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BEGIN:VEVENT
SUMMARY:Victoria Cantoral Farfán (Georg-August-Universität Göttingen)
DTSTART:20210628T142000Z
DTEND:20210628T151000Z
DTSTAMP:20260419T091948Z
UID:AFDRT/1
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/AFDRT/1/">To
 wards the motivic Nagao's conjecture and its connections with the Tate con
 jectures</a>\nby Victoria Cantoral Farfán (Georg-August-Universität Göt
 tingen) as part of Around Frobenius distributions and related topics II\n\
 n\nAbstract\nIn 1997\, Nagao conjectured that the rank of an elliptic surf
 ace could be given by a limit formula arising from a weighted average of F
 robenius traces from each fiber.\nDuring this talk\, I would like to repor
 t on a joint work with S. Kim where we introduced\, for the first time\, t
 he Motivic Nagao conjecture for pure motives. In addition\, I will highlig
 ht as well its links with some well-known conjectures in arithmetic geomet
 ry.\n
LOCATION:https://researchseminars.org/talk/AFDRT/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ananth Shankar (University of Wisconsin)
DTSTART:20210628T151000Z
DTEND:20210628T160000Z
DTSTAMP:20260419T091948Z
UID:AFDRT/2
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/AFDRT/2/">Ab
 elian varieties not isogenous to Jacobians over global fields</a>\nby Anan
 th Shankar (University of Wisconsin) as part of Around Frobenius distribut
 ions and related topics II\n\n\nAbstract\nLet K be the algebraic closure o
 f a global field of any characteristic. For every $g>3$ we prove that ther
 e exists a g-dimensional abelian variety over K which is not isogenous to 
 a Jacobian.  This is joint work with Jacob Tsimerman.\n
LOCATION:https://researchseminars.org/talk/AFDRT/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Elisa Lorenzo García (Université de Neuchâtel & Université de 
 Rennes 1)
DTSTART:20210628T160000Z
DTEND:20210628T165000Z
DTSTAMP:20260419T091948Z
UID:AFDRT/3
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/AFDRT/3/">Sa
 to-Tate distributions of twists of the Fermat and the Klein quartics</a>\n
 by Elisa Lorenzo García (Université de Neuchâtel & Université de Renne
 s 1) as part of Around Frobenius distributions and related topics II\n\n\n
 Abstract\nI will start by reviewing the Sato-Tate conjecture and its gener
 alisations. I will focus on the Sato-Tate distributions and computational 
 aspects. After reviewing the elliptic curves case and the genus 2 case I w
 ill move to my results on genus 3 with F. Fité and A. Sutherland. In this
  common work we determine the Sato-Tate groups and the Sato-Tate distribut
 ions of the twists of the Fermat and Klein quartics\, the two quartics wit
 h the largest automorphism group. This produces 60 different Sato-Tate dis
 tributions in genus 3\, which are already enough to see new phenomenons: f
 or instance in genus 3 the individual distribution of the coefficients of 
 the normalized Euler factor do not determine the Sato-Tate distribution.\n
LOCATION:https://researchseminars.org/talk/AFDRT/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andrew V. Sutherland (Massachusetts Institute of Technology)
DTSTART:20210628T180000Z
DTEND:20210628T185000Z
DTSTAMP:20260419T091948Z
UID:AFDRT/4
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/AFDRT/4/">St
 ronger arithmetic equivalence</a>\nby Andrew V. Sutherland (Massachusetts 
 Institute of Technology) as part of Around Frobenius distributions and rel
 ated topics II\n\n\nAbstract\nNumber fields K1 and K2 with the same Dedeki
