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BEGIN:VEVENT
SUMMARY:Stefan Steinerberger (University of Washington)
DTSTART:20200915T180000Z
DTEND:20200915T190000Z
DTSTAMP:20260404T095717Z
UID:RutgersNTS/1
DESCRIPTION:Title: Analytic Number Theory and Optimal Transport: an interesting con
nection\nby Stefan Steinerberger (University of Washington) as part of
Rutgers Number Theory Seminar\n\n\nAbstract\nOptimal Transport studies th
e problem of how to move one measure to another so that the "transport cos
t" is minimal. Think of one measure being products in a warehouse and the
other measure being how much people want to buy the product: the transpor
t distance would then be the amount of miles trucks have to drive (weighte
d by how much they carry). I will start by giving a gentle Introduction t
o this topic\, we do not actually need very much. My question then is: su
ppose one measure is the normalized counting measure in quadratic residues
in a finite field and the other is the uniform measure\, can the Transpor
t be estimated? Or maybe Dirac measures placed in irrational rotations on
the Torus: how cheap is it to transport them to the Lebesgue measure? An
d are these results interesting? (Spoiler: yes). And do they carry some u
seful meaning? (Spoiler: yes) Some recent advances in Optimal Transport a
llow these problems to be reduced to a simple exponential sum\; basic ingr
edients from Analytic Number Theory can then be used to get new insight at
relatively low technical cost. There are many\, many open questions.\n
LOCATION:https://stable.researchseminars.org/talk/RutgersNTS/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nikolay Bogachev (Skoltech & MIPT)
DTSTART:20200922T180000Z
DTEND:20200922T190000Z
DTSTAMP:20260404T095717Z
UID:RutgersNTS/2
DESCRIPTION:Title: Arithmetic and quasi-arithmetic hyperbolic reflection groups
\nby Nikolay Bogachev (Skoltech & MIPT) as part of Rutgers Number Theory S
eminar\n\n\nAbstract\nIn 1967\, Vinberg started a systematic study of hype
rbolic reflection groups. In particular\, he showed that Coxeter polytopes
are natural fundamental domains of hyperbolic reflection groups and devel
oped practically efficient methods that allow to determine compactness or
volume finiteness of a given Coxeter polytope by looking at its Coxeter di
agram. He also proved a (quasi-)arithmeticity criterion for hyperbolic lat
tices generated by reflections. In 1981\, Vinberg showed that there are no
compact Coxeter polytopes in hyperbolic spaces H^n for n>29. Also\, he sh
owed that there are no arithmetic hyperbolic reflection groups H^n for n>2
9\, either. Due to the results of Nikulin (2007) and Agol\, Belolipetsky\,
Storm\, and Whyte (2008) it became known that there are only finitely man
y maximal arithmetic hyperbolic reflection groups in all dimensions. These
results give hope that maximal arithmetic hyperbolic reflection groups ca
n be classified.\n\n \nA very interesting moment is that compact Coxeter p
olytopes are known only up to H^8\, and in H^7 and H^8 all the known examp
les are arithmetic. Thus\, besides the problem of classification of arithm
etic hyperbolic reflection groups (which remains open since 1970-80s) we h
ave another very natural question (which is again open since 1980s): do th
ere exist compact (both arithmetic and non-arithmetic) hyperbolic Coxeter
polytopes in H^n for n>8 ?\n \n\nThe talk will be devoted to the discussio
n of these two related problems. One part of the talk is based on the rece
nt preprint https://arxiv.org/abs/2003.11944v2 where some new geometric cl
assification method is described. The second part is based on a joint work
with Alexander Kolpakov https://arxiv.org/abs/2002.11445v2 where we prove
that each lower-dimensional face of a quasi-arithmetic Coxeter polytope\,
which happens to be itself a Coxeter polytope\, is also quasi-arithmetic.
