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BEGIN:VEVENT
SUMMARY:Victoria Cantoral
DTSTART;VALUE=DATE-TIME:20200727T163000Z
DTEND;VALUE=DATE-TIME:20200727T170000Z
DTSTAMP;VALUE=DATE-TIME:20200812T042615Z
UID:POINT/1
DESCRIPTION:Title: The Mumford—Tate conjecture implies the algebraic Sat
o—Tate conjecture\nby Victoria Cantoral as part of POINT: New Developmen
ts in Number Theory\n\n\nAbstract\nThe famous Mumford-Tate conjecture asse
rts that\, for every prime number $\\ell$\, Hodge cycles are $\\mathbb{Q}_
{\\ell}$-linear combinations of Tate cycles\, through Artin's comparisons
theorems between Betti and étale cohomology. The algebraic Sato-Tate conj
ecture\, introduced by Serre and developed later by Banaszak and Kedlaya\,
is a powerful tool in order to prove new instances of the generalized Sat
o-Tate conjecture. This previous conjecture is related with the equidistri
bution of Frobenius traces.\n\nOur main goal is to prove that the Mumford-
Tate conjecture for an abelian variety A implies the algebraic Sato-Tate c
onjecture for A. The relevance of this result lies mainly in the fact that
the list of known cases of the Mumford-Tate conjecture was up to now a lo
t longer than the list of known cases of the algebraic Sato-Tate conjectur
e. This is a joint work with Johan Commelin.\n\nIf you like to attend the
talk\, please register here: https://umich.zoom.us/meeting/register/tJAufu
qtqDksG9fEmjTbWHM4QOEUad6Ke-DE.\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Rahul Dalal
DTSTART;VALUE=DATE-TIME:20200727T170000Z
DTEND;VALUE=DATE-TIME:20200727T173000Z
DTSTAMP;VALUE=DATE-TIME:20200812T042615Z
UID:POINT/2
DESCRIPTION:Title: Statistics of Automorphic Representations through Simpl
ified Trace Formulas\nby Rahul Dalal as part of POINT: New Developments in
Number Theory\n\n\nAbstract\nAutomorphic representations encode informati
on about a broad range of interesting mathematical objects. They are very
difficult to study individually so it is often good to study them in famil
ies instead. The Arthur-Selberg trace formula is a powerful tool for this.
For certain very nice families (discrete series at infinity)\, the invari
ant and stable versions of the trace formula take on a simpler form\, allo
wing us to much more easily prove distributional results. I will discuss s
ome of these results and the techniques used for the required trace formul
a computations.\n\nIf you like to attend the talk\, please register here:
https://umich.zoom.us/meeting/register/tJAufuqtqDksG9fEmjTbWHM4QOEUad6Ke-D
E.\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:TBA
DTSTART;VALUE=DATE-TIME:20200824T130000Z
DTEND;VALUE=DATE-TIME:20200824T133000Z
DTSTAMP;VALUE=DATE-TIME:20200812T042615Z
UID:POINT/5
DESCRIPTION:by TBA as part of POINT: New Developments in Number Theory\n\n
Abstract: TBA\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:TBA
DTSTART;VALUE=DATE-TIME:20200824T133000Z
DTEND;VALUE=DATE-TIME:20200824T140000Z
DTSTAMP;VALUE=DATE-TIME:20200812T042615Z
UID:POINT/6
DESCRIPTION:by TBA as part of POINT: New Developments in Number Theory\n\n
Abstract: TBA\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:TBA
DTSTART;VALUE=DATE-TIME:20200909T000000Z
DTEND;VALUE=DATE-TIME:20200909T003000Z
DTSTAMP;VALUE=DATE-TIME:20200812T042615Z
UID:POINT/7
DESCRIPTION:by TBA as part of POINT: New Developments in Number Theory\n\n
