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BEGIN:VEVENT
SUMMARY:Emmanuel Breuillard (University of Cambridge)
DTSTART:20200918T161500Z
DTEND:20200918T173000Z
DTSTAMP:20260404T111215Z
UID:NEDNT/1
DESCRIPTION:Title: A subspace theorem for manifolds\nby Emmanuel Breuillard (Univers
ity of Cambridge) as part of New England Dynamics and Number Theory Semina
r\n\n\nAbstract\nSchmidt’s subspace theorem is a fundamental result in d
iophantine approximation and a natural generalization of Roth’s celebrat
ed theorem. In this talk I will discuss a geometric understanding of this
theorem that blends homogeneous dynamics and geometric invariant theory. C
ombined with the Kleinbock-Margulis quantitative non-divergence estimates
this yields a natural generalization of the subspace theorem to systems of
linear forms that depend nicely on a parameter. I will also present sever
al applications and consequences of the main result. Joint work with Nicol
as de Saxcé.\n
LOCATION:https://stable.researchseminars.org/talk/NEDNT/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yotam Smilansky (Rutgers University)
DTSTART:20200925T161500Z
DTEND:20200925T173000Z
DTSTAMP:20260404T111215Z
UID:NEDNT/2
DESCRIPTION:Title: Multiscale substitution tilings\nby Yotam Smilansky (Rutgers Univ
ersity) as part of New England Dynamics and Number Theory Seminar\n\n\nAbs
tract\nMultiscale substitution tilings are a new family of tilings of Eucl
idean space that are generated by multiscale substitution rules. Unlike th
e standard setup of substitution tilings\, which is a basic object of stud
y within the aperiodic order community and includes examples such as the P
enrose and the pinwheel tilings\, multiple distinct scaling constants are
allowed\, and the defining process of inflation and subdivision is a conti
nuous one. Under a certain irrationality assumption on the scaling constan
ts\, this construction gives rise to a new class of tilings\, tiling space
s and tiling dynamical systems\, which are intrinsically different from th
ose that arise in the standard setup. In the talk I will describe these ne
w objects and discuss various structural\, geometrical\, statistical and d
ynamical results. Based on joint work with Yaar Solomon.\n
LOCATION:https://stable.researchseminars.org/talk/NEDNT/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Samantha Fairchild (University of Washington)
DTSTART:20201002T161500Z
DTEND:20201002T173000Z
DTSTAMP:20260404T111215Z
UID:NEDNT/3
DESCRIPTION:Title: Counting social interactions for discrete subsets of the plane\nb
y Samantha Fairchild (University of Washington) as part of New England Dyn
amics and Number Theory Seminar\n\n\nAbstract\nGiven a discrete subset V i
n the plane\, how many points would you expect there to be in a ball of ra
dius 100? What if the radius is 10\,000? Due to the results of Fairchild a
nd forthcoming work with Burrin\, when V arises as orbits of non-uniform l
attice subgroups of SL(2\,R)\, we can understand asymptotic growth rate wi
th error terms of the number of points in V for a broad family of sets. A
crucial aspect of these arguments and similar arguments is understanding h
ow to count pairs of saddle connections with certain properties determinin
g the interactions between them\, like having a fixed determinant or havin
g another point in V nearby. We will focus on a concrete case used to stat
e the theorem and highlight the proof strategy. We will also discuss some
ongoing work and ideas which advertise the generality and strength of this
argument.\n
LOCATION:https://stable.researchseminars.org/talk/NEDNT/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nattalie Tamam (University of California\, San Diego)
DTSTART:20201009T161500Z
DTEND:20201009T173000Z
DTSTAMP:20260404T111215Z
UID:NEDNT/4
DESCRIPTION:Title: Effective equidistribution of horospherical flows in infinite volume<
/a>\nby Nattalie Tamam (University of California\, San Diego) as part of N
ew England Dynamics and Number Theory Seminar\n\nLecture held in Online.\n
\nAbstract\nWe want to provide effective information about averages of orb
its of the horospherical subgroup acting on a hyperbolic manifold of infin
ite volume. We start by presenting the setting and results for manifolds w
ith finite volume. Then\, discuss the difficulties that arise when studyin
g the infinite volume setting\, and the measures that play a crucial role
in it. This is joint work with Jacqueline Warren.\n
LOCATION:https://stable.researchseminars.org/talk/NEDNT/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Douglas Lind (University of Washington)
DTSTART:20201016T161500Z
DTEND:20201016T173000Z
DTSTAMP:20260404T111215Z
UID:NEDNT/5
DESCRIPTION:Title: Decimation limits of algebraic actions\nby Douglas Lind (Universi
ty of Washington) as part of New England Dynamics and Number Theory Semina
r\n\nLecture held in Online.\n\nAbstract\nThis is intended to be an exposi
tory talk using simple examples to illustrate what’s going on\, and so w
ill (hopefully) be a gentle introduction to these topics. Given a polynomi
al in d commuting variables we can define an algebraic action of ℤ^d by
commuting automorphisms of a compact subgroup of 𝕋^(ℤ^d). Restricting
the coordinates of points in this group to finite-index subgroups of ℤ^
d gives other algebraic actions\, defined by polynomials whose support gro
ws polynomially and whose coefficients grow exponentially. But by “renor
malizing” we can obtain a limiting object that is a concave function on
ℝ^d with interesting properties\, e.g. its maximum value is the entropy
of the action. For some polynomials this function also arises in statistic
al mechanics models as the “surface tension” of a random surface via a
variational principle. In joint work with Arzhakova\, Schmidt\, and Verbi
tskiy\, we establish this limiting behavior\, and identify the limit in te
rms of the Legendre transform of the Ronkin function of the polynomial. Th
e proof is based on Mahler’s estimates on polynomial coefficients using
Mahler measure\, and an idea used by Boyd to prove that Mahler measure is
continuous in the coefficients of the polynomial. Refinements of convergen
ce questions involve diophantine issues that I will discuss\, together wit
h some open problems.\n
LOCATION:https://stable.researchseminars.org/talk/NEDNT/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mishel Skenderi (Brandeis University)
DTSTART:20201023T161500Z
DTEND:20201023T173000Z
DTSTAMP:20260404T111215Z
UID:NEDNT/6
DESCRIPTION:Title: Small values at integer points of generic subhomogeneous functions\nby Mishel Skenderi (Brandeis University) as part of New England Dynamic
s and Number Theory Seminar\n\nLecture held in Online.\n\nAbstract\nThis t
alk will be based on joint work with Dmitry Kleinbock that has been motiva
ted by several recent papers (among them\, those of Athreya-Margulis\, Bou
rgain\, Ghosh-Gorodnik-Nevo\, Kelmer-Yu). Given a certain sort of group $G
$ and certain sorts of functions $f: \\mathbb{R}^n \\to \\mathbb{R}$ and $
\\psi : \\mathbb{R}^n \\to \\mathbb{R}_{>0}\,$ we obtain necessary and suf
ficient conditions so that for Haar-almost every $g \\in G\,$ there exist
infinitely many (respectively\, finitely many) $v \\in \\mathbb{Z}^n$ for
which $|(f \\circ g)(v)| \\leq \\psi(\\|v\\|)\,$ where $\\|\\cdot\\|$ is a
n arbitrary norm on $\\mathbb{R}^n.$ We also give a sufficient condition i
n the setting of uniform approximation. As a consequence of our methods\,
we obtain generalizations to the case of vector-valued (simultaneous) appr
oximation with no additional effort. In our work\, we use probabilistic re
sults in the geometry of numbers that go back several decades to the work
of Siegel\, Rogers\, and W. Schmidt\; these results have recently found ne
w life thanks to a 2009 paper of Athreya-Margulis.\n
LOCATION:https://stable.researchseminars.org/talk/NEDNT/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anthony Sanchez (University of Washington)
DTSTART:20201030T161500Z
DTEND:20201030T173000Z
DTSTAMP:20260404T111215Z
UID:NEDNT/7
DESCRIPTION:Title: Gaps of saddle connection directions for some branched covers of tori
\nby Anthony Sanchez (University of Washington) as part of New England
Dynamics and Number Theory Seminar\n\nLecture held in Online.\n\nAbstract
\nConsider the class of translation surfaces given by gluing two identical
tori along a slit. Every such surface has genus two and two cone-type sin
gularities of angle $4\\pi$. There is a distinguished set of geodesics cal
led saddle connections that are the geodesics between cone points. We can
recover a vector in the plane representing the saddle connection by keepin
g track of the amount that the saddle connection moves in the vertical and
horizontal direction. How random is the set of saddle connections? \nWe m
otivate the gap distribution of slopes as a measure of randomness and comp
ute the gap distribution of slopes of saddle connections for the class of
translation surfaces given by gluing two identical tori along a slit.\n
LOCATION:https://stable.researchseminars.org/talk/NEDNT/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Byungchul Cha (Muhlenberg College)
DTSTART:20201106T171500Z
DTEND:20201106T183000Z
DTSTAMP:20260404T111215Z
UID:NEDNT/8
DESCRIPTION:Title: Intrinsic Diophantine Approximation of circles\nby Byungchul Cha
(Muhlenberg College) as part of New England Dynamics and Number Theory Sem
inar\n\nLecture held in Online.\n\nAbstract\nLet $S^1$ be the unit circle
in $\\mathbb{R}^2$ centered at the origin and let $Z$ be a countable dense
subset of $S^1$\, for instance\, the set $Z = S^1(\\mathbb{Q})$ of all ra
tional points in $S^1$. We give a complete description of an initial discr
ete part of the Lagrange spectrum of $S^1$ in the sense of intrinsic Dioph
antine approximation. This is an analogue of the classical result of Marko
ff in 1879\, where he characterized the most badly approximable real numbe
rs via the periods of their continued fraction expansions. Additionally\,
we present similar results for a few different subsets $Z$ of $S^1$. This
is joint work with Dong Han Kim.\n
LOCATION:https://stable.researchseminars.org/talk/NEDNT/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jacqueline Warren (University of California\, San Diego)
DTSTART:20201113T171500Z
DTEND:20201113T183000Z
DTSTAMP:20260404T111215Z
UID:NEDNT/9
DESCRIPTION:Title: Joining classification and factor rigidity in infinite volume\nby
Jacqueline Warren (University of California\, San Diego) as part of New E
