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BEGIN:VEVENT
SUMMARY:Stefan Steinerberger (University of Washington)
DTSTART:20200915T180000Z
DTEND:20200915T190000Z
DTSTAMP:20260422T225929Z
UID:RutgersNTS/1
DESCRIPTION:Title: Analytic Number Theory and Optimal Transport: an interesting connection
\nby Stefan Steinerberger (University of Washington) as part of Rutger
s Number Theory Seminar\n\n\nAbstract\nOptimal Transport studies the probl
em of how to move one measure to another so that the "transport cost" is m
inimal. Think of one measure being products in a warehouse and the other
measure being how much people want to buy the product: the transport dista
nce would then be the amount of miles trucks have to drive (weighted by ho
w much they carry). I will start by giving a gentle Introduction to this
topic\, we do not actually need very much. My question then is: suppose o
ne measure is the normalized counting measure in quadratic residues in a f
inite field and the other is the uniform measure\, can the Transport be es
timated? Or maybe Dirac measures placed in irrational rotations on the To
rus: how cheap is it to transport them to the Lebesgue measure? And are t
hese results interesting? (Spoiler: yes). And do they carry some useful m
eaning? (Spoiler: yes) Some recent advances in Optimal Transport allow th
ese problems to be reduced to a simple exponential sum\; basic ingredients
from Analytic Number Theory can then be used to get new insight at relati
vely low technical cost. There are many\, many open questions.\n
LOCATION:https://researchseminars.org/talk/RutgersNTS/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nikolay Bogachev (Skoltech & MIPT)
DTSTART:20200922T180000Z
DTEND:20200922T190000Z
DTSTAMP:20260422T225929Z
UID:RutgersNTS/2
DESCRIPTION:Title: Arithmetic and quasi-arithmetic hyperbolic reflection groups\nby Ni
kolay Bogachev (Skoltech & MIPT) as part of Rutgers Number Theory Seminar\
n\n\nAbstract\nIn 1967\, Vinberg started a systematic study of hyperbolic
reflection groups. In particular\, he showed that Coxeter polytopes are na
tural fundamental domains of hyperbolic reflection groups and developed pr
actically efficient methods that allow to determine compactness or volume
finiteness of a given Coxeter polytope by looking at its Coxeter diagram.
He also proved a (quasi-)arithmeticity criterion for hyperbolic lattices g
enerated by reflections. In 1981\, Vinberg showed that there are no compac
t Coxeter polytopes in hyperbolic spaces H^n for n>29. Also\, he showed th
at there are no arithmetic hyperbolic reflection groups H^n for n>29\, eit
her. Due to the results of Nikulin (2007) and Agol\, Belolipetsky\, Storm\
, and Whyte (2008) it became known that there are only finitely many maxim
al arithmetic hyperbolic reflection groups in all dimensions. These result
s give hope that maximal arithmetic hyperbolic reflection groups can be cl
assified.\n\n \nA very interesting moment is that compact Coxeter polytope
s are known only up to H^8\, and in H^7 and H^8 all the known examples are
arithmetic. Thus\, besides the problem of classification of arithmetic hy
perbolic reflection groups (which remains open since 1970-80s) we have ano
ther very natural question (which is again open since 1980s): do there exi
st compact (both arithmetic and non-arithmetic) hyperbolic Coxeter polytop
es in H^n for n>8 ?\n \n\nThe talk will be devoted to the discussion of th
ese two related problems. One part of the talk is based on the recent prep
rint https://arxiv.org/abs/2003.11944v2 where some new geometric classific
ation method is described. The second part is based on a joint work with A
lexander Kolpakov https://arxiv.org/abs/2002.11445v2 where we prove that e
ach lower-dimensional face of a quasi-arithmetic Coxeter polytope\, which
happens to be itself a Coxeter polytope\, is also quasi-arithmetic. We als
o provide a few illustrative examples.\n
LOCATION:https://researchseminars.org/talk/RutgersNTS/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kim Klinger-Logan (Rutgers University)
DTSTART:20200929T180000Z
DTEND:20200929T190000Z
DTSTAMP:20260422T225929Z
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\nAbstract
\nHilbert and Polya quipped that to prove RH\, one can realize the zeros o
f zeta as spectral parameters for a self-adjoint operator. The Friedrichs
extension provides method of transforming a symmetric\, unbounded operato
r into a self-adjoint one. We will discuss applications of the Friedrichs
extension to the problem of zeros of L-functions. One such application is
an extension of recent work of Bombieri and Garrett.\n
