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BEGIN:VEVENT
SUMMARY:Chao Li (Columbia University)
DTSTART:20200409T203000Z
DTEND:20200409T213000Z
DTSTAMP:20260404T094801Z
UID:PrincetonIASNT/1
DESCRIPTION:Title: On the Kudla-Rapoport conjecture\nby Chao Li (Columbia U
niversity) as part of Princeton/IAS number theory seminar\n\nLecture held
in 214 Fine Hall (Princeton) or SH101 (IAS).\n\nAbstract\nThe Kudla-Rapopo
rt conjecture predicts a precise identity between the arithmetic intersect
ion number of special cycles on unitary Rapoport-Zink spaces and the deriv
ative of local representation densities of hermitian forms. It is a key lo
cal ingredient to establish the arithmetic Siegel-Weil formula and the ari
thmetic Rallis inner product formula\, relating the height of special cycl
es on Shimura varieties to the derivative of Siegel Eisenstein series and
L-functions. We will motivate this conjecture\, explain a proof and discus
s global applications.\n\nThis is joint work with Wei Zhang.\n
LOCATION:https://stable.researchseminars.org/talk/PrincetonIASNT/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ana Caraiani (Imperial College\, London)
DTSTART:20200416T190000Z
DTEND:20200416T200000Z
DTSTAMP:20260404T094801Z
UID:PrincetonIASNT/2
DESCRIPTION:Title: Local-global compatibility in the crystalline case\nby A
na Caraiani (Imperial College\, London) as part of Princeton/IAS number th
eory seminar\n\n\nAbstract\nLet F be a CM field. Scholze constructed Galoi
s representations associated to classes in the cohomology of locally symme
tric spaces for GL_n/F with p-torsion coefficients. These Galois represent
ations are expected to satisfy local-global compatibility at primes above
p. Even the precise formulation of this property is subtle in general\, an
d uses Kisin’s potentially semistable deformation rings. However\, this
property is crucial for proving modularity lifting theorems. I will discus
s joint work with J. Newton\, where we establish local-global compatibilit
y in the crystalline case under mild technical assumptions. This relies on
a new idea of using P-ordinary parts\, and improves on earlier results ob
tained in joint work with P. Allen\, F. Calegari\, T. Gee\, D. Helm\, B. L
e Hung\, J. Newton\, P. Scholze\, R. Taylor\, and J. Thorne in certain Fon
taine-Laffaille cases.\n
LOCATION:https://stable.researchseminars.org/talk/PrincetonIASNT/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jack Thorne (University of Cambridge)
DTSTART:20200423T130000Z
DTEND:20200423T140000Z
DTSTAMP:20260404T094801Z
UID:PrincetonIASNT/3
DESCRIPTION:Title: Symmetric power functoriality for holomorphic modular forms<
/a>\nby Jack Thorne (University of Cambridge) as part of Princeton/IAS num
ber theory seminar\n\n\nAbstract\nLanglands’s functoriality conjectures
predict the existence of “liftings” of automorphic representations alo
ng morphisms of L-groups. A basic case of interest comes from the irreduci
ble algebraic representations of GL(2)\, thought of as the L-group of the
reductive group GL(2) over Q. I will discuss the proof\, joint with James
Newton\, of the existence of the corresponding functorial liftings for a
broad class of holomorphic modular forms\, including Ramanujan’s Delta f
unction.\n
LOCATION:https://stable.researchseminars.org/talk/PrincetonIASNT/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Henrik Gustafsson (IAS)
DTSTART:20200430T203000Z
DTEND:20200430T213000Z
DTSTAMP:20260404T094801Z
UID:PrincetonIASNT/4
DESCRIPTION:Title: Eulerianity of Fourier coefficients of automorphic forms
\nby Henrik Gustafsson (IAS) as part of Princeton/IAS number theory semina
r\n\nLecture held in 214 Fine Hall (Princeton) or SH101 (IAS).\n\nAbstract
\nThe factorization of Fourier coefficients of automorphic forms plays an
important role in a wide range of topics\, from the study of L-functions t
o the interpretation of scattering amplitudes in string theory.\n\nIn this
talk I will present a transfer theorem which derives the Eulerianity of c
ertain Fourier coefficients from that of another coefficient. I will also
discuss some applications of this theorem to Fourier coefficients of autom
orphic forms in minimal and next-to-minimal representations.\n\nBased on r
ecent work with Dmitry Gourevitch\, Axel Kleinschmidt\, Daniel Persson and
Siddhartha Sahi.\n
LOCATION:https://stable.researchseminars.org/talk/PrincetonIASNT/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jayce Robert Getz (Duke University)
DTSTART:20200507T203000Z
DTEND:20200507T213000Z
DTSTAMP:20260404T094801Z
UID:PrincetonIASNT/5
DESCRIPTION:Title: On triple product L-functions\nby Jayce Robert Getz (Duk
e University) as part of Princeton/IAS number theory seminar\n\nLecture he
ld in 214 Fine Hall (Princeton) or SH101 (IAS).\n\nAbstract\nEstablishing
the conjectured analytic properties of triple product L-functions is a cru
cial case of Langlands functoriality. However\, little is known. I will
present work in progress on the case of triples of automorphic representat
ions on GL_3\; in some sense this is the smallest case that appears out of
reach via standard techniques. The approach is based on a the beautiful
fibration method of Braverman and Kazhdan for constructing Schwartz spaces
and proving analogues of the Poisson summation formula.\n
LOCATION:https://stable.researchseminars.org/talk/PrincetonIASNT/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mladen Dimitrov (Université de Lille)
DTSTART:20200514T183000Z
DTEND:20200514T193000Z
DTSTAMP:20260404T094801Z
UID:PrincetonIASNT/6
DESCRIPTION:Title: A geometric view on Iwasawa theory\nby Mladen Dimitrov (
Université de Lille) as part of Princeton/IAS number theory seminar\n\nLe
cture held in 214 Fine Hall (Princeton) or SH101 (IAS).\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/PrincetonIASNT/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Xin Wan (Morningside Center of Mathematics)
DTSTART:20200521T130000Z
DTEND:20200521T140000Z
DTSTAMP:20260404T094801Z
UID:PrincetonIASNT/7
DESCRIPTION:Title: Iwasawa theory and Bloch-Kato conjecture for unitary groups<
/a>\nby Xin Wan (Morningside Center of Mathematics) as part of Princeton/I
AS number theory seminar\n\nLecture held in 214 Fine Hall (Princeton) or S
H101 (IAS).\n\nAbstract\nWe describe a new method to study Eisenstein fami
ly and Iwasawa theory on unitary groups over totally real fields of genera