ngland Dynamics and Number Theory Seminar\n\nLecture held in Online.\n\nAb
stract\nFor a group acting on two spaces\, a joining of these systems is a
measure on the product space that is invariant under the diagonal action
and projects to the original measures on each space. As an important step
towards her celebrated measure classification theorem\, Ratner proved an e
arly landmark result classifying joinings for horocycle flows on finite vo
lume quotients of PSL(2\,R). In this talk\, I will discuss joining classif
ication for horospherical flows in the infinite volume\, rank one setting\
, as well as a key factor rigidity theorem that is used in the proof.\n
LOCATION:https://stable.researchseminars.org/talk/NEDNT/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Shahriar Mirzadeh (Michigan State University)
DTSTART:20201120T171500Z
DTEND:20201120T183000Z
DTSTAMP:20260404T111215Z
UID:NEDNT/10
DESCRIPTION:Title: On the dimension drop conjecture for diagonal flows on the space of
lattices\nby Shahriar Mirzadeh (Michigan State University) as part of
New England Dynamics and Number Theory Seminar\n\nLecture held in Online.\
n\nAbstract\nConsider the set of points in a homogeneous space X=G/Gamma w
hose g_t orbit misses a fixed open set. It has measure zero if the flow is
ergodic. It has been conjectured that this set has Hausdorff dimension st
rictly smaller than the dimension of X. This conjecture is proved when X i
s compact or when it has real rank 1. In this talk we will prove the conje
cture for probably the most important example of the higher rank case\, na
mely: G=SL(m+n\, R)\, Gamma=SL(m+n\,Z)\, and g_t = diag(exp(t/m)\, …\, e
xp(t/m)\, exp(-t/n)\, …\, exp(-t/n)). We can also use our main result to
produce new applications to Diophantine approximation. This project is jo
int work with Dmitry Kleinbock.\n
LOCATION:https://stable.researchseminars.org/talk/NEDNT/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anthony Sanchez (University of Washington)
DTSTART:20201211T171500Z
DTEND:20201211T183000Z
DTSTAMP:20260404T111215Z
UID:NEDNT/12
DESCRIPTION:Title: Gaps of saddle connection directions for some branched covers of tor
i\nby Anthony Sanchez (University of Washington) as part of New Englan
d Dynamics and Number Theory Seminar\n\nLecture held in Online.\n\nAbstrac
t\nHolonomy vectors of translation surfaces provide a geometric generaliza
tion for higher genus surfaces of (primitive) integer lattice points. The
counting and distribution properties of holonomy vectors on translation su
rfaces have been studied extensively. In this talk\, we consider the follo
wing question: How random are the holonomy vectors of a translation surfac
e? We motivate the gap distribution of slopes of holonomy vectors as a mea
sure of randomness and compute the gap distribution for the class of trans
lation surfaces given by gluing two identical tori along a slit. No prior
background on translation surfaces or gap distributions will be assumed.\n
LOCATION:https://stable.researchseminars.org/talk/NEDNT/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Osama Khalil (University of Utah)
DTSTART:20201204T171500Z
DTEND:20201204T183000Z
DTSTAMP:20260404T111215Z
UID:NEDNT/13
DESCRIPTION:Title: Large centralizers and counting integral points on affine varieties<
/a>\nby Osama Khalil (University of Utah) as part of New England Dynamics
and Number Theory Seminar\n\nLecture held in Online.\n\nAbstract\nDuke-Rud
nick-Sarnak and Eskin-McMullen initiated the use of ergodic methods to cou
nt integral points on affine homogeneous varieties. They reduced the probl
em to one of studying limiting distributions of translates of periods of r
eductive groups on homogeneous spaces. The breakthrough of Eskin\, Mozes a
nd Shah provided a rather complete understanding of this question in the c
ase the reductive group has a “small centralizer” inside the ambient g
roup. In this talk\, we describe work in progress giving new results on th
e equidistribution of generic translates of closed orbits of semisimple gr
oups with “large centralizers”. The key new ingredient is an algebraic
description of a partial compactification (for lack of a better word) of
the set of intermediate groups which act as obstructions to equidistributi
on. This allows us to employ tools from geometric invariant theory to stud
y the avoidance problem.\n
LOCATION:https://stable.researchseminars.org/talk/NEDNT/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Cagri Sert (Universität Zürich)
DTSTART:20210201T171500Z
DTEND:20210201T183000Z
DTSTAMP:20260404T111215Z
UID:NEDNT/14
DESCRIPTION:Title: Expanding measures and random walks on homogeneous spaces\nby Ca
gri Sert (Universität Zürich) as part of New England Dynamics and Number
Theory Seminar\n\nLecture held in Online.\n\nAbstract\nWe will start by r
eviewing some recent works on random walks on homogeneous spaces. We will
continue by discussing the notion of a H-expanding probability measure on
a connected semisimple Lie group H\, that we introduce inspired by these d
evelopments. As we shall see\, for a H-expanding µ with H < G\, on the on
e hand\, one can obtain a description of µ-stationary probability measure
s on the homogeneous space G/Λ using the measure classification results o
f Eskin– Lindenstrauss\, and on the other hand\, the recurrence techniqu
es of Benoist–Quint can be generalized to this setting. As a result\, we
will deduce equidistribution and orbit closure description results simult
aneously for a class of subgroups which contains Zariski-dense subgroups a
nd some epimorphic subgroups of H. If time allows\, we will see how\, usin
g an idea of Simmons–Weiss\, this allows also us to deduce Birkhoff gene
ricity of a class of fractal measures with respect to expanding diagonal a
ctions. Joint work with Roland Prohaska and Ronggang Shi.\n
LOCATION:https://stable.researchseminars.org/talk/NEDNT/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Barak Weiss (Tel Aviv University)
DTSTART:20210208T171500Z
DTEND:20210208T183000Z
DTSTAMP:20260404T111215Z
UID:NEDNT/15
DESCRIPTION:Title: Classification and statistics of cut-and-project sets\nby Barak
Weiss (Tel Aviv University) as part of New England Dynamics and Number The
ory Seminar\n\nLecture held in Online.\n\nAbstract\nWe introduce a class o
f so-called “Ratner-Marklof-Strombergsson measures”. These are probabi
lity measures supported on cut-and-project sets in Euclidean space of dime
nsion d>1 which are invariant and ergodic for the action of the groups ASL
_d(R) or SL_d(R) (affine or linear maps preserving orientation and volume)
. We classify the measures that can arise in terms of algebraic groups and
homogeneous dynamics. Using the classification\, we prove analogues of re
sults of Siegel\, Weil and Rogers about a Siegel summation formula and ide
ntities and bounds involving higher moments. We deduce results about asymp
totics\, with error estimates\, of point-counting and patch-counting for t
ypical cut-and-project sets. Joint work with Rene Ruehr and Yotam Smilansk
y.\n
LOCATION:https://stable.researchseminars.org/talk/NEDNT/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tsviqa Lakrec (The Hebrew University of Jerusalem)
DTSTART:20210222T171500Z
DTEND:20210222T183000Z
DTSTAMP:20260404T111215Z
UID:NEDNT/16
DESCRIPTION:Title: Equidistribution of affine random walks on some nilmanifolds\nby
Tsviqa Lakrec (The Hebrew University of Jerusalem) as part of New England
Dynamics and Number Theory Seminar\n\nLecture held in Online.\n\nAbstract
\nWe consider the action of the group of affine transformations on a nilma
nifold. Given a probability measure on this group and a starting point\, a
random walk on the nilmanifold is defined. We study quantitative equidist
ribution in law of such affine random walks on nilmanifolds. Under certain
assumptions\, we show that a failure to have fast equidistribution on a n
ilmanifold is due to a failure on some factor nilmanifold. Combined with e
quidistribution results on the torus\, this leads to an equidistribution s
tatement on some nilmanifolds\, such as Heisenberg nilmanifolds.\nThis tal
k is based on joint works with Weikun He and Elon Lindenstrauss.\n
LOCATION:https://stable.researchseminars.org/talk/NEDNT/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Maxim Kirsebom (University of Hamburg)
DTSTART:20210315T161500Z
DTEND:20210315T173000Z
DTSTAMP:20260404T111215Z
UID:NEDNT/17
DESCRIPTION:Title: Towards an extreme value law for the deepest cusp excursions of the
unipotent flow\nby Maxim Kirsebom (University of Hamburg) as part of N
ew England Dynamics and Number Theory Seminar\n\nLecture held in Online.\n
\nAbstract\nThe unipotent flow on the unit tangent bundle of the modular s
urface is a classic example of a homogeneous flow when understood through
the identification with PSL_2(R)/PSL_2(Z). The ergodicity of the flow impl
ies that almost every orbit is dense in the space and hence must eventuall
y make excursions deeper and deeper into the cusp. We are interested in un
derstanding the nature of these excursions. In the described setting\, and
more generally\, Athreya and Margulis proved that the maximal excursions
obey the logarithm law almost surely\, meaning that their growth rate scal
es the logarithm of the time. In this work we focus on a more precise desc
ription of this behaviour\, namely determining the probability that the de
epest excursion fails to outperform the expected asymptotic behaviour by a
n additive amount. This question may be phrased in the language of extreme
value statistics and we establish some results towards a complete extreme
value law in this setting. The methods used are based on classical ideas
from geometry of numbers. This is work in progress\, joint with Keivan Mal
lahi-Karai.\n
LOCATION:https://stable.researchseminars.org/talk/NEDNT/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Peter Varju (University of Cambridge)
DTSTART:20210322T161500Z
DTEND:20210322T173000Z
DTSTAMP:20260404T111215Z
UID:NEDNT/18
DESCRIPTION:Title: On the dimension of self-similar measures\nby Peter Varju (Unive
rsity of Cambridge) as part of New England Dynamics and Number Theory Semi
nar\n\nLecture held in Online.\n\nAbstract\nLet $f_1$\,…\,$f_n$ be a col
lection of contracting similarities on $\\mathbb{R}$\, and let $p_1$\,…\
,$p_n$ be a probability vector. There is a unique probability measure mu o
n $\\mathbb{R}$ that satisfies the identity\n$\\mu = p_1 f_1(\\mu) + … +
p_n f_n(\\mu)$.\nThis measure is called self-similar. The maps $f_1$\,…
\,$f_n$ are said to satisfy the no exact overlaps condition if they genera
