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BEGIN:VEVENT
SUMMARY:Alain Connes (IHES\, College de France\, Ohio State University)
DTSTART;VALUE=DATE-TIME:20201008T210000Z
DTEND;VALUE=DATE-TIME:20201008T220000Z
DTSTAMP;VALUE=DATE-TIME:20211209T064741Z
UID:JNTS/1
DESCRIPTION:Title: The
semi-local adele class space and Weil positivity\nby Alain Connes (IH
ES\, College de France\, Ohio State University) as part of Columbia CUNY N
YU number theory seminar\n\n\nAbstract\nI will explain the results of two
recent papers in collaboration with Katia Consani: First on a strong inequ
ality showing that for the single archimedean place the Weil local contrib
ution is larger than the trace of the scaling action on the Sonin space. S
econd showing that the products of ratios of local factors are quasi-inner
functions (a notion that extends the usual notion of inner functions) and
this gives the analytic prerequisites to treat the Weil positivity in the
semi-local case using the Hilbert space framework associated to a finite
set of places in my selecta paper of 1998.\n
LOCATION:https://researchseminars.org/talk/JNTS/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alireza Salehi Golsefidy (UCSD)
DTSTART;VALUE=DATE-TIME:20201015T210000Z
DTEND;VALUE=DATE-TIME:20201015T220000Z
DTSTAMP;VALUE=DATE-TIME:20211209T064741Z
UID:JNTS/2
DESCRIPTION:Title: Spe
ctral gap in perfect algebraic groups over prime fields\nby Alireza Sa
lehi Golsefidy (UCSD) as part of Columbia CUNY NYU number theory seminar\n
\n\nAbstract\nSuppose $G$ is a connected algebraic $\\Bbb Q$-group which i
s perfect\; that means $G=[G\,G].$ Let $H$ be the largest semisimple quoti
ent of $G.$ We show that a family of Cayley graphs of $G(F_p)$ is a family
of expander graphs if and only if their quotients as Cayley graphs of $H(
F_p)$ form a family of expanders. This work extends a result of Lindenstra
uss and Varju where they prove a similar statement for the group of specia
l affine transformations. In combination with a result of Breuillard and G
amburd\, one gets new families of finite groups with strong uniform expans
ion. \n\n\\vskip 4pt\nIn the talk after defining the relevant terms\, we d
iscuss the method developed by Bourgain and Gamburd for studying random wa
lks in finite groups. Roughly this method says in the absence of large app
roximate subgroups in a group $G$\, a random walk in $G$ has spectral gap
if it can gain an initial entropy and has a Diophantine property. Next in
the talk it will be explain why in our problem we only need to prove the n
eeded Diophantine property. I will present how certain exponential cancell
ations\, uniform convexity of $\\Cal L^p$-spaces\, and a type of hypercont
ractivity inequality can help us obtain such a Diophantine property. \n\n\
\vskip 4pt\n\nThis is joint work with Srivatsa Srinivas.\n
LOCATION:https://researchseminars.org/talk/JNTS/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Federico Scavia (University of British Columbia)
DTSTART;VALUE=DATE-TIME:20201022T210000Z
DTEND;VALUE=DATE-TIME:20201022T220000Z
DTSTAMP;VALUE=DATE-TIME:20211209T064741Z
UID:JNTS/3
DESCRIPTION:Title: Mot
ivic classes of classifying stacks of algebraic groups\nby Federico Sc
avia (University of British Columbia) as part of Columbia CUNY NYU number
theory seminar\n\n\nAbstract\nThe Grothendieck ring of algebraic stacks wa
s introduced by Ekedahl in \n2009. It may be viewed as a localization of t
he more classical Grothendieck \nring of varieties. If $G$ is a finite gro
up\, then the class\n $\\{BG\\}$ of its \nclassifying stack $BG$ is equal
to 1 in many cases\, but there are examples \nfor which $\\{BG\\}\\neq 1.$
When $G$ is connected\, $\\{BG\\}$ has been computed in many \ncases in
a long series of papers\, and it always turned out that $\\{BG\\}*\\{G\\}
=1.$ \nWe exhibit the first example of a connected group $G$ for which $\\
{BG\\}*\\{G\\}\\neq \n1.$ As a consequence\, we produce an infinite famil
y of non-constant finite \n\\'etale group schemes $A$ such that $\\{BA\\}\
\neq 1.$\n
LOCATION:https://researchseminars.org/talk/JNTS/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:James Newton (Kings College London)
DTSTART;VALUE=DATE-TIME:20201029T210000Z
DTEND;VALUE=DATE-TIME:20201029T220000Z
DTSTAMP;VALUE=DATE-TIME:20211209T064741Z
UID:JNTS/5
DESCRIPTION:Title: Sym
metric power functoriality for modular forms\nby James Newton (Kings C
ollege London) as part of Columbia CUNY NYU number theory seminar\n\n\nAbs
