BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Jayce Getz (Duke) DTSTART:20200423T193000Z DTEND:20200423T203000Z DTSTAMP:20260404T092654Z UID:WisconsinNTS/1 DESCRIPTION:Title: On triple product $L$-functions\nby Jayce Getz (Duke) as p art of Number theory / representation theory seminar\n\n\nAbstract\nEstabl ishing the conjectured analytic properties of triple product $L$-functions is a crucial case of Langlands functoriality. However\, little is known. I will present work in progress on the case of triples of automorphic repr esentations on $\\mathrm{GL}_3$\; in some sense this is the smallest case that appears out of reach via standard techniques. The approach involves a relative trace formula and Poisson summation on spherical varieties in th e sense of Braverman-Kazhdan\, Ngo\, and Sakellaridis.\n LOCATION:https://stable.researchseminars.org/talk/WisconsinNTS/1/ END:VEVENT BEGIN:VEVENT SUMMARY:Noah Taylor (University of Chicago) DTSTART:20200430T193000Z DTEND:20200430T203000Z DTSTAMP:20260404T092654Z UID:WisconsinNTS/2 DESCRIPTION:Title: The Sato Tate Conjecture on Abelian Surfaces\nby Noah Tayl or (University of Chicago) as part of Number theory / representation theor y seminar\n\n\nAbstract\nThe Sato-Tate conjecture says that the normalized point counts of genus $g$ curves are equidistributed with respect to a ce rtain measure. We will construct the Sato-Tate group\, state the conjectur e precisely\, prove a case\, and in the cases where not everything is know n\, we will discuss how much we can say about the point counts anyway.\n LOCATION:https://stable.researchseminars.org/talk/WisconsinNTS/2/ END:VEVENT BEGIN:VEVENT SUMMARY:Aaron Landesman (Stanford) DTSTART:20200507T193000Z DTEND:20200507T203000Z DTSTAMP:20260404T092654Z UID:WisconsinNTS/3 DESCRIPTION:Title: The geometric distribution of Selmer groups of elliptic curves over function fields\nby Aaron Landesman (Stanford) as part of Number theory / representation theory seminar\n\n\nAbstract\nBhargava\, Kane\, L enstra\, Poonen\, and Rains proposed heuristics for the distribution of ar ithmetic data relating to elliptic curves\, such as their ranks\, Selmer g roups\, and Tate-Shafarevich groups. As a special case of their heuristics \, they obtain the minimalist conjecture\, which predicts that 50% of elli ptic curves have rank 0 and 50% of elliptic curves have rank 1. After surv eying these conjectures\, we will explain joint work with Tony Feng and Er ic Rains\, verifying many of these conjectures over function fields of the form $\\mathbb F_q(t)$\, after taking a certain large $q$ limit.\n LOCATION:https://stable.researchseminars.org/talk/WisconsinNTS/3/ END:VEVENT BEGIN:VEVENT SUMMARY:Yifeng Liu (Yale) DTSTART:20200903T193000Z DTEND:20200903T203000Z DTSTAMP:20260404T092654Z UID:WisconsinNTS/4 DESCRIPTION:Title: Beilinson-Bloch conjecture and arithmetic inner product formul a\nby Yifeng Liu (Yale) as part of Number theory / representation theo ry seminar\n\n\nAbstract\nIn this talk\, we study the Chow group of the mo tive associated to a tempered global L-packet $\\pi$ of unitary groups of even rank with respect to a CM extension\, whose global root number is -1. We show that\, under some restrictions on the ramification of $\\pi$\, if the central derivative $L'(1/2\,\\pi)$ is nonvanishing\, then the $\\pi$- nearly isotypic localization of the Chow group of a certain unitary Shimur a variety over its reflex field does not vanish. This proves part of the B eilinson--Bloch conjecture for Chow groups and L-functions. Moreover\, ass uming the modularity of Kudla's generating functions of special cycles\, w e explicitly construct elements in a certain $\\pi$-nearly isotypic subspa ce of the Chow group by arithmetic theta lifting\, and compute their heigh ts in terms of the central derivative $L'(1/2\,\\pi)$ and local doubling z eta integrals. This is a joint work with Chao Li.\n LOCATION:https://stable.researchseminars.org/talk/WisconsinNTS/4/ END:VEVENT BEGIN:VEVENT SUMMARY:Yufei Zhao (MIT) DTSTART:20200910T193000Z DTEND:20200910T203000Z DTSTAMP:20260404T092654Z UID:WisconsinNTS/5 DESCRIPTION:Title: The joints problem for varieties\nby Yufei Zhao (MIT) as p art of Number theory / representation theory seminar\n\n\nAbstract\nWe gen eralize the Guth-Katz joints theorem from lines to varieties. A special ca se of our result says that N planes (2-flats) in 6 dimensions (over any fi eld) have $O(N^{3/2})$ joints\, where a joint is a point contained in a tr iple of these planes not all lying in some hyperplane. Our most general re sult gives upper bounds\, tight up to constant factors\, for joints with m ultiplicities for several sets of varieties of arbitrary dimensions (known as Carbery's conjecture).\n\nOur main innovation is a new way to extend t he polynomial method to higher dimensional objects. A simple\, yet key ste p in many applications of the polynomial method is the "vanishing lemma": a single-variable degree-d polynomial has at most d zeros. In this talk\, I will explain how we generalize the vanishing lemma to multivariable poly nomials\, for our application to the joints problem.\n\nJoint work with Jo nathan Tidor and Hung-Hsun Hans Yu (https://arxiv.org/abs/2008.01610)\n LOCATION:https://stable.researchseminars.org/talk/WisconsinNTS/5/ END:VEVENT BEGIN:VEVENT SUMMARY:Ziquan Yang (Harvard) DTSTART:20200917T193000Z DTEND:20200917T203000Z DTSTAMP:20260404T092654Z UID:WisconsinNTS/6 DESCRIPTION:Title: A Crystalline Torelli Theorem for Supersingular K3^[n]-type Va rieties\nby Ziquan Yang (Harvard) as part of Number theory / represent ation theory seminar\n\nAbstract: TBA\n LOCATION:https://stable.researchseminars.org/talk/WisconsinNTS/6/ END:VEVENT END:VCALENDAR