te a free semigroup (i.e. all compositions are distinct). Under this condi
tion\, the dimension of mu is conjectured to be the minimum of 1 and the r
atio of the entropy of $p_1$\,…\,$p_n$ and the average logarithmic contr
action factor of the $f_i$. This conjecture has been recently established
in some special cases\, including when $n=2$ and $f_1$ and $f_2$ have the
same contraction factor. In the talk I will discuss recent progress by Ari
el Rapaport and myself in the case $n=3$. In this case new difficulties ar
ise as was demonstrated by recent examples of Baker and Barany\, Kaenmaki
of IFS’s with arbitrarily weak separation properties.\n
LOCATION:https://stable.researchseminars.org/talk/NEDNT/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tushar Das (University of Wisconsin - La Crosse)
DTSTART:20210419T161500Z
DTEND:20210419T173000Z
DTSTAMP:20260404T111215Z
UID:NEDNT/19
DESCRIPTION:Title: Using templates to study problems in dynamics and number theory\
nby Tushar Das (University of Wisconsin - La Crosse) as part of New Englan
d Dynamics and Number Theory Seminar\n\nLecture held in Online.\n\nAbstrac
t\nTemplates may be viewed as a combinatorial device that helps study\nasy
mptotic properties of lattice successive minima. This simple idea\,\nintro
duced in joint work with Lior Fishman\, David Simmons\, and Mariusz\nUrban
ski\, promises to be useful in several areas beyond our current\napplicati
ons. The latter lie at the fertile interface along Dani’s\ncorrespondenc
e principle between Diophantine approximation and\nhomogeneous flows\, dee
pened by Kleinbock & Margulis\; and Schmidt &\nSummerer’s parametric geo
metry of numbers\, deepened by Roy. Templates\nare at the heart of our var
iational principle (arXiv:1901.06602)\,\nwhich provides a unified framewor
k to compute the Hausdorff and\npacking dimensions of a variety of sets of
dynamical and\nnumber-theoretic interest. We will introduce and give some
flavor for\nour project\, hint at a few new directions\, and hope to pres
ent several\nopen problems of varying depth to reward participants of this
\nwonderful seminar!\n
LOCATION:https://stable.researchseminars.org/talk/NEDNT/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Minju Lee (Yale University)
DTSTART:20210308T171500Z
DTEND:20210308T183000Z
DTSTAMP:20260404T111215Z
UID:NEDNT/20
DESCRIPTION:Title: Orbit closures of unipotent flows for hyperbolic manifolds with Fuch
sian ends\nby Minju Lee (Yale University) as part of New England Dynam
ics and Number Theory Seminar\n\nLecture held in Online.\n\nAbstract\nThis
is joint work with Hee Oh. We establish an analogue of Ratner’s orbit c
losure theorem for any connected closed subgroup generated by unipotent el
ements in $\\mathrm{SO}(d\,1)$ acting on the space $\\Gamma\\backslash\\ma
thrm{SO}(d\,1)$\, assuming that the associated hyperbolic manifold $M=\\Ga
mma\\backslash\\mathbb{H}^d$ is a convex cocompact manifold with Fuchsian
ends. For $d = 3$\, this was proved earlier by McMullen\, Mohammadi and Oh
. In a higher dimensional case\, the possibility of accumulation on closed
orbits of intermediate subgroups causes serious issues\, but in the end\,
all orbit closures of unipotent flows are relatively homogeneous. Our res
ults imply the following: for any $k\\geq 1$\,\n(1) the closure of any $k$
-horosphere in $M$ is a properly immersed submanifold\;\n(2) the closure o
f any geodesic $(k+1)$-plane in $M$ is a properly immersed submanifold\;\n
(3) an infinite sequence of maximal properly immersed geodesic $(k+1)$-pla
nes intersecting $\\mathrm{core} M$ becomes dense in $M$.\n
LOCATION:https://stable.researchseminars.org/talk/NEDNT/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Han Yu (University of Cambridge)
DTSTART:20210412T161500Z
DTEND:20210412T173000Z
DTSTAMP:20260404T111215Z
UID:NEDNT/21
DESCRIPTION:Title: Rational numbers near self-similar sets\nby Han Yu (University o
f Cambridge) as part of New England Dynamics and Number Theory Seminar\n\n
Lecture held in Online.\n\nAbstract\nWe will discuss a problem on counting
rational numbers near\nself-similar sets. In particular\, we will show th
at the set of rational\nnumbers is ‘reasonably well distributed’ aroun
d the middle $p$-th Cantor\nset when $p$ is a large integer. Our approach
is via Fourier analysis\nand we will also discuss some problems on Fourier
transform of\nself-similar measures which are of independent interest. As
a result\, it\nis possible to show that $p=5$ satisfies the previous stat
ement. The\nmaterials come from various working-in-progress projects with
D. Allen\,\nS. Chow and P. Varju.\n
LOCATION:https://stable.researchseminars.org/talk/NEDNT/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nicolas Chevallier (Université de Haute Alsace)
DTSTART:20210405T161500Z
DTEND:20210405T173000Z
DTSTAMP:20260404T111215Z
UID:NEDNT/22
DESCRIPTION:Title: Minimal vectors in $\\C^2$ and best constant for Dirichlet theorem o
ver $\\C$\nby Nicolas Chevallier (Université de Haute Alsace) as part
of New England Dynamics and Number Theory Seminar\n\nLecture held in Onli
ne.\n\nAbstract\nWe study minimal vectors in lattices over Gaussian intege
rs in $\\C^2$.We show that the index of the sub-lattice generated by two c
onsecutive minimal vectors in a lattice of $\\C^2$\, can be either $1$ or
$2$.Next\, we describe the constraints on pairs of consecutive minimal vec
tors. These constraints make it possible to find the best constant for Di
richlet theorem about approximations of complex numbers by quotient of Gau
ssian integers.\n
LOCATION:https://stable.researchseminars.org/talk/NEDNT/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Asaf Katz (University of Michigan)
DTSTART:20210426T161500Z
DTEND:20210426T173000Z
DTSTAMP:20260404T111215Z
UID:NEDNT/23
DESCRIPTION:Title: An application of Margulis’ inequality to effective equidistributi
on\nby Asaf Katz (University of Michigan) as part of New England Dynam
ics and Number Theory Seminar\n\nLecture held in Online.\n\nAbstract\nRatn
er’s celebrated equidistribution theorem states that the trajectory of a
ny point in a homogeneous space under a unipotent flow is getting equidist
ributed with respect to some algebraic measure. In the case where the acti
on is horospherical\, one can deduce an effective equidistribution result
by mixing methods\, an idea that goes back to Margulis’ thesis. When the
homogeneous space is non-compact\, one needs to impose further “diophan
tine conditions” over the base point\, quantifying some recurrence rates
\, in order to get a quantified equidistribution result. In the talk I wil
l discuss certain diophantine conditions\, and in particular I will show h
ow a new Margulis’ type inequality for translates of horospherical orbit
s helps verify such conditions. This results in a quantified equidistribut
ion result for a large class of points\, akin to the results of A. Strombr
eggson dealing with the \\textrm{SL}_2 case. In particular we deduce a ful
ly effective quantitative equidistribution for horospherical trajectories
of lattices defined over number fields\, without pertaining to the strong
subspace theorem.\n
LOCATION:https://stable.researchseminars.org/talk/NEDNT/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:No Talk
DTSTART:20210329T161500Z
DTEND:20210329T173000Z
DTSTAMP:20260404T111215Z
UID:NEDNT/24
DESCRIPTION:by No Talk as part of New England Dynamics and Number Theory S
eminar\n\nLecture held in Online.\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/NEDNT/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pratyush Sarkar (Yale University)
DTSTART:20210503T161500Z
DTEND:20210503T173000Z
DTSTAMP:20260404T111215Z
UID:NEDNT/25
DESCRIPTION:Title: Generalization of Selberg’s 3⁄16 theorem for convex cocompact th
in subgroups of SO(n\, 1)\nby Pratyush Sarkar (Yale University) as par
t of New England Dynamics and Number Theory Seminar\n\nLecture held in Onl
ine.\n\nAbstract\nSelberg’s 3/16 theorem for congruence covers of the mo
dular surface is a beautiful theorem which has a natural dynamical interpr
etation as uniform exponential mixing. Bourgain-Gamburd-Sarnak’s breakth
rough works initiated many recent developments to generalize Selberg’s t
heorem for infinite volume hyperbolic manifolds. One such result is by Oh-
Winter establishing uniform exponential mixing for convex cocompact hyperb
olic surfaces. These are not only interesting in and of itself but can als
o be used for a wide range of applications including uniform resonance fre
e regions for the resolvent of the Laplacian\, affine sieve\, and prime ge
odesic theorems. I will present a further generalization to higher dimensi
ons and some of these immediate consequences.\n
LOCATION:https://stable.researchseminars.org/talk/NEDNT/25/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Seungki Kim (University of Cincinnati)
DTSTART:20210510T161500Z
DTEND:20210510T173000Z
DTSTAMP:20260404T111215Z
UID:NEDNT/26
DESCRIPTION:Title: Counting problems on a random lattice\nby Seungki Kim (Universit
y of Cincinnati) as part of New England Dynamics and Number Theory Seminar
\n\nLecture held in Online.\n\nAbstract\nA random lattice is a random elem
ent of SL(n\,Z) \\ SL(n\,R) equipped with the probability measure inherite
d from the Haar measure of SL(n\,R). Analogous to the usual lattice point-
counting\, one tries to “count” — more precisely\, study the statist
ics of — the random lattice points inside a ball or other shapes. I’ll
give a gentle introduction to this topic\, discussing the early works of
Siegel\, Rogers and Schmidt and some of the recent results\, as well as th
eir applications.\n
LOCATION:https://stable.researchseminars.org/talk/NEDNT/26/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jayadev Athreya (University of Washington)
DTSTART:20210923T161500Z
DTEND:20210923T173000Z
DTSTAMP:20260404T111215Z
UID:NEDNT/28
DESCRIPTION:Title: Geometric Structures and Point Processes\nby Jayadev Athreya (Un
iversity of Washington) as part of New England Dynamics and Number Theory
Seminar\n\nLecture held in Online.\n\nAbstract\nIn this talk\, we will pro
ve the convergence part of Khitchine’s theorem on non-degenerate manifol
ds. This confirms a conjecture of Kleinbock and Margulis in 1998. Our appr
oach uses geometric and dynamical ideas together with a new technique of `
major and minor arcs’. In particular\, we establish sharp upper bounds f
or the number of rational points of bounded height lying near `major arcs
’ and give explicit exponentially small bounds for the measure of `minor