tract\nI will discuss some joint work with Jack Thorne on the symmetric po
wer lifting for modular forms. We prove the existence of all symmetric pow
er lifts for holomorphic Hecke eigenforms. We previously obtained this res
ult with an extra assumption on the ramification of the modular form (for
example\, square-free level)\, but can now remove this.\n
LOCATION:https://researchseminars.org/talk/JNTS/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kannan Soundararajan (Stanford University)
DTSTART;VALUE=DATE-TIME:20201105T220000Z
DTEND;VALUE=DATE-TIME:20201105T230000Z
DTSTAMP;VALUE=DATE-TIME:20211209T064741Z
UID:JNTS/6
DESCRIPTION:Title: Equ
idistribution from the Chinese Remainder Theorem\nby Kannan Soundarara
jan (Stanford University) as part of Columbia CUNY NYU number theory semin
ar\n\n\nAbstract\nSuppose for each prime $p$ we are given a set $A_p$ (pos
sibly\nempty) of residue classes mod $p$. Use these and the Chinese Remain
der\nTheorem to form a set $A_q$ of residue classes mod $q$\, for any inte
ger $q$.\nUnder very mild hypotheses\, we show that for a typical integer
$q$\, the\nresidue classes in $A_q$ will become equidistributed. The proto
typical\nexample (which this generalizes) is Hooley's theorem that the roo
ts of\na polynomial congruence mod $n$ are equidistributed on average over
$n$. I\nwill also discuss generalizations of such results to higher\ndime
nsions\, and when restricted to integers with a given number of\nprime fac
tors. (Joint work with Emmanuel Kowalski.)\n
LOCATION:https://researchseminars.org/talk/JNTS/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ramin Takloo-Bighash (University of Illinois at Chicago)
DTSTART;VALUE=DATE-TIME:20201112T220000Z
DTEND;VALUE=DATE-TIME:20201112T230000Z
DTSTAMP;VALUE=DATE-TIME:20211209T064741Z
UID:JNTS/7
DESCRIPTION:Title: Aut
omorphic forms on GSp(4)\nby Ramin Takloo-Bighash (University of Illin
ois at Chicago) as part of Columbia CUNY NYU number theory seminar\n\n\nAb
stract\nIn this talk I will survey some old and new results on automorphic
forms on the symplectic group of order four\, placing special emphasis on
period integrals and L-functions.\n
LOCATION:https://researchseminars.org/talk/JNTS/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Haruzo Hida (UCLA)
DTSTART;VALUE=DATE-TIME:20201119T220000Z
DTEND;VALUE=DATE-TIME:20201119T230000Z
DTSTAMP;VALUE=DATE-TIME:20211209T064741Z
UID:JNTS/8
DESCRIPTION:Title: Loc
al p-indecomposability of modular p-adic Galois representations\nby Ha
ruzo Hida (UCLA) as part of Columbia CUNY NYU number theory seminar\n\n\nA
bstract\nA conjecture by R. Greenberg asserts that a modular 2-dimensional
$p$-adic Galois representation of a cusp form of weight larger than or eq
ual to 2 is indecomposable over the $p$-inertia group unless it is induced
from an imaginary quadratic field. I start with a survey of the known res
ults and try to reach a brief description of new cases of indecomposabilit
y.\n
LOCATION:https://researchseminars.org/talk/JNTS/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Naser Sardari (Max Planck Institute for Mathematics)
DTSTART;VALUE=DATE-TIME:20201203T220000Z
DTEND;VALUE=DATE-TIME:20201203T230000Z
DTSTAMP;VALUE=DATE-TIME:20211209T064741Z
UID:JNTS/9
DESCRIPTION:Title: Van
ishing Fourier coefficients of Hecke eigenforms\nby Naser Sardari (Max
Planck Institute for Mathematics) as part of Columbia CUNY NYU number the
ory seminar\n\n\nAbstract\nWe prove that\, for fixed level~$(N\,p) = 1$ an
d prime~$p > 2$\, there are only finitely many Hecke eigenforms~$f$ of lev
el~$\\Gamma_1(N)$ and even weight with~$a_p(f) = 0$ (p-th Fourier coeffici
ent) which are not CM. This is joint work with Frank Calegari.\n
LOCATION:https://researchseminars.org/talk/JNTS/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alex Kontorovich (Rutgers University)
DTSTART;VALUE=DATE-TIME:20201210T220000Z
DTEND;VALUE=DATE-TIME:20201210T230000Z
DTSTAMP;VALUE=DATE-TIME:20211209T064741Z
UID:JNTS/10
DESCRIPTION:Title: To
ric Orbits in the Affine Sieve\nby Alex Kontorovich (Rutgers Universit
y) as part of Columbia CUNY NYU number theory seminar\n\n\nAbstract\nWe gi
ve a heuristic model for the failure of "saturation" in instances of the A
ffine Sieve having toral Zariski closure. Based on this model\, we formula
te precise conjectures on several classical problems of arithmetic interes
t\, and test these against empirical data. As a special case\, we give new
conjectures about prime factorizations of Fibonacci and Mersenne numbers.