We also provide a few illustrative examples.\n
LOCATION:https://stable.researchseminars.org/talk/RutgersNTS/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kim Klinger-Logan (Rutgers University)
DTSTART:20200929T180000Z
DTEND:20200929T190000Z
DTSTAMP:20260404T095717Z
UID:RutgersNTS/3
DESCRIPTION:Title: How to fail to prove the Riemann Hypothesis\nby Kim Klinger-
Logan (Rutgers University) as part of Rutgers Number Theory Seminar\n\n\nA
bstract\nHilbert and Polya quipped that to prove RH\, one can realize the
zeros of zeta as spectral parameters for a self-adjoint operator. The Fri
edrichs extension provides method of transforming a symmetric\, unbounded
operator into a self-adjoint one. We will discuss applications of the Frie
drichs extension to the problem of zeros of L-functions. One such applica
tion is an extension of recent work of Bombieri and Garrett.\n
LOCATION:https://stable.researchseminars.org/talk/RutgersNTS/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Thomas Bloom (University of Cambridge)
DTSTART:20201020T180000Z
DTEND:20201020T190000Z
DTSTAMP:20260404T095717Z
UID:RutgersNTS/4
DESCRIPTION:Title: Additive structure in dense sets of integers\nby Thomas Bloo
m (University of Cambridge) as part of Rutgers Number Theory Seminar\n\n\n
Abstract\nHow much additive structure can we guarantee in sets of integers
\, knowing only their density? The study of which density thresholds are s
ufficient to guarantee the existence of various kinds of additive structur
es is an old and fascinating subject with connections to analytic number t
heory\, additive combinatorics\, and harmonic analysis.\n\nIn this talk we
will discuss recent progress on perhaps the most well-known of these thre
sholds: how large do we need a set of integers to be to guarantee the exis
tence of a three-term arithmetic progression? In recent joint work with Ol
of Sisask we broke through the logarithmic density barrier for this proble
m\, establishing in particular that if a set is dense enough such that the
sum of reciprocals diverges\, then it must contain a three-term arithmeti
c progression\, establishing the first case of an infamous conjecture of E
rdos.\n\nWe will give an introduction to this problem and sketch some of t
he recent ideas that have made this progress possible. We will also discus
s a recent application to the density threshold of a set containing no squ
are differences.\n
LOCATION:https://stable.researchseminars.org/talk/RutgersNTS/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dmitry Frolenkov (Steklov Mathematical Institute)
DTSTART:20201027T180000Z
DTEND:20201027T190000Z
DTSTAMP:20260404T095717Z
UID:RutgersNTS/5
DESCRIPTION:Title: Second moment of symmetric square $L$-functions over Gaussian in
tegers and the Prime Geodesic Theorem\nby Dmitry Frolenkov (Steklov Ma
thematical Institute) as part of Rutgers Number Theory Seminar\n\n\nAbstra
ct\nWe will discuss an upper bound for the second moment of Maass form sym
metric square $L$-functions defined over Gaussian integers with an applica
tion to the Prime Geodesic Theorem. Joint work with Olga Balkanova.\n
LOCATION:https://stable.researchseminars.org/talk/RutgersNTS/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Solomon Friedberg (Boston College)
DTSTART:20201117T190000Z
DTEND:20201117T200000Z
DTSTAMP:20260404T095717Z
UID:RutgersNTS/6
DESCRIPTION:Title: Langlands functoriality\, the converse theorem\, and the integra
l representations of L-functions\nby Solomon Friedberg (Boston College
) as part of Rutgers Number Theory Seminar\n\n\nAbstract\nLanglands functo
riality predicts maps between automorphic representations on different gro
ups\, dictated by a map of L-groups. One important class of such maps are
endoscopic liftings\, established by Arthur using the trace formula. In th
is talk I describe an approach to endoscopic lifting that does not use the
trace formula. Instead it follows the approach of Cogdell\, Kim\, Piatets
ki-Shapiro and Shahidi\, who handled (before Arthur) the case of endoscopi
c liftings of generic automorphic representations by studying L-functions
and using the converse theorem. Using a new integral representations of L