arcs’. This is joint work with Victor Beresnevich.\n
LOCATION:https://stable.researchseminars.org/talk/NEDNT/28/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sebastian Hurtado (University of Chicago)
DTSTART:20210930T161500Z
DTEND:20210930T173000Z
DTSTAMP:20260404T111215Z
UID:NEDNT/29
DESCRIPTION:Title: Height Gap\, an Arithmetic Margulis Lemma and Almost Laws\nby Se
bastian Hurtado (University of Chicago) as part of New England Dynamics an
d Number Theory Seminar\n\nLecture held in Online.\n\nAbstract\nWe provide
a new (more elementary) proof of a result of E. Breuillard\, which state
that a set of matrices with algebraic entries generating a non-virtually s
olvable group has a positive lower bound in its arithmetic height (we will
explain this notion)\, this is a non-abelian version of Lehmer’s proble
m. We also show that in arithmetic locally symmetric spaces\, short geodes
ics tend to be far from each other if the degree of the trace field is lar
ge. This lemma allows us to prove new results about growth of cohomology o
f sequences of locally symmetric spaces and to give a proof of a conjectur
e of Gelander. These results are works in progress with Joe Chen and Homin
Lee\, and with Mikolaj Fraczyk and Jean Raimbault.\n
LOCATION:https://stable.researchseminars.org/talk/NEDNT/29/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dubi Kelmer (Boston College)
DTSTART:20211021T161500Z
DTEND:20211021T173000Z
DTSTAMP:20260404T111215Z
UID:NEDNT/30
DESCRIPTION:Title: The light cone Siegel transform\, its moment formulas\, and their ap
plications\nby Dubi Kelmer (Boston College) as part of New England Dyn
amics and Number Theory Seminar\n\nLecture held in Online.\n\nAbstract\nIn
this talk I will describe an analogue of the Siegel transform where the r
ole of Euclidean space is replaced by a light cone corresponding to an ind
efinite quadratic form.In this case one can use results on the spectral th
eory of incomplete Eisenstein series to establish moment formulas analogou
s to the classical formulas of Siegel\, Rogers\, and Schmidt.I will then d
escribe several applications of these formulas to counting lattice points
on the light cone\, as well as for the distribution of rational points on
the sphere. All new results are based on joint work with Shucheng Yu.\n
LOCATION:https://stable.researchseminars.org/talk/NEDNT/30/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lei Yang (Sichuan University)
DTSTART:20211007T161500Z
DTEND:20211007T173000Z
DTSTAMP:20260404T111215Z
UID:NEDNT/31
DESCRIPTION:Title: Khintchine’s theorem on manifolds\nby Lei Yang (Sichuan Univer
sity) as part of New England Dynamics and Number Theory Seminar\n\nLecture
held in Online.\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/NEDNT/31/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pengyu Yang (ETH)
DTSTART:20211014T161500Z
DTEND:20211014T173000Z
DTSTAMP:20260404T111215Z
UID:NEDNT/32
DESCRIPTION:Title: Equidistribution of degenerate curves and Dirichlet improvability\nby Pengyu Yang (ETH) as part of New England Dynamics and Number Theory
Seminar\n\nLecture held in Online.\n\nAbstract\nIn the space of 3-lattices
\, we study the translates of a line segment under a diagonal flow. Sharp
conditions for non-divergence and equidistribution will be given. As an ap
plication\, we will show that Lebesgue-almost every point on a planar line
is Dirichlet non-improvable if and only if the line is irrational. This i
s joint work with Kleinbock\, de Saxcé and Shah. Generalizations to highe
r dimensions will also be discussed (work in progress with Shah).\n
LOCATION:https://stable.researchseminars.org/talk/NEDNT/32/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Demi Allen (University of Warwick)
DTSTART:20211028T161500Z
DTEND:20211028T173000Z
DTSTAMP:20260404T111215Z
UID:NEDNT/33
DESCRIPTION:Title: An inhomogeneous Khintchine-Groshev Theorem without monotonicity
\nby Demi Allen (University of Warwick) as part of New England Dynamics an
d Number Theory Seminar\n\nLecture held in Online.\n\nAbstract\nThe classi
cal (inhomogeneous) Khintchine-Groshev Theorem tells us that for a monoton
ic approximating function $\\psi: \\mathbb{N} \\to [0\,\\infty)$ the Lebes
gue measure of the set of (inhomogeneously) $\\psi$-well-approximable poin
ts in $\\mathbb{R}^{nm}$ is zero or full depending on\, respectively\, the
convergence or divergence of $\\sum_{q=1}^{\\infty}{q^{n-1}\\psi(q)^m}$.
In the homogeneous case\, it is now known that the monotonicity condition
on $\\psi$ can be removed whenever $nm>1$ and cannot be removed when $nm=1
$. In this talk I will discuss recent work with Felipe A. Ramírez (Wesley
an\, US) in which we show that the inhomogeneous Khintchine-Groshev Theore
m is true without the monotonicity assumption on $\\psi$ whenever $nm>2$.
This result brings the inhomogeneous theory almost in line with the comple
ted homogeneous theory. I will survey previous results towards removing mo
notonicity from the homogeneous and inhomogeneous Khintchine-Groshev Theor
em before discussing the main ideas behind the proof our recent result.\n
LOCATION:https://stable.researchseminars.org/talk/NEDNT/33/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexander Gorodnik (University of Zurich)
DTSTART:20211104T161500Z
DTEND:20211104T173000Z
DTSTAMP:20260404T111215Z
UID:NEDNT/34
DESCRIPTION:Title: Quantitative equidistribution and Randomness\nby Alexander Gorod
nik (University of Zurich) as part of New England Dynamics and Number Theo
ry Seminar\n\nLecture held in Online.\n\nAbstract\nWe discuss some results
on quantitative equidistribution on homogeneous spaces and related proble
ms about behaviour of arithmetic counting functions. This is a joint work
with Björklund and Fregoli.\n
LOCATION:https://stable.researchseminars.org/talk/NEDNT/34/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Chris Lutsko (Rutgers University)
DTSTART:20211111T171500Z
DTEND:20211111T183000Z
DTSTAMP:20260404T111215Z
UID:NEDNT/35
DESCRIPTION:Title: Pair correlation of monomial sequences modulo 1\nby Chris Lutsko
(Rutgers University) as part of New England Dynamics and Number Theory Se
minar\n\nLecture held in Online.\n\nAbstract\nFix $\\alpha\, \\theta > 0$\
, and consider the sequence $(\\alpha n^\\theta \\mod 1)_{n>0}$. Since the
seminal work of Rudnick-Sarnak (1998)\, and due to the Berry-Tabor conjec
ture in quantum chaos\, the fine-scale properties of these dilated mononom
ial sequences have been intensively studied. In this talk\, I will briefly
survey what is known about these sequences and present a recent result (j
oint with Sourmelidis and Technau) showing that for $\\theta \\le 1/3$\, a
nd $\\alpha > 0$\, the pair correlation function is Poissonian. While the
techniques we use are derived from analytic number theory\, the problem is
rooted in dynamics and relates to dynamical proofs for related problems.\
n
LOCATION:https://stable.researchseminars.org/talk/NEDNT/35/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ilya Khayutin (Northwestern University)
DTSTART:20211202T171500Z
DTEND:20211202T183000Z
DTSTAMP:20260404T111215Z
UID:NEDNT/36
DESCRIPTION:Title: Two-step equidistribution for bi-quadratic torus packets\nby Ily
a Khayutin (Northwestern University) as part of New England Dynamics and N
umber Theory Seminar\n\nLecture held in Online.\n\nAbstract\nA major chall
enge to the asymptotic analysis of a sequence of probability measures on a
homogeneous space\, invariant under diagonalizable groups\, is the possib
ility of accumulation on intermediate homogeneous subspaces. In this aspec
t higher rank homogeneous flows cannot be expected to share the rigidity p
roperties of unipotent ones. In particular\, the linearization technique f
ails for diagonalizable flows. \n\nIn a joint work in progress with A. Wie
ser we show how in favorable situations one can actually use the existence
of intermediate homogeneous spaces in our benefit. We show that periodic
measures on some packets of periodic torus orbits on PGL4(Z)\\PGL4(R) conv
erge in the limit to a measure with a non-trivial Haar component. The proo
f goes by establishing high entropy for the limit measure. The method util
izes the intermediate homogeneous space to split the analysis into two mor
e tractable steps.\n
LOCATION:https://stable.researchseminars.org/talk/NEDNT/36/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Michael Bersudsky (Technion)
DTSTART:20211209T171500Z
DTEND:20211209T183000Z
DTSTAMP:20260404T111215Z
UID:NEDNT/37
DESCRIPTION:Title: On the image in the torus of sparse points on expanding analytic cur
ves\nby Michael Bersudsky (Technion) as part of New England Dynamics a
nd Number Theory Seminar\n\nLecture held in Online.\n\nAbstract\nIt is kno
wn that the projection to the 2-torus of the normalised parameter measure
on a circle of radius $R$ in the plane becomes uniformly distributed as $R
$ grows to infinity. I will discuss the following natural discrete analogu
e for this problem. Starting from an angle and a sequence of radii {$R_n$}
which diverges to infinity\, I will consider the projection to the 2-toru
s of the n’th roots of unity rotated by this angle and dilated by a fact
or of $R_n$. The interesting regime in this problem is when $R_n$ is much
larger than n so that the dilated roots of unity appear sparsely on the di
lated circle.I will discuss 3 types of results:\n\nValidity of equidistrib
ution for all angles when the sparsity is polynomial.\nFailure of equidist
ribution for some super polynomial dilations.\nEquidistribution for almost
all angles for arbitrary dilations.\nI will discuss the above type of res
ults in greater generality and I will try to explain how the theory of o-m
inimal structures is related to the proof.\n
LOCATION:https://stable.researchseminars.org/talk/NEDNT/37/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Akshat Das (University of Houston)
DTSTART:20220203T171500Z
DTEND:20220203T183000Z
DTSTAMP:20260404T111215Z
UID:NEDNT/38
DESCRIPTION:Title: An adelic version of the three gap theorem\nby Akshat Das (Unive
rsity of Houston) as part of New England Dynamics and Number Theory Semina
r\n\nLecture held in Online.\n\nAbstract\nIn order to understand problems
in dynamics which are sensitive to arithmetic properties of return times t
o regions\, it is desirable to generalize classical results about rotation
s on the circle to the setting of rotations on adelic tori. One such resul
t is the classical three gap theorem\, which is also referred to as the th
ree distance theorem and as the Steinhaus problem. It states that\, for an