This is based on joint work with Jeff Lagarias.\n
LOCATION:https://researchseminars.org/talk/JNTS/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tonghai Yang (University of Wisconsin)
DTSTART;VALUE=DATE-TIME:20201217T220000Z
DTEND;VALUE=DATE-TIME:20201217T230000Z
DTSTAMP;VALUE=DATE-TIME:20211209T064741Z
UID:JNTS/11
DESCRIPTION:Title: On
a conjecture of Gross and Zagier on algebraicity\nby Tonghai Yang (Un
iversity of Wisconsin) as part of Columbia CUNY NYU number theory seminar\
n\n\nAbstract\nThe automorphic Green function $G_s(z_1\, z_2)$ for $SL_2(\
\Bbb Z)$\, also called the resolvent kernel function for $\\Gamma$\, plays
an important role in both analytic and algebra number theory\, e.g. in t
he Gross-Zagier formula and Gross-Kohnen-Zagier formula. It is transcenden
tal in nature\, even its CM values are transcendental. It is quite inter
esting to have the following conjectural algebraicity property. \nFor a we
akly holomorphic modular form $f(\\tau)=\\sum\\limits_{m} c_f(m) q^m$ of w
eight $-2j$ ($j \\ge 0$)\, consider the linear combination \n\\vskip -1pt\
n$$\nG_{1+j\, f}(z_1\, z_2) = \\sum_{m >0} c_f(-m) m^j G_{1+j}^m(z_1\, z_2
)\n$$\n\\vskip -1pt\n\\noindent\nwhere $G_s^m(z_1\, z_2)$ is the Hecke cor
respondence of $G_s(z_1\, z_2)$ under the Hecke operator $T_m$ on the firs
t (or second) variable. Gross-Zagier conjectured in 1980s that for any
two CM points $z_i$ of discriminants $d_i$\n$$\n(d_1 d_2)^{j/2} G_{j+1\, f
} (z_1\, z_2) = \\frac{w_{d_1}w_{d_2}}{4}\\cdot \\log|\\alpha|\n$$\nfor so
me algebraic number $\\alpha$\, where $w_i$ is the number of units in $O_
{d_i}$. In this talk\, I will describe some progress on this conjecture. I
f time permits\, I will also explain how one method to attack this conject
ure also produces an analogue of the Gross-Kohnen-Zagier theorem in Kuga v
arieties. \n\nIn the RTG talk\, I will explain regularized theta lifting (
Borcherds product) and their CM value formula.\n
LOCATION:https://researchseminars.org/talk/JNTS/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Emmanuel Breuillard (University of Cambridge)
DTSTART;VALUE=DATE-TIME:20210211T220000Z
DTEND;VALUE=DATE-TIME:20210211T230000Z
DTSTAMP;VALUE=DATE-TIME:20211209T064741Z
UID:JNTS/12
DESCRIPTION:Title: A
subspace theorem for manifolds\nby Emmanuel Breuillard (University of
Cambridge) as part of Columbia CUNY NYU number theory seminar\n\n\nAbstrac
t\nIn the late 90's Kleinbock and Margulis solved a long-standing conjectu
re due to Sprindzuk regarding diophantine approximation on submanifolds o
f $\\Bbb R^n$. Their method used homogeneous dynamics via the so-called n
on-divergence estimates for unipotent flows on the space of lattices. Thi
s new point of view has revolutionized metric diophantine approximation. I
n this talk I will discuss how these ideas can be used to revisit the cele
brated Subspace Theorem of W. Schimidt\, which deals diophantine approxima
tion for linear forms with algebraic coefficients and is a far-reaching ge
neralization of Roth's theorem. Combined with a certain understanding of t
he geometry at the heart of Schmidt's Subspace Theorem\, in particular the
notion of Harder-Narasimhan filtration and related ideas borrowed from Ge
ometric Invariant Theory\, the Kleinbock-Margulis method leads to a metric
version of the Subspace Theorem\, where the linear forms are allowed to d
epend on a parameter. This result encompasses much previous work about dio
phantine exponents of submanifolds. If time permits I will also discuss co
nsequences for diophantine approximation on Lie groups. Joint work with Ni
colas de Saxc\\'e (Paris 13).\n
LOCATION:https://researchseminars.org/talk/JNTS/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:David McKinnon (University of Waterloo)
DTSTART;VALUE=DATE-TIME:20210218T220000Z
DTEND;VALUE=DATE-TIME:20210218T230000Z
DTSTAMP;VALUE=DATE-TIME:20211209T064741Z
UID:JNTS/13
DESCRIPTION:Title: HO
W TO APPROXIMATE RATIONAL POINTS\nby David McKinnon (University of Wat
erloo) as part of Columbia CUNY NYU number theory seminar\n\n\nAbstract\nD
ue to covid-19\, rational points on algebraic varieties are being forced t
o socially distance themselves. In this talk\, we will explore some reason
s why this behavior might persist beyond the end of the pandemic\, relatin