-functions of Cai\, Friedberg\, Ginzburg and Kaplan\, I and my collaborato
rs are able to handle all cuspidal automorphic representations\, and even
to give some liftings outside the work of Arthur.\n
LOCATION:https://stable.researchseminars.org/talk/RutgersNTS/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tony Feng (MIT)
DTSTART:20201201T190000Z
DTEND:20201201T200000Z
DTSTAMP:20260404T095717Z
UID:RutgersNTS/7
DESCRIPTION:Title: The geometric distribution of Selmer groups over function fields
\nby Tony Feng (MIT) as part of Rutgers Number Theory Seminar\n\n\nAbs
tract\nMany interesting aspects of the arithmetic of elliptic curves over
global fields are governed by Selmer groups\, which are cohomological appr
oximations to the group of rational points. The statistical behavior of Se
lmer groups has been the focus of much recent study\, and there is a wide
gap between what we can prove and what we believe is true. On the one hand
\, work of Bhargava and Shankar computes the average size of 2\,3\,4\, and
5-Selmer groups. On the other hand\, Bhargava-Kane-Lenstra-Poonen-Rains c
onjecture a precise distribution for n-Selmer groups\, for any n. I will t
alk about a limiting situation\, in the function field context\, where the
BKLPR distribution can actually be proved to model the distribution of Se
lmer groups. This is joint work with Aaron Landesman and Eric Rains.\n
LOCATION:https://stable.researchseminars.org/talk/RutgersNTS/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Matthew Young (Texas A&M University)
DTSTART:20201013T180000Z
DTEND:20201013T190000Z
DTSTAMP:20260404T095717Z
UID:RutgersNTS/8
DESCRIPTION:Title: Moments and hybrid subconvexity for symmetric-square L-functions
\nby Matthew Young (Texas A&M University) as part of Rutgers Number Th
eory Seminar\n\n\nAbstract\nI will discuss some recent work on moment prob
lems for symmetric-square L-functions. One application of this work is a
hybrid subconvexity result for these L-functions\, and another is a short
interval Lindelof-on-average bound. I will also discuss some of the motiv
ation for these problems\, which relates these L-functions to the equidist
ribution of cusp forms on the modular surface.\n
LOCATION:https://stable.researchseminars.org/talk/RutgersNTS/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nattalie Tamam (UCSD)
DTSTART:20201103T190000Z
DTEND:20201103T200000Z
DTSTAMP:20260404T095717Z
UID:RutgersNTS/9
DESCRIPTION:Title: Effective equidistribution of horospherical flows in infinite vo
lume\nby Nattalie Tamam (UCSD) as part of Rutgers Number Theory Semina
r\n\n\nAbstract\nHorospherical flows in homogeneous spaces have been studi
ed intensively over the last several decades and have many surprising appl
ications in various fields. Many basic results are under the assumption th
at the volume of the space is finite\, which is crucial as many basic ergo
dic theorems fail in the setting of an infinite measure space. In the talk
we will discuss the infinite volume setting\, and specifically\, when can
we expect horospherical orbits to equidistribute. Our goal will be to pro
vide an effective equidistribution result\, with polynomial rate\, for hor
ospherical orbits in the frame bundle of certain infinite volume hyperboli
c manifolds. This is a joint work with Jacqueline Warren.\n
LOCATION:https://stable.researchseminars.org/talk/RutgersNTS/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tim Trudgian (UNSW Canberra at ADFA)
DTSTART:20201110T190000Z
DTEND:20201110T200000Z
DTSTAMP:20260404T095717Z
UID:RutgersNTS/10
DESCRIPTION:Title: Zeta Zeroes… Mind the Gap!\nby Tim Trudgian (UNSW Canberr
a at ADFA) as part of Rutgers Number Theory Seminar\n\n\nAbstract\nThis wo
rk\, joint with Aleks Simonic and Caroline Turnage-Butterbaugh\, is hot of
f the presses. I'll outline a problem in obtaining large and small gaps be
tween zeroes of $\\zeta(s)$. See arXiv:2010.10675 for further details.\n
LOCATION:https://stable.researchseminars.org/talk/RutgersNTS/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yotam Smilansky (Rutgers University)
DTSTART:20210126T190000Z
DTEND:20210126T200000Z
DTSTAMP:20260404T095717Z
UID:RutgersNTS/11
DESCRIPTION:Title: Classification and statistics of cut-and-project sets\nby Y
