BEGIN:VCALENDAR
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PRODID:researchseminars.org
CALSCALE:GREGORIAN
X-WR-CALNAME:researchseminars.org
BEGIN:VEVENT
SUMMARY:Giada Grossi
DTSTART:20201019T113000Z
DTEND:20201019T124000Z
DTSTAMP:20260404T095039Z
UID:HUJI-BGU-NTS/1
DESCRIPTION:Title: The p-part of BSD for rational elliptic curves at Eisenstein p
rimes.\nby Giada Grossi as part of HUJI-BGU Number Theory Seminar\n\n\
nAbstract\nLet E be an elliptic curve over the rationals and p an odd prim
e such that E admits a rational p-isogeny satisfying some assumptions. In
a joint work with F. Castella\, J. Lee and C. Skinner\, we study the anti
cyclotomic Iwasawa theory for E/K for some suitable quadratic imaginary fi
eld K. I will explain our strategy and how our results\, combined with com
plex and p-adic Gross-Zagier formulae\, allow us to prove a p-converse to
the theorem of Gross--Zagier and Kolyvagin and the p-part of the Birch-Swi
nnerton--Dyer formula in analytic rank\n
LOCATION:https://stable.researchseminars.org/talk/HUJI-BGU-NTS/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:James Maynard
DTSTART:20201026T123000Z
DTEND:20201026T134000Z
DTSTAMP:20260404T095039Z
UID:HUJI-BGU-NTS/2
DESCRIPTION:Title: Title: The Duffin-Schaeffer Conjecture\nby James Maynard a
s part of HUJI-BGU Number Theory Seminar\n\n\nAbstract\nHow well can you a
pproximate real numbers by rationals with denominators coming from a given
set? Although this old question has applications in many areas\, in gener
al this question seems impossibly hard - we don’t even know whether e+pi
is rational or not!\n\nIf you allow for a tiny number of bad exceptions\,
then a beautiful dichotomy occurs - either almost everything can be appro
ximated or almost nothing. I’ll talk about this problem and recent joint
work with Dimitris Koukoulopoulos which classifies when these options occ
ur\, answering an old question of Duffin and Schaeffer. This relies on a f
un blend of different ideas\, including ergodic theory\, analytic number t
heory and graph theory.\n
LOCATION:https://stable.researchseminars.org/talk/HUJI-BGU-NTS/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Cong Xue
DTSTART:20201102T123000Z
DTEND:20201102T134000Z
DTSTAMP:20260404T095039Z
UID:HUJI-BGU-NTS/3
DESCRIPTION:Title: Title: Smoothness of the cohomology sheaves of stacks of shtuk
as\nby Cong Xue as part of HUJI-BGU Number Theory Seminar\n\nAbstract:
TBA\n
LOCATION:https://stable.researchseminars.org/talk/HUJI-BGU-NTS/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yifeng Liu
DTSTART:20201109T123000Z
DTEND:20201109T134000Z
DTSTAMP:20260404T095039Z
UID:HUJI-BGU-NTS/4
DESCRIPTION:Title: Beilinson-Bloch conjecture and arithmetic inner product formul
a\nby Yifeng Liu as part of HUJI-BGU Number Theory Seminar\n\n\nAbstra
ct\nIn this talk\, we study the Chow group of the motive associated to a t
empered global L-packet \\pi of unitary groups of even rank with respect t
o a CM extension\, whose global root number is -1. We show that\, under so
me restrictions on the ramification of \\pi\, if the central derivative L'
(1/2\,\\pi) is nonvanishing\, then the \\pi-nearly isotypic localization o
f the Chow group of a certain unitary Shimura variety over its reflex fiel
d does not vanish. This proves part of the Beilinson--Bloch conjecture for
Chow groups and L-functions. Moreover\, assuming the modularity of Kudla'
s generating functions of special cycles\, we explicitly construct element
s in a certain \\pi-nearly isotypic subspace of the Chow group by arithmet
ic theta lifting\, and compute their heights in terms of the central deriv
ative L'(1/2\,\\pi) and local doubling zeta integrals. This is a joint wor
k with Chao Li.\n
LOCATION:https://stable.researchseminars.org/talk/HUJI-BGU-NTS/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andrea Sartori (TAU)
DTSTART:20201116T123000Z
DTEND:20201116T134000Z
DTSTAMP:20260404T095039Z
