-Champaign) X Let be a finitely generated, non-elementary Fuchsian group of the second kind, and be two primitive vectors in . We consider the set , where is the standard inner product in . Using Hardy-Littlewood circle method and some infinite co-volume lattice point counting techniques developed by Bourgain, Kontorovich and Sarnak, together with Gamburd's 5/6 spectral gap, we show that if has parabolic elements, and the critical exponent of exceeds 0.995371, then a density-one subset of all admissible integers (i.e. integers passing all local obstructions) are actually in , with a power savings on the size of the exceptional set (i.e. the set of admissible integers failing to appear in ). This supplements a result of Bourgain-Kontorovich, which proves a density-one statement for the case when is free, finitely generated, has no parabolics and has critical exponent . Finding integers from orbits of thin subgroups of SL(2, Z)
Oct. 11, 2016 1pm (MATH 220)	Grad Algebra/Logic Agnes Szendrei (CU Boulder) Taylor Terms, Part 3: Olsak's Theorem
Oct. 11, 2016 2pm (MATH 220)	Mark Pullins (CU) An Introduction to Groups of Finite Morley Rank, 2
Oct. 11, 2016 2pm (MATH 350)	Lie Theory Scott Andrews (Boise State) X The symmetric group is sometimes referred to as "the general linear group over the field with one element." Although this statement is not mathematically precise, it motivates us to extend results about the symmetric group to the general linear groups over finite fields. I will present a standard construction of the irreducible modules of the symmetric group and show how it can be extended in a natural way to construct the unipotent modules of the finite general linear groups. I will also discuss related open problems. Irreducible modules of symmetric groups and finite general linear groups Sponsored by the Meyer Fund
Oct. 11, 2016 3pm (MATH 350)	Topology Agnes Beaudry (CU Boulder) Derived Categories

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