otam Smilansky (Rutgers University) as part of Rutgers Number Theory Semin
ar\n\n\nAbstract\nCut-and-project point sets are constructed by identifyin
g a strip of a fixed n-dimensional lattice (the "cut")\, and projecting th
e lattice points in that strip to a d-dimensional subspace (the "project
”)\, and are a well-studied model of aperiodic order. Dynamical results
concerning the translation action on the hull of a cut-and-project set are
known to shed light on certain properties of the point set itself\, but w
hat happens when instead of restricting to translations we consider all vo
lume preserving linear actions? \n\nA homogenous space of cut-and-project
sets is defined by fixing a cut-and-project construction and varying the n
-dimensional grid according to an ASL(d\,R) action. In the talk\, which is
based on joint work with René Rühr and Barak Weiss (https://arxiv.org/a
bs/2012.13299)\, I will discuss this construction and introduce the class
of Ratner-Marklof-Strömbergsson measures\, which are probability measures
supported on cut-and-project spaces that are invariant and ergodic for th
e group action. A classification of these measures is described in terms o
f data of algebraic groups\, and is used to prove analogues of results abo
ut a Siegel summation formula and identities and bounds involving higher m
oments. These in turn imply results about asymptotics\, with error estimat
es\, of point-counting and patch-counting statistics for typical cut-and-p
roject sets.\n
LOCATION:https://stable.researchseminars.org/talk/RutgersNTS/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Francisco Arana Herrera (Stanford University)
DTSTART:20210223T190000Z
DTEND:20210223T200000Z
DTSTAMP:20260404T095717Z
UID:RutgersNTS/12
DESCRIPTION:Title: Effective mapping class group dynamics\nby Francisco Arana
Herrera (Stanford University) as part of Rutgers Number Theory Seminar\n\n
\nAbstract\nMuch is known about the dynamics of the mapping class group on
different spaces: Teichmüller space\, the space of singular measured fol
iations\, the space of geodesic currents. However\, very little is known a
bout its effective dynamics. In this talk I will discuss work in progress
that aims at clearing up this picture. Applications to counting problems o
n surfaces\, including a partial solution to an open problem of Wright\, w
ill also be discussed. No previous knowledge of any of these topics will b
e assumed.\n
LOCATION:https://stable.researchseminars.org/talk/RutgersNTS/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sarah Peluse (Princeton University)
DTSTART:20210202T190000Z
DTEND:20210202T200000Z
DTSTAMP:20260404T095717Z
UID:RutgersNTS/13
DESCRIPTION:Title: An asymptotic version of the prime power conjecture for perfect
difference sets\nby Sarah Peluse (Princeton University) as part of Ru
tgers Number Theory Seminar\n\n\nAbstract\nA subset D of a finite cyclic g
roup Z/mZ is called a "perfect difference set" if every nonzero element of
Z/mZ can be written uniquely as the difference of two elements of D. If s
uch a set exists\, then a simple counting argument shows that m=n^2+n+1 fo
r some nonnegative integer n. Singer constructed examples of perfect diffe
rence sets in Z/(n^2+n+1)Z whenever n is a prime power\, and it is an old
conjecture that these are the only such n for which a perfect difference s
et exists. 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 con
tains a perfect difference set is ~N/log(N).\n
LOCATION:https://stable.researchseminars.org/talk/RutgersNTS/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Frank Thorne (University of South Carolina)
DTSTART:20210302T190000Z
DTEND:20210302T200000Z
DTSTAMP:20260404T095717Z
UID:RutgersNTS/14
DESCRIPTION:Title: Upper Bounds for Counting Number Fields\nby Frank Thorne (U
niversity of South Carolina) as part of Rutgers Number Theory Seminar\n\n\
nAbstract\nHow many number fields are there of fixed degree and bounded di
scriminant?\n\nThis will be a two-part talk. In the first part\, I will gi
ve an overview of what is expected and what is known -- often in the case
where the Galois group is specified. In the second part I will give an ove
