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SUMMARY:Jayce Getz (Duke)
DTSTART;VALUE=DATE-TIME:20200423T193000Z
DTEND;VALUE=DATE-TIME:20200423T203000Z
DTSTAMP;VALUE=DATE-TIME:20201031T034824Z
UID:WisconsinNTS/1
DESCRIPTION:Title: On triple product $L$-functions\nby Jayce Getz (Duke) a
s part of Number theory / representation theory seminar\n\n\nAbstract\nEst
ablishing the conjectured analytic properties of triple product $L$-functi
ons is a crucial case of Langlands functoriality. However\, little is know
n. I will present work in progress on the case of triples of automorphic r
epresentations on $\\mathrm{GL}_3$\; in some sense this is the smallest ca
se that appears out of reach via standard techniques. The approach involve
s a relative trace formula and Poisson summation on spherical varieties in
the sense of Braverman-Kazhdan\, Ngo\, and Sakellaridis.\n
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BEGIN:VEVENT
SUMMARY:Noah Taylor (University of Chicago)
DTSTART;VALUE=DATE-TIME:20200430T193000Z
DTEND;VALUE=DATE-TIME:20200430T203000Z
DTSTAMP;VALUE=DATE-TIME:20201031T034824Z
UID:WisconsinNTS/2
DESCRIPTION:Title: The Sato Tate Conjecture on Abelian Surfaces\nby Noah T
aylor (University of Chicago) as part of Number theory / representation th
eory seminar\n\n\nAbstract\nThe Sato-Tate conjecture says that the normali
zed point counts of genus $g$ curves are equidistributed with respect to a
certain measure. We will construct the Sato-Tate group\, state the conjec
ture precisely\, prove a case\, and in the cases where not everything is k
nown\, we will discuss how much we can say about the point counts anyway.\
n
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SUMMARY:Aaron Landesman (Stanford)
DTSTART;VALUE=DATE-TIME:20200507T193000Z
DTEND;VALUE=DATE-TIME:20200507T203000Z
DTSTAMP;VALUE=DATE-TIME:20201031T034824Z
UID:WisconsinNTS/3
DESCRIPTION:Title: The geometric distribution of Selmer groups of elliptic
curves over function fields\nby Aaron Landesman (Stanford) as part of Num
ber theory / representation theory seminar\n\n\nAbstract\nBhargava\, Kane\
, Lenstra\, Poonen\, and Rains proposed heuristics for the distribution of
arithmetic data relating to elliptic curves\, such as their ranks\, Selme
r groups\, and Tate-Shafarevich groups. As a special case of their heurist
ics\, they obtain the minimalist conjecture\, which predicts that 50% of e
lliptic curves have rank 0 and 50% of elliptic curves have rank 1. After s
urveying these conjectures\, we will explain joint work with Tony Feng and
Eric Rains\, verifying many of these conjectures over function fields of
the form $\\mathbb F_q(t)$\, after taking a certain large $q$ limit.\n
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SUMMARY:Yifeng Liu (Yale)
DTSTART;VALUE=DATE-TIME:20200903T193000Z
DTEND;VALUE=DATE-TIME:20200903T203000Z
DTSTAMP;VALUE=DATE-TIME:20201031T034824Z
UID:WisconsinNTS/4
DESCRIPTION:Title: Beilinson-Bloch conjecture and arithmetic inner product
formula\nby Yifeng Liu (Yale) as part of Number theory / representation t
heory seminar\n\n\nAbstract\nIn this talk\, we study the Chow group of the
motive 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 $\\p
i$-nearly isotypic localization of the Chow group of a certain unitary Shi
mura variety over its reflex field does not vanish. This proves part of th
e Beilinson--Bloch conjecture for Chow groups and L-functions. Moreover\,
assuming the modularity of Kudla's generating functions of special cycles\
, we explicitly construct elements in a certain $\\pi$-nearly isotypic sub
space of the Chow group by arithmetic theta lifting\, and compute their he
ights in terms of the central derivative $L'(1/2\,\\pi)$ and local doublin
g zeta integrals. This is a joint work with Chao Li.\n
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SUMMARY:Yufei Zhao (MIT)
DTSTART;VALUE=DATE-TIME:20200910T193000Z
DTEND;VALUE=DATE-TIME:20200910T203000Z
DTSTAMP;VALUE=DATE-TIME:20201031T034824Z
UID:WisconsinNTS/5
DESCRIPTION:Title: The joints problem for varieties\nby Yufei Zhao (MIT) a
s 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 our result says that N planes (2-flats) in 6 dimensions (over any
field) have $O(N^{3/2})$ joints\, where a joint is a point contained in a
triple of these planes not all lying in some hyperplane. Our most general
result gives upper bounds\, tight up to constant factors\, for joints wit
h multiplicities for several sets of varieties of arbitrary dimensions (kn
own as Carbery's conjecture).\n\nOur main innovation is a new way to exten
d the polynomial method to higher dimensional objects. A simple\, yet key
step 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 p
olynomials\, 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
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ziquan Yang (Harvard)
DTSTART;VALUE=DATE-TIME:20200917T193000Z
DTEND;VALUE=DATE-TIME:20200917T203000Z
DTSTAMP;VALUE=DATE-TIME:20201031T034824Z
UID:WisconsinNTS/6
DESCRIPTION:Title: A Crystalline Torelli Theorem for Supersingular K3^[n]-
type Varieties\nby Ziquan Yang (Harvard) as part of Number theory / repres
entation theory seminar\n\nAbstract: TBA\n
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