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BEGIN:VEVENT
SUMMARY:Alain Connes (IHES\, College de France\, Ohio State University)
DTSTART:20201008T210000Z
DTEND:20201008T220000Z
DTSTAMP:20260404T094554Z
UID:JNTS/1
DESCRIPTION:Title: The semi-local adele class space and Weil positivity\nby Alain Con
nes (IHES\, College de France\, Ohio State University) as part of Columbia
CUNY NYU number theory seminar\n\n\nAbstract\nI will explain the results
of two recent papers in collaboration with Katia Consani: First on a stron
g inequality showing that for the single archimedean place the Weil local
contribution is larger than the trace of the scaling action on the Sonin s
pace. Second showing that the products of ratios of local factors are quas
i-inner functions (a notion that extends the usual notion of inner functio
ns) 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://stable.researchseminars.org/talk/JNTS/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alireza Salehi Golsefidy (UCSD)
DTSTART:20201015T210000Z
DTEND:20201015T220000Z
DTSTAMP:20260404T094554Z
UID:JNTS/2
DESCRIPTION:Title: Spectral gap in perfect algebraic groups over prime fields\nby Ali
reza Salehi Golsefidy (UCSD) as part of Columbia CUNY NYU number theory se
minar\n\n\nAbstract\nSuppose $G$ is a connected algebraic $\\Bbb Q$-group
which is perfect\; that means $G=[G\,G].$ Let $H$ be the largest semisimpl
e quotient 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 Lin
denstrauss and Varju where they prove a similar statement for the group of
special affine transformations. In combination with a result of Breuillar
d and Gamburd\, one gets new families of finite groups with strong uniform
expansion. \n\n\\vskip 4pt\nIn the talk after defining the relevant terms
\, we discuss the method developed by Bourgain and Gamburd for studying ra
ndom walks in finite groups. Roughly this method says in the absence of la
rge approximate subgroups in a group $G$\, a random walk in $G$ has spectr
al gap if it can gain an initial entropy and has a Diophantine property. N
ext in the talk it will be explain why in our problem we only need to prov
e the needed Diophantine property. I will present how certain exponential
cancellations\, uniform convexity of $\\Cal L^p$-spaces\, and a type of hy
percontractivity inequality can help us obtain such a Diophantine property
. \n\n\\vskip 4pt\n\nThis is joint work with Srivatsa Srinivas.\n
LOCATION:https://stable.researchseminars.org/talk/JNTS/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Federico Scavia (University of British Columbia)
DTSTART:20201022T210000Z
DTEND:20201022T220000Z
DTSTAMP:20260404T094554Z
UID:JNTS/3
DESCRIPTION:Title: Motivic classes of classifying stacks of algebraic groups\nby Fede
rico Scavia (University of British Columbia) as part of Columbia CUNY NYU
number theory seminar\n\n\nAbstract\nThe Grothendieck ring of algebraic st
acks was introduced by Ekedahl in \n2009. It may be viewed as a localizati
on of the more classical Grothendieck \nring of varieties. If $G$ is a fin
ite group\, 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 \nc
ases 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 wh
ich $\\{BG\\}*\\{G\\}\\neq \n1.$ As a consequence\, we produce an infinit
e family of non-constant finite \n\\'etale group schemes $A$ such that $\\
{BA\\}\\neq 1.$\n
LOCATION:https://stable.researchseminars.org/talk/JNTS/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:James Newton (Kings College London)
DTSTART:20201029T210000Z
DTEND:20201029T220000Z
DTSTAMP:20260404T094554Z
UID:JNTS/5
DESCRIPTION:Title: Symmetric power functoriality for modular forms\nby James Newton (
Kings College London) as part of Columbia CUNY NYU number theory seminar\n
\n\nAbstract\nI will discuss some joint work with Jack Thorne on the symme
tric power lifting for modular forms. We prove the existence of all symmet
ric power lifts for holomorphic Hecke eigenforms. We previously obtained t
his result with an extra assumption on the ramification of the modular for
m (for example\, square-free level)\, but can now remove this.\n
LOCATION:https://stable.researchseminars.org/talk/JNTS/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kannan Soundararajan (Stanford University)
DTSTART:20201105T220000Z
DTEND:20201105T230000Z
DTSTAMP:20260404T094554Z
UID:JNTS/6
DESCRIPTION:Title: Equidistribution from the Chinese Remainder Theorem\nby Kannan Sou
ndararajan (Stanford University) as part of Columbia CUNY NYU number theor
y seminar\n\n\nAbstract\nSuppose for each prime $p$ we are given a set $A_
p$ (possibly\nempty) of residue classes mod $p$. Use these and the Chinese
Remainder\nTheorem to form a set $A_q$ of residue classes mod $q$\, for a
ny integer $q$.\nUnder very mild hypotheses\, we show that for a typical i
nteger $q$\, the\nresidue classes in $A_q$ will become equidistributed. Th
e prototypical\nexample (which this generalizes) is Hooley's theorem that
the roots of\na polynomial congruence mod $n$ are equidistributed on avera
ge over $n$. I\nwill also discuss generalizations of such results to highe
r\ndimensions\, and when restricted to integers with a given number of\npr
ime factors. (Joint work with Emmanuel Kowalski.)\n
LOCATION:https://stable.researchseminars.org/talk/JNTS/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ramin Takloo-Bighash (University of Illinois at Chicago)
DTSTART:20201112T220000Z
DTEND:20201112T230000Z