LOCATION:https://researchseminars.org/talk/RutgersNTS/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Thomas Bloom (University of Cambridge)
DTSTART:20201020T180000Z
DTEND:20201020T190000Z
DTSTAMP:20260422T225929Z
UID:RutgersNTS/4
DESCRIPTION:Title: Additive structure in dense sets of integers\nby Thomas Bloom (Univ
ersity of Cambridge) as part of Rutgers Number Theory Seminar\n\n\nAbstrac
t\nHow much additive structure can we guarantee in sets of integers\, know
ing only their density? The study of which density thresholds are sufficie
nt to guarantee the existence of various kinds of additive structures is a
n old and fascinating subject with connections to analytic number theory\,
additive combinatorics\, and harmonic analysis.\n\nIn this talk we will d
iscuss recent progress on perhaps the most well-known of these thresholds:
how large do we need a set of integers to be to guarantee the existence o
f a three-term arithmetic progression? In recent joint work with Olof Sisa
sk we broke through the logarithmic density barrier for this problem\, est
ablishing in particular that if a set is dense enough such that the sum of
reciprocals diverges\, then it must contain a three-term arithmetic progr
ession\, establishing the first case of an infamous conjecture of Erdos.\n
\nWe will give an introduction to this problem and sketch some of the rece
nt ideas that have made this progress possible. We will also discuss a rec
ent application to the density threshold of a set containing no square dif
ferences.\n
LOCATION:https://researchseminars.org/talk/RutgersNTS/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dmitry Frolenkov (Steklov Mathematical Institute)
DTSTART:20201027T180000Z
DTEND:20201027T190000Z
DTSTAMP:20260422T225929Z
UID:RutgersNTS/5
DESCRIPTION:Title: Second moment of symmetric square $L$-functions over Gaussian integers
and the Prime Geodesic Theorem\nby Dmitry Frolenkov (Steklov Mathemati
cal Institute) as part of Rutgers Number Theory Seminar\n\n\nAbstract\nWe
will discuss an upper bound for the second moment of Maass form symmetric
square $L$-functions defined over Gaussian integers with an application to
the Prime Geodesic Theorem. Joint work with Olga Balkanova.\n
LOCATION:https://researchseminars.org/talk/RutgersNTS/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Solomon Friedberg (Boston College)
DTSTART:20201117T190000Z
DTEND:20201117T200000Z
DTSTAMP:20260422T225929Z
UID:RutgersNTS/6
DESCRIPTION:Title: Langlands functoriality\, the converse theorem\, and the integral repre
sentations of L-functions\nby Solomon Friedberg (Boston College) as pa
rt of Rutgers Number Theory Seminar\n\n\nAbstract\nLanglands functoriality
predicts maps between automorphic representations on different groups\, d
ictated by a map of L-groups. One important class of such maps are endosco
pic liftings\, established by Arthur using the trace formula. In this talk
I describe an approach to endoscopic lifting that does not use the trace
formula. Instead it follows the approach of Cogdell\, Kim\, Piatetski-Shap
iro and Shahidi\, who handled (before Arthur) the case of endoscopic lifti
ngs of generic automorphic representations by studying L-functions and usi
ng the converse theorem. Using a new integral representations of L-functi
ons of Cai\, Friedberg\, Ginzburg and Kaplan\, I and my collaborators are
able to handle all cuspidal automorphic representations\, and even to give
some liftings outside the work of Arthur.\n
LOCATION:https://researchseminars.org/talk/RutgersNTS/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tony Feng (MIT)
DTSTART:20201201T190000Z
DTEND:20201201T200000Z
DTSTAMP:20260422T225929Z
UID:RutgersNTS/7
DESCRIPTION:Title: The geometric distribution of Selmer groups over function fields\nb
y Tony Feng (MIT) as part of Rutgers Number Theory Seminar\n\n\nAbstract\n
Many interesting aspects of the arithmetic of elliptic curves over global
fields are governed by Selmer groups\, which are cohomological approximati
ons to the group of rational points. The statistical behavior of Selmer gr
oups has been the focus of much recent study\, and there is a wide gap bet
ween 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-Selm
er groups. On the other hand\, Bhargava-Kane-Lenstra-Poonen-Rains conjectu
re a precise distribution for n-Selmer groups\, for any n. I will talk abo
ut a limiting situation\, in the function field context\, where the BKLPR
distribution can actually be proved to model the distribution of Selmer gr
oups. This is joint work with Aaron Landesman and Eric Rains.\n