UID:HUJI-BGU-NTS/5
DESCRIPTION:Title: Spectral quasi-correlations and Arithmetic Random Waves.\n
by Andrea Sartori (TAU) as part of HUJI-BGU Number Theory Seminar\n\n\nAbs
tract\nSpectral quasi-correlations are small sums of lattice points lying
on the same circle. In this talk\, I will first describe how these sums na
turally arise in the study of the small scales behaviour of (random) Lapla
ce eigenfunctions on the standard 2 dimensional torus\, also known as Arit
hmetic Random Waves. I will then discuss how to obtain bounds on the said
sums using the geometry of numbers and what these bounds tell us about Ari
thmetic Random Waves.\n
LOCATION:https://stable.researchseminars.org/talk/HUJI-BGU-NTS/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yunqing Tang
DTSTART:20201123T123000Z
DTEND:20201123T134000Z
DTSTAMP:20260404T095039Z
UID:HUJI-BGU-NTS/6
DESCRIPTION:Title: Reductions of K3 surfaces via intersections on GSpin Shimura v
arieties.\nby Yunqing Tang as part of HUJI-BGU Number Theory Seminar\n
\n\nAbstract\nFor a K3 surface X over a number field with potentially good
reduction everywhere\, we prove that there are infinitely many primes mod
ulo which the reduction of X has larger geometric Picard rank than that of
the generic fiber X. A similar statement still holds true for ordinary K3
surfaces with potentially good reduction everywhere over global function
fields. In this talk\, I will present the proofs via the (arithmetic) inte
rsection theory on good integral models (and its special fibers) of GSpin
Shimura varieties along with a potential application to a certain case of
the Hecke orbit conjecture of Chai and Oort. This talk is based on joint w
ork with Ananth Shankar\, Arul Shankar\, and Salim Tayou and with Davesh M
aulik and Ananth Shankar.\n
LOCATION:https://stable.researchseminars.org/talk/HUJI-BGU-NTS/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Natalia Cristina Garcia Fritz
DTSTART:20201130T123000Z
DTEND:20201130T134000Z
DTSTAMP:20260404T095039Z
UID:HUJI-BGU-NTS/7
DESCRIPTION:Title: Progress of Vojta's conjecture over function fields with a des
cription of the exceptional set\nby Natalia Cristina Garcia Fritz as p
art of HUJI-BGU Number Theory Seminar\n\n\nAbstract\nIn this talk we will
present some unconditional progress on Vojta's conjecture on surfaces with
truncated counting functions in the function field setting. In the cases
that we consider\, these results provide an explicit description of the ex
ceptional set.\nThe approach involves a local study of omega-integral curv
es and global estimates for intersection numbers. This builds on our earli
er work regarding the explicit computation of the exceptional set in the c
ontext of the Bombieri-Lang conjecture\, extending ideas by Vojta and Bogo
molov.\n
LOCATION:https://stable.researchseminars.org/talk/HUJI-BGU-NTS/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tal Horesh
DTSTART:20201207T123000Z
DTEND:20201207T134000Z
DTSTAMP:20260404T095039Z
UID:HUJI-BGU-NTS/8
DESCRIPTION:Title: Distribution of primitive lattices and flags of lattices in Z^
n\nby Tal Horesh as part of HUJI-BGU Number Theory Seminar\n\n\nAbstra
ct\nPrimitive lattices in Z^n are a generalization of the concept of primi
tive vectors: a rank d subgroup of Z^n is called primitive if there is no
other subgroup of the same rank that properly contains it. In two papers f
rom 1998 and from 2015\, Schmidt proved a counting statement for primitive
lattices of any rank 1 < d < n\, taking into account their shapes (simila
rity classes modulo rotation and re-scaling\, namely projections into SO(d
)\\SLd(R)/SLd(Z))\, and directions (the subspaces that they span\, namely
projections into the Grassmannian GR(d\,n)). We extend upon this counting
statement\, and also consider the shapes of the orthogonal complements of
these lattices. Moreover\, we introduce the concept of flags of primitive