g to the existence of superspreader rational curves.\n
LOCATION:https://researchseminars.org/talk/JNTS/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Benjamin Howard (Boston College)
DTSTART;VALUE=DATE-TIME:20210225T220000Z
DTEND;VALUE=DATE-TIME:20210225T230000Z
DTSTAMP;VALUE=DATE-TIME:20211209T064741Z
UID:JNTS/14
DESCRIPTION:Title: AR
ITHMETIC VOLUMES OF UNITARY SHIMURA VARIETIES\nby Benjamin Howard (Bos
ton College) as part of Columbia CUNY NYU number theory seminar\n\n\nAbstr
act\nThe integral model of a GU$(n-1\,1)$ Shimura variety carries a natura
l metrized line bundle of modular forms. Viewing this metrized line bundl
e as a class in the codimension one arithmetic Chow group\, one can define
its arithmetic volume as an iterated self-intersection. We show that thi
s volume can be expressed in terms of logarithmic derivatives of L-functio
ns at integer points. This is joint work with Jan Bruinier.\n
LOCATION:https://researchseminars.org/talk/JNTS/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alina Cojocaru (University of Illinois at Chicago)
DTSTART;VALUE=DATE-TIME:20210304T220000Z
DTEND;VALUE=DATE-TIME:20210304T230000Z
DTSTAMP;VALUE=DATE-TIME:20211209T064741Z
UID:JNTS/15
DESCRIPTION:Title: FR
OBENIUS TRACES FOR ABELIAN VARIETIES\nby Alina Cojocaru (University of
Illinois at Chicago) as part of Columbia CUNY NYU number theory seminar\n
\n\nAbstract\nIn the 1970s\, S. Lang and H. Trotter proposed a conjectural
asymptotic formula for the number of primes for which the Frobenius trace
of an elliptic curve defined over the rational equals a given integer. We
will discuss generalizations of this conjecture to higher dimensional abe
lian varieties and we will present recent results proven for abelian varie
ties that arise as products of non-isogenous non-CM elliptic curves. This
is joint work with Tian Wang (University of Illinois at Chicago).\n
LOCATION:https://researchseminars.org/talk/JNTS/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Paul Bourgade (NYU)
DTSTART;VALUE=DATE-TIME:20210311T220000Z
DTEND;VALUE=DATE-TIME:20210311T230000Z
DTSTAMP;VALUE=DATE-TIME:20211209T064741Z
UID:JNTS/16
DESCRIPTION:Title: TH
E FYODOROV-HIARY-KEATING CONJECTURE\nby Paul Bourgade (NYU) as part of
Columbia CUNY NYU number theory seminar\n\n\nAbstract\nFyodorov-Hiary-Kea
ting established a series of conjectures concerning large values of the Ri
emann zeta function in a random short interval. After reviewing the origin
s of these predictions through the random matrix analogy\, I will explain
recent work with Louis-Pierre Arguin and Maksym Radziwill\, which proves a
strong form of the upper bound for the maximum.\n
LOCATION:https://researchseminars.org/talk/JNTS/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Levent Alpoge (Columbia University)
DTSTART;VALUE=DATE-TIME:20210318T210000Z
DTEND;VALUE=DATE-TIME:20210318T220000Z
DTSTAMP;VALUE=DATE-TIME:20211209T064741Z
UID:JNTS/17
DESCRIPTION:Title: Ef
fective height bounds for odd-degree totally real points on some curves\nby Levent Alpoge (Columbia University) as part of Columbia CUNY NYU num
ber theory seminar\n\n\nAbstract\nLet $\\mathcal O$ be an order in a total
ly real field $F.$\n Let $K$ be an odd-degree totally real field. Let $S$
be a finite set of places of $K.$ We study $S$-integral $K$-points on inte
gral models $H_\\mathcal O$ of Hilbert modular varieties because not only
do said varieties admit complete curves (thus reducing questions about suc
h curves' $K$-rational points to questions about $S$-integral $K$-points o
n these integral models)\, they also have their $S$-integral $K$-points co
ntrolled by known cases of modularity\, in the following way. First assume
for clarity modularity of all $\\text{\\rm GL}_2$-type abelian varieties
over $K$ --- then all $S$-integral $K$-points on $H_{\\mathcal O}$ \n aris
e from K-isogeny factors of the \n $[F:\\mathbb Q]$-th power of the Jacobi
an of a single Shimura curve with level structure (by Jacquet-Langlands tr
ansfer). By a generalization of an argument of von Kanel\, isogeny estimat
es of Raynaud/Masser-Wustholz and Bost's lower bound on the Faltings heigh
t suffice to then bound the heights of all points in $H_{\\mathcal O}(\\ma