l signatures. As a consequence we prove that if the central $L$-value of a
cuspidal eigenform on the unitary group twisted by a CM character is 0\,
then the corresponding Selmer group has positive rank. The method also has
a byproduct the $p$-adic functional equations for $p$-adic $L$-functions
and $p$-adic families of Eisenstein series on unitary groups.\n
LOCATION:https://stable.researchseminars.org/talk/PrincetonIASNT/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Farrell Brumley\, (Université Sorbonne Paris Nord)
DTSTART:20200528T140000Z
DTEND:20200528T150000Z
DTSTAMP:20260404T094801Z
UID:PrincetonIASNT/8
DESCRIPTION:Title: Joint equidistribution of adelic torus orbits and families o
f twisted L-functions\nby Farrell Brumley\, (Université Sorbonne Pari
s Nord) as part of Princeton/IAS number theory seminar\n\n\nAbstract\nThe
classical Linnik problems are concerned with the equidistribution of adeli
c torus orbits on the homogeneous spaces attached to inner forms of GL2\,
as the discriminant of the torus gets large. When specialized\, these prob
lems admit beautiful classical interpretations\, such as the equidistribut
ion of integer points on spheres\, of Heegner points or packets of closed
geodesics on the modular surface\, or of supersingular reductions of CM el
liptic curves. In the mid 20th century\, Linnik and his school established
the equidistribution of many of these classical variants through his ergo
dic method\, under a congruence condition on the discriminants modulo a fi
xed auxiliary prime. More recently\, the Waldspurger formula and subconvex
estimates on L-functions were used to remove these congruence conditions\
, and provide effective power-savings rates.\n\nIn their 2006 ICM address\
, Michel and Venkatesh proposed a variant of this problem in which one con
siders the product of two distinct inner forms of GL2\, along with a diago
nally embedded torus. One can again specialize the setting to obtain inter
esting classical reformulations\, such as the joint equidistribution of in
teger points on the sphere\, together with the shape of the orthogonal lat
tice. This hybrid context has received a great deal of attention recently
in the dynamics community\, where\, for instance\, the latter problem was
solved by Aka\, Einsiedler\, and Shapira\, under supplementary congruence
conditions modulo two fixed primes\, using as critical input the joinings
theorem of Einsiedler and Lindenstrauss.\n\nIn joint (ongoing) work with V
alentin Blomer\, we remove the supplementary congruence conditions in the
joint equidistribution problem\, conditionally on the Riemann Hypothesis\
, while obtaining a logarithmic rate of convergence. The proof uses Waldsu
rger’s theorem and estimates of fractional moments of L-functions in the
family of class group twists.\n
LOCATION:https://stable.researchseminars.org/talk/PrincetonIASNT/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Florian Richter (Northwestern University)
DTSTART:20200604T190000Z
DTEND:20200604T200000Z
DTSTAMP:20260404T094801Z
UID:PrincetonIASNT/9
DESCRIPTION:Title: Dynamical generalizations of the Prime Number Theorem and di
sjointness of additive and multiplicative actions\nby Florian Richter
(Northwestern University) as part of Princeton/IAS number theory seminar\n
\n\nAbstract\nOne of the fundamental challenges in number theory is to und
erstand the intricate way in which the additive and multiplicative structu
res in the integers intertwine. We will explore a dynamical approach to th
is topic. After introducing a new dynamical framework for treating questio
ns in multiplicative number theory\, we will present an ergodic theorem wh
ich contains various classical number-theoretic results\, such as the Prim
e Number Theorem\, as special cases. This naturally leads to a formulation
of an extended form of Sarnak's conjecture\, which deals with the disjoin
tness of actions of (N\,+) and (N\,*). This talk is based on joint work wi
th Vitaly Bergelson.\n
LOCATION:https://stable.researchseminars.org/talk/PrincetonIASNT/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Rong Zhou (Imperial College London)
DTSTART:20200618T190000Z
DTEND:20200618T200000Z
DTSTAMP:20260404T094801Z
UID:PrincetonIASNT/10
DESCRIPTION:Title: Independence of $\\ell$ for Frobenius conjugacy classes att
ached to abelian varieties\nby Rong Zhou (Imperial College London) as
part of Princeton/IAS number theory seminar\n\n\nAbstract\nLet $A$ be an a
belian variety over a number field $E\\subset \\mathbb{C}$ and let $v$ be
a place of good reduction lying over a prime $p$. For a prime $\\ell\\neq
p$\, a result of Deligne implies that upon replacing $E$ by a finite exten
sion\, the Galois representation on the $\\ell$-adic Tate module of $A$ fa
ctors as $\\rho_\\ell:\\mathrm{Gal}(\\overline{E}/E)\\rightarrow G_A$\, wh
ere $G_A$ is the Mumford--Tate group of $A_{\\mathbb{C}}$. For $p>2$\, we
prove that the conjugacy class of $\\rho_\\ell(\\mathrm{Frob}_v)$ is defi
ned over $\\mathbb{Q}$ and independent of $\\ell$. This is joint work with
Mark Kisin.\n
LOCATION:https://stable.researchseminars.org/talk/PrincetonIASNT/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vesselin Dimitrov (University of Toronto)
DTSTART:20200611T190000Z
DTEND:20200611T200000Z
DTSTAMP:20260404T094801Z
UID:PrincetonIASNT/11
DESCRIPTION:Title: New constraints on the Galois configurations of algebraic i
ntegers in the complex plane\nby Vesselin Dimitrov (University of Toro
nto) as part of Princeton/IAS number theory seminar\n\n\nAbstract\nFekete
(1923) discovered the notion of transfinite diameter while studying the po
ssible configurations of Galois orbits of algebraic integers in the comple
x plane. Based purely on the fact that the discriminants of monic integer
irreducible polynomials $P(X) \\in \\mathbb{Z}[X]$ are at least $1$ in mag
nitude (since they are non-zero integers)\, he found that the incidences $
(\\mathcal{K}\, P)$ between these polynomials $P(X)$ and compacts $\\mathc
al{K} \\subset \\mathbb{C}$ of transfinite diameter $d(\\mathcal{K}) < 1$
have finite fibers over the argument $\\mathcal{K}$. Here we say that $\\m
athcal{K}$ and $P$ are in incidence if all the roots of $P$ belong to $\\m
athcal{K}$. The descendants of Fekete's theorem are vast and powerful\, no