DTSTAMP:20260404T094554Z
UID:JNTS/7
DESCRIPTION:Title: Automorphic forms on GSp(4)\nby Ramin Takloo-Bighash (University o
f Illinois at Chicago) as part of Columbia CUNY NYU number theory seminar\
n\n\nAbstract\nIn this talk I will survey some old and new results on auto
morphic forms on the symplectic group of order four\, placing special emph
asis on period integrals and L-functions.\n
LOCATION:https://stable.researchseminars.org/talk/JNTS/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Haruzo Hida (UCLA)
DTSTART:20201119T220000Z
DTEND:20201119T230000Z
DTSTAMP:20260404T094554Z
UID:JNTS/8
DESCRIPTION:Title: Local p-indecomposability of modular p-adic Galois representations
\nby Haruzo Hida (UCLA) as part of Columbia CUNY NYU number theory seminar
\n\n\nAbstract\nA conjecture by R. Greenberg asserts that a modular 2-dime
nsional $p$-adic Galois representation of a cusp form of weight larger tha
n or equal 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 kn
own results and try to reach a brief description of new cases of indecompo
sability.\n
LOCATION:https://stable.researchseminars.org/talk/JNTS/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Naser Sardari (Max Planck Institute for Mathematics)
DTSTART:20201203T220000Z
DTEND:20201203T230000Z
DTSTAMP:20260404T094554Z
UID:JNTS/9
DESCRIPTION:Title: Vanishing Fourier coefficients of Hecke eigenforms\nby Naser Sarda
ri (Max Planck Institute for Mathematics) as part of Columbia CUNY NYU num
ber theory seminar\n\n\nAbstract\nWe prove that\, for fixed level~$(N\,p)
= 1$ and prime~$p > 2$\, there are only finitely many Hecke eigenforms~$f$
of level~$\\Gamma_1(N)$ and even weight with~$a_p(f) = 0$ (p-th Fourier c
oefficient) which are not CM. This is joint work with Frank Calegari.\n
LOCATION:https://stable.researchseminars.org/talk/JNTS/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alex Kontorovich (Rutgers University)
DTSTART:20201210T220000Z
DTEND:20201210T230000Z
DTSTAMP:20260404T094554Z
UID:JNTS/10
DESCRIPTION:Title: Toric Orbits in the Affine Sieve\nby Alex Kontorovich (Rutgers Un
iversity) as part of Columbia CUNY NYU number theory seminar\n\n\nAbstract
\nWe give a heuristic model for the failure of "saturation" in instances o
f the Affine Sieve having toral Zariski closure. Based on this model\, we
formulate precise conjectures on several classical problems of arithmetic
interest\, and test these against empirical data. As a special case\, we g
ive new conjectures about prime factorizations of Fibonacci and Mersenne n
umbers. This is based on joint work with Jeff Lagarias.\n
LOCATION:https://stable.researchseminars.org/talk/JNTS/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tonghai Yang (University of Wisconsin)
DTSTART:20201217T220000Z
DTEND:20201217T230000Z
DTSTAMP:20260404T094554Z
UID:JNTS/11
DESCRIPTION:Title: On a conjecture of Gross and Zagier on algebraicity\nby Tonghai Y
ang (University of Wisconsin) as part of Columbia CUNY NYU number theory s
eminar\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 the Gross-Zagier formula and Gross-Kohnen-Zagier formula. It is tran
scendental in nature\, even its CM values are transcendental. It is quit
e interesting to have the following conjectural algebraicity property. \nF
or a weakly holomorphic modular form $f(\\tau)=\\sum\\limits_{m} c_f(m) q^
m$ of weight $-2j$ ($j \\ge 0$)\, consider the linear combination \n\\vski
p -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 He
cke correspondence of $G_s(z_1\, z_2)$ under the Hecke operator $T_m$ on t
he first (or second) variable. Gross-Zagier conjectured in 1980s that f
or 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 some 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 conjec
ture. If time permits\, I will also explain how one method to attack this
conjecture also produces an analogue of the Gross-Kohnen-Zagier theorem in
Kuga varieties. \n\nIn the RTG talk\, I will explain regularized theta li
fting (Borcherds product) and their CM value formula.\n
LOCATION:https://stable.researchseminars.org/talk/JNTS/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Emmanuel Breuillard (University of Cambridge)
DTSTART:20210211T220000Z
DTEND:20210211T230000Z
DTSTAMP:20260404T094554Z
UID:JNTS/12
DESCRIPTION:Title: A subspace theorem for manifolds\nby Emmanuel Breuillard (Univers
ity of Cambridge) as part of Columbia CUNY NYU number theory seminar\n\n\n
Abstract\nIn the late 90's Kleinbock and Margulis solved a long-standing c
onjecture due to Sprindzuk regarding diophantine approximation on submani
folds of $\\Bbb R^n$. Their method used homogeneous dynamics via the so-c
alled non-divergence estimates for unipotent flows on the space of lattic
es. This new point of view has revolutionized metric diophantine approxima
tion. In this talk I will discuss how these ideas can be used to revisit t
he celebrated Subspace Theorem of W. Schimidt\, which deals diophantine ap
proximation for linear forms with algebraic coefficients and is a far-reac
hing generalization of Roth's theorem. Combined with a certain understandi
ng of the geometry at the heart of Schmidt's Subspace Theorem\, in particu
lar the notion of Harder-Narasimhan filtration and related ideas borrowed
from Geometric Invariant Theory\, the Kleinbock-Margulis method leads to a
metric version of the Subspace Theorem\, where the linear forms are allow
ed to depend on a parameter. This result encompasses much previous work ab