Abstract: TBA\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:TBA
DTSTART;VALUE=DATE-TIME:20200909T003000Z
DTEND;VALUE=DATE-TIME:20200909T010000Z
DTSTAMP;VALUE=DATE-TIME:20200812T042615Z
UID:POINT/8
DESCRIPTION:by TBA as part of POINT: New Developments in Number Theory\n\n
Abstract: TBA\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:TBA
DTSTART;VALUE=DATE-TIME:20200921T163000Z
DTEND;VALUE=DATE-TIME:20200921T170000Z
DTSTAMP;VALUE=DATE-TIME:20200812T042615Z
UID:POINT/9
DESCRIPTION:by TBA as part of POINT: New Developments in Number Theory\n\n
Abstract: TBA\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:TBA
DTSTART;VALUE=DATE-TIME:20200921T170000Z
DTEND;VALUE=DATE-TIME:20200921T173000Z
DTSTAMP;VALUE=DATE-TIME:20200812T042615Z
UID:POINT/10
DESCRIPTION:by TBA as part of POINT: New Developments in Number Theory\n\n
Abstract: TBA\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Seoyoung Kim (Queen's University)
DTSTART;VALUE=DATE-TIME:20200810T163000Z
DTEND;VALUE=DATE-TIME:20200810T170000Z
DTSTAMP;VALUE=DATE-TIME:20200812T042615Z
UID:POINT/11
DESCRIPTION:Title: From the Birch and Swinnerton-Dyer conjecture to Nagao'
s conjecture\nby Seoyoung Kim (Queen's University) as part of POINT: New D
evelopments in Number Theory\n\n\nAbstract\nLet $E$ be an elliptic curve o
ver $\\mathbb{Q}$ with discriminant\, and let $a_p$ be the Frobenius trace
for each prime p. In 1965\, Birch and Swinnerton-Dyer formulated a conjec
ture which implies\n\n$\\lim\\limits_{x \\rightarrow \\infty} \\frac{1}{\\
log x} \\sum_{p< x} \\frac{a_p\\log p}{p}=-r+\\frac{1}{2}\,$\n\nwhere $r$
is the order of the zero of the $L$-function of $E$ at $s=1$\, which is pr
edicted to be the Mordell-Weil rank of $E(\\mathbb{Q})$. We show that if t
he above limit exits\, then the limit equals $-r+\\frac{1}{2}$\, and study
the connections to Riemann hypothesis for $E$. We also relate this to Nag
ao's conjecture. This is a recent joint work with M. Ram Murty.\n\nPlease
register for the talks on August 10 here:\nhttps://fordham.zoom.us/meeting
/register/tJwpde2srTgqHdYG6NMu5WmgzPiDnNJQMTsM\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sachi Hashimoto (Boston University)
DTSTART;VALUE=DATE-TIME:20200810T170000Z
DTEND;VALUE=DATE-TIME:20200810T173000Z
DTSTAMP;VALUE=DATE-TIME:20200812T042615Z
UID:POINT/12
DESCRIPTION:Title: Computing rational points on databases of curves\nby Sa
chi Hashimoto (Boston University) as part of POINT: New Developments in Nu
mber Theory\n\n\nAbstract\nFor a curve of genus at least $2$\, we know fro
m Faltings's theorem that its set of rational points is finite. A major ch
allenge is to provably determine\, for a given curve\, this set of rationa
l points. One promising method is the Chabauty-Coleman method\, which uses
$p$-adic (Coleman) integrals to compute a finite set of p-adic points on
the curve including the rational points. We will discuss computations usin
g the Chabauty-Coleman method to provably determine rational point sets fo
r databases of certain genus $3$ superelliptic curves. This is joint work
with Maria de Frutos Fernandez and Travis Morrison.\n\nPlease register for
the talks on August 10 here:\nhttps://fordham.zoom.us/meeting/register/tJ
wpde2srTgqHdYG6NMu5WmgzPiDnNJQMTsM\n
END:VEVENT
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