LOCATION:https://researchseminars.org/talk/RutgersNTS/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Matthew Young (Texas A&M University)
DTSTART:20201013T180000Z
DTEND:20201013T190000Z
DTSTAMP:20260422T225929Z
UID:RutgersNTS/8
DESCRIPTION:Title: Moments and hybrid subconvexity for symmetric-square L-functions\nb
y Matthew Young (Texas A&M University) as part of Rutgers Number Theory Se
minar\n\n\nAbstract\nI will discuss some recent work on moment problems fo
r symmetric-square L-functions. One application of this work is a hybrid
subconvexity result for these L-functions\, and another is a short interva
l Lindelof-on-average bound. I will also discuss some of the motivation f
or these problems\, which relates these L-functions to the equidistributio
n of cusp forms on the modular surface.\n
LOCATION:https://researchseminars.org/talk/RutgersNTS/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nattalie Tamam (UCSD)
DTSTART:20201103T190000Z
DTEND:20201103T200000Z
DTSTAMP:20260422T225929Z
UID:RutgersNTS/9
DESCRIPTION:Title: Effective equidistribution of horospherical flows in infinite volume\nby Nattalie Tamam (UCSD) as part of Rutgers Number Theory Seminar\n\n\n
Abstract\nHorospherical flows in homogeneous spaces have been studied inte
nsively over the last several decades and have many surprising application
s in various fields. Many basic results are under the assumption that the
volume of the space is finite\, which is crucial as many basic ergodic the
orems fail in the setting of an infinite measure space. In the talk we wil
l discuss the infinite volume setting\, and specifically\, when can we exp
ect horospherical orbits to equidistribute. Our goal will be to provide an
effective equidistribution result\, with polynomial rate\, for horospheri
cal orbits in the frame bundle of certain infinite volume hyperbolic manif
olds. This is a joint work with Jacqueline Warren.\n
LOCATION:https://researchseminars.org/talk/RutgersNTS/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tim Trudgian (UNSW Canberra at ADFA)
DTSTART:20201110T190000Z
DTEND:20201110T200000Z
DTSTAMP:20260422T225929Z
UID:RutgersNTS/10
DESCRIPTION:Title: Zeta Zeroes… Mind the Gap!\nby Tim Trudgian (UNSW Canberra at AD
FA) as part of Rutgers Number Theory Seminar\n\n\nAbstract\nThis work\, jo
int with Aleks Simonic and Caroline Turnage-Butterbaugh\, is hot off the p
resses. I'll outline a problem in obtaining large and small gaps between z
eroes of $\\zeta(s)$. See arXiv:2010.10675 for further details.\n
LOCATION:https://researchseminars.org/talk/RutgersNTS/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yotam Smilansky (Rutgers University)
DTSTART:20210126T190000Z
DTEND:20210126T200000Z
DTSTAMP:20260422T225929Z
UID:RutgersNTS/11
DESCRIPTION:Title: Classification and statistics of cut-and-project sets\nby Yotam Sm
ilansky (Rutgers University) as part of Rutgers Number Theory Seminar\n\n\
nAbstract\nCut-and-project point sets are constructed by identifying a str
ip of a fixed n-dimensional lattice (the "cut")\, and projecting the latti
ce points in that strip to a d-dimensional subspace (the "project”)\, an
d are a well-studied model of aperiodic order. Dynamical results concernin
g 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 what happe
ns when instead of restricting to translations we consider all volume pres
erving linear actions? \n\nA homogenous space of cut-and-project sets is d
efined by fixing a cut-and-project construction and varying the n-dimensio
nal 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/abs/2012.1
3299)\, I will discuss this construction and introduce the class of Ratner
-Marklof-Strömbergsson measures\, which are probability measures supporte
d on cut-and-project spaces that are invariant and ergodic for the group a
ction. A classification of these measures is described in terms of data of
algebraic groups\, and is used to prove analogues of results about a Sieg
el summation formula and identities and bounds involving higher moments. T
hese in turn imply results about asymptotics\, with error estimates\, of p
oint-counting and patch-counting statistics for typical cut-and-project se
ts.\n
LOCATION:https://researchseminars.org/talk/RutgersNTS/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Francisco Arana Herrera (Stanford University)
DTSTART:20210223T190000Z
DTEND:20210223T200000Z
DTSTAMP:20260422T225929Z
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\nAbstr
act\nMuch is known about the dynamics of the mapping class group on differ
ent spaces: Teichmüller space\, the space of singular measured foliations
\, the space of geodesic currents. However\, very little is known about it