out diophantine exponents of submanifolds. If time permits I will also dis
cuss consequences for diophantine approximation on Lie groups. Joint work
with Nicolas de Saxc\\'e (Paris 13).\n
LOCATION:https://stable.researchseminars.org/talk/JNTS/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:David McKinnon (University of Waterloo)
DTSTART:20210218T220000Z
DTEND:20210218T230000Z
DTSTAMP:20260404T094554Z
UID:JNTS/13
DESCRIPTION:Title: HOW TO APPROXIMATE RATIONAL POINTS\nby David McKinnon (University
of Waterloo) as part of Columbia CUNY NYU number theory seminar\n\n\nAbst
ract\nDue to covid-19\, rational points on algebraic varieties are being f
orced to socially distance themselves. In this talk\, we will explore some
reasons why this behavior might persist beyond the end of the pandemic\,
relating to the existence of superspreader rational curves.\n
LOCATION:https://stable.researchseminars.org/talk/JNTS/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Benjamin Howard (Boston College)
DTSTART:20210225T220000Z
DTEND:20210225T230000Z
DTSTAMP:20260404T094554Z
UID:JNTS/14
DESCRIPTION:Title: ARITHMETIC VOLUMES OF UNITARY SHIMURA VARIETIES\nby Benjamin Howa
rd (Boston College) as part of Columbia CUNY NYU number theory seminar\n\n
\nAbstract\nThe integral model of a GU$(n-1\,1)$ Shimura variety carries a
natural metrized line bundle of modular forms. Viewing this metrized lin
e bundle as a class in the codimension one arithmetic Chow group\, one can
define its arithmetic volume as an iterated self-intersection. We show t
hat this volume can be expressed in terms of logarithmic derivatives of L-
functions at integer points. This is joint work with Jan Bruinier.\n
LOCATION:https://stable.researchseminars.org/talk/JNTS/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alina Cojocaru (University of Illinois at Chicago)
DTSTART:20210304T220000Z
DTEND:20210304T230000Z
DTSTAMP:20260404T094554Z
UID:JNTS/15
DESCRIPTION:Title: FROBENIUS TRACES FOR ABELIAN VARIETIES\nby Alina Cojocaru (Univer
sity of Illinois at Chicago) as part of Columbia CUNY NYU number theory se
minar\n\n\nAbstract\nIn the 1970s\, S. Lang and H. Trotter proposed a conj
ectural asymptotic formula for the number of primes for which the Frobeniu
s trace of an elliptic curve defined over the rational equals a given inte
ger. We will discuss generalizations of this conjecture to higher dimensio
nal abelian varieties and we will present recent results proven for abelia
n varieties 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://stable.researchseminars.org/talk/JNTS/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Paul Bourgade (NYU)
DTSTART:20210311T220000Z
DTEND:20210311T230000Z
DTSTAMP:20260404T094554Z
UID:JNTS/16
DESCRIPTION:Title: THE FYODOROV-HIARY-KEATING CONJECTURE\nby Paul Bourgade (NYU) as
part of Columbia CUNY NYU number theory seminar\n\n\nAbstract\nFyodorov-Hi
ary-Keating established a series of conjectures concerning large values of
the Riemann zeta function in a random short interval. After reviewing the
origins of these predictions through the random matrix analogy\, I will e
xplain recent work with Louis-Pierre Arguin and Maksym Radziwill\, which p
roves a strong form of the upper bound for the maximum.\n
LOCATION:https://stable.researchseminars.org/talk/JNTS/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Levent Alpoge (Columbia University)
DTSTART:20210318T210000Z
DTEND:20210318T220000Z
DTSTAMP:20260404T094554Z
UID:JNTS/17
DESCRIPTION:Title: Effective height bounds for odd-degree totally real points on some cu
rves\nby Levent Alpoge (Columbia University) as part of Columbia CUNY
NYU number theory seminar\n\n\nAbstract\nLet $\\mathcal O$ be an order in
a totally real field $F.$\n Let $K$ be an odd-degree totally real field. L
et $S$ be a finite set of places of $K.$ We study $S$-integral $K$-points
on integral models $H_\\mathcal O$ of Hilbert modular varieties because no
t only do said varieties admit complete curves (thus reducing questions ab
out such curves' $K$-rational points to questions about $S$-integral $K$-p
oints on these integral models)\, they also have their $S$-integral $K$-po
ints controlled by known cases of modularity\, in the following way. First
assume for clarity modularity of all $\\text{\\rm GL}_2$-type abelian var
ieties over $K$ --- then all $S$-integral $K$-points on $H_{\\mathcal O}$
\n arise from K-isogeny factors of the \n $[F:\\mathbb Q]$-th power of the
Jacobian of a single Shimura curve with level structure (by Jacquet-Langl
ands transfer). By a generalization of an argument of von Kanel\, isogeny
estimates of Raynaud/Masser-Wustholz and Bost's lower bound on the Falting
s height suffice to then bound the heights of all points in $H_{\\mathcal
O}(\\mathcal O_{K\,S}).$ \n As for the assumption\, though modularity is o
f course not known in this generality\, by following Taylor's (sufficientl
y explicit for us) proof of his potential modularity theorem we are able t
o 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 bound
s apply. Specifically\, we prove that\, for $a\\in \\overline{\\Bbb Q}^\\t
imes$\ntotally 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 i
s an effectively computable $c = c_{a\,{\\scriptscriptstyle L}\,{\\scripts
criptstyle S}}\\in \\Bbb Z^+$ such that all $x\,y\\in L$ satisfying $x^6
+ 4y^3 = a^2 $ satisfy $h(x) < c.$ Note that this gives infinitely many cu