lattices\, and extend this counting statement to them as well.\n
LOCATION:https://stable.researchseminars.org/talk/HUJI-BGU-NTS/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Michele Fornea
DTSTART:20201214T143000Z
DTEND:20201214T154000Z
DTSTAMP:20260404T095039Z
UID:HUJI-BGU-NTS/9
DESCRIPTION:Title: The arithmetic of plectic Jacobians\nby Michele Fornea as
part of HUJI-BGU Number Theory Seminar\n\n\nAbstract\nHeegner points play
a pivotal role in our understanding of the arithmetic of modular elliptic
curves. They control the Mordell-Weil group of elliptic curves of rank 1\,
and they arise as CM points on Jacobians of Shimura curves. \nThe work of
Bertolini\, Darmon and their schools has shown that p-adic methods can be
successfully employed to generalize the definition of Heegner points to q
uadratic extension that are not necessarily CM. Notably\, Guitart\, Masdeu
and Sengun have defined and numerically computed Stark-Heegner (SH) point
s in great generality. Their computations strongly support the belief that
SH points completely control the Mordell-Weil group of elliptic curves of
rank 1.\n\nInspired by Nekovar and Scholl’s plectic conjectures\, Lenna
rt Gehrmann and I recently proposed a plectic generalization of SH points:
a cohomological construction of local points on elliptic curves that conj
ecturally control Mordell-Weil groups of higher rank. In this talk\, focus
ing on the quadratic CM case\, I will present an alternative speculative f
ramework that can be used to cast the definition of plectic Heegner points
in geometric terms.\n\nplease note the unusual time\n
LOCATION:https://stable.researchseminars.org/talk/HUJI-BGU-NTS/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tung Nguyen
DTSTART:20201221T143000Z
DTEND:20201221T154000Z
DTSTAMP:20260404T095039Z
UID:HUJI-BGU-NTS/10
DESCRIPTION:Title: Heights and Tamagawa number of motives.\nby Tung Nguyen a
s part of HUJI-BGU Number Theory Seminar\n\n\nAbstract\nThe class number f
ormula is an inspiring pillar of number theory. By the work of many mathem
aticians\, notably Deligne\, Beilinson\, Bloch\, Kato\, Fontaine\, Perrin-
Riou\, Jannsen\, and many others\, we now have a quite general (conjectura
l) class number formulas for motives\, i.e.\, the Tamagawa number conjectu
re of Bloch-Kato. Recently\, Kato has proposed a new approach to this prob
lem using heights of motives. In this talk\, we will give an overview of t
his approach. In particular\, we will show a precise relation between heig
hts to Tamagawa numbers of motives. We also partially answer some of Kato'
s questions about the number of mixed motives of bounded heights in the ca
se of mixed Tate motives.\n
LOCATION:https://stable.researchseminars.org/talk/HUJI-BGU-NTS/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Arvind Kumar
DTSTART:20201228T123000Z
DTEND:20201228T134000Z
DTSTAMP:20260404T095039Z
UID:HUJI-BGU-NTS/11
DESCRIPTION:Title: Strong multiplicity one for Siegel cusp forms of degree two\nby Arvind Kumar as part of HUJI-BGU Number Theory Seminar\n\n\nAbstrac
t\nThe classical multiplicity one theorem has been strengthened significan
tly for modular forms by Rajan. He has shown that if two normalized eigenf
orms have the same (normalized) Hecke eigenvalues for primes of positive u
pper density\, then one is the character twist of the other. This is calle
d a strong multiplicity one theorem. The first result in the direction of
multiplicity one result for Siegel modular forms of degree two was obtaine
d only recently in 2018 by Schmidt. By following the approach of Rajan\, w
e will prove a strong multiplicity one theorem for Siegel cuspidal eigenfo
rms of degree two and level one. The methods involve Galois representation
s associated to Siegel cusp forms\, a multiplicity one result for Galois r
epresentations\, and finally the result due to Schmidt. This is based on j
oint work with J. Meher and K. D. Shankhadhar.\n
