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SUMMARY:Jayce Getz (Duke)
DTSTART;VALUE=DATE-TIME:20200423T193000Z
DTEND;VALUE=DATE-TIME:20200423T203000Z
DTSTAMP;VALUE=DATE-TIME:20241016T062859Z
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;VALUE=DATE-TIME:20200430T193000Z
DTEND;VALUE=DATE-TIME:20200430T203000Z
DTSTAMP;VALUE=DATE-TIME:20241016T062859Z
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/
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SUMMARY:Aaron Landesman (Stanford)
DTSTART;VALUE=DATE-TIME:20200507T193000Z
DTEND;VALUE=DATE-TIME:20200507T203000Z
DTSTAMP;VALUE=DATE-TIME:20241016T062859Z
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/
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SUMMARY:Yifeng Liu (Yale)
DTSTART;VALUE=DATE-TIME:20200903T193000Z
DTEND;VALUE=DATE-TIME:20200903T203000Z
DTSTAMP;VALUE=DATE-TIME:20241016T062859Z
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/
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SUMMARY:Yufei Zhao (MIT)
DTSTART;VALUE=DATE-TIME:20200910T193000Z
DTEND;VALUE=DATE-TIME:20200910T203000Z
DTSTAMP;VALUE=DATE-TIME:20241016T062859Z
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/
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BEGIN:VEVENT
SUMMARY:Ziquan Yang (Harvard)
DTSTART;VALUE=DATE-TIME:20200917T193000Z
DTEND;VALUE=DATE-TIME:20200917T203000Z
DTSTAMP;VALUE=DATE-TIME:20241016T062859Z
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/
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