rves for each of which Faltings' theorem is now effective over infinitely
many number fields.\n
LOCATION:https://stable.researchseminars.org/talk/JNTS/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:William Chen (Columbia University)
DTSTART:20210325T210000Z
DTEND:20210325T220000Z
DTSTAMP:20260404T094554Z
UID:JNTS/18
DESCRIPTION:Title: MARKOFF TRIPLES\, NIELSON EQUIVALENCE\, AND NONABELIAN LEVEL STRUCTUR
ES\nby William Chen (Columbia University) as part of Columbia CUNY NYU
number theory seminar\n\n\nAbstract\nFollowing Bourgain\, Gamburd\, and S
arnak\, we say that the Markoff equation $x^2 + y^2 + z^2 − 3xyz = 0$ sa
tisfies strong approximation at a prime p if its integral points surject o
nto its $F_p$ points. In 2016\, Bourgain\, Gamburd\, and Sarnak were able
to establish strong approximation at all but a sparse (but infinite) set o
f primes\, and conjectured that it holds at all primes. Building on their
results\, in this talk I will explain how to establish strong approximatio
n for all but a finite and effectively computable set of primes\, thus red
ucing the conjecture to a finite computation. Using the connection between
the Markoff surface and the character variety of SL(2) representations of
the fundamental group of a punctured torus\, this result becomes a coroll
ary of a more general divisibility theorem on the cardinalities of Nielsen
equivalence classes of generating pairs of finite groups\, which in turn
follows from a simple observation regarding the degree of a certain line b
undle on the moduli stack of elliptic curves with nonabelian level structu
res. As time allows we will also describe some applications.\n
LOCATION:https://stable.researchseminars.org/talk/JNTS/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Romyar Sharifi (UCLA)
DTSTART:20210401T210000Z
DTEND:20210401T220000Z
DTSTAMP:20260404T094554Z
UID:JNTS/19
DESCRIPTION:Title: EISENSTEIN COCYCLES IN MOTIVIC COHOMOLOGY\nby Romyar Sharifi (UCL
A) as part of Columbia CUNY NYU number theory seminar\n\n\nAbstract\nI wil
l discuss describe joint work with Akshay Venkatesh on the construction of
$\\text{\\rm GL}_2(\\mathbb Z)$-cocycles valued in second $K$-groups of t
he function fields of the squares of the multiplicative group over the rat
ionals and of a universal elliptic curve over a modular curve. I'll explai
n how these cocycles respectively specialize to explicit homomorphisms tak
ing modular symbols for congruence subgroups to special elements in second
cohomology groups of cyclotomic fields and modular curves\, and I’ll di
scuss how our methods can be used to prove an Eisenstein property and Heck
e-equivariance of the respective maps.\n
LOCATION:https://stable.researchseminars.org/talk/JNTS/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kiran Kedlaya (UC San Diego)
DTSTART:20210408T210000Z
DTEND:20210408T220000Z
DTSTAMP:20260404T094554Z
UID:JNTS/20
DESCRIPTION:Title: BANACH BUNDLES\nby Kiran Kedlaya (UC San Diego) as part of Columb
ia CUNY NYU number theory seminar\n\n\nAbstract\nTate's theory of rigid an
alytic spaces includes a theory of coherent\nsheaves described by Kiehl. W
e describe an extension of this\nconstruction to what we call ``Banach bun
dles" on rigid analytic spaces\,\nand more general adic spaces such as per
fectoid spaces\; this builds upon\nprevious work with Ruochuan Liu. As an
application\, we obtain a\nGAGA-style theorem for vector bundles on a prod
uct of Fargues-Fontaine\ncurves.\n
LOCATION:https://stable.researchseminars.org/talk/JNTS/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lillian Pierce (Duke University)
DTSTART:20210415T210000Z
DTEND:20210415T220000Z
DTSTAMP:20260404T094554Z
UID:JNTS/21
DESCRIPTION:Title: ON BURGESS BOUND AND SUPERORTHOGONALITY\nby Lillian Pierce (Duke
University) as part of Columbia CUNY NYU number theory seminar\n\n\nAbstra
ct\nThe Burgess bound is a well-known upper bound for short multiplicative
character sums\, with a curious proof. It implies\, for example\, a subco
nvexity bound for Dirichlet L-functions. In this talk we will present two
types of new work on Burgess bounds. First\, we will describe new Burgess
bounds in multi-dimensional settings. Second\, we will present a new persp
ective on Burgess's method of proof. Indeed\, in order to try to improve a
method\, it makes sense to understand the bigger “proofscape” in whic
h a method fits. We will show that it can be regarded as an application of
superorthogonality. This perspective turns out to unify many topics rangi
ng across harmonic analysis and number theory. We will survey these connec
tions\, with a focus on the number-theoretic side.\n
LOCATION:https://stable.researchseminars.org/talk/JNTS/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Edgar Costa (MIT)
DTSTART:20210422T210000Z
DTEND:20210422T220000Z
DTSTAMP:20260404T094554Z
UID:JNTS/22
DESCRIPTION:Title: EFFECTIVE OBSTRUCTION TO LIFTING ALGEBRAIC CLASSES FROM POSITIVE CHAR
ACTERISTIC\nby Edgar Costa (MIT) as part of Columbia CUNY NYU number t
heory seminar\n\n\nAbstract\nWe will present two methods to compute upper
bounds on the number of algebraic cycles that lift from characteristic $p$
to characteristic zero. For an abelian variety\, we show that we can reco
ver the decomposition of its endomorphism algebra from two well-chosen Fro
benius polynomials. We then focus on how to obtain similar bounds by relyi
ng on a single prime reduction\, and instead consider p-adic thickenings.