y real number\, a\, and positive integer\, N\, the collection of points na
mod 1\, where n runs from 1 to N\, partitions the circle into component
arcs having one of at most three distinct lengths. Since the 1950s\, when
this theorem was first proved independently by multiple authors\, it has b
een reproved numerous times and generalized in many ways. One of the more
recent proofs has been given by Marklof and Strömbergsson using a lattice
based approach to gaps problems in Diophantine approximation. In this tal
k\, we use an adaptation of this approach to the adeles to prove a natural
generalization of the classical three gap theorem for rotations on adelic
tori. This is joint work with Alan Haynes.\n
LOCATION:https://stable.researchseminars.org/talk/NEDNT/38/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jiyoung Han (TIFR)
DTSTART:20220210T171500Z
DTEND:20220210T183000Z
DTSTAMP:20260404T111215Z
UID:NEDNT/39
DESCRIPTION:Title: The asymptotic distribution of the joint values of the integral latt
ice points for a system of a quadratic form and a linear form\nby Jiyo
ung Han (TIFR) as part of New England Dynamics and Number Theory Seminar\n
\nLecture held in Online.\n\nAbstract\nLet Q be a quadratic form and let L
be a linear form on the n-dimensional real vector space. We are intereste
d in the distribution of the image of the integral lattice under the map (
Q\, L). Developing the celebrated work of Eskin\, Margulis\, and Mozes in
1998\, we provide the conditions of systems of forms which satisfy that th
e number of integral vectors in the ball of radius T whose joint values ar
e contained in a given bounded set converges asymptotically to the volume
of the region given by the level sets of the quadratic form and the linear
form\, intersecting with the ball of radius T\, as T goes to infinity. Th
is condition is introduced by Gorodnik in 2004.\nFor this\, we need to cla
ssify all intermediate subgroups between the special orthogonal group pres
erving Q and L and the special linear group. Among them\, only two closed
subgroups are of our concern. We will introduce Siegel integral formulas a
nd equidistribution theorems for each subgroup\, and show how to reach our
main theorem. This is joint work with Seonhee Lim and Keivan Mallahi-Kara
i.\n
LOCATION:https://stable.researchseminars.org/talk/NEDNT/39/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Julien Trevisan (Institut de Mathématiques de Jussieu)
DTSTART:20220217T171500Z
DTEND:20220217T183000Z
DTSTAMP:20260404T111215Z
UID:NEDNT/40
DESCRIPTION:Title: Limit laws in the lattice counting problem. The case of ellipses.\nby Julien Trevisan (Institut de Mathématiques de Jussieu) as part of N
ew England Dynamics and Number Theory Seminar\n\nLecture held in Online.\n
\nAbstract\nLet E be an ellipse centered around 0. We are interested in th
e asymptotic distribution\nof the error of the number of unimodular lattic
e points that fall into tE when the lattice is random\nand when t goes to
infinity.\nBuilding on previous works by Bleher and by Fayad and Dolgopyat
\, we show that the error term\, when normalized by the square root of t\,
converges in distribution towards an explicit distribution.\nFor this\, w
e first use harmonic analysis to reduce the study of the normalized error
to the study of a Siegel transform that depends on t.\nThen\, and this is
the key part of our proof\, we show that\, when t goes to infinity\, this
last Siegel transform behaves in distribution as\, what we call\, a modifi
ed Siegel transform with random weights. Such objects often appear in aver
age counting problems.\nFinally\, we show that this last quantity converge
s almost surely\, and we study the existence of the moments of its law.\nT
his work was supervised by Bassam Fayad.\n
LOCATION:https://stable.researchseminars.org/talk/NEDNT/40/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Irving Calderón (Université Paris-Saclay)
DTSTART:20220303T171500Z
DTEND:20220303T183000Z
DTSTAMP:20260404T111215Z
UID:NEDNT/41
DESCRIPTION:Title: S-adic quadratic forms and Homogeneous Dynamics\nby Irving Calde
rón (Université Paris-Saclay) as part of New England Dynamics and Number
Theory Seminar\n\nLecture held in Online.\n\nAbstract\nWe present two new
quantitative results about quadratic forms.\nLet $S = {\\infty} \\cup S_f
$ be a finite set of places of Q. Consider the ring $Z_S$ of S-integers\,
and $Q_S = \\prod{p \\in S} Q_p$. The first is a solution to the problem o
f deciding if any given integral quadratic forms $Q_1$ and $Q_2$ are $Z_S$
-equivalent. The proof is based on a reformulation of the problem in terms
of the action of $O(Q_1\, Q_S)$ on the space $X{d\,S}$ of lattices of $Q_
{S\,d}$. A key tool are explicit mixing rates for the action of O(Q1\, QS)
on closed orbits in X{d\,S}. As an application we obtain\, for any S-inte
gral orthogonal group\, polynomial bounds on the S-norms of the elements o
f a finite generating set.\nThese two results and the methods of proof are
based on the work of H. Li and G. Margulis for $S = { \\infty }$.\n
LOCATION:https://stable.researchseminars.org/talk/NEDNT/41/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nattalie Tamam (University of Michigan)
DTSTART:20220310T171500Z
DTEND:20220310T183000Z
DTSTAMP:20260404T111215Z
UID:NEDNT/42
DESCRIPTION:Title: Classification of divergence of trajectories\nby Nattalie Tamam
(University of Michigan) as part of New England Dynamics and Number Theory
Seminar\n\nLecture held in Online.\n\nAbstract\nAs shown by Dani\, diopha
ntine approximations are in direct correspondence to the behavior of orbit
s in certain homogeneous spaces. We will discuss the interpretation of the
divergent trajectories and the obvious ones\, the ones diverging due to a
purely algebraic reason. As conjectured by Barak Weiss\, there is a compl
ete classification of divergent trajectories when considering the action o
f subgroups of the diagonal group. We will discuss the last part of this c
onjecture\, showing that for a ‘large enough’ such subgroup\, every di
vergent trajectory diverges obviously. This is a joint work with Omri Sola
n.\n
LOCATION:https://stable.researchseminars.org/talk/NEDNT/42/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nate Hughes (University of Exeter)
DTSTART:20220317T161500Z
DTEND:20220317T173000Z
DTSTAMP:20260404T111215Z
UID:NEDNT/43
DESCRIPTION:Title: Effective Counting and Spiralling of Lattice Approximates\nby Na
te Hughes (University of Exeter) as part of New England Dynamics and Numbe
r Theory Seminar\n\nLecture held in Online.\n\nAbstract\nWe will prove an
effective version of Dirichlet’s approximation theorem\, giving the erro
r between the number of rational approximations to a real vector with deno
minator less than some real number T and the asymptotic growth of this cou
nt. Additional results for linear forms can be obtained\, as well as resul
ts measuring the direction of these approximates\, known as ‘spiralling
of lattice approximates’. These results are obtained by reformulating th
e number-theoretic problem to the context of homogeneous spaces of unimodu
lar lattices. The advantage of this reformulation is that we have more too
ls to deal with the problem\, such as Siegel’s mean value theorem and Ro
gers’ higher moment formula. The proof involves using the ergodic proper
ties of diagonal flows on this homogeneous space to calculate the number o
f lattice approximates\, bounding the second moment of the count\, then ap
plying an effective ergodic theorem due to Gaposhkin. Particular attention
is paid to the case of primitive lattices in two-dimensions\, where Roger
s’ theorem fails. In this case\, we apply a new theorem by Kleinbock and
Yu to obtain a better error term than previous results due to Schmidt.\n
LOCATION:https://stable.researchseminars.org/talk/NEDNT/43/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Simon Machado (the University of Cambridge)
DTSTART:20220324T161500Z
DTEND:20220324T173000Z
DTSTAMP:20260404T111215Z
UID:NEDNT/44
DESCRIPTION:Title: Superrigidity and arithmeticity for some aperiodic subsets in higher
-rank simple Lie groups\nby Simon Machado (the University of Cambridge
) as part of New England Dynamics and Number Theory Seminar\n\nLecture hel
d in Online.\n\nAbstract\nMeyer sets are fascinating objects: they are ape
riodic subsets of Euclidean spaces that nonetheless exhibit long-range ape
riodic order. Sets of vertices of the Penrose tiling (P3) and Pisot-Vijara
yaghavan numbers of a real number field are some of the most well-known ex
amples. In his pioneering work\, Meyer provided a powerful and elegant cha
racterisation of Meyer sets. Years later\, Lagarias proved a similar chara
cterisation starting from what seemed to be considerably weaker assumption
s.\nA fascinating question asks whether Meyer’s and Lagarias’ results
may be extended to more general ambient groups. In fact\, a first result i
n that direction was already obtained in Meyer’s work: he proved a sum-p
roduct phenomenon which\, implicitly\, boiled down to a classification of
Meyer sets in the group of affine transformations of the line.\nI will tal
k about a generalisation of both Meyer’s and Lagarias’ theorems to dis
crete subsets of higher-rank simple Lie groups. I will explain how this re
sult can be seen as a generalisation of Margulis’ arithmeticity theorem
and how it can be deduced from Zimmer’s cocycle superrigidity. We will s
ee that\, surprisingly\, Pisot-Vijarayaghavan numbers appear naturally in
this context too.\n
LOCATION:https://stable.researchseminars.org/talk/NEDNT/44/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Johannes Schleischitz (Middle East Technical University)
DTSTART:20220331T161500Z
DTEND:20220331T173000Z
DTSTAMP:20260404T111215Z
UID:NEDNT/45
DESCRIPTION:Title: Exact uniform approximation and Dirichlet spectrum\nby Johannes
Schleischitz (Middle East Technical University) as part of New England Dyn
amics and Number Theory Seminar\n\nLecture held in Online.\n\nAbstract\nWe
consider the Dirichlet spectrum\, with respect to maximum norm and simult
aneous approximation. It is basically the analogue of the famous (multi-di
mensional) Lagrange spectrum with respect to uniform approximation. By Dir
ichlet’s Theorem it is contained in [0\,1]. The central new result is th
at it equals the entire interval [0\,1] when the number of variables is tw
o or more. We thereby get a new\, constructive proof of a recent result by
Beresnevich\, Guan\, Marnat\, Ramirez and Velani that there are Dirichlet
improvable vectors that are neither bad nor singular\, in any dimension.