 nd zeta function\nare said to be arithmetically equivalent.  Such number f
 ields\nnecessarily have the same degree\, signature\, unit group\, discrim
 inant\,\nand Galois closure\, and the distributions of their Frobenius ele
 ments\nare compatible in a strong sense: for every unramified prime p the 
 base\nchange of the Q-algebras K1 and K2 to Qp are isomorphic.  This need 
 not\nhold at ramified primes\, so the adele rings of K1 and K2 need not be
 \nisomorphic\, and global invariants such as the regulator and class numbe
 r\nmay differ.\n\nMotivated by a recent result of Prasad\, I will discuss 
 three stronger\nnotions of arithmetic equivalence that force isomorphisms 
 of some or all\nof these invariants without forcing an isomorphism of numb
 er fields\, and\npresent examples that address questions of Scott and of G
 uralnick and\nWeiss\, and shed some light on a question of Prasad. These r
 esults also\nhave applications to the construction of curves with the same
  L-function\n(due to Prasad)\, isospectral Riemannian manifolds (due to Su
 nada)\, and\nisospectral graphs (due to Halbeisen and Hungerbuhler).\n\nPr
 eprint: https://arxiv.org/abs/2104.01956\n
LOCATION:https://researchseminars.org/talk/AFDRT/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Daniel Fiorilli (CNRS Université Paris-Saclay)
DTSTART:20210628T185000Z
DTEND:20210628T194000Z
DTSTAMP:20260419T091948Z
UID:AFDRT/5
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/AFDRT/5/">Di
 stribution of Frobenius elements in families of Galois extensions</a>\nby 
 Daniel Fiorilli (CNRS Université Paris-Saclay) as part of Around Frobeniu
 s distributions and related topics II\n\n\nAbstract\nThis is joint work wi
 th Florent Jouve. I will discuss three\ntypes of results: Linnik type ques
 tions on the prime ideal of least norm\nwith prescribed Frobenius\, the ge
 neric order of magnitude of the error\nterm in the Chebotarev density theo
 rem\, and unconditional instances of\nChebyshev's bias in number fields.\n
LOCATION:https://researchseminars.org/talk/AFDRT/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Seoyoung Kim (Queen's University)
DTSTART:20210628T194000Z
DTEND:20210628T203000Z
DTSTAMP:20260419T091948Z
UID:AFDRT/6
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/AFDRT/6/">Fr
 om the Birch and Swinnerton-Dyer conjecture to Nagao's conjecture</a>\nby 
 Seoyoung Kim (Queen's University) as part of Around Frobenius distribution
 s and related topics II\n\n\nAbstract\nLet E be an elliptic curve over Q\,
  and let a_p be the Frobenius trace for each prime p. In 1965\, Birch and 
 Swinnerton-Dyer formulated a conjecture which implies the convergence of t
 he Nagao-Mestre sum\n$lim_{x->infty} (1/log x) \\sum_{p < x}(a_p log p)/p=
 -r+1/2\,$\nwhere r is the order of the zero of the L-function of E at s=1\
 , which is predicted to be the Mordell-Weil rank of E(Q). We show that if 
 the above limit exists\, then the limit equals -r+1/2\, and study the conn
 ections to the Riemann hypothesis for E. We also relate this to Nagao's co
 njecture for elliptic curves. Furthermore\, we discuss a generalization of
  the above results for the Selberg classes and hence (conjecturally) for t
 he L-function of abelian varieties\, and their relations to the generalize
 d Nagao's conjecture. This is a joint work with M. Ram Murty.\n
LOCATION:https://researchseminars.org/talk/AFDRT/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bjorn Poonen (Massachusetts Institute of Technology)