thcal O_{K\,S}).$ \n As for the assumption\, though modularity is of cours
e not known in this generality\, by following Taylor's (sufficiently expli
cit for us) proof of his potential modularity theorem we are able to make
the above unconditional.\n\n\n \nFinally we use the hypergeometric abelian
varieties associated to the arithmetic triangle group $\\Delta(3\,6\,6)$
to give explicit examples of curves to which the above height bounds apply
. Specifically\, we prove that\, for $a\\in \\overline{\\Bbb Q}^\\times$\n
totally real of odd degree (e.g. $a = 1$)\, for all $L/\\Bbb Q(a)$ totally
real of odd degree and $S$ a finite set of places of $L\,$ there is an ef
fectively computable $c = c_{a\,{\\scriptscriptstyle L}\,{\\scriptscriptst
yle S}}\\in \\Bbb Z^+$ such that all $x\,y\\in L$ satisfying $x^6 + 4y^3
= a^2 $ satisfy $h(x) < c.$ Note that this gives infinitely many curves fo
r each of which Faltings' theorem is now effective over infinitely many nu
mber fields.\n
LOCATION:https://researchseminars.org/talk/JNTS/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:William Chen (Columbia University)
DTSTART;VALUE=DATE-TIME:20210325T210000Z
DTEND;VALUE=DATE-TIME:20210325T220000Z
DTSTAMP;VALUE=DATE-TIME:20211209T064741Z
UID:JNTS/18
DESCRIPTION:Title: MA
RKOFF TRIPLES\, NIELSON EQUIVALENCE\, AND NONABELIAN LEVEL STRUCTURES\
nby William Chen (Columbia University) as part of Columbia CUNY NYU number
theory seminar\n\n\nAbstract\nFollowing Bourgain\, Gamburd\, and Sarnak\,
we say that the Markoff equation $x^2 + y^2 + z^2 − 3xyz = 0$ satisfies
strong approximation at a prime p if its integral points surject onto its
$F_p$ points. In 2016\, Bourgain\, Gamburd\, and Sarnak were able to esta
blish strong approximation at all but a sparse (but infinite) set of prime
s\, and conjectured that it holds at all primes. Building on their results
\, in this talk I will explain how to establish strong approximation for a
ll but a finite and effectively computable set of primes\, thus reducing t
he conjecture to a finite computation. Using the connection between the Ma
rkoff surface and the character variety of SL(2) representations of the fu
ndamental group of a punctured torus\, this result becomes a corollary of
a more general divisibility theorem on the cardinalities of Nielsen equiva
lence classes of generating pairs of finite groups\, which in turn follows
from a simple observation regarding the degree of a certain line bundle o
n the moduli stack of elliptic curves with nonabelian level structures. As
time allows we will also describe some applications.\n
LOCATION:https://researchseminars.org/talk/JNTS/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Romyar Sharifi (UCLA)
DTSTART;VALUE=DATE-TIME:20210401T210000Z
DTEND;VALUE=DATE-TIME:20210401T220000Z
DTSTAMP;VALUE=DATE-TIME:20211209T064741Z
UID:JNTS/19
DESCRIPTION:Title: EI
SENSTEIN COCYCLES IN MOTIVIC COHOMOLOGY\nby Romyar Sharifi (UCLA) as p
art of Columbia CUNY NYU number theory seminar\n\n\nAbstract\nI will discu
ss describe joint work with Akshay Venkatesh on the construction of $\\tex
t{\\rm GL}_2(\\mathbb Z)$-cocycles valued in second $K$-groups of the func
tion fields of the squares of the multiplicative group over the rationals
and of a universal elliptic curve over a modular curve. I'll explain how t
hese cocycles respectively specialize to explicit homomorphisms taking mod
ular symbols for congruence subgroups to special elements in second cohomo
logy groups of cyclotomic fields and modular curves\, and I’ll discuss h
ow our methods can be used to prove an Eisenstein property and Hecke-equiv
ariance of the respective maps.\n
LOCATION:https://researchseminars.org/talk/JNTS/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kiran Kedlaya (UC San Diego)
DTSTART;VALUE=DATE-TIME:20210408T210000Z
DTEND;VALUE=DATE-TIME:20210408T220000Z
DTSTAMP;VALUE=DATE-TIME:20211209T064741Z
UID:JNTS/20
DESCRIPTION:Title: BA
NACH BUNDLES\nby Kiran Kedlaya (UC San Diego) as part of Columbia CUNY
NYU number theory seminar\n\n\nAbstract\nTate's theory of rigid analytic
spaces includes a theory of coherent\nsheaves described by Kiehl. We descr
ibe an extension of this\nconstruction to what we call ``Banach bundles" o
n rigid analytic spaces\,\nand more general adic spaces such as perfectoid