LOCATION:https://stable.researchseminars.org/talk/HUJI-BGU-NTS/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mark Shusterman
DTSTART:20210104T143000Z
DTEND:20210104T154000Z
DTSTAMP:20260404T095039Z
UID:HUJI-BGU-NTS/12
DESCRIPTION:by Mark Shusterman as part of HUJI-BGU Number Theory Seminar\n
\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/HUJI-BGU-NTS/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:no seminar
DTSTART:20210111T123000Z
DTEND:20210111T134000Z
DTSTAMP:20260404T095039Z
UID:HUJI-BGU-NTS/13
DESCRIPTION:by no seminar as part of HUJI-BGU Number Theory Seminar\n\nAbs
tract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/HUJI-BGU-NTS/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Danny Neftin
DTSTART:20210315T123000Z
DTEND:20210315T134000Z
DTSTAMP:20260404T095039Z
UID:HUJI-BGU-NTS/14
DESCRIPTION:Title: The parametric dimension\nby Danny Neftin as part of HUJI
-BGU Number Theory Seminar\n\n\nAbstract\nThe essential dimension measures
the complexity of algebraic objects. The parametric dimension\, an arithm
etic analogue\, measures the complexity of those objects defined over the
rationals. We describe what appears to be a significant difference between
the two dimensions for field extensions and other algebraic objects.\n
LOCATION:https://stable.researchseminars.org/talk/HUJI-BGU-NTS/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Martin Raum
DTSTART:20210322T123000Z
DTEND:20210322T134000Z
DTSTAMP:20260404T095039Z
UID:HUJI-BGU-NTS/15
DESCRIPTION:by Martin Raum as part of HUJI-BGU Number Theory Seminar\n\nAb
stract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/HUJI-BGU-NTS/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pol van Hoften
DTSTART:20210405T113000Z
DTEND:20210405T124000Z
DTSTAMP:20260404T095039Z
UID:HUJI-BGU-NTS/16
DESCRIPTION:Title: Mod p points on Shimura varieties of parahoric level\nby
Pol van Hoften as part of HUJI-BGU Number Theory Seminar\n\n\nAbstract\nAb
stract: The conjecture of Langlands-Rapoport gives a conjectural descripti
on of the mod p points of Shimura varieties\, with applications towards co
mputing the (semi-simple) zeta function of these Shimura varieties. The co
njecture was proven by Kisin for abelian type Shimura varieties at primes
of (hyperspecial) good reduction\, after having constructed smooth integra
l models. For primes of (parahoric) bad reduction\, Kisin and Pappas have
constructed a good integral model and the conjecture was generalised to th
is setting by Rapoport. In this talk I will discuss recent results towards
the conjecture for these integral models\, under minor hypothesis\, build
ing on earlier work of Zhou. Along the way we will see irreducibility resu
lts for various stratifications on special fibers of Shimura varieties\, i
ncluding irreducibility of central leaves and Ekedahl-Oort strata.\n
LOCATION:https://stable.researchseminars.org/talk/HUJI-BGU-NTS/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jef Laga
DTSTART:20210419T130000Z
DTEND:20210419T140000Z
DTSTAMP:20260404T095039Z
UID:HUJI-BGU-NTS/17
DESCRIPTION:Title: Rational points and Selmer groups of some families of genus 3
curves and abelian surfaces\nby Jef Laga as part of HUJI-BGU Number T
heory Seminar\n\n\nAbstract\nManjul Bhargava and Arul Shankar have determi
ned the average size of the n-Selmer group of the family of all elliptic c
urves over Q ordered by height\, for n at most 5. In this talk we will con
sider a family of nonhyperelliptic genus 3 curves\, and bound the average
size of the 2-Selmer group of their Jacobians. This implies that a majorit
y of curves in this family have relatively few rational points. We also co
nsider a family of abelian surfaces which are not principally polarized an
d obtain similar results.\n
LOCATION:https://stable.researchseminars.org/talk/HUJI-BGU-NTS/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mahesh Kakde
DTSTART:20210426T113000Z
DTEND:20210426T124000Z