More precisely\, we show how to compute a $p$-adic approximation of the ob
struction map on the algebraic classes of a finite reduction for an abelia
n variety or a smooth hypersurface. This gives an upper bound on the “mi
ddle Picard number” of a hypersurface or similarly an upper bound on the
endomorphism algebra or the Neron-Severi group of an abelian variety.\nTh
is is joint work with: Davide Lombardo\, Nicolas Mascot\, Jeroen Sijsling\
, Emre Sertöz\, and John Voight.\n
LOCATION:https://stable.researchseminars.org/talk/JNTS/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Shou-Wu Zhang (Princeton)
DTSTART:20210429T210000Z
DTEND:20210429T220000Z
DTSTAMP:20260404T094554Z
UID:JNTS/23
DESCRIPTION:Title: EQUIDISTRIBUTION OF SMALL POINTS ON QUASI-PROJECTIVE VARIETIES\nb
y Shou-Wu Zhang (Princeton) as part of Columbia CUNY NYU number theory sem
inar\n\n\nAbstract\nFor quasi-projective varieties over finitely generated
fields\, we develop a theory of adelic line bundles including an equidist
ribution theorem for Galois orbits of small points. In this lecture\, we w
ill explain this theory and its application to arithmetic of abelian varie
ties\, dynamical systems\, and their moduli. This is a joint work with Xin
yi Yuan.\n
LOCATION:https://stable.researchseminars.org/talk/JNTS/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Eun Hye Lee (Stony Brook University)
DTSTART:20211007T213000Z
DTEND:20211007T223000Z
DTSTAMP:20260404T094554Z
UID:JNTS/24
DESCRIPTION:Title: Subconvexity of Shintani Zeta Functions\nby Eun Hye Lee (Stony Br
ook University) as part of Columbia CUNY NYU number theory seminar\n\n\nAb
stract\nIn this talk\, I will introduce the Shintani zeta function and the
problem of subconvexity. And then\, I will survey the recent results of m
yself and R. Hough.\n
LOCATION:https://stable.researchseminars.org/talk/JNTS/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Maksym Radziwill (Caltech)
DTSTART:20211014T213000Z
DTEND:20211014T223000Z
DTSTAMP:20260404T094554Z
UID:JNTS/25
DESCRIPTION:Title: Bias in cubic Gauss sums\nby Maksym Radziwill (Caltech) as part o
f Columbia CUNY NYU number theory seminar\n\n\nAbstract\nI will discuss re
cent work with Alex Dunn. Conditionally on the Generalized Riemann Hypothe
sis we establish a conjecture of S. Patterson from 1978 concerning the exi
stence of a bias in cubic Gauss sums. This explains a well-known numerical
bias first observed by Kummer in 1846. The proof relies on the use of met
aplectic forms for the cubic cover of $GL_2$ and on a new ”dispersion”
estimate 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 w
ill explain the tools alluded to above\, the rationale for the tools and t
he main moments of the proof.\n
LOCATION:https://stable.researchseminars.org/talk/JNTS/25/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Karol Koziol (University of Michigan)
DTSTART:20211021T213000Z
DTEND:20211021T223000Z
DTSTAMP:20260404T094554Z
UID:JNTS/26
DESCRIPTION:Title: Poincare duality for modular representations of p-adic groups and Hec
ke algebras\nby Karol Koziol (University of Michigan) as part of Colum
bia CUNY NYU number theory seminar\n\n\nAbstract\nThe mod-$p$ representati
ons theory 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
Langlands program. However\, many constructions from the case of complex c
oefficients are quite poorly behaved in the mod-$p$ setting\, and it becom
es necessary to use derived functors. In this talk\, I'll describe how thi
s situation looks for the functor of smooth duality on mod-$p$ representat
ions\, and discuss the construction of a Poincare duality spectral sequenc
e relating Kohlhaase's functors of higher smooth duals with modules over t
he (pro-$p$) Iwahori-Hecke algebra.\n
LOCATION:https://stable.researchseminars.org/talk/JNTS/26/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Wei Zhang (MIT)
DTSTART:20211028T213000Z
DTEND:20211028T223000Z
DTSTAMP:20260404T094554Z
UID:JNTS/27
DESCRIPTION:Title: p-Adic heights of the arithmetic diagonal cycles\nby Wei Zhang (M
IT) as part of Columbia CUNY NYU number theory seminar\n\n\nAbstract\nThis
is a work in progress joint with Daniel Disegni. We formulate a p-adic an
alogue of the Arithmetic Gan–Gross–Prasad conjecture for unitary group
s\, relating the p-adic height pairing of the arithmetic diagonal cycles t
o the first central derivative (along the cyclotomic direction) of a p-adi
c Rankin–Selberg L-function associated to cuspidal automorphic represent
ations. 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 app
lications to the p-adic version of the Bloch-Kato conjecture.\n
LOCATION:https://stable.researchseminars.org/talk/JNTS/27/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Michael Magee (Durham University)
DTSTART:20211104T213000Z
DTEND:20211104T223000Z
DTSTAMP:20260404T094554Z
UID:JNTS/28
DESCRIPTION:Title: The maximal spectral gap of a hyperbolic surface\nby Michael Mage
e (Durham University) as part of Columbia CUNY NYU number theory seminar\n
\n\nAbstract\nA hyperbolic surface is a surface with metric of constant cu
rvature -1. The spectral gap between the first two eigenvalues of the Lapl
acian on a closed hyperbolic surface contains a good deal of information a
bout the surface\, including its connectivity\, dynamical properties of it
s geodesic flow\, and error terms in geodesic counting problems. For arith
metic hyperbolic surfaces the spectral gap is also the subject of one of t
he biggest open problems in automorphic forms: Selberg’s eigenvalue conj
ecture.\n\nIt was an open problem from the 1970s whether there exist a seq
uence of closed hyperbolic surfaces with genera tending to infinity and sp