spaces\; this builds upon\nprevious work with Ruochuan Liu. As an applica
tion\, we obtain a\nGAGA-style theorem for vector bundles on a product of
Fargues-Fontaine\ncurves.\n
LOCATION:https://researchseminars.org/talk/JNTS/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lillian Pierce (Duke University)
DTSTART;VALUE=DATE-TIME:20210415T210000Z
DTEND;VALUE=DATE-TIME:20210415T220000Z
DTSTAMP;VALUE=DATE-TIME:20211209T064741Z
UID:JNTS/21
DESCRIPTION:Title: ON
BURGESS BOUND AND SUPERORTHOGONALITY\nby Lillian Pierce (Duke Univers
ity) as part of Columbia CUNY NYU number theory seminar\n\n\nAbstract\nThe
Burgess bound is a well-known upper bound for short multiplicative charac
ter sums\, with a curious proof. It implies\, for example\, a subconvexity
bound for Dirichlet L-functions. In this talk we will present two types o
f new work on Burgess bounds. First\, we will describe new Burgess bounds
in multi-dimensional settings. Second\, we will present a new perspective
on Burgess's method of proof. Indeed\, in order to try to improve a method
\, it makes sense to understand the bigger “proofscape” in which a met
hod fits. We will show that it can be regarded as an application of supero
rthogonality. This perspective turns out to unify many topics ranging acro
ss harmonic analysis and number theory. We will survey these connections\,
with a focus on the number-theoretic side.\n
LOCATION:https://researchseminars.org/talk/JNTS/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Edgar Costa (MIT)
DTSTART;VALUE=DATE-TIME:20210422T210000Z
DTEND;VALUE=DATE-TIME:20210422T220000Z
DTSTAMP;VALUE=DATE-TIME:20211209T064741Z
UID:JNTS/22
DESCRIPTION:Title: EF
FECTIVE OBSTRUCTION TO LIFTING ALGEBRAIC CLASSES FROM POSITIVE CHARACTERIS
TIC\nby Edgar Costa (MIT) as part of Columbia CUNY NYU number theory s
eminar\n\n\nAbstract\nWe will present two methods to compute upper bounds
on the number of algebraic cycles that lift from characteristic $p$ to cha
racteristic zero. For an abelian variety\, we show that we can recover the
decomposition of its endomorphism algebra from two well-chosen Frobenius
polynomials. We then focus on how to obtain similar bounds by relying on a
single prime reduction\, and instead consider p-adic thickenings. More pr
ecisely\, we show how to compute a $p$-adic approximation of the obstructi
on map on the algebraic classes of a finite reduction for an abelian varie
ty or a smooth hypersurface. This gives an upper bound on the “middle Pi
card number” of a hypersurface or similarly an upper bound on the endomo
rphism algebra or the Neron-Severi group of an abelian variety.\nThis is j
oint work with: Davide Lombardo\, Nicolas Mascot\, Jeroen Sijsling\, Emre
Sertöz\, and John Voight.\n
LOCATION:https://researchseminars.org/talk/JNTS/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Shou-Wu Zhang (Princeton)
DTSTART;VALUE=DATE-TIME:20210429T210000Z
DTEND;VALUE=DATE-TIME:20210429T220000Z
DTSTAMP;VALUE=DATE-TIME:20211209T064741Z
UID:JNTS/23
DESCRIPTION:Title: EQ
UIDISTRIBUTION OF SMALL POINTS ON QUASI-PROJECTIVE VARIETIES\nby Shou-
Wu Zhang (Princeton) as part of Columbia CUNY NYU number theory seminar\n\
n\nAbstract\nFor quasi-projective varieties over finitely generated fields
\, we develop a theory of adelic line bundles including an equidistributio
n theorem for Galois orbits of small points. In this lecture\, we will exp
lain this theory and its application to arithmetic of abelian varieties\,
dynamical systems\, and their moduli. This is a joint work with Xinyi Yuan
.\n
LOCATION:https://researchseminars.org/talk/JNTS/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Eun Hye Lee (Stony Brook University)
DTSTART;VALUE=DATE-TIME:20211007T213000Z
DTEND;VALUE=DATE-TIME:20211007T223000Z
DTSTAMP;VALUE=DATE-TIME:20211209T064741Z
UID:JNTS/24
DESCRIPTION:Title: Su
bconvexity of Shintani Zeta Functions\nby Eun Hye Lee (Stony Brook Uni
versity) as part of Columbia CUNY NYU number theory seminar\n\n\nAbstract\
nIn this talk\, I will introduce the Shintani zeta function and the proble
m of subconvexity. And then\, I will survey the recent results of myself a
nd R. Hough.\n
LOCATION:https://researchseminars.org/talk/JNTS/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Maksym Radziwill (Caltech)
