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        "event_title":"Orbit transversality for abelian varieties",
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        "description":"The dynamical Mordell\u2013Lang problem asks how one forward orbit intersects a subvariety. We consider a complementary question over number fields, allowing passage to a suitable finite extension: can a proper Zariski-closed subset meet every rational grand orbit?\nAssuming a Zariski-dense forward orbit, Pasten and Silverman answered this question negatively for linear automorphisms of projective space and for self-morphisms of geometrically simple abelian varieties. We will see that the answer is no for every dominant self-morphism of an abelian variety, without the dense-orbit assumption. If time permits, we will also discuss the case of projective space.",
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        "event_title":"The Cohomology of a Smooth Projective Toric Variety is a Permutation Representation",
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        "combined_title":"The Cohomology of a Smooth Projective Toric Variety is a Permutation Representation: Rui Xiong",
        "event_subtitle":"Rui Xiong",
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        "description":"Let a finite group act on a smooth projective toric variety via lattice automorphism. We show that its cohomology is a permutation representation: it is induced from a group action on a set. This answers a question of Stanley, for all smooth projective toric varieties, without the usual properness assumption. The proof uses ideas from mirror symmetry. Joint with Tao Gui, Chushi Qin, and Kaizhe Shen.",
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