tably including the equidistribution theorems of Bilu\, Rumely and Szpiro-
Ullmo-Zhang or -- in a different line of development -- the root separatio
n bound of Mahler. But the input on the discriminant is sometimes too coar
se to be useful: in reality one expects\, but cannot prove\, that discrimi
nants of polynomials are large\, and dropping them by integrality is too c
rude in certain finer questions such as Lehmer's. \n\nBreusch (1951) solve
d the non-reciprocal case of the Lehmer problem by taking up a lossless ar
ithmetic input from resultants rather than discriminants. In this talk\, I
will present some further lossless constraints that derive from certain w
hole infinite sequences of Hankel determinants attached to the polynomial
$P(X)$ by algebraic operations. This will allow us to update on Fekete's t
heorem on the incidences $(\\mathcal{K}\,P)$\, by focusing this time on th
e fibers over the argument $P$ for compacts $\\mathcal{K}$ that are made o
f finite unions of Jordan arcs continua covering the roots of $P$ with cer
tain congruence conditions on $P$ and on the connected components of $\\ma
thcal{K}$. The ensuing taming on Galois orbits turn out to be sufficiently
severe to resolve the conjecture of Schinzel and Zassenhaus (I will expla
in this case in detail)\, amidst certain other cases of the Lehmer problem
that are far off from Salem's extreme. In a geometric formulation for $\\
mathcal{A}_g$ with its Kobayashi metric\, the root spacing constraints are
likewise sufficiently severe to furthermore yield the exact $\\mathcal{A}
_g$ analogs of the well-known polynomial counting theorems of Penner and L
eininger-Margalit on the "$L$-short" geodesics of moduli space $\\mathcal{
M}_g$.\n
LOCATION:https://stable.researchseminars.org/talk/PrincetonIASNT/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sarah Peluse (IAS)
DTSTART:20200910T203000Z
DTEND:20200910T213000Z
DTSTAMP:20260404T094801Z
UID:PrincetonIASNT/12
DESCRIPTION:Title: An asymptotic version of the prime power conjecture for per
fect difference sets\nby Sarah Peluse (IAS) as part of Princeton/IAS n
umber theory seminar\n\n\nAbstract\nA subset D of a finite cyclic group Z/
mZ is called a "perfect difference set" if every nonzero element of Z/mZ c
an be written uniquely as the difference of two elements of D. If such a s
et exists\, then a simple counting argument shows that m=n^2+n+1 for some
nonnegative integer n. Singer constructed examples of perfect difference s
ets in Z/(n^2+n+1)Z whenever n is a prime power\, and it is an old conject
ure that these are the only such n for which a perfect difference set exis
ts. In this talk\, I will discuss a proof of an asymptotic version of this
conjecture: the number of n less than N for which Z/(n^2+n+1)Z contains a
perfect difference set is ~N/log(N).\n
LOCATION:https://stable.researchseminars.org/talk/PrincetonIASNT/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tony Feng (MIT and IAS)
DTSTART:20200917T180000Z
DTEND:20200917T190000Z
DTSTAMP:20260404T094801Z
UID:PrincetonIASNT/13
DESCRIPTION:Title: Equivariant localization\, parity sheaves\, and cyclic base
change\nby Tony Feng (MIT and IAS) as part of Princeton/IAS number th
eory seminar\n\n\nAbstract\nLafforgue and Genestier-Lafforgue have const
ructed the global and (semisimplified) local Langlands correspondences fo
r arbitrary reductive groups over function fields. I will explain some re
cently established properties of these correspondences regarding base chan
ge functoriality: existence of transfers for mod p automorphic forms throu
gh p-cyclic base change in the global correspondence\, and Tate cohomology
realizes p-cyclic base change in the mod p local correspondence. The proo
fs are based on a combination of equivariant localization arguments (inspi
red by work of Treumann-Venkatesh) and the theory of parity sheaves (due t
o Juteau-Mautner-Williamson).\n
LOCATION:https://stable.researchseminars.org/talk/PrincetonIASNT/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Abhishek Oswal (IAS)
DTSTART:20200924T203000Z
DTEND:20200924T213000Z
DTSTAMP:20260404T094801Z
UID:PrincetonIASNT/14
DESCRIPTION:Title: A non-Archimedean definable Chow theorem\nby Abhishek O
swal (IAS) as part of Princeton/IAS number theory seminar\n\n\nAbstract\nI
n recent years\, o-minimality has found some striking applications to diop
hantine geometry. The utility of o-minimal structures originates from the
remarkably tame topological properties satisfied by sets definable in such
structures. Despite the rigidity that it imposes\, the theory is sufficie
ntly flexible to allow for a range of analytic constructions. An illustrat
ion of this `tame' property is the following surprising generalization of
Chow's theorem proved by Peterzil and Starchenko - A closed analytic subs
et of a complex algebraic variety that is also definable in an o-minimal s
tructure\, is in fact algebraic. While the o-minimal machinery aims to cap
ture the archimedean order topology of the real line\, it is natural to wo
nder if such a machinery can be set up over non-archimedean fields. In thi
s talk\, we shall explore a non-archimedean analogue of an o-minimal struc
ture and a version of the definable Chow theorem in this context.\n
LOCATION:https://stable.researchseminars.org/talk/PrincetonIASNT/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jessica Fintzen (IAS and Duke University)
DTSTART:20201008T180000Z
DTEND:20201008T190000Z
DTSTAMP:20260404T094801Z
UID:PrincetonIASNT/15
DESCRIPTION:Title: Representations of p-adic groups and applications\nby J
essica Fintzen (IAS and Duke University) as part of Princeton/IAS number t
heory seminar\n\n\nAbstract\nThe Langlands program is a far-reaching colle
ction of conjectures that relate different areas of mathematics including
number theory and representation theory. A fundamental problem on the repr
esentation theory side of the Langlands program is the construction of all
(irreducible\, smooth\, complex) representations of p-adic groups.\nI wil
l provide an overview of our understanding of the representations of p-adi
c groups\, with an emphasis on recent progress.\nI will also outline how n
ew results about the representation theory of p-adic groups can be used to
obtain congruences between arbitrary automorphic forms and automorphic fo
rms which are supercuspidal at p\, which is joint work with Sug Woo Shin.
