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:20260422T212704Z UID:WisconsinNTS/1 DESCRIPTION:Title: On triple product $L$-functions\nby Jayce Getz (Duke) as part of Number theory / representation theory seminar\n\n\nAbstract\nEstablishing the conjectured analytic properties of triple product $L$-functions is a c rucial case of Langlands functoriality. However\, little is known. I will present work in progress on the case of triples of automorphic representat ions on $\\mathrm{GL}_3$\; in some sense this is the smallest case that ap pears out of reach via standard techniques. The approach involves a relati ve trace formula and Poisson summation on spherical varieties in the sense of Braverman-Kazhdan\, Ngo\, and Sakellaridis.\n LOCATION:https://researchseminars.org/talk/WisconsinNTS/1/ END:VEVENT BEGIN:VEVENT SUMMARY:Noah Taylor (University of Chicago) DTSTART:20200430T193000Z DTEND:20200430T203000Z DTSTAMP:20260422T212704Z UID:WisconsinNTS/2 DESCRIPTION:Title: The Sato Tate Conjecture on Abelian Surfaces\nby Noah Taylor (Uni versity of Chicago) as part of Number theory / representation theory semin ar\n\n\nAbstract\nThe Sato-Tate conjecture says that the normalized point counts of genus $g$ curves are equidistributed with respect to a certain m easure. We will construct the Sato-Tate group\, state the conjecture preci sely\, prove a case\, and in the cases where not everything is known\, we will discuss how much we can say about the point counts anyway.\n LOCATION:https://researchseminars.org/talk/WisconsinNTS/2/ END:VEVENT BEGIN:VEVENT SUMMARY:Aaron Landesman (Stanford) DTSTART:20200507T193000Z DTEND:20200507T203000Z DTSTAMP:20260422T212704Z UID:WisconsinNTS/3 DESCRIPTION:Title: The geometric distribution of Selmer groups of elliptic curves over f unction fields\nby Aaron Landesman (Stanford) as part of Number theory / representation theory seminar\n\n\nAbstract\nBhargava\, Kane\, Lenstra\ , Poonen\, and Rains proposed heuristics for the distribution of arithmeti c data relating to elliptic curves\, such as their ranks\, Selmer groups\, and Tate-Shafarevich groups. As a special case of their heuristics\, they obtain the minimalist conjecture\, which predicts that 50% of elliptic cu rves have rank 0 and 50% of elliptic curves have rank 1. After surveying t hese conjectures\, we will explain joint work with Tony Feng and Eric Rain s\, 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://researchseminars.org/talk/WisconsinNTS/3/ END:VEVENT BEGIN:VEVENT SUMMARY:Yifeng Liu (Yale) DTSTART:20200903T193000Z DTEND:20200903T203000Z DTSTAMP:20260422T212704Z UID:WisconsinNTS/4 DESCRIPTION:Title: Beilinson-Bloch conjecture and arithmetic inner product formula\n by Yifeng Liu (Yale) as part of Number theory / representation theory semi nar\n\n\nAbstract\nIn this talk\, we study the Chow group of the motive as sociated to a tempered global L-packet $\\pi$ of unitary groups of even ra nk with respect to a CM extension\, whose global root number is -1. We sho w that\, under some restrictions on the ramification of $\\pi$\, if the ce ntral derivative $L'(1/2\,\\pi)$ is nonvanishing\, then the $\\pi$-nearly isotypic localization of the Chow group of a certain unitary Shimura varie ty over its reflex field does not vanish. This proves part of the Beilinso n--Bloch conjecture for Chow groups and L-functions. Moreover\, assuming t he modularity of Kudla's generating functions of special cycles\, we expli citly construct elements in a certain $\\pi$-nearly isotypic subspace of t he Chow group by arithmetic theta lifting\, and compute their heights in t erms of the central derivative $L'(1/2\,\\pi)$ and local doubling zeta int egrals. This is a joint work with Chao Li.\n LOCATION:https://researchseminars.org/talk/WisconsinNTS/4/ END:VEVENT BEGIN:VEVENT SUMMARY:Yufei Zhao (MIT) DTSTART:20200910T193000Z DTEND:20200910T203000Z DTSTAMP:20260422T212704Z UID:WisconsinNTS/5 DESCRIPTION:Title: The joints problem for varieties\nby Yufei Zhao (MIT) as part of Number theory / representation theory seminar\n\n\nAbstract\nWe generalize the Guth-Katz joints theorem from lines to varieties. A special case of o ur result says that N planes (2-flats) in 6 dimensions (over any field) ha ve $O(N^{3/2})$ joints\, where a joint is a point contained in a triple of these planes not all lying in some hyperplane. Our most general result gi ves upper bounds\, tight up to constant factors\, for joints with multipli cities for several sets of varieties of arbitrary dimensions (known as Car bery's conjecture).\n\nOur main innovation is a new way to extend the poly nomial method to higher dimensional objects. A simple\, yet key step in ma ny applications of the polynomial method is the "vanishing lemma": a singl e-variable degree-d polynomial has at most d zeros. In this talk\, I will explain how we generalize the vanishing lemma to multivariable polynomials \, for our application to the joints problem.\n\nJoint work with Jonathan Tidor and Hung-Hsun Hans Yu (https://arxiv.org/abs/2008.01610)\n LOCATION:https://researchseminars.org/talk/WisconsinNTS/5/ END:VEVENT BEGIN:VEVENT SUMMARY:Ziquan Yang (Harvard) DTSTART:20200917T193000Z DTEND:20200917T203000Z DTSTAMP:20260422T212704Z UID:WisconsinNTS/6 DESCRIPTION:Title: A Crystalline Torelli Theorem for Supersingular K3^[n]-type Varieties \nby Ziquan Yang (Harvard) as part of Number theory / representation t heory seminar\n\nAbstract: TBA\n LOCATION:https://researchseminars.org/talk/WisconsinNTS/6/ END:VEVENT END:VCALENDAR