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BEGIN:VEVENT
SUMMARY:Chandrashekhar Khare
DTSTART:20200608T160000Z
DTEND:20200608T170000Z
DTSTAMP:20260422T225721Z
UID:UNYONTC/1
DESCRIPTION:Title:
Serre-type conjectures for projective representations\nby Chandrashekh
ar Khare as part of Upstate New York Online Number Theory Colloquium\n\n\n
Abstract\nWe consider automorphy of many representations of the form $\\b
ar \\rho:G_K \\rightarrow PGL_2(k)$ with $K$ a CM field and $k=F_3\,F_5$.
In particular we prove (under some mild conditions) that for $F$ totally
real\, a surjective representation $\\bar \\rho:G_F \\rightarrow PGL_2(F_
5)$ with totally odd sign character arises from a Hilbert modular form of
weight $(2\,\\ldots\, 2)$. This is joint work with Patrick Allen and Jack
Thorne.\n
LOCATION:https://researchseminars.org/talk/UNYONTC/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Maxim Mornev
DTSTART:20200622T160000Z
DTEND:20200622T170000Z
DTSTAMP:20260422T225721Z
UID:UNYONTC/2
DESCRIPTION:Title:
Tate conjectures in function field arithmetic\nby Maxim Mornev as part
of Upstate New York Online Number Theory Colloquium\n\n\nAbstract\nMany v
ersions of Tate conjectures were proved for Drinfeld modules and\nfor thei
r higher-dimensional generalizations\, the t-modules of Anderson.\nThe und
erpinning of this success is a technically simple but powerful\ntheory of
t-motives pioneered by Anderson. In this talk I shall describe\nan approac
h to Tate conjectures for t-modules which implies all the\nknown versions
and explains why some variants of the conjectures fail.\nThe approach comb
ines the theory of t-motives with the t-adic\ncounterpart of the theory of
overconvergent F-isocrystals.\n
LOCATION:https://researchseminars.org/talk/UNYONTC/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Florian Sprung
DTSTART:20200706T180000Z
DTEND:20200706T190000Z
DTSTAMP:20260422T225721Z
UID:UNYONTC/3
DESCRIPTION:Title:
Subleading terms of L-functions of elliptic curves\nby Florian Sprung
as part of Upstate New York Online Number Theory Colloquium\n\n\nAbstract\
nThe leading term of the L-function of an elliptic curve encodes\nsome of
its arithmetic via BSD. What about the subleading term? Wuthrich\nproved t
hat this subleading term is related to the leading one as a\nconsequence o
f the functional equation. Bianchi gave a p-adic analogue of\nthis result\
, and also found another consequence of the functional equation\nconcernin
g Iwasawa's mu-invariant\, assuming p is ordinary. This talk\npresents joi
nt work with C. Dion\, in which we extend the results of\nBianchi/Wuthrich
in various directions: First\, we discuss what happens in\nthe supersingu
lar (not ordinary) case. In this case\, there is a pair of\namenable funct
ions\, for which we prove Bianchi's/Wuthrich's ideas can be\napplied. Sinc
e we now have a pair of functions\, we can do something new: We\ncan relat
e their orders of vanishing to each other. If there is time\, we\nalso hop
e to discuss a result concerning lambda-invariants (for which p can\nbe or
dinary or supersingular).\n
LOCATION:https://researchseminars.org/talk/UNYONTC/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Michael Filaseta
DTSTART:20200720T160000Z
DTEND:20200720T170000Z
DTSTAMP:20260422T225721Z
UID:UNYONTC/4
DESCRIPTION:Title:
On a dense universal Hilbert set\nby Michael Filaseta as part of Upsta
te New York Online Number Theory Colloquium\n\n\nAbstract\nA $universal\\
Hilbert\\ set$\nis an infinite set $\\mathcal S \\subseteq \\mathbb Z$\n
having the property that for every $F(x\,y) \\in \\mathbb Z[x\,y]$\nwhich