We provide several generalizations\, including metrical claims.\n
LOCATION:https://stable.researchseminars.org/talk/NEDNT/45/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Emilio Corso (ETH)
DTSTART:20220407T161500Z
DTEND:20220407T173000Z
DTSTAMP:20260404T111215Z
UID:NEDNT/46
DESCRIPTION:Title: Asymptotics of the equidistribution rate of expanding circles on com
pact hyperbolic quotients and applications\nby Emilio Corso (ETH) as p
art of New England Dynamics and Number Theory Seminar\n\nLecture held in O
nline.\n\nAbstract\nEquidistribution properties of translates of orbits fo
r subgroup actions on homogeneous spaces are intimately linked to the mixi
ng features of the global action of the ambient group. The connection appe
ars already in Margulis’ thesis (1969)\, displaying its full potential i
n the work of Eskin and McMullen during the nineties. On a quantitative le
vel\, the philosophy underpinning this linkage allows to transfer mixing r
ates to effective estimates for the rate of equidistribution\, albeit at t
he cost of a sizeable loss in the exponent. In joint work with Ravotti\, w
e instead resort to a spectral method\, pioneered by Ratner in her study o
f quantitative mixing of geodesic and horocycle flows\, in order to obtain
the precise asymptotic behaviour of averages of regular observables along
expanding circles on compact hyperbolic surfaces. The primary goal of the
talk is to outline the salient traits of this method\, illustrating how i
t leads to the relevant asymptotic expansion. In addition\, we shall also
present applications of the main result to distributional limit theorems a
nd to quantitative error estimates on the corresponding hyperbolic lattice
point counting problem\, the latter having been examined\, to date\, only
through number-theoretical methods in works of Selberg\, Lax-Phillips and
Phillips-Rudnick.\n
LOCATION:https://stable.researchseminars.org/talk/NEDNT/46/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mikolaj Fraczyk (University of Chicago)
DTSTART:20220414T161500Z
DTEND:20220414T173000Z
DTSTAMP:20260404T111215Z
UID:NEDNT/47
DESCRIPTION:Title: Thin part of the arithmetic orbifolds\nby Mikolaj Fraczyk (Unive
rsity of Chicago) as part of New England Dynamics and Number Theory Semina
r\n\nLecture held in Online.\n\nAbstract\nLet X be a symmetric space. The
collar lemma\, also known as the Margulis lemma\, says that there exists a
n epsilon=epsilon(X)\, such that the epsilon-thin part of a locally symmet
ric space X/\\Gamma looks locally like a quotient by a virtually unipotent
subgroup. It turns out that in the arithmetic setting we can improve this
lemma by making the epsilon grow linearly in the degree of the number fil
ed generated by the traces of elements of \\Gamma. I will explain why this
is the case and present several applications\, including the proof of the
fact that an arithmetic locally symmetric manifold M is homotopy equivale
nt to a simplicial complex of size bounded linearly in the volume of M and
degrees of all vertices bounded uniformly in terms of X. Based on a joint
work with Sebastian Hurtado and Jean Raimbault.\n
LOCATION:https://stable.researchseminars.org/talk/NEDNT/47/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ian Hoover (Boston College)
DTSTART:20220428T161500Z
DTEND:20220428T173000Z
DTSTAMP:20260404T111215Z
UID:NEDNT/48
DESCRIPTION:Title: Effective Equidistribution on Hilbert Modular Surfaces\nby Ian H
oover (Boston College) as part of New England Dynamics and Number Theory S
eminar\n\nLecture held in Online.\n\nAbstract\nWhile ineffective equidistr
ibution has been understood much more generally\, effective results for no
n-compact orbits have been more scarce. I will give effective (polynomial)
error rates for the translates of diagonal orbits on Hilbert modular surf
aces. This work follows as a higher dimensional extension of the work of K
elmer and Kontorovich.\n
LOCATION:https://stable.researchseminars.org/talk/NEDNT/48/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jiajie Zheng (Brandeis University)
DTSTART:20220505T161500Z
DTEND:20220505T173000Z
DTSTAMP:20260404T111215Z
UID:NEDNT/49
DESCRIPTION:Title: Dynamical Borel–Cantelli Lemma for Lipschitz Twists\nby Jiajie
Zheng (Brandeis University) as part of New England Dynamics and Number Th
eory Seminar\n\nLecture held in Online.\n\nAbstract\nIn the study of some
dynamical systems\, the limit superior of a sequence of measurable sets is
often of interest. The shrinking targets and recurrence are two of the mo
st commonly studied problems that concern limit superior sets. However\, t
he zero-one laws for the shrinking targets and recurrence are usually trea
ted separately and proved differently. In this talk\, we construct a gener
alized definition that can specialize into the shrinking targets and recur
rence and our approach gives a unified proof to the zero-one laws for the
two problems.\n
LOCATION:https://stable.researchseminars.org/talk/NEDNT/49/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Simon Baker (University of Birmingham)
DTSTART:20220922T161500Z
DTEND:20220922T173000Z
DTSTAMP:20260404T111215Z
UID:NEDNT/50
DESCRIPTION:Title: Overlapping iterated function systems from the perspective of Metric
Number Theory\nby Simon Baker (University of Birmingham) as part of N
ew England Dynamics and Number Theory Seminar\n\nLecture held in Online.\n
\nAbstract\nKhintchine’s theorem is a classical result from metric numbe
r theory which relates the Lebesgue measure of certain limsup sets with th
e divergence of naturally occurring volume sums. Importantly this result p
rovides a quantitative description of how the rationals are distributed wi
thin the reals. In this talk I will discuss some recent work where I prove
that a similar Khintchine like phenomenon occurs typically within many fa
milies of overlapping iterated function systems. Families of iterated func
tion systems these results apply to include those arising from Bernoulli c
onvolutions\, the 0\,1\,3 problem\, and affine contractions with varying t
ranslation parameters. \nTime permitting I also will discuss a particular
family of iterated function systems for which we can be more precise. Our
analysis of this family shows that by studying the metric properties of li
msup sets\, we can distinguish between the overlapping behaviour of iterat
ed function systems in a way that is not available to us by simply studyin
g properties of self-similar measures.\n
LOCATION:https://stable.researchseminars.org/talk/NEDNT/50/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Juno Seong (UC San Diego)
DTSTART:20221006T161500Z
DTEND:20221006T173000Z
DTSTAMP:20260404T111215Z
UID:NEDNT/51
DESCRIPTION:Title: An avoidance principle and Margulis functions for expanding translat
es of unipotent orbits\nby Juno Seong (UC San Diego) as part of New En
gland Dynamics and Number Theory Seminar\n\nLecture held in Online.\n\nAbs
tract\nAvoidance principles — quantifying how much time trajectories avo
id certain subsets of the ambient space — have been fruitful in the stud
y of dynamical systems. We prove an avoidance principle for expanding tran
slates of unipotent orbits for some semisimple homogeneous spaces. In addi
tion\, we prove a quantitative isolation result of closed orbits and give
an upper bound on the number of closed orbits of bounded volume. The proof
of our results relies on the construction of a Margulis function and the
theory of finite dimensional representations of semisimple Lie groups. Thi
s is joint work with Anthony Sanchez.\n
LOCATION:https://stable.researchseminars.org/talk/NEDNT/51/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Chris Lutsko (Rutgers University)
DTSTART:20221013T161500Z
DTEND:20221013T173000Z
DTSTAMP:20260404T111215Z
UID:NEDNT/52
DESCRIPTION:Title: A Spectral Approach to Counting and Equidistribution\nby Chris L
utsko (Rutgers University) as part of New England Dynamics and Number Theo
ry Seminar\n\nLecture held in Online.\n\nAbstract\nSince the early 20th ce
ntury\, spectral methods have been used to obtain effective counting theor
ems for various objects of interest in number theory\, geometry and group
theory. In this talk I’ll start by introducing two classical problems: t
he Gauss circle problem\, and the Apollonian counting problem. By surveyin
g results on these problems (and some generalizations)\, I’ll demonstrat
e how to use spectral methods to obtain effective asymptotics for some ver
y classical problems. Then I will try and explain how to generalize this m
ethod to apply to certain horospherical equidistribution theorems.\n
LOCATION:https://stable.researchseminars.org/talk/NEDNT/52/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lam Pham (Brandeis University)
DTSTART:20221020T161500Z
DTEND:20221020T173000Z
DTSTAMP:20260404T111215Z
UID:NEDNT/53
DESCRIPTION:Title: Short closed geodesics in higher rank arithmetic locally symmetric s
paces\nby Lam Pham (Brandeis University) as part of New England Dynami
cs and Number Theory Seminar\n\nLecture held in Online.\n\nAbstract\nA wel
l-known conjecture of Margulis predicts that there is a uniform lower boun
d on the systole of any irreducible arithmetic locally symmetric space. Re
cently\, in joint work with Mikolaj Fraczyk\, we show that for simple Lie
groups of higher rank\, this conjecture is equivalent to a well-known conj
ecture in number theory: that Salem numbers are uniformly bounded away fro
m 1. I will discuss our proof and some tools used\, and some additional re
sults which hold unconditionally and highlight the structure of the bottom
of the length spectrum.\n
LOCATION:https://stable.researchseminars.org/talk/NEDNT/53/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Shreyasi Datta (University of Michigan)
DTSTART:20221103T161500Z
DTEND:20221103T173000Z
DTSTAMP:20260404T111215Z
UID:NEDNT/54
DESCRIPTION:Title: p-Adic Diophantine approximation with respect to fractal measures\nby Shreyasi Datta (University of Michigan) as part of New England Dynam
ics and Number Theory Seminar\n\nLecture held in Online.\n\nAbstract\nI wi
ll give an introduction to Diophantine approximation problems starting wit
h the famous Sprindzuk Conjecture (which is now a theorem by Kleinbock and
Margulis\, who solved this using homogeneous dynamics).\nNext\, I will ta
lk about p-adic Diophantine approximation and how it is different than the
real case. In a very recent work with Anish Ghosh and Victor Beresnevich
we solved a conjecture of Kleinbock and Tomanov\, which shows pushforward
of a fractal measure by ‘nice’ functions exhibits ‘nice’ Diophanti
ne properties. In particular\, we prove p-adic analogue of a result by Kle
inbock\, Lindenstrauss and Weiss on friendly measures. I will talk about h
ow lack of the mean value theorem makes life difficult in the p-adic field
s. (No prior knowledge on this subject will be assumed!)\n
LOCATION:https://stable.researchseminars.org/talk/NEDNT/54/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nikolay Moshchevitin (Lomonosov Moscow State University)
DTSTART:20221110T171500Z
DTEND:20221110T183000Z
DTSTAMP:20260404T111215Z
UID:NEDNT/55
DESCRIPTION:Title: On inhomogeneous Diophantine approximation\nby Nikolay Moshchevi
tin (Lomonosov Moscow State University) as part of New England Dynamics an
d Number Theory Seminar\n\nLecture held in Online.\n\nAbstract\nWe will di
scuss some classical and modern results related to systems of inhomogeneou
s linear forms. We will begin with Kronecker approximation theorem and fa
mous results by Khintchine and continue with rather modern problems\, in p
articular related to weighted setting and coprime approximation.\n
LOCATION:https://stable.researchseminars.org/talk/NEDNT/55/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nicolas de Saxce (Université Paris-Nord)
DTSTART:20221117T171500Z
DTEND:20221117T183000Z
DTSTAMP:20260404T111215Z
UID:NEDNT/56
DESCRIPTION:Title: Rational approximations to linear subspaces\nby Nicolas de Saxce
(Université Paris-Nord) as part of New England Dynamics and Number Theor
y Seminar\n\nLecture held in Online.\n\nAbstract\nUsing diagonal orbits on
the space of lattices\, we revisit some old questions of Schmidt concerni
ng diophantine approximation on Grassmann varieties\, and in particular\,
we prove a version of Dirichlet’s principle in that setting.\n
LOCATION:https://stable.researchseminars.org/talk/NEDNT/56/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tariq Osman (Brandeis University)
DTSTART:20221201T171500Z
DTEND:20221201T183000Z
DTSTAMP:20260404T111215Z
UID:NEDNT/57
DESCRIPTION:Title: Tail Asymptotics for Generalised Theta Sums with Rational Parameters
\nby Tariq Osman (Brandeis University) as part of New England Dynamics
and Number Theory Seminar\n\nLecture held in Online.\n\nAbstract\nWe defi
ne generalised theta sums as exponential sums of the form S^f_N(x\; \\alph
a\, \\beta) := \\sum_{n \\in \\mathbb Z} f(n/N) e((1/2 n^2 + \\beta n)x +
\\alpha n)\, where e(z) = e^{2 \\pi i z}. If \\alpha and \\beta are fixed
real numbers\, and x is chosen randomly from the unit interval\, we may us
e homogeneous dynamics to show that N^{-1/2} S^f_N$ possesses a limiting d
istribution as N goes to infinity\, provided f is sufficiently regular. In
joint work with F. Cellarosi\, we prove that for specific rational pairs
(\\alpha\, \\beta) this limiting distribution is compactly supported and t
hat all other rational pairs lead to a limiting distribution with heavy ta
ils. This complements the existing work of F. Cellarosi and J. Marklof whe
re at least one of \\alpha or \\beta is irrational.\n
LOCATION:https://stable.researchseminars.org/talk/NEDNT/57/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sam Chow (University of Warwick)
DTSTART:20221208T171500Z
DTEND:20221208T183000Z
DTSTAMP:20260404T111215Z
UID:NEDNT/58
DESCRIPTION:Title: Counting rationals and diophantine approximation on fractals\nby
Sam Chow (University of Warwick) as part of New England Dynamics and Numb
er Theory Seminar\n\nLecture held in Online.\n\nAbstract\nWe count rationa
ls in missing-digit sets\, with applications to diophantine approximation.