DTSTAMP:20260404T095039Z
UID:HUJI-BGU-NTS/18
DESCRIPTION:Title: On the Brumer—Stark conjecture and application to Hilbert
’s 12th problem\nby Mahesh Kakde as part of HUJI-BGU Number Theory S
eminar\n\n\nAbstract\nI will report on my joint work with Samit Dasgupta o
n the Brumer-Stark conjecture proving existence of the Brumer-Stark units
and on a conjecture of Dasgupta giving a p-adic analytic formula for these
units. I will present a sketch of our proof of the Brumer-Stark conjectur
e and also mention applications to Hilbert's 12th problem i.e. explicit cl
ass field theory.\n
LOCATION:https://stable.researchseminars.org/talk/HUJI-BGU-NTS/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Johannes Girsch
DTSTART:20210503T113000Z
DTEND:20210503T124000Z
DTSTAMP:20260404T095039Z
UID:HUJI-BGU-NTS/19
DESCRIPTION:Title: The Doubling Method in Algebraic Families\nby Johannes Gi
rsch as part of HUJI-BGU Number Theory Seminar\n\n\nAbstract\nLocal consta
nts are an important concept in the complex representation theory of reduc
tive $p$-adic groups\, for example they are pivotal in the formulation of
the Local Langlands correspondence. In recent years there has been progres
s in defining such constants for modular representations or in even more g
eneral settings. For example\, Moss was able to define $\\gamma$-factors f
or representations of $\\GL_n(\\mathbb Q_p)$ with coefficients in general
noetherian rings and subsequently together with Helm was able to prove a c
onverse theorem\, which was crucial for the proof of the Local Langlands c
orrespondence in families for $\\GL_n$. The aim of this talk is to show ho
w one can extend the Doubling Method of Piateski-Shapiro and Rallis to fam
ilies of representations of classical groups. In this setting we will intr
oduce and prove a rationality result for the Doubling Zeta integrals. Subs
equently we will show that these zeta integrals satisfy a functional equat
ion from which one obtains $\\gamma$-factors.\n
LOCATION:https://stable.researchseminars.org/talk/HUJI-BGU-NTS/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Olivier Fouquet
DTSTART:20210524T113000Z
DTEND:20210524T124000Z
DTSTAMP:20260404T095039Z
UID:HUJI-BGU-NTS/20
DESCRIPTION:Title: The Iwasawa Main Conjecture for modular motives (especially t
hose with very bad reduction)\nby Olivier Fouquet as part of HUJI-BGU
Number Theory Seminar\n\n\nAbstract\nAbstract: The Iwasawa Main Conjecture
for modular motives is a conjecture of Barry Mazur\, Ralph Greenberg and
Kazuya Kato describing the variation of special values of L-functions of e
igencuspforms under twists by cyclotomic characters. In this talk\, I will
explain its statement and meaning as well as outline its proof (under mil
d hypothesis on the residual Galois representation)\, and especially how t
o deduce the conjecture in general from the case of good reduction. This i
s joint work with Xin Wan.\n
LOCATION:https://stable.researchseminars.org/talk/HUJI-BGU-NTS/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jessica Fintzen
DTSTART:20210531T113000Z
DTEND:20210531T124000Z
DTSTAMP:20260404T095039Z
UID:HUJI-BGU-NTS/21
DESCRIPTION:Title: Representations of p-adic groups\nby Jessica Fintzen as p
art of HUJI-BGU Number Theory Seminar\n\n\nAbstract\nThe Langlands program
is a far-reaching collection of conjectures that relate different areas o
f mathematics including number theory and representation theory. A fundame
ntal problem on the representation theory side of the Langlands program is
the construction of all (irreducible\, smooth\, complex or mod-$\\ell$) r
epresentations of p-adic groups. I will provide an overview of our underst
anding of the representations of p-adic groups\, with an emphasis on recen
t progress\, and outline some applications.\n
LOCATION:https://stable.researchseminars.org/talk/HUJI-BGU-NTS/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Carlo Pagano
DTSTART:20210607T113000Z