is irreducible in $\\mathbb Q[x\,y]$ and satisfies $\\deg_{x} (F) \\ge 1$\
, \nwe have that for all but finitely many $y_{0} \\in \\mathcal S$\, th
e polynomial \n$F(x\,y_{0})$ is irreducible in $\\mathbb Q[x]$. \nThe exi
stence of universal Hilbert sets is due to P.C. Gilmore and A. Robinson in
1955\,\nand since then a number of explicit examples have been given. \n
Universal Hilbert sets of density $1$ in the integers have been shown to e
xist \nby Y. Bilu in 1996 and P. D\\`ebes and U. Zannier in 1998.\nIn this
talk\, we discuss a connection between universal Hilbert sets and \nSiege
l's Lemma on the finiteness of integral points on a curve\nof genus $\\ge
1$\, and explain how a result of K.Ford (2008) implies\nthe existence of a
universal Hilbert set $\\mathcal S$ satisfying\n\\[\n|\\{ m \\in \\mathbb
Z: m \\not\\in \\mathcal S\, |m| \\le X \\}| \\ll \\dfrac{X}{(\\log X)^{\
\delta}}\,\n\\]\nwhere $\\delta = 1 - (1+\\log\\log 2)/(\\log 2) = 0.08607
1\\ldots$. This is joint work with Robert Wilcox.\n
LOCATION:https://researchseminars.org/talk/UNYONTC/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Daqing Wan
DTSTART:20200803T160000Z
DTEND:20200803T170000Z
DTSTAMP:20260422T225721Z
UID:UNYONTC/5
DESCRIPTION:Title:
Slopes in Z_p-towers of curves\nby Daqing Wan as part of Upstate New Y
ork Online Number Theory Colloquium\n\n\nAbstract\nThis is an expository l
ecture. We shall review basic questions\, results and ideas on slopes for
zeta functions of curves over finite fields of characteristic p. The empha
sis will be on the slope variation when the curve varies in a $Z_p$-tower.
\n
LOCATION:https://researchseminars.org/talk/UNYONTC/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andrew Granville
DTSTART:20200817T160000Z
DTEND:20200817T170000Z
DTSTAMP:20260422T225721Z
UID:UNYONTC/6
DESCRIPTION:Title:
Understanding the distribution of primes in (very) short intervals\nby
Andrew Granville as part of Upstate New York Online Number Theory Colloqu
ium\n\n\nAbstract\nIn joint work with Alyssa Lumley we explore the maximum
number\nof primes in short intervals\, both from a heuristic and a comput
ational\npoint-of-view. This leads naturally to questions in sieve theory
and\nprobability theory which we will also explore.\n
LOCATION:https://researchseminars.org/talk/UNYONTC/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dustin Clausen
DTSTART:20200831T160000Z
DTEND:20200831T170000Z
DTSTAMP:20260422T225721Z
UID:UNYONTC/7
DESCRIPTION:Title:
On the quadratic reciprocity law\nby Dustin Clausen as part of Upstate
New York Online Number Theory Colloquium\n\n\nAbstract\nI'll describe a r
ather idiosyncratic proof of the quadratic reciprocity\nlaw. This talk ca
n also be seen as a small introduction to algebraic K-theory and\nthe use
of homotopy theory in arithmetic.\n
LOCATION:https://researchseminars.org/talk/UNYONTC/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hé\;lè\;ne Esnault
DTSTART:20200928T160000Z
DTEND:20200928T170000Z
DTSTAMP:20260422T225721Z
UID:UNYONTC/8
DESCRIPTION:Title:
Bounding ramification with covers and curves\nby Hé\;lè\;n
e Esnault as part of Upstate New York Online Number Theory Colloquium\n\n\
nAbstract\nIn positive characteristic\, there is no curve with the propert
y that its fundamental\ngroup covers the one of a given variety $X$ (Lefsc
hetz property). Deligne asked\nwhether over an algebraically closed field
there is such a curve which preserves the\nmonodromy groups of ${\\bar \\
mathbb{Q}}_\\ell$ local systems in bounded rank and\nramification on $X$.