This simplifies earlier constructions of attaching Galois representations
to automorphic representations\, i.e. the global Langlands correspondence\
, for general linear groups. Moreover\, our results apply to general p-adi
c groups and have therefore the potential to become widely applicable beyo
nd the case of the general linear group.\n
LOCATION:https://stable.researchseminars.org/talk/PrincetonIASNT/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Carney Alexander (University of Rochester)
DTSTART:20201015T203000Z
DTEND:20201015T213000Z
DTSTAMP:20260404T094801Z
UID:PrincetonIASNT/16
DESCRIPTION:Title: Heights and dynamics over arbitrary fields\nby Carney A
lexander (University of Rochester) as part of Princeton/IAS number theory
seminar\n\n\nAbstract\n"Classically\, heights are defined over number fiel
ds or transcendence degree one function fields. This is so that the Northc
ott property\, which says that sets of points with bounded height are fini
te\, holds. Here\, expanding on work of Moriwaki and Yuan-Zhang\, we show
how to define arithmetic intersections and heights relative to any finitel
y generated field extension K/k\, and construct canonical heights for pola
rizable arithmetic dynamical systems f:X->X. These heights have a correspo
nding Northcott property when k is Q or F_q. When k is larger\, we show th
at Northcott for canonical heights is conditional on the non-isotriviality
of f:X->X\, generalizing work of Lang-Neron\, Baker\, and Chatzidakis-Hru
shovski. Additionally\, we prove the Hodge Index Theorem for arithmetic in
tersections relative to K/k. Since\, when Northcott holds\, preperiodic po
ints are the same as height zero points\, this has applications to dynamic
al systems. By the Lefschetz principle\, these results can be applied over
any field.\n"\n
LOCATION:https://stable.researchseminars.org/talk/PrincetonIASNT/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tasho Kaletha (University of Michigan and IAS)
DTSTART:20201029T203000Z
DTEND:20201029T213000Z
DTSTAMP:20260404T094801Z
UID:PrincetonIASNT/17
DESCRIPTION:Title: An explicit supercuspidal local Langlands correspondence\nby Tasho Kaletha (University of Michigan and IAS) as part of Princeton/
IAS number theory seminar\n\n\nAbstract\nWe will give an explicit construc
tion and description of a supercuspidal local Langlands correspondence for
any p-adic group G that splits over a tame extension\, provided p does no
t divide the order of the Weyl group. This construction matches any discre
te Langlands parameters with trivial monodromy to an L-packet consisting o
f supercuspidal representations\, and describes the internal structure of
these L-packets.\n\nThe construction has two parts. The depth-zero part in
volves generalizing to disconnected groups results of Lusztig on the decom
position of a non-singular Deligne-Lusztig induction. Higher multiplicitie
s occur in this decomposition and are handled using work of Bonnafe-Dat-Ro
uquier. The positive-depth part involves functorial transfer from a twiste
d Levi subgroup\, which is made possible by an improvement of Yu's constru
ction of supercuspidal representations obtained in recent joint work with
Fintzen and Spice\, and consideration of Harish-Chandra characters.\n\nWe
will also discuss ongoing work towards related conjectures: Shahidi's gene
ric L-packet conjecture\, Hiraga-Ichino-Ikeda formal degree conjecture\,
stability and endoscopic transfer.\n
LOCATION:https://stable.researchseminars.org/talk/PrincetonIASNT/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Shai Evra (Princeton)
DTSTART:20201119T213000Z
DTEND:20201119T223000Z
DTSTAMP:20260404T094801Z
UID:PrincetonIASNT/18
DESCRIPTION:Title: Ramanujan Conjecture and the Density Hypothesis\nby Sha
i Evra (Princeton) as part of Princeton/IAS number theory seminar\n\n\nAbs
tract\nThe Generalized Ramanujan Conjecture (GRC) for GL(n) is a central o
pen problem in modern number theory. Its resolution is known to yield seve
ral important applications. For instance\, the Ramanujan-Petersson conject
ure for GL(2)\, proven by Deligne\, was a key ingredient in the work of Lu
botzky-Phillips-Sarnak on Ramanujan graphs.\nOne can also state analogues
(Naive) Ramanujan Conjectures (NRC) for other reductive groups. However\,
in the 70's Kurokawa and Howe-Piatetski-Shapiro proved that the (NRC) fail
s even for quasi-split classical groups.\nIn the 90's Sarnak-Xue put forth
a Density Hypothesis version of the (NRC)\, which serves as a replacement
of the (NRC) in applications.\nIn this talk I will describe a possible ap
proach to proving the Density Hypothesis for definite classical groups\, b
y invoking deep and recent results coming from the Langlands program: The
endoscopic classification of automorphic representations of classical grou
ps due to Arthur\, and the proof of the Generalized Ramanujan-Petersson Co
njecture.\n
LOCATION:https://stable.researchseminars.org/talk/PrincetonIASNT/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:William Chen (Columbia University)
DTSTART:20201105T213000Z
DTEND:20201105T223000Z
DTSTAMP:20260404T094801Z
UID:PrincetonIASNT/19
DESCRIPTION:Title: Strong approximation for the Markoff equation via nonabelia
n level structures on elliptic curves\nby William Chen (Columbia Unive
rsity) as part of Princeton/IAS number theory seminar\n\n\nAbstract\nFollo
wing 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 it
s integral points surject onto its F_p points. In 2016\, Bourgain\, Gambur
d\, and Sarnak were able to establish strong approximation at all but a sp
arse (but infinite) set of primes\, and conjecture that it holds at all pr
imes. Building on their results\, in this talk I will explain how to obtai
n strong approximation for all but a finite and effectively computable set
of primes\, thus reducing the conjecture to a finite computation. The key
result amounts to establishing a congruence on the degree of a certain li
ne bundle on the moduli stack of elliptic curves with SL(2\,p)-structures.