ectral gap tending to 1/4. (The value 1/4 here is the asymptotically optim
al one.) Recently we proved that this is indeed possible. I’ll discuss t
he very interesting background of this problem in detail as well as some i
deas of the proof.\n\nThis is joint work with Will Hide.\n
LOCATION:https://stable.researchseminars.org/talk/JNTS/28/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Myrto Mavraki (Harvard)
DTSTART:20211111T223000Z
DTEND:20211111T233000Z
DTSTAMP:20260404T094554Z
UID:JNTS/29
DESCRIPTION:Title: Uniformity in the dynamical Bogomolov conjecture\nby Myrto Mavrak
i (Harvard) as part of Columbia CUNY NYU number theory seminar\n\n\nAbstra
ct\nZhang has proposed dynamical versions of the classical Manin- Mumford
and Bogomolov conjectures. A special case of these conjectures\, for ‘sp
lit’ maps\, has recently been established by Nguyen\, Ghioca and Ye. In
particular\, they show that two rational maps have at most finitely many c
ommon preperiodic points\, unless they are ‘related’. In this talk we
discuss uniform versions of their results across 1-parameter families of c
ertain split maps and curves. This is joint work with Harry Schmidt.\n
LOCATION:https://stable.researchseminars.org/talk/JNTS/29/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Melanie Wood (Harvard)
DTSTART:20211118T223000Z
DTEND:20211118T233000Z
DTSTAMP:20260404T094554Z
UID:JNTS/30
DESCRIPTION:Title: The average size of 3-torsion in class groups of 2-extensions\nby
Melanie Wood (Harvard) as part of Columbia CUNY NYU number theory seminar
\n\n\nAbstract\nThe $p$-torsion in the class group of a number field $K$ i
s conjectured to\nbe small: of size at most $|\\text{Disc}\\\,K |^\\epsilo
n$\, and to have constant\naverage size in families with a given Galois cl
osure group (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-torsion in quadratic\nfields (Davenport and Heilbronn\, 1971) and 2-tor
sion in non-Galois\ncubic fields (Bhargava\, 2005). We prove that the 3-t
orsion is\nconstant on average for fields with Galois closure group any 2-
group\nwith a transposition\, including\, e.g. quartic $D_4$ fields. We w
ill\ndiscuss the main inputs into the proof with an eye towards giving an\
nintroduction to the tools in the area. This is joint work with Robert\nL
emke Oliver and Jiuya Wang.\n
LOCATION:https://stable.researchseminars.org/talk/JNTS/30/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Elena Fuchs & Kristin Lauter (UC Davis & Facebook AI Research)
DTSTART:20211202T223000Z
DTEND:20211202T233000Z
DTSTAMP:20260404T094554Z
UID:JNTS/31
DESCRIPTION:Title: Cryptographic hash functions from Markoff triples\nby Elena Fuchs
& Kristin Lauter (UC Davis & Facebook AI Research) as part of Columbia CU
NY NYU number theory seminar\n\n\nAbstract\nIn this talk\, we discuss how
mod-$p$ Markoff graphs can be used to construct cryptographic hash functio
ns. We present potential path finding algorithms in these graphs\, which w
ill also lead to questions about lifts of mod $p$ solutions to the Markoff
equation will come up as well. This is joint work with M. Litman and A. T
ran\, as well as with E. Bellah and L. Ye.\n
LOCATION:https://stable.researchseminars.org/talk/JNTS/31/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Levent Alpoge (Harvard University)
DTSTART:20211209T223000Z
DTEND:20211209T233000Z
DTSTAMP:20260404T094554Z
UID:JNTS/32
DESCRIPTION:Title: A "height-free" effective isogeny estimate for GL(2)-type abelian var
ieties\nby Levent Alpoge (Harvard University) as part of Columbia CUNY
NYU number theory seminar\n\n\nAbstract\nWe prove a ”height-free” eff
ective isogeny estimate for abelian varieties of GL(2)-type.\nMore precise
ly\, let g ∈ Z\n+\, K a number field\, S a finite set of places of K\, a
nd\nA\, B/K g-dimensional abelian varieties with good reduction outside S
which are\nK-isogenous and of GL(2)-type over $\\bar \\text{Q}$. We show t
hat there is a K-isogeny A → B\nof degree effectively bounded in terms o
f g\, K\, and S only.\nWe deduce an effective open image theorem for these
abelian varieties\, as well\nas an effective upper bound on the number of
S-integral K-points on a Hilbert\nmodular variety\n
LOCATION:https://stable.researchseminars.org/talk/JNTS/32/
END:VEVENT
BEGIN:VEVENT
SUMMARY:David Hansen (Max Planck Institute)
DTSTART:20211216T223000Z
DTEND:20211216T233000Z
DTSTAMP:20260404T094554Z
UID:JNTS/33
DESCRIPTION:Title: Local Shimura varieties and their cohomology\nby David Hansen (Ma
x Planck Institute) as part of Columbia CUNY NYU number theory seminar\n\n
\nAbstract\nLocal Shimura varieties are non-archimedean analytic spaces an
alogous to Shimura varieties\, whose cohomology is expected to realize (in
a precise sense) both the local Langlands correspondence and the local Ja
cquet-Langlands correspondence. I'll give a gentle introduction to the the
ory of local Shimura varieties\, and explain some results that can be prov
en about their cohomology using current technology. Some of this material
is joint work with Tasho Kaletha and Jared Weinstein.\n
LOCATION:https://stable.researchseminars.org/talk/JNTS/33/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Matthew de Courcy-Ireland (EPFL)
DTSTART:20220210T223000Z
DTEND:20220210T233000Z
DTSTAMP:20260404T094554Z
UID:JNTS/34
DESCRIPTION:Title: Markoff graphs mod p\nby Matthew de Courcy-Ireland (EPFL) as part
of Columbia CUNY NYU number theory seminar\n\n\nAbstract\nWe discuss a fa
mily of cubic surfaces defined by $$x^2+y^2+z^2=xyz+k$$ modulo prime numbe
rs. The solutions form a graph\, where each vertex $(x\,y\,z)$ is joined t
o the other solution of the same quadratic in any of the three variables.