DTSTART:20210629T142000Z
DTEND:20210629T151000Z
DTSTAMP:20260419T091948Z
UID:AFDRT/7
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/AFDRT/7/">Ab
 elian varieties of prescribed order over finite fields</a>\nby Bjorn Poone
 n (Massachusetts Institute of Technology) as part of Around Frobenius dist
 ributions and related topics II\n\n\nAbstract\nWe give several new constru
 ctions of Weil polynomials to show that given a prime power q and n >> 1\,
  every integer in a large subinterval of the Hasse-Weil interval is realiz
 ed as #A(F_q) for some n-dimensional abelian variety A over F_q.  Moreover
 \, we can make A geometrically simple\, ordinary\, and principally polariz
 ed.  On the one hand\, our work generalizes a theorem of Howe and Kedlaya 
 for F_2.  On the other hand\, it improves upon theorems of DiPippo and How
 e\; Aubry\, Haloui\, and Lachaud\; and Kadets.  This talk will focus on on
 e construction that leads to explicit (and nearly best possible) bounds\, 
 in terms of q\, on the largest integer that is not A(F_q) for any A.  This
  is joint work with Raymond van Bommel\, Edgar Costa\, Wanlin Li\, and Ale
 xander Smith.\n
LOCATION:https://researchseminars.org/talk/AFDRT/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexander Smith (Massachusetts Institute of Technology)
DTSTART:20210629T151000Z
DTEND:20210629T160000Z
DTSTAMP:20260419T091948Z
UID:AFDRT/8
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/AFDRT/8/">To
 tally positive integers of small trace and extreme orders of abelian varie
 ties over finite fields</a>\nby Alexander Smith (Massachusetts Institute o
 f Technology) as part of Around Frobenius distributions and related topics
  II\n\n\nAbstract\nOutside of finitely many exceptions\, we show that the 
 average real valuation of a totally positive algebraic integer is at least
  $1.80$\, improving the prior best of $1.7919$. As a consequence\, for a s
 ufficiently large square prime power $q$\, we show that all but finitely m
 any simple abelian varieties $A/\\mathbb{F}_q$ satisfy\n\\[(q - 2q^{1/2} +
  2.8)^{\\dim A}  \\le \\#A(\\mathbb{F}_q) \\le (q + 2q^{1/2} - 0.8)^{\\dim
  A}\,\\]\nand we explain how are approach can be adapted to other $q$. We 
 will also give some evidence that there are infinitely many totally positi
 ve algebraic integers whose average valuation is less than $1.82$ and expl
 ain the implications of such a result for abelian varieties over finite fi
 elds.\n\nOur starting point is the fact that the discriminant of a rationa
 l integer polynomial must be a rational integer. We are able to take advan
 tage of this fact in our computational approach by using logarithmic poten
 tial theory.\n
LOCATION:https://researchseminars.org/talk/AFDRT/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tian Wang (University of Illinois at Chicago)
DTSTART:20210629T180000Z
DTEND:20210629T185000Z
DTSTAMP:20260419T091948Z
UID:AFDRT/9
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/AFDRT/9/">Bo
 unds for the distribution of the Frobenius traces associated to products o
 f non-CM elliptic curves</a>\nby Tian Wang (University of Illinois at Chic
 ago) as part of Around Frobenius distributions and related topics II\n\n\n
 Abstract\nLet $A/\\mathbb{Q}$ be an abelian variety that is isogenous over
  $\\mathbb{Q}$ to the product $E_1 \\times \\ldots \\times E_g$ of ellipti
 c curves $E_1/\\mathbb{Q}$\, $\\ldots$\, $E_g/\\mathbb{Q}$ without complex
  multiplication and pairwise non-isogenous over $\\overline{\\mathbb{Q}}$.
