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BEGIN:VEVENT
SUMMARY:Grzegorz Banaszak (Uniwersytet im. Adama Mickiewicza)
DTSTART:20200523T142000Z
DTEND:20200523T153000Z
DTSTAMP:20260415T205459Z
UID:AFroDis2020/1
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/AFroDis2020/
 1/">Algebraic Sato-Tate and Sato Tate conjectures</a>\nby Grzegorz Banasza
 k (Uniwersytet im. Adama Mickiewicza) as part of Around Frobenius distribu
 tions and related topics\n\n\nAbstract\nLet $K$ be a number field and let 
 $\\rho_{l} : G_{K} \\rightarrow GL(V_l)$ be a strictly compatible family o
 f $l$-adic representations\, according to Serre\, associated with a pure\,
  polarized\, rational Hodge structure. In the lecture I will introduce Alg
 ebraic Sato-Tate and Sato-Tate conjectures in this general framework. I wi
 ll explain how these conjectures are related to the motivic approach by Se
 rre to generalize the classical Sato-Tate conjecture. Previously this work
  concerned abelian varieties and more generally\, motives of odd weight in
  the Deligne's  motivic category for absolute Hodge cycles. Now the result
 s are extended to other motivic categories and to motives of arbitrary wei
 ght\; the case of even weight introduces some parity considerations that d
 o not appear for odd weight. This is joint work in progress with Kiran Ked
 laya.\n
LOCATION:https://researchseminars.org/talk/AFroDis2020/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dorota Blinkiewicza (Uniwersytet im. Adama Mickiewicza)
DTSTART:20200523T153000Z
DTEND:20200523T163000Z
DTSTAMP:20260415T205459Z
UID:AFroDis2020/2
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/AFroDis2020/
 2/">Frobenius elements in $\\ell$-adic\, Galois representations associated
  with semi-abelian varieties</a>\nby Dorota Blinkiewicza (Uniwersytet im. 
 Adama Mickiewicza) as part of Around Frobenius distributions and related t
 opics\n\n\nAbstract\nIn my lecture\, I will talk about results concerning 
 linear relations in the Mordell-Weil group of a semi-abelian variety isoge
 neous to product of a torus and an abelian variety. I will show that to ge
 t these results one can use only finite number of reductions which amount 
 to constructing Frobenius elements with special arithmetic properties in t
 he l-adic representation associated with the semi-abelian variety under in
 vestigation.\n
LOCATION:https://researchseminars.org/talk/AFroDis2020/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Francesc Fité (MIT)
DTSTART:20200523T170000Z
DTEND:20200523T180000Z
DTSTAMP:20260415T205459Z
UID:AFroDis2020/3
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/AFroDis2020/
 3/">Ordinary primes for some abelian varieties with extra endomorphisms</a
 >\nby Francesc Fité (MIT) as part of Around Frobenius distributions and r
 elated topics\n\n\nAbstract\nIt is a conjecture often attributed to Serre 
 that for any abelian variety defined over a number field there exists a no
 nzero 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 density of or
 dinary primes in the case of surfaces). I will discuss some current discov
 erings on the abundance of ordinary primes for certain types of abelian va
 rieties of dimensions 3 and 4 which possess extra endomorphisms.\n
LOCATION:https://researchseminars.org/talk/AFroDis2020/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ram M. Murty (Queen's University)
DTSTART:20200523T180000Z
DTEND:20200523T190000Z
DTSTAMP:20260415T205459Z
UID:AFroDis2020/4
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/AFroDis2020/
 4/">Some remarks on the Birch and Swinnerton-Dyer conjecture</a>\nby Ram M
 . Murty (Queen's University) as part of Around Frobenius distributions and
  related topics\n\n\nAbstract\nIn the 1960's\, Birch and Swinnerton-Dyer f
 ormulated several conjectures relating the\nrank r of the elliptic curve E
  to the order of the zero of the L-series attached to E at s=1.\nTheir ori