We can not prove this in general\, instead we give weaker\nstatements whi
ch enable one to tamify local systems. \n\nJoint work with Vasudevan Srini
vas.\n
LOCATION:https://researchseminars.org/talk/UNYONTC/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Wadim Zudilin
DTSTART:20200914T160000Z
DTEND:20200914T170000Z
DTSTAMP:20260422T225721Z
UID:UNYONTC/9
DESCRIPTION:Title:
Creative microscoping\nby Wadim Zudilin as part of Upstate New York On
line Number Theory Colloquium\n\n\nAbstract\nLet $A_k=2^{-6k}{\\binom{2k}k
}^3$ for $k=0\,1\,\\dots$\,.\nThough traditional techniques of establishin
g the hypergeometric evaluation\n\n$\\sum \\limits_{k=0}^\\infty(-1)^k(4k+
1)A_k =\\frac2\\pi$\n\nand (super)congruences\n\n$\\sum \\limits_{k=0}^{p-
1}(-1)^k(4k+1)A_k \\equiv p(-1)^{(p-1)/2}\\pmod{p^3} \\quad\\text{for\npri
mes}\\\; p>2$\n\nshare certain similarities\, they do not display intrinsi
c reasons for the two to be\nrelated.\nIn my talk I will outline basic ing
redients of a method developed in joint works\nwith Victor Guo\, which doe
s the missing part\, also for many other instances of such\narithmetic dua
lity.\nThe main idea is constructing suitable $q$-deformations of the infi
nite sum (and\nmany such sums are already recorded in the $q$-literature)\
,\nand then look at the asymptotics of that at roots of unity.\nInterestin
gly enough\, the $q$-deformations may offer more.\nFor example\, the $q$-d
eformation of the above infinite sum also implies\n$$\n\\sum_{k=0}^\\infty
A_k\n=\\frac{\\Gamma(1/4)^4}{4\\pi^3}\n=\\frac{8L(f\,1)}{\\pi}\n\\quad\\t
ext{and}\\quad\n\\sum_{k=0}^{p-1}A_k\\equiv a(p)\\pmod{p^2}\n$$\n(in fact\
, the latter congruences in their stronger modulo $p^3$ form proven by Lon
g\nand Ramakrishna)\,\nwhere $a(p)$ is the $p$-th Fourier coefficient of (
the weight 3 modular form)\n$f=q\\prod_{m=1}^\\infty(1-q^{4m})^6$.\n\n($NB
:$ The variable $q$ in the last definition is related to the modular\npara
meter $\\tau$ through $q=e^{2\\pi i\\tau}$ and has nothing to do with the
$q$ in\nthe $q$-deformation.)\n
LOCATION:https://researchseminars.org/talk/UNYONTC/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Michel Waldschmidt
DTSTART:20201012T160000Z
DTEND:20201012T170000Z
DTSTAMP:20260422T225721Z
UID:UNYONTC/10
DESCRIPTION:Title: Some variants of Seshadri's constant\nby Michel Waldschmidt as part o
f Upstate New York Online Number Theory Colloquium\n\n\nAbstract\nSeshadri
's constant is related to a conjecture due to Nagata. Another conjecture\,
\nalso due to Nagata and solved by Bombieri in 1970\, is related with alge
braic values\nof meromorphic functions. The main argument of Bombieri's pr
oof leads to a Schwarz\nLemma in several variables\, the proof of which gi
ves rise to another invariant\nassociated with symbolic powers of the idea
l of functions vanishing on a finite set\nof points. This invariant is an
asymptotic measure of the least degree of a\npolynomial in several variabl
es with given order of vanishing on a finite set of\npoints. Recent works
on the resurgence of ideals of points and the containment\nproblem compare
powers and symbolic powers of ideals.\n
LOCATION:https://researchseminars.org/talk/UNYONTC/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Chantal David
DTSTART:20201026T160000Z
DTEND:20201026T170000Z
DTSTAMP:20260422T225721Z
UID:UNYONTC/11
DESCRIPTION:Title: Moments and non-vanishing of cubic Dirichlet L-functions at s=1/2\nby
Chantal David as part of Upstate New York Online Number Theory Colloquium
\n\n\nAbstract\nA famous conjecture of Chowla predicts that $L(\\frac{1}{2
}\,\\chi)\\neq 0$ for all Dirichlet L-functions\nattached to primitive ch
aracters $\\chi$. It was conjectured first in the case where $\\chi$ is a
quadratic\ncharacter\, which is the most studied case. For quadratic Diric
hlet L-functions\, Soundararajan\nproved that at least 87.5% of the quadra
tic Dirichlet L-functions do not vanish at $s=\\frac{1}{2}.$\n\nUnder GRH\
, there are slightly stronger results by Ozlek and Snyder.\nWe present in
this talk the first result showing a positive proportion of cubic Dirichle
t\nL-functions non-vanishing at s = 1/2 for the non-Kummer case over funct
ion fields. This\ncan be achieved by using the recent breakthrough work on