These moves are related to a nonlinear action of the modular group PGL(2\,
$\\mathbb{Z}$) on the surface. We outline some ways these equations arise\
, and how we became interested in showing that the associated graphs canno
t be embedded in the plane. We describe constructions showing that the gra
phs for $k=0$ are not planar if the prime is congruent to 1 modulo 4\, or
congruent to a quadratic residue 1\, 2\, or 4 modulo 7. We also sketch a p
roof of non-planarity for all sufficiently large primes.\n
LOCATION:https://stable.researchseminars.org/talk/JNTS/34/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vytautas Paskunas (University of Duisberg-Essen)
DTSTART:20220224T223000Z
DTEND:20220224T233000Z
DTSTAMP:20260404T094554Z
UID:JNTS/35
DESCRIPTION:Title: On local Galois deformation rings\nby Vytautas Paskunas (Universi
ty of Duisberg-Essen) as part of Columbia CUNY NYU number theory seminar\n
\n\nAbstract\nWe show that framed deformation rings of mod $p$ representat
ions of the absolute Galois group of a $p$-adic local field are complete i
ntersections of expected dimension. We determine their irreducible compone
nts and show that they and their special fibres are normal and complete in
tersection. As an application we prove density results of loci with prescr
ibed $p$-adic Hodge theoretic properties.\n\n(joint work with Gebhard Boec
kle and Ashwin Iyengar. The preprint is available at https://arxiv.org/abs
/2110.01638 ).\n
LOCATION:https://stable.researchseminars.org/talk/JNTS/35/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yunqing Tang (Princeton University)
DTSTART:20220217T223000Z
DTEND:20220217T233000Z
DTSTAMP:20260404T094554Z
UID:JNTS/36
DESCRIPTION:Title: Basic reductions of abelian varieties\nby Yunqing Tang (Princeton
University) as part of Columbia CUNY NYU number theory seminar\n\n\nAbstr
act\nElkies proved that an elliptic curve over $\\mathbb Q$ has infinitely
many supersingular reductions. The generalization of the 0-dimensional su
persingular locus of the modular curve is the so called basic locus of a S
himura curve at a good prime. In this talk\, we generalize Elkies’s theo
rem to some abelian varieties over totally real fields parametrized by cer
tain unitary Shimura curves\; these Shimura curves arise from the moduli s
paces of cyclic covers of the projective line ramified at 4 points. This i
s joint work (in progress) with Wanlin Li\, Elena Mantovan\, and Rachel Pr
ies.\n
LOCATION:https://stable.researchseminars.org/talk/JNTS/36/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Joseph Silverman (Brown University)
DTSTART:20220303T223000Z
DTEND:20220303T233000Z
DTSTAMP:20260404T094554Z
UID:JNTS/37
DESCRIPTION:Title: Orbits on tri-involutive K3 surfaces\nby Joseph Silverman (Brown
University) as part of Columbia CUNY NYU number theory seminar\n\n\nAbstra
ct\nLet $\\mathcal W$ be a surface in $\\mathbb P^1 \\times \\mathbb P^1 \
\times \\mathbb P^1$ given by the vanishing of a (2\,2\,2) form. The thre
e projections $\\mathcal W \\to \\mathbb P^1 \\times \\mathbb P^1$ are
double covers that induce three non-commuting involutions on $\\mathcal W.
$ Let $G$ be the group of automorphisms of $\\mathcal W$ generated by the
se involutions. We investigate the $G$-orbit structure of the points of $\
\mathcal W$. In particular\, we study $G$-orbital components over finite f
ields and finite $G$-orbits in characteristic 0. This is joint work with E
lena Fuchs\, Matthew Litman\, and Austin Tran.\n
LOCATION:https://stable.researchseminars.org/talk/JNTS/37/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Matthias Strauch (Indiana University Bloomington)
DTSTART:20220310T223000Z
DTEND:20220310T233000Z
DTSTAMP:20260404T094554Z
UID:JNTS/38
DESCRIPTION:Title: p-adic Banach space representations of SL(2\, Q_p)\nby Matthias S
trauch (Indiana University Bloomington) as part of Columbia CUNY NYU numbe
r theory seminar\n\n\nAbstract\nWe explain how to deduce a classification
of admissible\nunitary representations of SL$(2\, \\mathbb Q_p)$ on Banach
spaces over (finite\nextensions of) $\\mathbb Q_p$ from the $p$-adic Lang
lands correspondence for\nGL$(2\, \\mathbb Q_p)$. The latter was establish
ed by Colmez and \nColmez-Dospinescu-Paskunas. When the representation is
"de Rham''\, we relate the\ncorresponding L-packet to the L-packet of asso
ciated smooth\nrepresentations. When compared to the case of smooth repres
entations\,\ninteresting similarities as well as dissimilarities can be ob
served.\n
LOCATION:https://stable.researchseminars.org/talk/JNTS/38/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Peter Humphries (University of Virginia)
DTSTART:20220317T213000Z
DTEND:20220317T223000Z
DTSTAMP:20260404T094554Z
UID:JNTS/39
DESCRIPTION:Title: Spectral reciprocity and applications\nby Peter Humphries (Univer
sity of Virginia) as part of Columbia CUNY NYU number theory seminar\n\n\n
Abstract\nSpectral reciprocity is a phenomenon in which certain moments of
L-functions are shown to be exactly equal to other moments of L-functions
. A quintessential example is Motohashi's formula\, which relates the four
th moment of the Riemann zeta function to the third moment of L-functions
associated to GL(2) automorphic forms. I will discuss generalisations of M
otohashi's formula\, how to prove these formulae using tools from the theo
ry of automorphic forms\, and applications of these formulae to problems i
n analytic number theory\, including the $L^4$-norm problem for automorphi
c forms.\n
LOCATION:https://stable.researchseminars.org/talk/JNTS/39/
END:VEVENT
BEGIN:VEVENT
SUMMARY:William Duke (UCLA)
DTSTART:20220324T213000Z
DTEND:20220324T223000Z
DTSTAMP:20260404T094554Z
UID:JNTS/40