In the process\, we develop the theory of Fourier \\ell^1 dimension\, inc
luding the computational aspect.\n
LOCATION:https://stable.researchseminars.org/talk/NEDNT/58/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Omri Solan (Hebrew University of Jerusalem)
DTSTART:20230921T161500Z
DTEND:20230921T173000Z
DTSTAMP:20260404T111215Z
UID:NEDNT/59
DESCRIPTION:Title: Birkhoff generic points on curves\nby Omri Solan (Hebrew Univers
ity of Jerusalem) as part of New England Dynamics and Number Theory Semina
r\n\nLecture held in Online.\n\nAbstract\nLet $a_t$ be a diagonal flow on
the space X of unimodular lattices in R^n. A point x in X is called Birkho
ff generic if a_t.x equidistributes in X as t\\to \\infty. By Birkhoff erg
odic theorem\, almost every point x in X is Birkhoff generic. One may ask
whether the same is true when the point x is sampled according to a measur
e singular to Lebesgue. \nIn a joint work with Andreas Wieser\, we discuss
the case of a generic point x in an analytic curve in X\, and show that u
nder certain conditions\, it must be Birkhoff generic. This Birkhoff gener
icity result has various applications in Diophantine approximation. In thi
s talk we will relate Birkhoff genericity to approximations of real number
s by algebraic numbers of degree at most n.\n
LOCATION:https://stable.researchseminars.org/talk/NEDNT/59/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Zach Selk (Queen’s University)
DTSTART:20230928T161500Z
DTEND:20230928T173000Z
DTSTAMP:20260404T111215Z
UID:NEDNT/60
DESCRIPTION:Title: Stochastic Calculus for the Theta Process\nby Zach Selk (Queen
’s University) as part of New England Dynamics and Number Theory Seminar
\n\nLecture held in Online.\n\nAbstract\nThe Theta process\, $X(t)$\, is a
complex valued stochastic process of number theoretical origin arising as
a scaling limit of quadratic Weyl sums $$\\sum_{n=1}^N e^{2\\pi i \\left(
\\frac{1}{2}(n^2+\\beta)x+\\alpha n\\right)}\,$$ where $(\\alpha\,\\beta)\
\in \\mathbb R^2 \\setminus \\mathbb Q^2$ and $x\\in \\mathbb R$ is chosen
at random according to any law absolutely continuous with respect to Lebe
sgue measure. The Theta process can be explicitly represented as $X(t)=\\s
qrt{t} \\Theta(\\Gamma g \\Phi^{2 \\log t})$ where $\\Theta$ is an automor
phic function defined on Lie group $G$\, invariant under left multiplicati
on under lattice $\\Gamma$. Additionally\, $g\\in \\Gamma \\setminus G$ is
chosen Haar uniformly at random and $\\Phi$ is the geodesic flow on $\\Ga
mma \\setminus G$. The Theta process shares several similar properties wit
h the Brownian motion. In particular\, both lack differentiability and hav
e the same $p$ variation and H\\”older properties.\nSimilarly to Brownia
n motion\, standard calculus and even Young/Riemann-Stieltjes calculus tec
hniques do not work. However\, Brownian motion is what is known as a marti
ngale allowing for a classical theory of It\\^o calculus which makes use o
f cancellations “on average”. The It\\^o calculus can be used to prove
several properties of Brownian motion such as its conformal invariance\,
bounds on its running maximum in terms of its quadratic variation\, absolu
tely continuous changes in measure and much more. \nUnfortunately\, we sho
w that the Theta process $X$ is not a (semi)martingale\, therefore It\\^o
techniques don’t work. However\, a new theory introduced in 1998 by Terr
y Lyons called rough paths theory handles processes with the same analytic
regularity as $X$. The key idea in rough paths theory is that constructin
g stochastic calculus for a signal can be reduced to constructing the “i
terated integrals” of the signal. In this talk\, we will show the constr
uction of the iterated integrals – the “rough path” – above the pr
ocess $X$. Joint with Francesco Cellarosi.\n
LOCATION:https://stable.researchseminars.org/talk/NEDNT/60/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yuval Yifrach (Technion)
DTSTART:20231005T161500Z
DTEND:20231005T173000Z
DTSTAMP:20260404T111215Z
UID:NEDNT/61
DESCRIPTION:Title: A variation on the p-adic Littlewood Conjecture\nby Yuval Yifrac
h (Technion) as part of New England Dynamics and Number Theory Seminar\n\n
Lecture held in Online.\n\nAbstract\nWe consider a variation on the p-adic
Littlewood Conjecture where instead of using powers of one prime\, we use
arbitrarily large primes. We examine this conjecture from two viewpoints:
the Diophantine-approximation one and the dynamical one. Using the dynami
cal viewpoint\, we rephrase the conjecture using Hecke neighbors and prove
a partial statement towards the conjecture. Namely\, we prove that the Ha
usdorff dimension of the exception set is strictly smaller than 1. Our too
ls for the proof are mainly the effective equidistribution of Hecke neighb
ors due to Oh et al and to expander properties of $SL_2(Z/pZ)$ due to Bour
gain-Gamburd. This talk is based on an ongoing joint work with Erez Neshar
im.\n
LOCATION:https://stable.researchseminars.org/talk/NEDNT/61/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hao Xing (Ohio State University)
DTSTART:20231019T161500Z
DTEND:20231019T173000Z
DTSTAMP:20260404T111215Z
UID:NEDNT/62
DESCRIPTION:Title: Equidistribution problem in the space of Euclidean sublattices\n
by Hao Xing (Ohio State University) as part of New England Dynamics and Nu
mber Theory Seminar\n\nLecture held in Online.\n\nAbstract\nConsider the s
pace of covolume-one sublattices of a fixed rank m in the Euclidean space
ℝd. How do the orbits behave under the action of the lattice subgroups o
f SL(d\,ℝ) (e.g. SL(d\,ℤ))? In a recent joint work with Michael Bers
udsky\, we established an equidistribution phenomenon of such orbits when
d=m+1. However\, there are many more unsolved problems along this directi
on which might be of interest not only to homogeneous dynamicists\, but al
so to number theorists and analysts as well. In this talk\, I will explain
the problem\, our result\, an overview of methods and further directions
of research in a user-friendly way.\n
LOCATION:https://stable.researchseminars.org/talk/NEDNT/62/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Noy Soffer Aranov (Technion)
DTSTART:20231026T161500Z
DTEND:20231026T173000Z
DTSTAMP:20260404T111215Z
UID:NEDNT/63
DESCRIPTION:Title: Covering Radii in Positive Characteristic\nby Noy Soffer Aranov
(Technion) as part of New England Dynamics and Number Theory Seminar\n\nLe
cture held in Online.\n\nAbstract\nA fascinating question in geometry of n
umber pertains to the covering radius of lattice with respect to an intere
sting function. For example\, given a convex body C and a lattice L in R^d
\, it is interesting to ask what is the infimal r ≥ 0 such that L + rC =
R^d. Another interesting covering radius is the multiplicative covering r
adius\, which connects to dynamics due to its invariance under the diagona
l group. It was conjectured by Minkowski that the multiplicative covering
radius is bounded above by 2^{-d} and that this upper bound is obtained on
ly on AZ^d. In this talk I will discuss surprising results pertaining to c
overing radii in the positive characteristic setting and discover several
surprising results. Some of my results include explicitly connecting betwe
en the covering radii with respect to convex bodies and successive minima
and proving a positive characteristic analogue of Minkowski’s function.\
n
LOCATION:https://stable.researchseminars.org/talk/NEDNT/63/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alon Agin (Tel Aviv University)
DTSTART:20231102T161500Z
DTEND:20231102T173000Z
DTSTAMP:20260404T111215Z
UID:NEDNT/64
DESCRIPTION:Title: Constructing best approximation vectors\nby Alon Agin (Tel Aviv
University) as part of New England Dynamics and Number Theory Seminar\n\nL
ecture held in Online.\n\nAbstract\nFor v in R^d and arbitrary norm\, we d
efine the best approximation sequence of v and the displacement vectors se
quence of v. We will discuss classical and recent works in Diophantine app
roximations in the language of these objects – focusing on their length\
, direction and congruence class.\n
LOCATION:https://stable.researchseminars.org/talk/NEDNT/64/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sam Chow (Warwick)
DTSTART:20231109T171500Z
DTEND:20231109T183000Z
DTSTAMP:20260404T111215Z
UID:NEDNT/65
DESCRIPTION:Title: Dispersion and Littlewood’s conjecture\nby Sam Chow (Warwick)
as part of New England Dynamics and Number Theory Seminar\n\nLecture held
in Online.\n\nAbstract\nI’ll discuss some problems related to Littlewood
’s conjecture in diophantine approximation\, and the role hitherto playe
d by discrepancy theory. I’ll explain why our new dispersion-theoretic a
pproach should\, and does\, deliver stronger results. Our dispersion estim
ate is proved using Poisson summation and diophantine inequalities. Joint
with Niclas Technau.\n
LOCATION:https://stable.researchseminars.org/talk/NEDNT/65/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mikey Chow (Mikey Chow)