sharp upper bounds for moments\nof Soundararajan\, Harper and Lester-Radz
iwill. Our results would transfer over number\nfields (but we would need t
o assume GRH in this case).\nThe talk will be accessible to a general audi
ence of number theorists and graduate students\nin number theory.\n\nJoint
work with A. Florea and M. Lalin.\n
LOCATION:https://researchseminars.org/talk/UNYONTC/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexandru Buium
DTSTART:20201123T170000Z
DTEND:20201123T180000Z
DTSTAMP:20260422T225721Z
UID:UNYONTC/12
DESCRIPTION:Title: Solutions to arithmetic differential equations in the p-adic complex fiel
d\nby Alexandru Buium as part of Upstate New York Online Number Theory
Colloquium\n\n\nAbstract\nArithmetic differential equations are analogues
of differential equations\nin which derivatives of functions are replaced
by Fermat quotients of numbers.\nIn its original form this theory would o
nly allow the consideration of solutions to\nsuch equations in unramified
extensions of the p-adic integers. Recently\, L.Miller\nand the author sh
owed that the `main examples' of arithmetic differential equations\nin the
theory possess a remarkable differential overconvergence property. This\n
allows the consideration (and study) of their solutions in the ring of int
egers of\nthe p-adic complex field.\n
LOCATION:https://researchseminars.org/talk/UNYONTC/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Matt Baker
DTSTART:20201207T170000Z
DTEND:20201207T180000Z
DTSTAMP:20260422T225721Z
UID:UNYONTC/13
DESCRIPTION:Title: The Algebra of Forgetfulness\nby Matt Baker as part of Upstate New Yo
rk Online Number Theory Colloquium\n\n\nAbstract\nThere are a several theo
rems in algebra where one purposely forgets\ncertain information about the
coefficients of a polynomial and then sees whether\ncertain properties of
the roots can still be determined. A prototypical example is\nDescartes
’ Rule of Signs\, where we forget everything about a polynomial P except
for\nthe signs of its coefficients and then ask for information about the
signs of the\nreal roots of P. I will explain a novel algebraic framework
for systematically\nunderstanding results of this type. As time permits\,
I will discuss connections to\nmatroid theory\, including the algebraic f
oundations underlying the construction of a\n"moduli space of matroids". T
his is joint work with Oliver Lorscheid.\n
LOCATION:https://researchseminars.org/talk/UNYONTC/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Michael Larsen
DTSTART:20210222T170000Z
DTEND:20210222T180000Z
DTSTAMP:20260422T225721Z
UID:UNYONTC/14
DESCRIPTION:Title: Elliptic curves over fields with finitely generated Galois groups\nby
Michael Larsen as part of Upstate New York Online Number Theory Colloquiu
m\n\n\nAbstract\nLet K be a field in characteristic 0 with $Gal (\\bar{K}/
K)$\nfinitely generated. What can be said about the group of rational poin
ts\nof an elliptic curve E over K? I will discuss various approaches to th
is\nproblem\, via algebraic geometry\, algebraic combinatorics\, and analy
tic\nnumber theory.\n
LOCATION:https://researchseminars.org/talk/UNYONTC/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gerard van der Geer
DTSTART:20210308T170000Z
DTEND:20210308T180000Z
DTSTAMP:20260422T225721Z
UID:UNYONTC/15
DESCRIPTION:Title: Modular forms and invariant theory\nby Gerard van der Geer as part of
Upstate New York Online Number Theory Colloquium\n\n\nAbstract\nSiegel an
d Teichmueller modular forms of genus g are generalizations\nof the usual
elliptic modular forms\, the case g=1\, but live on the\nmoduli spaces of
abelian varieties and curves of genus g. These forms\, \nare just as intri
guing\, but more difficult to construct.\nWe intend to show how one can us
e invariant theory to describe in \nprinciple all such modular forms for g
enus 2 and 3 explicitly.\nThis is joint work with Fabien Clery and Carel F
aber.\n
LOCATION:https://researchseminars.org/talk/UNYONTC/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:David Harbater
DTSTART:20210322T160000Z
DTEND:20210322T170000Z
DTSTAMP:20260422T225721Z
UID:UNYONTC/16
DESCRIPTION:Title: Local-global principles over semi-global fields\nby David Harbater as
part of Upstate New York Online Number Theory Colloquium\n\n\nAbstract\nL