  For an  integer $t$ and a positive real number $x$\, denote by $\\pi_A(x\
 , t)$ the number of primes $p \\leq x$\, of good reduction for the abelian
  variety $A$\, for which the Frobenius trace associated to the reduction o
 f $A$ modulo $p$ equals $t$.\n\nBased on prior approaches to the Lang-Trot
 ter Conjecture for the Frobenius traces associated to reduction of \n\nan 
 elliptic curve\, under the RH and the GRH for  Dedekind zeta functions\, w
 e prove a non-trivial upper bound for $\\pi_A(x\, t)$.\n\nThis is joint wo
 rk with Alina Carmen Cojocaru.\n
LOCATION:https://researchseminars.org/talk/AFDRT/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Emmanuel Kowalski (ETH Zürich)
DTSTART:20210629T185000Z
DTEND:20210629T194000Z
DTSTAMP:20260419T091948Z
UID:AFDRT/10
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/AFDRT/10/">F
 ourier analysis over commutative algebraic groups and Frobenius distributi
 on</a>\nby Emmanuel Kowalski (ETH Zürich) as part of Around Frobenius dis
 tributions and related topics II\n\n\nAbstract\nIn ongoing joint work with
  A. Forey and J. Fresán\, we generalize to any\nconnected commutative alg
 ebraic group the convolution approach to\nequidistribution problems pionee
 red by Katz for the multiplicative\ngroup.\n\nThe lecture will survey the 
 general statements before focusing on\nconcrete examples\, including a spe
 cial case related to lines on cubic\nthreefolds\, where the exceptional gr
 oup E_6 appears.\n
LOCATION:https://researchseminars.org/talk/AFDRT/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mihran Papikian (Pennsylvania State University)
DTSTART:20210629T194000Z
DTEND:20210629T203000Z
DTSTAMP:20260419T091948Z
UID:AFDRT/11
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/AFDRT/11/">C
 omputing endomorphism rings and Frobenius matrices of Drinfeld modules</a>
 \nby Mihran Papikian (Pennsylvania State University) as part of Around Fro
 benius distributions and related topics II\n\n\nAbstract\nLet $\\mathbb{F}
 _q[T]$ be the polynomial ring over a finite field $\\mathbb{F}_q$. We stud
 y the endomorphism rings of Drinfeld $\\mathbb{F}_q[T]$-modules of arbitra
 ry rank over finite fields. We compare the endomorphism rings to their sub
 rings generated by the Frobenius endomorphism and deduce from this a recip
 rocity law for the division fields of Drinfeld modules. We then use these 
 results to give an efficient algorithm for computing the endomorphism ring
 s and discuss some interesting examples produced by our algorithm. This is
  a joint work with Sumita Garai.\n
LOCATION:https://researchseminars.org/talk/AFDRT/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Margaret Bilu (IST Austria)
DTSTART:20210629T133000Z
DTEND:20210629T142000Z
DTSTAMP:20260419T091948Z
UID:AFDRT/12
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/AFDRT/12/">Z
 eta statistics</a>\nby Margaret Bilu (IST Austria) as part of Around Frobe
 nius distributions and related topics II\n\n\nAbstract\nIn this talk\, we 
 will introduce several different topologies in which a\nsequence of zeta f
 unctions of varieties over a finite field can be taken\nto converge. These
  topologies will be defined in terms of the sizes of\nthe coefficients of 
 the power series expansions at zero or in terms of\nthe zeros and poles. W
 e will explain how these types of convergence can\nbe interpreted arithmet
 ically and/or geometrically\, and how this leads\nto a conjectural way of 
 unifying arithmetic and motivic statistics. As\nevidence for our conjectur
 es we will mention some convergence results\nfor spaces of zero-cycles. Th
 is is joint work with Ronno Das and Sean Howe.\n
LOCATION:https://researchseminars.org/talk/AFDRT/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Will Sawin (Columbia University)
DTSTART:20210628T133000Z
DTEND:20210628T142000Z
DTSTAMP:20260419T091948Z
UID:AFDRT/13
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/AFDRT/13/">F
 robenius distribution in number theory over function fields</a>\nby Will S
 awin (Columbia University) as part of Around Frobenius distributions and r
 elated topics II\n\n\nAbstract\nThere exists a natural analogue of the Che
 botarev density \ntheorem for the field of rational functions in one varia
 ble over a \nfinite field\, or extensions of it. Because of the additional
  geometric \nflexibility of that setting\, this theorem can be used to pro
 ve \nnumber-theoretic statements over that field which have little or no \
 napparent relationship to Chebotarev. I will explain an example of this \n
 phenomenon in my work with Michael Lipnowski and Jacob Tsimerman on \nthe 
 Cohen-Lenstra heuristics over function fields.\n
LOCATION:https://researchseminars.org/talk/AFDRT/13/
END:VEVENT
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