To make contact with the Markoff equation\, we use the fact that the Mark
off surface is a level set of the character variety for SL(2) representati
ons of the fundamental group of a punctured torus\, and that the strong ap
proximation conjecture can be expressed in terms of the mapping class grou
p action on the character variety\, which in turn also determines the geom
etry of the moduli stack of elliptic curves with SL(2\,p)-structures. As t
ime allows we will also describe a number of applications.\n
LOCATION:https://stable.researchseminars.org/talk/PrincetonIASNT/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Levent Alpoge (Columbia University)
DTSTART:20201112T213000Z
DTEND:20201112T223000Z
DTSTAMP:20260404T094801Z
UID:PrincetonIASNT/20
DESCRIPTION:Title: Effective height bounds for odd-degree totally real points
on some curves\nby Levent Alpoge (Columbia University) as part of Prin
ceton/IAS number theory seminar\n\n\nAbstract\nLet $\\mathfrak o$ be an or
der in a totally real field\, say $F$. Let $K$ be an odd-degree totally re
al field. Let $S$ be a finite set of places of $K$. We study $S$-integral
$K$-points on integral models $H_\\mathfrak o$ of Hilbert modular varietie
s because not only do said varieties admit complete curves (thus reducing
questions about such curves' $K$-rational points to questions about $S$-in
tegral $K$-points on these integral models)\, they also have their $S$-int
egral $K$-points controlled by known cases of modularity\, in the followin
g way. First assume for clarity modularity of all $\\GL_2$-type abelian va
rieties over $K$ --- then all $S$-integral $K$-points on $H_\\mathfrak o$
arise from $K$-isogeny factors of the $[F:\\mathbb Q]$-th power of the Jac
obian of a single Shimura curve with level structure (by Jacquet-Langlands
transfer). By a generalization of an argument of von Känel\, isogeny est
imates of Raynaud/Masser-Wüstholz and Bost's lower bound on the Faltings
height suffice to then bound the heights of all points in $H_\\mathfrak o(
\\mathfrak o_{K\,S})$. As for the assumption\, though modularity is of cou
rse not known in this generality\, by following Taylor's (sufficiently exp
licit for us) proof of his potential modularity theorem we are able to mak
e the above unconditional.\n\nFinally we use the hypergeometric abelian va
rieties associated to the arithmetic triangle group $\\Delta(3\,6\,6)$ to
give explicit examples of curves to which the above height bounds apply. S
pecifically\, we prove that\, for $a\\in \\overline{\\mathbb Q}^\\times$ t
otally real of odd degree (e.g. $a = 1$) and $L/\\mathbb Q(a)$ totally rea
l of odd degree\, there is an effectively computable $c = c_{a\,L}\\in \\Z
^+$ 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 for each of which Falti
ngs' theorem is now effective over infinitely many number fields.\n
LOCATION:https://stable.researchseminars.org/talk/PrincetonIASNT/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jingwei Xiao (Princeton University and IAS)
DTSTART:20201203T213000Z
DTEND:20201203T223000Z
DTSTAMP:20260404T094801Z
UID:PrincetonIASNT/21
DESCRIPTION:Title: A unitary analogy of Friedberg-Jacquet and Guo-Jacquet peri
ods and central values of standard L functions on GL(2n)\nby Jingwei X
iao (Princeton University and IAS) as part of Princeton/IAS number theory
seminar\n\n\nAbstract\nLet G be a reductive group over a number field F an
d H a subgroup. Automorphic periods study the integrals of cuspidal automo
rphic forms on G over H(F)\\H(A_F). They are often related to special valu
es of certain L functions. One of the most notable case is when (G\,H)=(U(
n+1)☓U(n)\, U(n))\, and these periods are related to central values of R
ankin-Selberg L functions on GL(n+1)☓GL(n). In this talk\, I will explai
n my work in progress with Wei Zhang that studies central values of standa
rd L functions on GL(2n) using (G\,H)=(U(2n)\, U(n)☓U(n)) and some varia
nts. I shall explain the conjecture and a relative trace formula approach
to study it. We prove the required fundamental lemma using a limit of the
Jacquet-Rallis fundamental lemma and Hironaka’s characterization of sphe
rical functions on the space of non degenerate Hermitian matrices. Also\,
the question admits an arithmetic analogy.\n
LOCATION:https://stable.researchseminars.org/talk/PrincetonIASNT/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Joni Teravainen (Oxford)
DTSTART:20201210T213000Z
DTEND:20201210T223000Z
DTSTAMP:20260404T094801Z
UID:PrincetonIASNT/22
DESCRIPTION:Title: On the Liouville function at polynomial arguments\nby J
oni Teravainen (Oxford) as part of Princeton/IAS number theory seminar\n\n
\nAbstract\nLet λ be the Liouville function and P(x) any polynomial that
is not a square. An open problem formulated by Chowla and others asks to s
how that the sequence λ(P(n)) changes sign infinitely often. We present a
solution to this problem for new classes of polynomials P\, including any
product of linear factors or any product of quadratic factors of a certai
n type. The proofs also establish some nontrivial cancellation in Chowla a
nd Elliott type correlation averages.\n
LOCATION:https://stable.researchseminars.org/talk/PrincetonIASNT/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lue Pan (University of Chicago)
DTSTART:20201022T203000Z
DTEND:20201022T213000Z
DTSTAMP:20260404T094801Z
UID:PrincetonIASNT/23
DESCRIPTION:Title: On the locally analytic vectors of the completed cohomology
of modular curves\nby Lue Pan (University of Chicago) as part of Prin
ceton/IAS number theory seminar\n\n\nAbstract\nA classical result identifi
es holomorphic modular forms with highest weight vectors of certain repres
