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BEGIN:VEVENT
SUMMARY:Grzegorz Banaszak (Uniwersytet im. Adama Mickiewicza)
DTSTART;VALUE=DATE-TIME:20200523T142000Z
DTEND;VALUE=DATE-TIME:20200523T153000Z
DTSTAMP;VALUE=DATE-TIME:20200705T042513Z
UID:AFroDis2020/1
DESCRIPTION:Title: Algebraic Sato-Tate and Sato Tate conjectures\nby Grzeg
orz Banaszak (Uniwersytet im. Adama Mickiewicza) as part of Around Frobeni
us distributions and related topics\n\n\nAbstract\nLet $K$ be a number fie
ld and let $\\rho_{l} : G_{K} \\rightarrow GL(V_l)$ be a strictly compatib
le family of $l$-adic representations\, according to Serre\, associated wi
th a pure\, polarized\, rational Hodge structure. In the lecture I will in
troduce Algebraic Sato-Tate and Sato-Tate conjectures in this general fram
ework. I will explain how these conjectures are related to the motivic app
roach by Serre to generalize the classical Sato-Tate conjecture. Previousl
y this work concerned abelian varieties and more generally\, motives of od
d weight in the Deligne's motivic category for absolute Hodge cycles. Now
the results are extended to other motivic categories and to motives of ar
bitrary weight\; the case of even weight introduces some parity considerat
ions that do not appear for odd weight. This is joint work in progress wit
h Kiran Kedlaya.\n
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BEGIN:VEVENT
SUMMARY:Dorota Blinkiewicza (Uniwersytet im. Adama Mickiewicza)
DTSTART;VALUE=DATE-TIME:20200523T153000Z
DTEND;VALUE=DATE-TIME:20200523T163000Z
DTSTAMP;VALUE=DATE-TIME:20200705T042513Z
UID:AFroDis2020/2
DESCRIPTION:Title: Frobenius elements in $\\ell$-adic\, Galois representat
ions associated with semi-abelian varieties\nby Dorota Blinkiewicza (Uniwe
rsytet im. Adama Mickiewicza) as part of Around Frobenius distributions an
d related topics\n\n\nAbstract\nIn my lecture\, I will talk about results
concerning linear relations in the Mordell-Weil group of a semi-abelian va
riety isogeneous to product of a torus and an abelian variety. I will show
that to get these results one can use only finite number of reductions wh
ich amount to constructing Frobenius elements with special arithmetic prop
erties in the l-adic representation associated with the semi-abelian varie
ty under investigation.\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Francesc Fité (MIT)
DTSTART;VALUE=DATE-TIME:20200523T170000Z
DTEND;VALUE=DATE-TIME:20200523T180000Z
DTSTAMP;VALUE=DATE-TIME:20200705T042513Z
UID:AFroDis2020/3
DESCRIPTION:Title: Ordinary primes for some abelian varieties with extra e
ndomorphisms\nby Francesc Fité (MIT) as part of Around Frobenius distribu
tions and related topics\n\n\nAbstract\nIt is a conjecture often attribute
d to Serre that for any abelian variety defined over a number field there
exists a nonzero density set of primes of ordinary reduction. For elliptic
curves and abelian surfaces this has been known for a while and it is due
to Katz\, Ogus and Serre (recently Sawin has even determined the exact de
nsity of ordinary primes in the case of surfaces). I will discuss some cur
rent discoverings on the abundance of ordinary primes for certain types of
abelian varieties of dimensions 3 and 4 which possess extra endomorphisms
.\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ram M. Murty (Queen's University)
DTSTART;VALUE=DATE-TIME:20200523T180000Z
DTEND;VALUE=DATE-TIME:20200523T190000Z
DTSTAMP;VALUE=DATE-TIME:20200705T042513Z
UID:AFroDis2020/4
DESCRIPTION:Title: Some remarks on the Birch and Swinnerton-Dyer conjectur
e\nby Ram M. Murty (Queen's University) as part of Around Frobenius distri
butions and related topics\n\n\nAbstract\nIn the 1960's\, Birch and Swinne
rton-Dyer formulated several conjectures relating the\nrank r of the ellip
tic curve E to the order of the zero of the L-series attached to E at s=1.