DTSTART;VALUE=DATE-TIME:20211014T213000Z
DTEND;VALUE=DATE-TIME:20211014T223000Z
DTSTAMP;VALUE=DATE-TIME:20211209T064741Z
UID:JNTS/25
DESCRIPTION:Title: Bi
as in cubic Gauss sums\nby Maksym Radziwill (Caltech) as part of Colum
bia CUNY NYU number theory seminar\n\n\nAbstract\nI will discuss recent wo
rk with Alex Dunn. Conditionally on the Generalized Riemann Hypothesis we
establish a conjecture of S. Patterson from 1978 concerning the existence
of a bias in cubic Gauss sums. This explains a well-known numerical bias f
irst observed by Kummer in 1846. The proof relies on the use of metaplecti
c forms for the cubic cover of $GL_2$ and on a new ”dispersion” estima
te for cubic Gauss sums. Along the way we show that the cubic large sieve
of Heath-Brown is sharp\, contrary to widely held expectations. I will exp
lain the tools alluded to above\, the rationale for the tools and the main
moments of the proof.\n
LOCATION:https://researchseminars.org/talk/JNTS/25/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Karol Koziol (University of Michigan)
DTSTART;VALUE=DATE-TIME:20211021T213000Z
DTEND;VALUE=DATE-TIME:20211021T223000Z
DTSTAMP;VALUE=DATE-TIME:20211209T064741Z
UID:JNTS/26
DESCRIPTION:Title: Po
incare duality for modular representations of p-adic groups and Hecke alge
bras\nby Karol Koziol (University of Michigan) as part of Columbia CUN
Y NYU number theory seminar\n\n\nAbstract\nThe mod-$p$ representations the
ory of $p$-adic reductive groups (such as $\\textrm{GL}_2(\\mathbb{Q}_p)$)
is one of the foundations of the rapidly developing mod-$p$ local Langlan
ds program. However\, many constructions from the case of complex coeffici
ents are quite poorly behaved in the mod-$p$ setting\, and it becomes nece
ssary to use derived functors. In this talk\, I'll describe how this situa
tion looks for the functor of smooth duality on mod-$p$ representations\,
and discuss the construction of a Poincare duality spectral sequence relat
ing Kohlhaase's functors of higher smooth duals with modules over the (pro
-$p$) Iwahori-Hecke algebra.\n
LOCATION:https://researchseminars.org/talk/JNTS/26/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Wei Zhang (MIT)
DTSTART;VALUE=DATE-TIME:20211028T213000Z
DTEND;VALUE=DATE-TIME:20211028T223000Z
DTSTAMP;VALUE=DATE-TIME:20211209T064741Z
UID:JNTS/27
DESCRIPTION:Title: p-
Adic heights of the arithmetic diagonal cycles\nby Wei Zhang (MIT) as
part of Columbia CUNY NYU number theory seminar\n\n\nAbstract\nThis is a w
ork in progress joint with Daniel Disegni. We formulate a p-adic analogue
of the Arithmetic Gan–Gross–Prasad conjecture for unitary groups\, rel
ating the p-adic height pairing of the arithmetic diagonal cycles to the f
irst central derivative (along the cyclotomic direction) of a p-adic Ranki
n–Selberg L-function associated to cuspidal automorphic representations.
In the good ordinary case we are able to prove the conjecture\, at least
when the ramifications are mild at inert primes. We deduce some applicatio
ns to the p-adic version of the Bloch-Kato conjecture.\n
LOCATION:https://researchseminars.org/talk/JNTS/27/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Michael Magee (Durham University)
DTSTART;VALUE=DATE-TIME:20211104T213000Z
DTEND;VALUE=DATE-TIME:20211104T223000Z
DTSTAMP;VALUE=DATE-TIME:20211209T064741Z
UID:JNTS/28
DESCRIPTION:Title: Th
e maximal spectral gap of a hyperbolic surface\nby Michael Magee (Durh
am University) as part of Columbia CUNY NYU number theory seminar\n\n\nAbs
tract\nA hyperbolic surface is a surface with metric of constant curvature
-1. The spectral gap between the first two eigenvalues of the Laplacian o
n a closed hyperbolic surface contains a good deal of information about th
e surface\, including its connectivity\, dynamical properties of its geode
sic flow\, and error terms in geodesic counting problems. For arithmetic h
yperbolic surfaces the spectral gap is also the subject of one of the bigg
est open problems in automorphic forms: Selberg’s eigenvalue conjecture.
\n\nIt was an open problem from the 1970s whether there exist a sequence o
f closed hyperbolic surfaces with genera tending to infinity and spectral
gap tending to 1/4. (The value 1/4 here is the asymptotically optimal one.