entations of SL_2(\\mathbb{R}). We study locally analytic vectors of the (
p-adically) completed cohomology of modular curves and prove a p-adic anal
ogue of this result. As applications\, we are able to prove a classicality
result for overconvergent eigenforms and give a new proof of Fontaine-Maz
ur conjecture in the irregular case under some mild hypothesis. One techni
cal tool is relative Sen theory which allows us to relate infinitesimal gr
oup action with Hodge(-Tate) structure.\n
LOCATION:https://stable.researchseminars.org/talk/PrincetonIASNT/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Joel Nagloo (City University of New York)
DTSTART:20210121T213000Z
DTEND:20210121T223000Z
DTSTAMP:20260404T094801Z
UID:PrincetonIASNT/24
DESCRIPTION:Title: Ax-Lindemann-Weierstrass Theorem (ALW) for Fuchsian automor
phic functions\nby Joel Nagloo (City University of New York) as part o
f Princeton/IAS number theory seminar\n\n\nAbstract\nOver the last decades
\, following works around the Pila-Wilkie counting theorem in the context
of o-minimality\, there has been a surge in interest around functional tra
nscendence results\, in part due to their connection with special points c
onjectures. A prime example is Pila's modular ALW Theorem and its role in
his proof of the André-Oort conjecture. \n\nIn this talk we will discuss
how an entirely new approach\, using the model theory of differential fiel
ds\, can be used to prove the Ax-Lindemann-Weierstrass (ALW) Theorem with
derivatives for Fuchsian automorphic functions - a direct generalization o
f Pila’s ALW theorem. We will also explain how new cases of the André-P
ink conjecture can be obtained using this new approach. This is joint work
with G. Casale and J. Freitag.\n
LOCATION:https://stable.researchseminars.org/talk/PrincetonIASNT/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mathilde Gerbelli-Gauthier (IAS)
DTSTART:20210211T213000Z
DTEND:20210211T223000Z
DTSTAMP:20260404T094801Z
UID:PrincetonIASNT/25
DESCRIPTION:Title: Cohomology of Arithmetic Groups and Endoscopy\nby Mathi
lde Gerbelli-Gauthier (IAS) as part of Princeton/IAS number theory seminar
\n\n\nAbstract\nHow fast do Betti numbers grow in a congruence tower of co
mpact arithmetic manifolds? The dimension of the middle degree of cohomolo
gy is proportional to the volume of the manifold\, but away from the middl
e the growth is known to be sub-linear in the volume. I will explain how a
utomorphic representations and the phenomenon of endoscopy provide a frame
work to understand and quantify this slow growth. Specifically\, I will di
scuss how to obtain some explicit bounds in the case of unitary groups usi
ng Arthur’s stable trace formula.\n
LOCATION:https://stable.researchseminars.org/talk/PrincetonIASNT/25/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Salim Tayou (IAS)
DTSTART:20210218T213000Z
DTEND:20210218T223000Z
DTSTAMP:20260404T094801Z
UID:PrincetonIASNT/26
DESCRIPTION:Title: Exceptional jumps of Picard rank of K3 surfaces over number
fields\nby Salim Tayou (IAS) as part of Princeton/IAS number theory s
eminar\n\n\nAbstract\nGiven a K3 surface X over a number field K\, we prov
e that the set of primes of K where the geometric Picard rank jumps is inf
inite\, assuming that X has everywhere potentially good reduction. This re
sult is formulated in the general framework of GSpin Shimura varieties and
I will explain other applications to abelian surfaces. I will also discus
s applications to the existence of rational curves on K3 surfaces. The res
ults in this talk are joint work with Ananth Shankar\, Arul Shankar and Yu
nqing Tang.\n
LOCATION:https://stable.researchseminars.org/talk/PrincetonIASNT/26/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hang Xue (The University of Arizona)
DTSTART:20210325T203000Z
DTEND:20210325T213000Z
DTSTAMP:20260404T094801Z
UID:PrincetonIASNT/27
DESCRIPTION:Title: The local Gan-Gross-Prasad conjecture for real unitary grou
ps\nby Hang Xue (The University of Arizona) as part of Princeton/IAS n
umber theory seminar\n\n\nAbstract\nA classical branching theorem of Weyl
describes how an irreducible representation of compact U(n+1) decomposes w
hen restricted to U(n). The local Gan-Gross-Prasad conjecture provides a c
onjectural extension to the setting of representations of noncompact unita
ry groups lying in a generic L-packet. We prove this conjecture. Previousl
y Beuzart-Plessis proved the ''multiplicity one in a Vogan packet'' part o
f the conjecture for tempered L-packets using the local trace formula appr
oach initiated by Waldspurger. Our proof uses theta lifts instead\, and is
independent of the trace formula argument.\n
LOCATION:https://stable.researchseminars.org/talk/PrincetonIASNT/27/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sam Mundy (Columbia University)
DTSTART:20210401T203000Z
DTEND:20210401T213000Z
DTSTAMP:20260404T094801Z
UID:PrincetonIASNT/28
DESCRIPTION:Title: Eisenstein series\, $p$-adic deformations\, Galois represen
tations\, and the group $G_2$.\nby Sam Mundy (Columbia University) as
part of Princeton/IAS number theory seminar\n\n\nAbstract\nI will explain
some recent work on special cases of the Bloch-Kato conjecture for the sym
metric cube of certain modular Galois representations. Under certain stand
ard conjectures\, this work constructs nontrivial elements in the Selmer g
roups of these symmetric cube Galois representations\; this works by $p$-a
dically deforming critical Eisenstein series in a generically cuspidal fam
ily of automorphic representations\, and then constructing a lattice in th
e associated family of Galois representations\, all for the exceptional gr
oup $G_2$. While I will touch on all of these aspects of the construction\