s effective dynamics. In this talk I will discuss work in progress that ai
ms at clearing up this picture. Applications to counting problems on surfa
ces\, including a partial solution to an open problem of Wright\, will als
o be discussed. No previous knowledge of any of these topics will be assum
ed.\n
LOCATION:https://researchseminars.org/talk/RutgersNTS/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sarah Peluse (Princeton University)
DTSTART:20210202T190000Z
DTEND:20210202T200000Z
DTSTAMP:20260422T225929Z
UID:RutgersNTS/13
DESCRIPTION:Title: An asymptotic version of the prime power conjecture for perfect differ
ence sets\nby Sarah Peluse (Princeton University) as part of Rutgers 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://researchseminars.org/talk/RutgersNTS/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Frank Thorne (University of South Carolina)
DTSTART:20210302T190000Z
DTEND:20210302T200000Z
DTSTAMP:20260422T225929Z
UID:RutgersNTS/14
DESCRIPTION:Title: Upper Bounds for Counting Number Fields\nby Frank Thorne (Universi
ty of South Carolina) as part of Rutgers Number Theory Seminar\n\n\nAbstra
ct\nHow many number fields are there of fixed degree and bounded discrimin
ant?\n\nThis will be a two-part talk. In the first part\, I will give an o
verview of what is expected and what is known -- often in the case where t
he Galois group is specified. In the second part I will give an overview o
f recent work with Robert Lemke Oliver\, which improves upon the best know
n general upper bounds.\n
LOCATION:https://researchseminars.org/talk/RutgersNTS/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:David Lowry-Duda (ICERM)
DTSTART:20210209T190000Z
DTEND:20210209T200000Z
DTSTAMP:20260422T225929Z
UID:RutgersNTS/15
DESCRIPTION:Title: Computing and verifying Maass forms\nby David Lowry-Duda (ICERM) a
s part of Rutgers Number Theory Seminar\n\n\nAbstract\nIn this talk\, I de
scribe theoretical and practical aspects of the computation of GL2 Maass f
orms. We'll describe Hejhal's algorithm to compute the Maass forms and rec
ent methods of Booker\, Stromberg\, and Venkatesh to certify correctness o
f these forms. This is part of an ongoing project to rigorously implement
and compute Maass forms on a large scale for the L-function and Modular Fo
rm Database (LMFDB.org).\n
LOCATION:https://researchseminars.org/talk/RutgersNTS/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Adam Harper
DTSTART:20210216T190000Z
DTEND:20210216T200000Z
DTSTAMP:20260422T225929Z
UID:RutgersNTS/16
DESCRIPTION:Title: Large fluctuations of random multiplicative functions\nby Adam Har
per as part of Rutgers Number Theory Seminar\n\n\nAbstract\nRandom multipl
icative functions $f(n)$ are a well studied random model for deterministic
multiplicative functions like Dirichlet characters or the Mobius function
. 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 remains an op
en question to sharply determine the size of these fluctuations\, and in t
his 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://researchseminars.org/talk/RutgersNTS/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ian Whitehead (Swarthmore College)
DTSTART:20210413T180000Z
DTEND:20210413T190000Z
DTSTAMP:20260422T225929Z
UID:RutgersNTS/17
DESCRIPTION:Title: Apollonian Packings and Kac-Moody Root Systems\nby Ian Whitehead (
Swarthmore College) as part of Rutgers Number Theory Seminar\n\n\nAbstract
\nFix four mutually tangent circles in the plane. Fill in the spaces betwe
en these circles with additional tangent circles. By repeating this proces
s ad infinitum\, on smaller and smaller scales\, we obtain an Apollonian c
ircle packing. I will define a four-variable generating function for curva
tures that appear in an Apollonian packing. This function is essentially a
character for a rank 4 indefinite Kac-Moody root system. I will relate th
is generating function to certain automorphic forms\, including theta func
tions on SL(2) and a Siegel automorphic form on Sp(4). And I will discuss
its domain of convergence\, the Tits cone of the root system\, which inher
its the rich geometry of Apollonian packings.\n
LOCATION:https://researchseminars.org/talk/RutgersNTS/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anders Södergren (Chalmers University of Technology)
DTSTART:20210420T180000Z
DTEND:20210420T190000Z
DTSTAMP:20260422T225929Z
UID:RutgersNTS/18
DESCRIPTION:Title: Can a random lattice and its dual be independent?\nby Anders Söde
rgren (Chalmers University of Technology) as part of Rutgers Number Theory
Seminar\n\n\nAbstract\nIn this talk I will discuss Rogers' mean value for