) Recently we proved that this is indeed possible. I’ll discuss the very
interesting background of this problem in detail as well as some ideas of
the proof.\n\nThis is joint work with Will Hide.\n
LOCATION:https://researchseminars.org/talk/JNTS/28/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Myrto Mavraki (Harvard)
DTSTART;VALUE=DATE-TIME:20211111T223000Z
DTEND;VALUE=DATE-TIME:20211111T233000Z
DTSTAMP;VALUE=DATE-TIME:20211209T064741Z
UID:JNTS/29
DESCRIPTION:Title: Un
iformity in the dynamical Bogomolov conjecture\nby Myrto Mavraki (Harv
ard) as part of Columbia CUNY NYU number theory seminar\n\n\nAbstract\nZha
ng has proposed dynamical versions of the classical Manin- Mumford and Bog
omolov conjectures. A special case of these conjectures\, for ‘split’
maps\, has recently been established by Nguyen\, Ghioca and Ye. In particu
lar\, they show that two rational maps have at most finitely many common p
reperiodic points\, unless they are ‘related’. In this talk we discuss
uniform versions of their results across 1-parameter families of certain
split maps and curves. This is joint work with Harry Schmidt.\n
LOCATION:https://researchseminars.org/talk/JNTS/29/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Melanie Wood (Harvard)
DTSTART;VALUE=DATE-TIME:20211118T223000Z
DTEND;VALUE=DATE-TIME:20211118T233000Z
DTSTAMP;VALUE=DATE-TIME:20211209T064741Z
UID:JNTS/30
DESCRIPTION:Title: Th
e average size of 3-torsion in class groups of 2-extensions\nby Melani
e Wood (Harvard) as part of Columbia CUNY NYU number theory seminar\n\n\nA
bstract\nThe $p$-torsion in the class group of a number field $K$ is conje
ctured to\nbe small: of size at most $|\\text{Disc}\\\,K |^\\epsilon$\, an
d to have constant\naverage size in families with a given Galois closure g
roup (when $p$\ndoesn't divide the order of the group). In general\, the
best upper\nbound we have is $|\\text{Disc}\\\, K|^{1/2+\\epsilon}$\, and
previously the only two\ncases known with constant average were for 3-tors
ion in quadratic\nfields (Davenport and Heilbronn\, 1971) and 2-torsion in
non-Galois\ncubic fields (Bhargava\, 2005). We prove that the 3-torsion
is\nconstant on average for fields with Galois closure group any 2-group\n
with a transposition\, including\, e.g. quartic $D_4$ fields. We will\ndi
scuss the main inputs into the proof with an eye towards giving an\nintrod
uction to the tools in the area. This is joint work with Robert\nLemke Ol
iver and Jiuya Wang.\n
LOCATION:https://researchseminars.org/talk/JNTS/30/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Elena Fuchs & Kristin Lauter (UC Davis & Facebook AI Research)
DTSTART;VALUE=DATE-TIME:20211202T223000Z
DTEND;VALUE=DATE-TIME:20211202T233000Z
DTSTAMP;VALUE=DATE-TIME:20211209T064741Z
UID:JNTS/31
DESCRIPTION:Title: Cr
yptographic hash functions from Markoff triples\nby Elena Fuchs & Kris
tin Lauter (UC Davis & Facebook AI Research) as part of Columbia CUNY NYU
number theory seminar\n\n\nAbstract\nIn this talk\, we discuss how mod-$p$
Markoff graphs can be used to construct cryptographic hash functions. We
present potential path finding algorithms in these graphs\, which will als
o lead to questions about lifts of mod $p$ solutions to the Markoff equati
on will come up as well. This is joint work with M. Litman and A. Tran\, a
s well as with E. Bellah and L. Ye.\n
LOCATION:https://researchseminars.org/talk/JNTS/31/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Levent Alpoge (Harvard University)
DTSTART;VALUE=DATE-TIME:20211209T223000Z
DTEND;VALUE=DATE-TIME:20211209T233000Z
DTSTAMP;VALUE=DATE-TIME:20211209T064741Z
UID:JNTS/32
DESCRIPTION:Title: A
"height-free" effective isogeny estimate for GL(2) abelian varieties\
nby Levent Alpoge (Harvard University) as part of Columbia CUNY NYU number
theory seminar\n\nInteractive livestream: https://columbiauniversity.zoom
.us/j/96523128411\nPassword hint: the order of the group PGL(2\, $F_5$) or
$S_5$\n\nAbstract\nWe prove a ”height-free” effective isogeny estimat
e for abelian varieties of GL2-type.\nMore precisely\, let g ∈ Z\n+\, K
a number field\, S a finite set of places of K\, and\nA\, B/K g-dimensiona
l abelian varieties with good reduction outside S which are\nK-isogenous a
nd of GL2-type over Q. We show that there is a K-isogeny A → B\nof degre
e effectively bounded in terms of g\, K\, and S only.\nWe deduce an effect
ive open image theorem for these abelian varieties\, as well\nas an effect
ive upper bound on the number of S-integral K-points on a Hilbert\nmodular
variety\n
LOCATION:https://researchseminars.org/talk/JNTS/32/
URL:https://columbiauniversity.zoom.us/j/96523128411
END:VEVENT
END:VCALENDAR