 ginal conjecture connected the limiting behavior of the product over prime
 s $p < x$\nof $N_p/p$\, where $N_p$ is the number of points of E (mod p) w
 ith the rank r of E.  We will show\nthat if the limit exists\, then the va
 lue of the limit is as predicted by Birch and Swinnerton-Dyer.  We will al
 so make some remarks on how this is related to a conjecture of Nagao.\nThi
 s is a report on recent joint work with Seoyoung Kim.\n
LOCATION:https://researchseminars.org/talk/AFroDis2020/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Marc Hindry (Université de Paris)
DTSTART:20200524T143000Z
DTEND:20200524T153000Z
DTSTAMP:20260415T205459Z
UID:AFroDis2020/5
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/AFroDis2020/
 5/">Torsion points on abelian varieties and Galois action</a>\nby Marc Hin
 dry (Université de Paris) as part of Around Frobenius distributions and r
 elated topics\n\n\nAbstract\nI will give a brief survey about torsion poin
 ts on an abelian variety A over a number field K and their associated Galo
 is representation before presenting some recent results and discuss future
  investigations. Topic involves naturally the uniform bound conjecture ("f
 ixing K\, varying A") and\nMumford-Tate conjecture ("fixing A\, varying K"
 ).\n
LOCATION:https://researchseminars.org/talk/AFroDis2020/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alina Cojocaru (UIC)
DTSTART:20200524T153000Z
DTEND:20200524T163000Z
DTSTAMP:20260415T205459Z
UID:AFroDis2020/6
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/AFroDis2020/
 6/">The growth of the absolute discriminant of a rank 2 generic elliptic m
 odule</a>\nby Alina Cojocaru (UIC) as part of Around Frobenius distributio
 ns and related topics\n\n\nAbstract\nFor an elliptic module of rank 2 and 
 generic characteristic\, with trivial endomorphism ring\, we study the gro
 wth of the absolute discriminant of the endomorphism ring associated to it
 s reduction modulo a prime. We prove that the absolute discriminant grows 
 with the norm of the prime defining the reduction\, and that\, for a densi
 ty one of primes\, this growth is as close as possible to the natural uppe
 r bound. This is joint work with Mihran Papikian.\n
LOCATION:https://researchseminars.org/talk/AFroDis2020/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Edgar Costa (MIT)
DTSTART:20200524T170000Z
DTEND:20200524T180000Z
DTSTAMP:20260415T205459Z
UID:AFroDis2020/7
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/AFroDis2020/
 7/">From Frobenius polynomials to geometry</a>\nby Edgar Costa (MIT) as pa
 rt of Around Frobenius distributions and related topics\n\n\nAbstract\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 Frobenius polynomi
 als.\nIn the case of an abelian variety\, we show how to obtain the decomp
 osition of the endomorphism algebra\, the corresponding dimensions\, and c
 enters.\nSimilarly\,  by studying the variation of the geometric Picard ra
 nk\, we obtain a sufficient criterion for the existence of infinitely many
  rational curves on a K3 surface of even geometric Picard rank.\n
LOCATION:https://researchseminars.org/talk/AFroDis2020/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kiran Kedlaya (UCSD)
DTSTART:20200524T180000Z
DTEND:20200524T190000Z
DTSTAMP:20260415T205459Z
UID:AFroDis2020/8
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/AFroDis2020/
 8/">Towards explicit realizations of the Sato-Tate groups of abelian three
 folds</a>\nby Kiran Kedlaya (UCSD) as part of Around Frobenius distributio
 ns and related topics\n\n\nAbstract\nI report on ongoing joint work with F
 rancesc Fite and Drew Sutherland on\nSato-Tate groups of abelian threefold
 s. There are known to be 410 such\ngroups\, but it is not yet known how ma
 ny groups occur for principally\npolarized abelian threefolds or for Jacob
 ians\; we report on progress\ntowards answering these questions.\n
LOCATION:https://researchseminars.org/talk/AFroDis2020/8/
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