ocal-global principles have classically been studied in the \ncontext of g
lobal fields\; i.e.\, number fields or function fields of \ncurves over fi
nite fields. In recent years\, they have also been studied \nover what ha
ve come to be known as semi-global fields\, a class that \nincludes functi
on fields of p-adic curves. Classical results such as the \nHasse-Minkowsk
i theorem have been carried over to this context\, though \nwith very diff
erent proofs. The talk will present results in this \ndirection\, includin
g ongoing work of the speaker with J-L. \nColliot-Thélène\, J. Hartmann\
, D. Krashen\, R. Parimala\, and V. Suresh.\n
LOCATION:https://researchseminars.org/talk/UNYONTC/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Florian Pop
DTSTART:20210405T160000Z
DTEND:20210405T170000Z
DTSTAMP:20260422T225721Z
UID:UNYONTC/17
DESCRIPTION:Title: Towards minimalistic forms of the Neukirch and Uchida Theorem\nby Flo
rian Pop as part of Upstate New York Online Number Theory Colloquium\n\n\n
Abstract\nRecall that the famous Neukirch and Uchida Theorem (and its vari
ants) show that the isomorphism type of global fields is functorially enco
ded in their absolute and/or solvable Galois theory. Inspired by the very
recent work of Saidi-Tamagawa on the topic\, and work by Harry Smit relate
d to the subject\, I will present some work in progress on quite "minimali
stic" forms of the Neukirch and Uchida Theorem and its generalizations. Th
is work in progress is collaboration with Adam Topaz.\n
LOCATION:https://researchseminars.org/talk/UNYONTC/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yuri Tschinkel
DTSTART:20210419T160000Z
DTEND:20210419T170000Z
DTSTAMP:20260422T225721Z
UID:UNYONTC/18
DESCRIPTION:Title: Equivariant birational types\nby Yuri Tschinkel as part of Upstate Ne
w York Online Number Theory Colloquium\n\n\nAbstract\nI will discuss new r
esults and constructions in equivariant birational geometry.\n
LOCATION:https://researchseminars.org/talk/UNYONTC/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Minhyong Kim
DTSTART:20210503T160000Z
DTEND:20210503T170000Z
DTSTAMP:20260422T225721Z
UID:UNYONTC/19
DESCRIPTION:Title: Recent Progress on Diophantine Equations in Two Variables\nby Minhyon
g Kim as part of Upstate New York Online Number Theory Colloquium\n\n\nAbs
tract\nThe study of rational or integral solutions to polynomial equations
$f(x_1\, x_2\,..\, x_n)=0$ is among the oldest subjects in mathematics. A
fter a brief description of its modern history\, we will review a few of t
he breakthroughs of the last few decades and some recent geometric approac
hes to describing sets of solutions when the number of variables is 2.\n
LOCATION:https://researchseminars.org/talk/UNYONTC/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jason Bell
DTSTART:20210517T160000Z
DTEND:20210517T170000Z
DTSTAMP:20260422T225721Z
UID:UNYONTC/20
DESCRIPTION:Title: Transcendental dynamical degrees of birational maps\nby Jason Bell as
part of Upstate New York Online Number Theory Colloquium\n\n\nAbstract\nT
he degree of a dominant rational map $f:\\mathbb{P}^n\\to \\mathbb{P}^n$ i
s\nthe common degree of its homogeneous components. By considering iterat
es of $f$\,\none can form a sequence ${\\rm deg}(f^n)$\, which is submulti
plicative and hence has\nthe property that there is some $\\lambda\\ge 1$
such that $({\\rm deg}(f^n))^{1/n}\\to\n\\lambda$. The quantity $\\lambda
$ is called the first dynamical degree of $f$. \nWe’ll give an overview
of the significance of the dynamical degree in complex\ndynamics and descr
ibe recent examples in which this dynamical degree is provably\ntranscende
ntal. This is joint work with Jeffrey Diller\, Mattias Jonsson\, and Holl
y\nKrieger.\n
LOCATION:https://researchseminars.org/talk/UNYONTC/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dino Lorenzini
DTSTART:20211108T183000Z
DTEND:20211108T193000Z
DTSTAMP:20260422T225721Z
UID:UNYONTC/21
DESCRIPTION:Title: Torsion and Tamagawa numbers\nby Dino Lorenzini as part of Upstate Ne
w York Online Number Theory Colloquium\n\n\nAbstract\nAssociated with an a
belian variety $A/K$ over a number field $K$ is a finite\nset of integers
greater than $1$ called the local Tamagawa numbers of $A/K$. Assuming\ntha
t the abelian variety $A/K$ has a $K$-rational torsion point of prime orde