DESCRIPTION:Title: On a theorem of Legendre\nby William Duke (UCLA) as part of Colum
bia CUNY NYU number theory seminar\n\n\nAbstract\nI will explain that the
primitive zeros of certain indefinite ternary quadratic forms fall into a
single orbit under automorphs of the form.\nOne ingredient in the proof is
a characterization and count of classes of zeros of the form consisting p
rimitive triples of Gaussian binary quadratic forms\, where triples are a
cted on by the extended modular group.\nAnother is an application of Eisen
stein series for an associated Fuchsian group.\n
LOCATION:https://stable.researchseminars.org/talk/JNTS/40/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Elden Elmanto (Harvard University)
DTSTART:20220331T213000Z
DTEND:20220331T223000Z
DTSTAMP:20260404T094554Z
UID:JNTS/41
DESCRIPTION:Title: On the motivic cohomology of schemes\nby Elden Elmanto (Harvard
University) as part of Columbia CUNY NYU number theory seminar\n\n\nAbstra
ct\nI will report on joint work with Matthew Morrow. Using ideas from topo
logical cyclic homology and $p$-adic Hodge theory\, we construct a theory
of $p$-adic motivic complexes for any qcqs scheme in characteristic $p$. T
his can be viewed as a generalization of algebraic cycles to singular\, po
ssibly nonreduced\, schemes. A key result is an agreement of this construc
tion with Bloch cycle complexes on smooth varieties which\, time permittin
g\, I will explain a proof of.\n
LOCATION:https://stable.researchseminars.org/talk/JNTS/41/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ye Tian (Morningside Center of Math.\, Beijing)
DTSTART:20220407T213000Z
DTEND:20220407T223000Z
DTSTAMP:20260404T094554Z
UID:JNTS/42
DESCRIPTION:Title: On Tunnell-Gross type formulae\nby Ye Tian (Morningside Center of
Math.\, Beijing) as part of Columbia CUNY NYU number theory seminar\n\n\n
Abstract\nFor a weight 2 cuspidal newform $f\,$ we prove an explicit vers
ion of Waldspurger's theorem\, which relates L-values of quadratic twists
of $f$ to certain ternary quadratic forms. Gross gave a geometric proof
of such a formula assuming (i) the conductor of $f $ is a prime (ii) L(1\
, $f$) is nonzero. Gross' work was generalized by Bocherer and Schulze-Pil
lot to square-free conductors based on their investigation of Yoshida lift
. Via a different approach\, Mao generalized Gross' work only assuming (i
). In this talk\, we outline the proof of an explicit formula in the gene
ral case. Joint work with W. He and W. Xiong.\n
LOCATION:https://stable.researchseminars.org/talk/JNTS/42/
END:VEVENT
BEGIN:VEVENT
SUMMARY:John Voight (Dartmouth)
DTSTART:20220414T213000Z
DTEND:20220414T223000Z
DTSTAMP:20260404T094554Z
UID:JNTS/43
DESCRIPTION:Title: A family of Jacobians with definite QM\nby John Voight (Dartmouth
) as part of Columbia CUNY NYU number theory seminar\n\n\nAbstract\nWe inv
estigate explicitly a family of hyperelliptic curves of genus four whose J
acobians have definite quaternionic multiplication. This family has many i
nteresting features\, including: they give infinitely many examples where
the ell-adic monodromy groups are disconnected over the field of definitio
n of the endomorphism ring. This is joint work with Victoria Cantoral-Farf
an and Davide Lombardo.\n
LOCATION:https://stable.researchseminars.org/talk/JNTS/43/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Igor Shparlinski (UNSW\, Australia)
DTSTART:20220421T213000Z
DTEND:20220421T223000Z
DTSTAMP:20260404T094554Z
UID:JNTS/44
DESCRIPTION:Title: Characteristic Polynomials and Multiplicative Dependence of Integer M
atrices\nby Igor Shparlinski (UNSW\, Australia) as part of Columbia CU
NY NYU number theory seminar\n\n\nAbstract\nWe consider the set $\\mathca
l{M}_n(\\mathbb{Z}\; H))$ of $n\\times n$-matrices with \ninteger elements
of size at most $H$ and obtain upper and lower bounds on the number of $
s$-tuples\nof matrices from $\\mathcal{M}_n(\\mathbb{Z}\; H)$\, satisfyin
g various multiplicative relations\, including \n multiplicative depend
ence\, commutativity and \n bounded generation of a subgroup of $\\text{\\
rm GL}_n(\\mathbb{Q})$. These problems generalise those studied \nin the
scalar case $n=1$ by F. Pappalardi\, M. Sha\, I. E. Shparlinski and C. L.
Stewart (2018) with an \nobvious distinction due to the non-commutativity
of matrices. \nAs a part of our method\, we obtain a new upper bound on t
he number of matrices from $\\mathcal{M}_n(\\mathbb{Z}\; H)$\nwith a give
n characteristic polynomial $f \\in\\mathbb{Z}[X]$\, which is uniform wit
h respect to $f$. This complements \nthe asymptotic formula of A. Eskin\,
S. Mozes and N. Shah (1996) in which $f$ has to be fixed and irreducible.
\n\nJoint work with Alina Ostafe.\n
LOCATION:https://stable.researchseminars.org/talk/JNTS/44/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Francesc Castella (UC Santa Barbara)
DTSTART:20220428T213000Z
DTEND:20220428T223000Z
DTSTAMP:20260404T094554Z
UID:JNTS/45
DESCRIPTION:Title: On Mazur's main conjecture at Eisenstein primes\nby Francesc Cast
ella (UC Santa Barbara) as part of Columbia CUNY NYU number theory seminar
\n\n\nAbstract\nLet $E$ be a rational elliptic curve\, and $p$ an odd prim
e of good ordinary reduction for $E.$ In 1972\, Mazur formulated an analog
ue of Iwasawa’s main conjecture for the $p$-primary Selmer group of $E$
over the cyclotomic $\\mathbb Z_p$-extension of $\\mathbb Q$. In this talk
I’ll report on recent progress towards Mazur’s main conjecture (joint
with Giada Grossi and Chris Skinner\, building on an earlier joint work a
lso with Jaehoon Lee) in the case where $E$ admits a rational $p$-isogeny.
\n
LOCATION:https://stable.researchseminars.org/talk/JNTS/45/
END:VEVENT
END:VCALENDAR