, I will mainly focus on the Galois side in this talk.\n
LOCATION:https://stable.researchseminars.org/talk/PrincetonIASNT/28/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Chao Li (Columbia University)
DTSTART:20210415T203000Z
DTEND:20210415T213000Z
DTSTAMP:20260404T094801Z
UID:PrincetonIASNT/29
DESCRIPTION:Title: Beilinson-Bloch conjecture for unitary Shimura varieties\nby Chao Li (Columbia University) as part of Princeton/IAS number theory
seminar\n\n\nAbstract\nFor certain automorphic representations $\\pi$ on
unitary groups\, we show that if $L(s\, \\pi)$ vanishes to order one at th
e center $s=1/2$\, then the associated $\\pi$-localized Chow group of a un
itary Shimura variety is nontrivial. This proves part of the Beilinson-Blo
ch conjecture for unitary Shimura varieties\, which generalizes the BSD co
njecture. Assuming Kudla's modularity conjecture\, we further prove the ar
ithmetic inner product formula for $L'(1/2\, \\pi)$\, which generalizes th
e Gross-Zagier formula. We will motivate these conjectures and discuss som
e aspects of the proof. We will also mention recent extensions applicable
to symmetric power L-functions of elliptic curves. This is joint work with
Yifeng Liu.\n
LOCATION:https://stable.researchseminars.org/talk/PrincetonIASNT/29/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yves André (CNRS)
DTSTART:20210429T200000Z
DTEND:20210429T210000Z
DTSTAMP:20260404T094801Z
UID:PrincetonIASNT/30
DESCRIPTION:Title: On the canonical\, fpqc and finite topologies: classical qu
estions\, new answers (and conversely)\nby Yves André (CNRS) as part
of Princeton/IAS number theory seminar\n\n\nAbstract\nUp to a finite cover
ing\, a sequence of nested subvarieties of an affine algebraic variety jus
t looks like a flag of vector spaces (Noether)\; understanding this « up
to » is a primary motivation for a fine study of finite coverings. \n\nTh
e aim of this talk is to give a bird-eye view of some fundamental question
s about them\, which took root in Algebraic Geometry (descent problems etc
.)\, then motivated major trends in Commutative Algebra (F-singularities e
tc.)\, and recently found complete solutions using p-adic methods (perfect
oids). Rather than going into detail of the latter\, the emphasis will be
on synthesizing\, from the geometric viewpoint\, a rather scattered theme.
\n\nThis is based on joint work with Luisa Fiorot (https://doi.org/10.242
2/2036-2145.201912_006)\n
LOCATION:https://stable.researchseminars.org/talk/PrincetonIASNT/30/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gal Dor (Tel Aviv University)
DTSTART:20210304T213000Z
DTEND:20210304T223000Z
DTSTAMP:20260404T094801Z
UID:PrincetonIASNT/31
DESCRIPTION:Title: Monoidal Structures on GL(2)-Modules and Abstractly Automor
phic Representations\nby Gal Dor (Tel Aviv University) as part of Prin
ceton/IAS number theory seminar\n\n\nAbstract\nConsider the function field
F of a smooth curve over $F_q$\, with q>2.\n\nL-functions of automorphic
representations of GL(2) over F are important objects for studying the ari
thmetic properties of the field F. Unfortunately\, they can be defined in
two different ways: one by Godement-Jacquet\, and one by Jacquet-Langlands
. Classically\, one shows that the resulting L-functions coincide using a
complicated computation.\n\nEach of these L-functions is the GCD of a fami
ly of zeta integrals associated to test data. I will categorify the questi
on\, by showing that there is a correspondence between the two families of
zeta integrals\, instead of just their L-functions. The resulting compari
son of test data will induce an exotic symmetric monoidal structure on the
category of representations of GL(2).\n\nIt turns out that an appropriate
space of automorphic functions is a commutative algebra with respect to t
his symmetric monoidal structure. I will outline this construction\, and s
how how it can be used to construct a category of automorphic representati
ons.\n
LOCATION:https://stable.researchseminars.org/talk/PrincetonIASNT/31/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexandru Zaharescu (UIUC)
DTSTART:20210311T213000Z
DTEND:20210311T223000Z
DTSTAMP:20260404T094801Z
UID:PrincetonIASNT/32
DESCRIPTION:Title: Some remarks on Landau-Siegel zeros\nby Alexandru Zahar
escu (UIUC) as part of Princeton/IAS number theory seminar\n\nAbstract: TB
A\n
LOCATION:https://stable.researchseminars.org/talk/PrincetonIASNT/32/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Will Sawin (Columbia university)
DTSTART:20210318T203000Z
DTEND:20210318T213000Z
DTSTAMP:20260404T094801Z
UID:PrincetonIASNT/33
DESCRIPTION:Title: The Shafarevich Conjecture for Hypersurfaces in Abelian Var
ieties\nby Will Sawin (Columbia university) as part of Princeton/IAS n
umber theory seminar\n\n\nAbstract\nFaltings proved the statement\, previo
usly conjectured by Shafarevich\, that there are finitely many abelian var
ieties of dimension n\, defined over a fixed number field\, with good redu
ction outside a fixed finite set of primes\, up to isomorphism. In joint w
ork with Brian Lawrence\, we prove an analogous finiteness statement for h
ypersurfaces in a fixed abelian variety with good reduction outside a fini
te set of primes. I will give a broad introduction to some of the ideas in
the proof\, which builds on p-adic Hodge theory techniques from work of L
awrence and Venkatesh as well as sheaf convolution in algebraic geometry.\
n
LOCATION:https://stable.researchseminars.org/talk/PrincetonIASNT/33/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Adam Harper (University of Warwick)
DTSTART:20210408T203000Z
DTEND:20210408T213000Z
DTSTAMP:20260404T094801Z
UID:PrincetonIASNT/34
DESCRIPTION:Title: Low moments of character sums\nby Adam Harper (Universi