\nTheir original conjecture connected the limiting behavior of the product
over primes $p < x$\nof $N_p/p$\, where $N_p$ is the number of points of
E (mod p) with the rank r of E. We will show\nthat if the limit exists\,
then the value of the limit is as predicted by Birch and Swinnerton-Dyer.
We will also make some remarks on how this is related to a conjecture of
Nagao.\nThis is a report on recent joint work with Seoyoung Kim.\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Marc Hindry (Université de Paris)
DTSTART;VALUE=DATE-TIME:20200524T143000Z
DTEND;VALUE=DATE-TIME:20200524T153000Z
DTSTAMP;VALUE=DATE-TIME:20200705T042513Z
UID:AFroDis2020/5
DESCRIPTION:Title: Torsion points on abelian varieties and Galois action\n
by Marc Hindry (Université de Paris) as part of Around Frobenius distribu
tions and related topics\n\n\nAbstract\nI will give a brief survey about t
orsion points on an abelian variety A over a number field K and their asso
ciated Galois representation before presenting some recent results and dis
cuss future investigations. Topic involves naturally the uniform bound con
jecture ("fixing K\, varying A") and\nMumford-Tate conjecture ("fixing A\,
varying K").\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alina Cojocaru (UIC)
DTSTART;VALUE=DATE-TIME:20200524T153000Z
DTEND;VALUE=DATE-TIME:20200524T163000Z
DTSTAMP;VALUE=DATE-TIME:20200705T042513Z
UID:AFroDis2020/6
DESCRIPTION:Title: The growth of the absolute discriminant of a rank 2 gen
eric elliptic module\nby Alina Cojocaru (UIC) as part of Around Frobenius
distributions and related topics\n\n\nAbstract\nFor an elliptic module of
rank 2 and generic characteristic\, with trivial endomorphism ring\, we st
udy the growth of the absolute discriminant of the endomorphism ring assoc
iated to its reduction modulo a prime. We prove that the absolute discrimi
nant grows with the norm of the prime defining the reduction\, and that\,
for a density one of primes\, this growth is as close as possible to the n
atural upper bound. This is joint work with Mihran Papikian.\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Edgar Costa (MIT)
DTSTART;VALUE=DATE-TIME:20200524T170000Z
DTEND;VALUE=DATE-TIME:20200524T180000Z
DTSTAMP;VALUE=DATE-TIME:20200705T042513Z
UID:AFroDis2020/7
DESCRIPTION:Title: From Frobenius polynomials to geometry\nby Edgar Costa
(MIT) as part of Around Frobenius distributions and related topics\n\n\nAb
stract\nIn this talk\, we will focus on how one can deduce some geometric
invariants of an abelian variety or a K3 surface by studying their Frobeni
us polynomials.\nIn the case of an abelian variety\, we show how to obtain
the decomposition of the endomorphism algebra\, the corresponding dimensi
ons\, and centers.\nSimilarly\, by studying the variation of the geometri
c Picard rank\, we obtain a sufficient criterion for the existence of infi
nitely many rational curves on a K3 surface of even geometric Picard rank.
\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kiran Kedlaya (UCSD)
DTSTART;VALUE=DATE-TIME:20200524T180000Z
DTEND;VALUE=DATE-TIME:20200524T190000Z
DTSTAMP;VALUE=DATE-TIME:20200705T042513Z
UID:AFroDis2020/8
DESCRIPTION:Title: Towards explicit realizations of the Sato-Tate groups o
f abelian threefolds\nby Kiran Kedlaya (UCSD) as part of Around Frobenius
distributions and related topics\n\n\nAbstract\nI report on ongoing joint
work with Francesc Fite and Drew Sutherland on\nSato-Tate groups of abelia
n threefolds. There are known to be 410 such\ngroups\, but it is not yet k
nown how many groups occur for principally\npolarized abelian threefolds o
r for Jacobians\; we report on progress\ntowards answering these questions
.\n
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