rview of recent work with Robert Lemke Oliver\, which improves upon the be
st known general upper bounds.\n
LOCATION:https://stable.researchseminars.org/talk/RutgersNTS/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:David Lowry-Duda (ICERM)
DTSTART:20210209T190000Z
DTEND:20210209T200000Z
DTSTAMP:20260404T095717Z
UID:RutgersNTS/15
DESCRIPTION:Title: Computing and verifying Maass forms\nby David Lowry-Duda (I
CERM) as part of Rutgers Number Theory Seminar\n\n\nAbstract\nIn this talk
\, I describe theoretical and practical aspects of the computation of GL2
Maass forms. We'll describe Hejhal's algorithm to compute the Maass forms
and recent methods of Booker\, Stromberg\, and Venkatesh to certify correc
tness of these forms. This is part of an ongoing project to rigorously imp
lement and compute Maass forms on a large scale for the L-function and Mod
ular Form Database (LMFDB.org).\n
LOCATION:https://stable.researchseminars.org/talk/RutgersNTS/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Adam Harper
DTSTART:20210216T190000Z
DTEND:20210216T200000Z
DTSTAMP:20260404T095717Z
UID:RutgersNTS/16
DESCRIPTION:Title: Large fluctuations of random multiplicative functions\nby A
dam Harper as part of Rutgers Number Theory Seminar\n\n\nAbstract\nRandom
multiplicative functions $f(n)$ are a well studied random model for determ
inistic multiplicative functions like Dirichlet characters or the Mobius f
unction. Arguably the first question ever studied about them\, by Wintner
in 1944\, was to obtain almost sure bounds for the largest fluctuations of
their partial $\\sum_{n \\leq x} f(n)$\, seeking to emulate the classical
Law of the Iterated Logarithm for independent random variables. It remain
s an open question to sharply determine the size of these fluctuations\, a
nd in this talk I will describe a new result in that direction. I hope to
get to some interesting details of the new proof in the latter part of the
talk\, but most of the discussion should be widely accessible.\n
LOCATION:https://stable.researchseminars.org/talk/RutgersNTS/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ian Whitehead (Swarthmore College)
DTSTART:20210413T180000Z
DTEND:20210413T190000Z
DTSTAMP:20260404T095717Z
UID:RutgersNTS/17
DESCRIPTION:Title: Apollonian Packings and Kac-Moody Root Systems\nby Ian Whit
ehead (Swarthmore College) as part of Rutgers Number Theory Seminar\n\n\nA
bstract\nFix four mutually tangent circles in the plane. Fill in the space
s between these circles with additional tangent circles. By repeating this
process ad infinitum\, on smaller and smaller scales\, we obtain an Apoll
onian circle packing. I will define a four-variable generating function fo
r curvatures that appear in an Apollonian packing. This function is essent
ially a character for a rank 4 indefinite Kac-Moody root system. I will re
late this generating function to certain automorphic forms\, including the
ta functions on SL(2) and a Siegel automorphic form on Sp(4). And I will d
iscuss its domain of convergence\, the Tits cone of the root system\, whic
h inherits the rich geometry of Apollonian packings.\n
LOCATION:https://stable.researchseminars.org/talk/RutgersNTS/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anders Södergren (Chalmers University of Technology)
DTSTART:20210420T180000Z
DTEND:20210420T190000Z
DTSTAMP:20260404T095717Z
UID:RutgersNTS/18
DESCRIPTION:Title: Can a random lattice and its dual be independent?\nby Ander
s Södergren (Chalmers University of Technology) as part of Rutgers Number
Theory Seminar\n\n\nAbstract\nIn this talk I will discuss Rogers' mean va
lue formula in the space of unimodular lattices as well as a recent genera
lization of Rogers' formula. In particular\, I will describe a formula for
mean values of products of Siegel transforms with arguments taken from bo
th a lattice and its dual lattice. The main application is a result on the
joint distribution of the vector lengths in a random lattice and its dual
lattice in the limit as the dimension of the lattices tends to infinity\,
and provides a partial affirmative answer to the question in the title. T
his is joint work with Andreas Strömbergsson.\n