ty of Warwick) as part of Princeton/IAS number theory seminar\n\n\nAbstrac
t\nSums of Dirichlet characters $\\sum_{n \\leq x}\\chi(n)$ (where $\\chi$
is a character modulo some prime $r$\, say) are one of the best studied o
bjects in analytic number theory. Their size is the subject of numerous re
sults and conjectures\, such as the P\\'olya--Vinogradov inequality and th
e Burgess bound. One way to get information about this is to study the pow
er moments $\\frac{1}{r−1}\\sum_{\\chi\\mod r}|\\sum_{n≤x}\\chi(n)|^{2
q}$\, which turns out to be quite a subtle question that connects with iss
ues in probability and physics. In this talk I will describe an upper boun
d for these moments when $0≤q≤1$. I will focus mainly on the number th
eoretic issues arising.\n
LOCATION:https://stable.researchseminars.org/talk/PrincetonIASNT/34/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andrei Rapinchuk (University of Virginia)
DTSTART:20210506T203000Z
DTEND:20210506T213000Z
DTSTAMP:20260404T094801Z
UID:PrincetonIASNT/35
DESCRIPTION:Title: Groups with bounded generation: old and new\nby Andrei
Rapinchuk (University of Virginia) as part of Princeton/IAS number theory
seminar\n\n\nAbstract\nA group is said to have bounded generation (BG) if
it is a finite product of cyclic subgroups. We will survey the known examp
les of groups with (BG) and their properties. We will then report on a rec
ent result (joint with P. Corvaja\, J. Ren and U. Zannier) that non-virtua
lly abelian anisotropic linear groups (i. e. those consisting entirely of
semi-simple elements) are not boundedly generated. The proofs rely on numb
er-theoretic techniques.\n
LOCATION:https://stable.researchseminars.org/talk/PrincetonIASNT/35/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Naomi Sweeting (Harvard)
DTSTART:20210422T203000Z
DTEND:20210422T213000Z
DTSTAMP:20260404T094801Z
UID:PrincetonIASNT/36
DESCRIPTION:Title: Kolyvagin's conjecture and higher congruences of modular fo
rms\nby Naomi Sweeting (Harvard) as part of Princeton/IAS number theor
y seminar\n\n\nAbstract\nGiven an elliptic curve E\, Kolyvagin used CM poi
nts on modular curves to construct a system of classes valued in the Galoi
s cohomology of the torsion points of E. Under the conjecture that not all
of these classes vanish\, he gave a description for the Selmer group of E
. This talk will report on recent work proving new cases of Kolyvagin's co
njecture. The proof builds on work of Wei Zhang\, who used congruences bet
ween modular forms to prove Kolyvagin's conjecture under some technical hy
potheses. We remove many of these hypotheses by considering congruences mo
dulo higher powers of p. The talk will explain the difficulties associated
with higher congruences of modular forms and how they can be overcome.\n
LOCATION:https://stable.researchseminars.org/talk/PrincetonIASNT/36/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexander Smith (MIT)
DTSTART:20210225T213000Z
DTEND:20210225T223000Z
DTSTAMP:20260404T094801Z
UID:PrincetonIASNT/37
DESCRIPTION:Title: Selmer groups and a Cassels-Tate pairing for finite Galois
modules\nby Alexander Smith (MIT) as part of Princeton/IAS number theo
ry seminar\n\n\nAbstract\nI will discuss some new results on the structure
of Selmer groups of finite Galois modules over global fields. Tate's defi
nition of the Cassels-Tate pairing can be extended to a pairing on such Se
lmer groups with little adjustment\, and many of the fundamental propertie
s of the Cassels-Tate pairing can be reproved with new methods in this set
ting. I will also give a general definition of the theta/Mumford group and
relate it to the structure of the Cassels-Tate pairing\, generalizing wor
k of Poonen and Stoll.\n
LOCATION:https://stable.researchseminars.org/talk/PrincetonIASNT/37/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Maksym Radziwiłł (Caltech)
DTSTART:20210513T203000Z
DTEND:20210513T213000Z
DTSTAMP:20260404T094801Z
UID:PrincetonIASNT/38
DESCRIPTION:Title: Expansion and parity\nby Maksym Radziwiłł (Caltech) a
s part of Princeton/IAS number theory seminar\n\n\nAbstract\nI will discus
s recent work with Harald Helfgott in which we establish roughly speaking
that the graph connecting n to n +/- p with p a prime dividing n is almost
"locally Ramanujan". As a result we obtain improvements of results of Tao
and Tao-Teravainen on logarithmic Chowla. I will discuss the main ideas i
n the proof and the connections with logarithmic Chowla.\n
LOCATION:https://stable.researchseminars.org/talk/PrincetonIASNT/38/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Michael Larsen (Indiana University Bloomington)
DTSTART:20210527T203000Z
DTEND:20210527T213000Z
DTSTAMP:20260404T094801Z
UID:PrincetonIASNT/39
DESCRIPTION:Title: Character estimates for classical finite simple groups\
nby Michael Larsen (Indiana University Bloomington) as part of Princeton/I
AS number theory seminar\n\n\nAbstract\nThis is intended to complement the
recent talk of Pham Huu Tiep in this seminar but will not assume familiar
ity with that talk. The estimates in the title are upper bounds of the fo
rm $|\\chi(g)| \\le \\chi(1)^\\alpha$\, where $\\chi$ is irreducible and $
\\alpha$ depends on the size of the centralizer of g. I will briefly disc
uss geometric applications of such bounds\, explain how probability theory
can be used to reduce to the case of elements g of small centralizer\, di
scuss the level theory of characters\, and conclude with the reduction to
the case of characters $\\chi$ of large degree. For such pairs (g\,$\\chi
$)\, exponential character bounds are trivial.\n
LOCATION:https://stable.researchseminars.org/talk/PrincetonIASNT/39/
END:VEVENT
END:VCALENDAR