DTEND:20210607T124000Z
DTSTAMP:20260404T095039Z
UID:HUJI-BGU-NTS/22
DESCRIPTION:Title: On the negative Pell conjecture\nby Carlo Pagano as part
of HUJI-BGU Number Theory Seminar\n\n\nAbstract\nHow often does the ring o
f integer of a real quadratic have a unit of negative norm? In 1995 Steven
hagen\, refining a conjecture of Nagell\, proposed a conjectural asymptoti
c formula describing how many such real quadratic fields should be out the
re when counted by discriminant. I will discuss an upcoming joint work wit
h Peter Koymans where we establish Stevenhagen's conjecture.\n
LOCATION:https://stable.researchseminars.org/talk/HUJI-BGU-NTS/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Umberto Zannier
DTSTART:20210614T113000Z
DTEND:20210614T123000Z
DTSTAMP:20260404T095039Z
UID:HUJI-BGU-NTS/23
DESCRIPTION:Title: Abelian varieties not isogenous to any Jacobian\nby Umber
to Zannier as part of HUJI-BGU Number Theory Seminar\n\n\nAbstract\nIt is
well known that in dimension g\\ge 4\nthere exist complex abelian varieti
es not isogenous to\n any Jacobian. A question of Katz and Oort asked whe
ther\n one can find such examples over the field of algebraic numbers.\n
This was answered affirmatively by Oort-Chai under the\n Andre'-Oort conj
ecture\, and by Tsimerman unconditionally.\n They gave examples within Co
mplex Multiplication.\n In joint work with Masser\, by means of a comple
tely\n different method\, we proved that in a sense the "general\n abelia
n variety over \\overline\\Q is indeed not isogenous\n to any Jacobian. I
shall illustrate the context and the\nbasic principles\n of the proofs.\n
LOCATION:https://stable.researchseminars.org/talk/HUJI-BGU-NTS/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tangli Ge
DTSTART:20210621T113000Z
DTEND:20210621T123000Z
DTSTAMP:20260404T095039Z
UID:HUJI-BGU-NTS/24
DESCRIPTION:Title: Uniformity of quadratic points\nby Tangli Ge as part of H
UJI-BGU Number Theory Seminar\n\n\nAbstract\nHarris-Silverman showed as a
corollary of Faltings’ Theorem in dimension two that a non-hyperelliptic
non-bielliptic curve over some number field has only finitely many quadra
tic points. In this talk\, I will explain how to get a uniform bound on th
e number of quadratic points of such curves\, in terms of the Mordell-Weil
ranks. The result relies on the uniform Mordell-Lang conjecture in dimens
ion two. This is motivated by the recent work on the uniform Mordell-Lang
conjecture by Dimitrov-Gao-Habegger and Kühne. I will also briefly introd
uce the uniformity conjecture in general\, as shown in a joint work with Z
iyang Gao and Lars Kühne.\n
LOCATION:https://stable.researchseminars.org/talk/HUJI-BGU-NTS/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jan Bruinier
DTSTART:20210628T113000Z
DTEND:20210628T123000Z
DTSTAMP:20260404T095039Z
UID:HUJI-BGU-NTS/25
DESCRIPTION:Title: CM values of higher automorphic Green functions\nby Jan B
ruinier as part of HUJI-BGU Number Theory Seminar\n\n\nAbstract\nThe autom
orphic Green function for a modular curve $X$ is a function on\n$X\\times
X$ with a logarithmic singularity along the diagonal which is a\nresolvent
kernel of the hyperbolic Laplacian. It plays an important role\nin the an
alytic theory of automorphic forms and in the Arakelov geometry\nof modula
r curves. Gross and Zagier conjectured that for positive integral\nspectra
l parameter $s$ the values at CM points of certain linear\ncombinations of
Hecke translates of this Green function are given by\nlogarithms of algeb
raic numbers in suitable class fields. In certain cases\nthis conjecture w
as proved by Mellit and Viazovska. We report on joint\nwork with S. Ehlen
and T. Yang in which we establish new cases of the\nconjecture. We also di
scuss generalizations to orthogonal groups of\nsignature $(n\,2)$ and poss
ible applications.\n
LOCATION:https://stable.researchseminars.org/talk/HUJI-BGU-NTS/25/
END:VEVENT
END:VCALENDAR