LOCATION:https://stable.researchseminars.org/talk/RutgersNTS/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hung Bui (The University of Manchester)
DTSTART:20210330T180000Z
DTEND:20210330T190000Z
DTSTAMP:20260404T095717Z
UID:RutgersNTS/19
DESCRIPTION:Title: Analytic ranks of automorphic L-functions and Landau-Siegel zer
os\nby Hung Bui (The University of Manchester) as part of Rutgers Numb
er Theory Seminar\n\n\nAbstract\nBrumer and Ram Murty independently conjec
tured that almost all newforms of weight 2 and level q have analytic rank
<= 1. In this talk we will relate this problem to the study of Landau-Sieg
el zeros. In particular\, we show that either Landau-Siegel zeros do not e
xist\, or that almost all such newforms with q prime have analytic rank <=
2. This is joint work with Kyle Pratt and Alexandru Zaharescu.\n
LOCATION:https://stable.researchseminars.org/talk/RutgersNTS/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Olivia Beckwith (The University of Illinois at Urbana-Champaign)
DTSTART:20210323T180000Z
DTEND:20210323T190000Z
DTSTAMP:20260404T095717Z
UID:RutgersNTS/20
DESCRIPTION:Title: Zero density estimates and fractional imaginary parts of zeros
of GL(2) L-functions\nby Olivia Beckwith (The University of Illinois a
t Urbana-Champaign) as part of Rutgers Number Theory Seminar\n\n\nAbstract
\nWe prove an analogue of Selberg's density estimate for the Riemann zeta
function that holds for GL(2) L-functions. We use this estimate to study t
he distribution of scalar multiples of imaginary parts of zeros of GL(2) L
-functions modulo 1. This is joint work with Di Liu\, Jesse Thorner\, and
Alexandru Zaharescu.\n
LOCATION:https://stable.researchseminars.org/talk/RutgersNTS/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yusheng Luo (The University of Michigan)
DTSTART:20210406T180000Z
DTEND:20210406T190000Z
DTSTAMP:20260404T095717Z
UID:RutgersNTS/21
DESCRIPTION:Title: Circle packings\, kissing reflection group and critically fixed
anti-rational maps\nby Yusheng Luo (The University of Michigan) as pa
rt of Rutgers Number Theory Seminar\n\n\nAbstract\nCircle packings appear
frequently in the studies of dynamics\, geometry and number theory. One ca
n naturally associate a reflection group to a finite circle packing\, gene
rated by reflections along the corresponding circles. In this talk\, we wi
ll establish an explicit correspondence between such reflection groups wit
h anti-holomorphic proper maps of the Riemann sphere where all the critica
l points are fixed. We will explore the correspondence both in the dynamic
al plane and the parameter spaces. In particular\, we will explain how the
analogue of Thurston’s compactness theorem for acylindrical hyperbolic
3-manifold holds for critically fixed anti-rational maps.\nWe will also br
iefly discuss some open questions motivated by the correspondence.\n
LOCATION:https://stable.researchseminars.org/talk/RutgersNTS/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yiannis Petridis (University College London)
DTSTART:20210427T180000Z
DTEND:20210427T190000Z
DTSTAMP:20260404T095717Z
UID:RutgersNTS/22
DESCRIPTION:Title: Arithmetic statistics of modular symbols\nby Yiannis Petrid
is (University College London) as part of Rutgers Number Theory Seminar\n\
n\nAbstract\nThe central value of the L-function of an elliptic curve has
been the object of extensive studies in the last 50 years. Associated with
such a curve we wish to understand also families of twists of it\, leadin
g to the study of twisted L-functions. On the other hand modular symbols h
ave been a useful tool to study the space of holomorphic cusp forms of wei
ght 2\, and the homology of modular curves. They have been the object of e
xtensive investigations by many mathematicians including Birch\, Manin\, a
nd Cremona. Mazur\, Rubin\, and Stein have recently formulated a series of
conjectures about statistical properties of modular symbols in order to u
nderstand central values of twists of elliptic curve L-functions. We discu
ss some of these conjectures and the recent progress and resolution of the
m. This is joint work with M. S. Risager.\n
LOCATION:https://stable.researchseminars.org/talk/RutgersNTS/22/
END:VEVENT
END:VCALENDAR