mula in the space of unimodular lattices as well as a recent generalizatio
n of Rogers' formula. In particular\, I will describe a formula for mean v
alues of products of Siegel transforms with arguments taken from both a la
ttice 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 lattic
e in the limit as the dimension of the lattices tends to infinity\, and pr
ovides a partial affirmative answer to the question in the title. This is
joint work with Andreas Strömbergsson.\n
LOCATION:https://researchseminars.org/talk/RutgersNTS/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hung Bui (The University of Manchester)
DTSTART:20210330T180000Z
DTEND:20210330T190000Z
DTSTAMP:20260422T225929Z
UID:RutgersNTS/19
DESCRIPTION:Title: Analytic ranks of automorphic L-functions and Landau-Siegel zeros\
nby Hung Bui (The University of Manchester) as part of Rutgers Number Theo
ry Seminar\n\n\nAbstract\nBrumer and Ram Murty independently conjectured t
hat almost all newforms of weight 2 and level q have analytic rank <= 1. I
n this talk we will relate this problem to the study of Landau-Siegel zero
s. In particular\, we show that either Landau-Siegel zeros do not exist\,
or that almost all such newforms with q prime have analytic rank <= 2. Thi
s is joint work with Kyle Pratt and Alexandru Zaharescu.\n
LOCATION:https://researchseminars.org/talk/RutgersNTS/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Olivia Beckwith (The University of Illinois at Urbana-Champaign)
DTSTART:20210323T180000Z
DTEND:20210323T190000Z
DTSTAMP:20260422T225929Z
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 at Urban
a-Champaign) as part of Rutgers Number Theory Seminar\n\n\nAbstract\nWe pr
ove an analogue of Selberg's density estimate for the Riemann zeta functio
n that holds for GL(2) L-functions. We use this estimate to study the dist
ribution of scalar multiples of imaginary parts of zeros of GL(2) L-functi
ons modulo 1. This is joint work with Di Liu\, Jesse Thorner\, and Alexand
ru Zaharescu.\n
LOCATION:https://researchseminars.org/talk/RutgersNTS/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yusheng Luo (The University of Michigan)
DTSTART:20210406T180000Z
DTEND:20210406T190000Z
DTSTAMP:20260422T225929Z
UID:RutgersNTS/21
DESCRIPTION:Title: Circle packings\, kissing reflection group and critically fixed anti-r
ational maps\nby Yusheng Luo (The University of Michigan) as part of R
utgers Number Theory Seminar\n\n\nAbstract\nCircle packings appear frequen
tly in the studies of dynamics\, geometry and number theory. One can natur
ally associate a reflection group to a finite circle packing\, generated b
y reflections along the corresponding circles. In this talk\, we will esta
blish an explicit correspondence between such reflection groups with anti-
holomorphic proper maps of the Riemann sphere where all the critical point
s are fixed. We will explore the correspondence both in the dynamical plan
e and the parameter spaces. In particular\, we will explain how the analog
ue of Thurston’s compactness theorem for acylindrical hyperbolic 3-manif
old holds for critically fixed anti-rational maps.\nWe will also briefly d
iscuss some open questions motivated by the correspondence.\n
LOCATION:https://researchseminars.org/talk/RutgersNTS/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yiannis Petridis (University College London)
DTSTART:20210427T180000Z
DTEND:20210427T190000Z
DTSTAMP:20260422T225929Z
UID:RutgersNTS/22
DESCRIPTION:Title: Arithmetic statistics of modular symbols\nby Yiannis Petridis (Uni
versity College London) as part of Rutgers Number Theory Seminar\n\n\nAbst
ract\nThe central value of the L-function of an elliptic curve has been th
e object of extensive studies in the last 50 years. Associated with such a
curve we wish to understand also families of twists of it\, leading to th
e study of twisted L-functions. On the other hand modular symbols have bee
n a useful tool to study the space of holomorphic cusp forms of weight 2\,
and the homology of modular curves. They have been the object of extensiv
e investigations by many mathematicians including Birch\, Manin\, and Crem
ona. Mazur\, Rubin\, and Stein have recently formulated a series of conjec
tures about statistical properties of modular symbols in order to understa
nd central values of twists of elliptic curve L-functions. We discuss some
of these conjectures and the recent progress and resolution of them. This
is joint work with M. S. Risager.\n
LOCATION:https://researchseminars.org/talk/RutgersNTS/22/
END:VEVENT
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