r $N$\, we can\nask whether it is possible for none of the local Tamagawa
numbers to be divisible by\n$N$. The ratio $\\textrm{(product of the Tamag
awa numbers)}/ |\\textrm{Torsion in }E(K) |$ appears in the\nconjectural l
eading term of the L-function of $A$ in the Birch and Swinnerton-Dyer\ncon
jecture\, and we are thus interested in understanding whether there are of
ten\ncancellation in this ratio.\n\nWe will present some finiteness result
s on this question in the case of elliptic\ncurves. More precisely\, let $
d > 0$ be an integer\, and assume that there exist\ninfinitely many fields
$K/\\mathbb{Q}$ of degree $d$ with an elliptic curve $E/K$ having a $K$-r
ational\npoint of order $N$. We will show that for certain such pairs $(d\
,N)$\, there are only\nfinitely many fields $K/\\mathbb{Q}$ of degree $d$
such that there exists an elliptic curve $E/K$\nhaving a $K$-rational poin
t of order $N$ and none of the local Tamagawa numbers are\ndivisible by $N
$. The lists of known exceptions are surprisingly small when $d$ is at\nmo
st $7$.\n
LOCATION:https://researchseminars.org/talk/UNYONTC/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Winnie Li
DTSTART:20211011T173000Z
DTEND:20211011T183000Z
DTSTAMP:20260422T225721Z
UID:UNYONTC/22
DESCRIPTION:Title: Pair arithmetical equivalence for quadratic fields\nby Winnie Li as p
art of Upstate New York Online Number Theory Colloquium\n\n\nAbstract\nGiv
en two nonisomorphic number fields K and M\, and two finite \norder Hecke
characters $\\chi$ of K and $\\eta$ of M respectively\, we say \nthat the
pairs $(\\chi\, K)$ and $(\\eta\, M)$ are arithmetically equivalent \nif t
he associated L-functions coincide: $L(s\, \\chi\, K) = L(s\, \\eta\, M)$.
\nWhen the characters are trivial\, this reduces to the question of field
s \nwith the same Dedekind zeta function\, investigated by Gassmann in 192
6\, \nwho found such fields of degree 180\, and by Perlis in 1977 and othe
rs\, \nwho showed that there are no arithmetically equivalent fields of de
gree \nless than 7.\n\nIn this talk we discuss arithmetically equivalent p
airs where the fields \nare quadratic. They give rise to dihedral automorp
hic forms induced from \ncharacters of different quadratic fields. We char
acterize when a given \npair is arithmetically equivalent to another pair\
, explicitly construct \nsuch pairs for infinitely many quadratic extensio
ns with odd class \nnumber\, and classify such characters of order 2.\n\nT
his is a joint work with Zeev Rudnick.\n
LOCATION:https://researchseminars.org/talk/UNYONTC/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yakov Varshavsky
DTSTART:20211026T173000Z
DTEND:20211026T183000Z
DTSTAMP:20260422T225721Z
UID:UNYONTC/23
DESCRIPTION:Title: The Hrushovski-Lang-Weil's estimates\nby Yakov Varshavsky as part of
Upstate New York Online Number Theory Colloquium\n\n\nAbstract\nIn the tal
k I am going to outline an algebro-geometric proof\nof Hrushovski's genera
lization of the Lang-Weil estimates on the\nnumber of points in the inters
ection of a correspondence with the\ngraph of Frobenius. This is a joint w
ork with K. V. Shuddhodan.\n
LOCATION:https://researchseminars.org/talk/UNYONTC/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Matt Papanikolas
DTSTART:20211207T183000Z
DTEND:20211207T193000Z
DTSTAMP:20260422T225721Z
UID:UNYONTC/24
DESCRIPTION:Title: Product formulas for periods of Drinfeld modules\nby Matt Papanikolas
as part of Upstate New York Online Number Theory Colloquium\n\n\nAbstract
\nWe investigate new formulas for periods and quasi-periods of Drinfeld\nm
odules\, similar to the product formula for the fundamental period of the
Carlitz\nmodule obtained through the Anderson-Thakur function. To these en
ds we develop tools\nfor constructing rigid analytic trivializations for D
rinfeld modules as infinite\nproducts of Frobenius twists of matrices\, fr
om which we recover the rigid analytic\ntrivialization given by Pellarin i
n terms of Anderson generating functions. One\nparticular advantage is tha
t the terms of these infinite products can be determined\nfrom only a fini
te amount of initial explicit calculation. Joint with C. Khaochim.\n
LOCATION:https://researchseminars.org/talk/UNYONTC/24/
END:VEVENT
END:VCALENDAR