DTSTART:20231116T171500Z
DTEND:20231116T183000Z
DTSTAMP:20260404T111215Z
UID:NEDNT/66
DESCRIPTION:Title: Jordan and Cartan spectra in higher rank with applications to correl
ations\nby Mikey Chow (Mikey Chow) as part of New England Dynamics and
Number Theory Seminar\n\nLecture held in Online.\n\nAbstract\nThe celebra
ted prime geodesic theorem for a closed hyperbolic surface says that the n
umber of closed geodesics of length at most t is asymptotically e^t/t. For
a closed surface equipped with two different hyperbolic structures\, Schw
artz and Sharp (’93) showed that the number of free homotopy classes of
length about t in both hyperbolic structures is asymptotically a constant
multiple of e^{ct} /t^{3/2} for some 0Primitive rational points on expanding horospheres: effective joint
equidistribution\nby Daniel El-Baz (TU Graz) as part of New England Dy
namics and Number Theory Seminar\n\nLecture held in Online.\n\nAbstract\nI
will present joint work with Min Lee and Andreas Strömbergsson. Using te
chniques from analytic number theory\, spectral theory\, geometry of numbe
rs as well as a healthy dose of linear algebra and building on a previous
work by Bingrong Huang\, Min Lee and myself\, we furnish a new proof of a
2016 theorem by Einsiedler\, Mozes\, Shah and Shapira. That theorem concer
ns the equidistribution of primitive rational points on certain homogeneou
s spaces and our proof has the added benefit of yielding a rate of converg
ence. It turns out to have several (perhaps surprising) applications to nu
mber theory and combinatorics\, which I shall also discuss.\n
LOCATION:https://stable.researchseminars.org/talk/NEDNT/67/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Florian Richter (EPFL)
DTSTART:20231207T171500Z
DTEND:20231207T183000Z
DTSTAMP:20260404T111215Z
UID:NEDNT/68
DESCRIPTION:by Florian Richter (EPFL) as part of New England Dynamics and
Number Theory Seminar\n\nLecture held in Online.\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/NEDNT/68/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Oleksiy Klurman (University of Bristol)
DTSTART:20231214T171500Z
DTEND:20231214T183000Z
DTSTAMP:20260404T111215Z
UID:NEDNT/69
DESCRIPTION:Title: Finding Infinite arithmetic structures in sets of positive density\nby Oleksiy Klurman (University of Bristol) as part of New England Dyna
mics and Number Theory Seminar\n\nLecture held in Online.\n\nAbstract\nIs
there a partition of the natural numbers into finitely many pieces\, none
of which contains a Pythagorean triple (i.e. a solution to the equation x^
2 + y^2 = z^2)? This is one of the simplest (to state!) questions in arith
metic Ramsey theory which is still widely open. I will talk about a recent
partial result\, showing that “Pythagorean pairs” are partition regul
ar\, that is in any finite partition of the natural numbers there are two
numbers x\,y in the same cell of the partition\, such that x^2 + y^2 = z^2
for some integer z (which may be coloured differently). The proof is a bl
end of ideas from ergodic theory and multiplicative number theory. Based o
n a joint work with N. Frantzikinakis and J. Moreira.\n
LOCATION:https://stable.researchseminars.org/talk/NEDNT/69/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lei Yang (IAS)
DTSTART:20240229T171500Z
DTEND:20240229T183000Z
DTSTAMP:20260404T111215Z
UID:NEDNT/70
DESCRIPTION:Title: Incidence geometry and effective equidistribution in homogeneous dyn
amics\nby Lei Yang (IAS) as part of New England Dynamics and Number Th
eory Seminar\n\nLecture held in Online.\n\nAbstract\nI will explain my pro
of of an effective version of Ratner’s equidistribution theorem for unip
otent orbits in SL(3\,R)/SL(3\,Z). The proof combines new ideas from harmo
nic analysis and incidence geometry. In particular\, the proof is based on
a bootstrapping argument improving the local dimension of measures genera
ted by unipotent orbits. The key is to relate the behavior of the unipoten
t orbits to a Kakeya model.\n
LOCATION:https://stable.researchseminars.org/talk/NEDNT/70/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gaurav Aggarwal (TIFR)
DTSTART:20240307T171500Z
DTEND:20240307T183000Z
DTSTAMP:20260404T111215Z
UID:NEDNT/71
DESCRIPTION:Title: Joint Equidistribution of Approximates\nby Gaurav Aggarwal (TIFR
) as part of New England Dynamics and Number Theory Seminar\n\nLecture hel
d in Online.\n\nAbstract\nThe distribution of integer points on varieties
has occupied mathematicians for centuries. In the 1950’s Linnik used an
“ergodic method” to prove the equidistribution of integer points on la
rge spheres under a congruence condition. As shown by Maaß\, this problem
is closely related to modular forms. Subsequently\, there were spectacula
r developments both from the analytic as well as ergodic side. I will disc
uss a more refined problem\, namely the joint distribution of lattice poin
ts in conjunction with other arithmetic data. An example of such data is t
he “shape” of an associated lattice\, or in number theoretic language\
, a Heegner point. In a completely different direction\, a “Poincaré se
ction” is a classical and useful tool in ergodic theory and dynamical sy
stems. Recently\, Shapira and Weiss\, constructed a Poincaré section for
the geodesic flow on the moduli space of lattices to study joint equidistr
ibution properties. Their work in fact is very general but crucially uses
the fact that the acting group has rank one. In joint work with Anish Ghos
h\, we develop a new method to deal with actions of higher rank groups. I
will explain this and\, if time permits\, some corollaries in Diophantine
analysis.\n
LOCATION:https://stable.researchseminars.org/talk/NEDNT/71/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Shreyasi Datta (Uppsala University)
DTSTART:20240314T161500Z
DTEND:20240314T173000Z
DTSTAMP:20260404T111215Z
UID:NEDNT/72
DESCRIPTION:Title: Bad is null via constant invariance\nby Shreyasi Datta (Uppsala
University) as part of New England Dynamics and Number Theory Seminar\n\nL
ecture held in Online.\n\nAbstract\nThe set of badly approximable vectors
in Diophantine approximation plays a significant role. In a recent work wi
th Victor Beresnevich\, Anish Ghosh\, and Ben Ward\, we developed a genera
l framework to show a `constant invariance’ property for a large class o
f limsup sets of neighbourhoods of subsets of a metric measure space. As a
consequence\, we get that the set of badly approximable points has measur
e zero in a metric space equipped with certain natural measures. In partic
ular\, given any C^2 manifold\, we show almost every point is not badly ap
proximable.\n
LOCATION:https://stable.researchseminars.org/talk/NEDNT/72/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Carsten Peterson (Paderborn University)
DTSTART:20240411T161500Z
DTEND:20240411T173000Z
DTSTAMP:20260404T111215Z
UID:NEDNT/73
DESCRIPTION:Title: Quantum ergodicity on the Bruhat-Tits building for PGL(3) in the Ben
jamini-Schramm limit\nby Carsten Peterson (Paderborn University) as pa
rt of New England Dynamics and Number Theory Seminar\n\nLecture held in On
line.\n\nAbstract\nOriginally\, quantum ergodicity concerned equidistribut
ion properties of Laplacian eigenfunctions with large eigenvalue on manifo
lds for which the geodesic flow is ergodic. More recently\, several author
s have investigated quantum ergodicity for sequences of spaces which “co
nverge” to their common universal cover and when one restricts to eigenf
unctions with eigenvalues in a fixed range. Previous authors have consider
ed this type of quantum ergodicity in the settings of regular graphs\, ran
k one symmetric spaces\, and some higher rank symmetric spaces. We prove a
nalogous results in the case when the underlying common universal cover is
the Bruhat-Tits building associated to \\textrm{PGL}(3\, F) where F is a
non-archimedean local field. This may be seen as both a higher rank analog
ue of the regular graphs setting as well as a non-archimedean analogue of
the symmetric space setting\n
LOCATION:https://stable.researchseminars.org/talk/NEDNT/73/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nikolay Moshchevitin (Technion)
DTSTART:20240418T161500Z
DTEND:20240418T173000Z
DTSTAMP:20260404T111215Z
UID:NEDNT/74
DESCRIPTION:Title: Bounded ratios and badly approximability\nby Nikolay Moshcheviti
n (Technion) as part of New England Dynamics and Number Theory Seminar\n\n
Lecture held in Online.\n\nAbstract\nWe will discuss relatively new criter
ia of badly approximability in terms of ratios of best approximations. Let
qν be convergents of continued fractions to real irrational α. It is we
ll known that\n\nα is badly approximable iff supν qν+1/qν is f
inite iff infν||qν+1α||/||qνα||>0.\n\nWe will discuss how thi
s property may be generalised to Diophantine Approximation in higher dimen
sions. The answer seems to be rather non-trivial. Some of the related prop
erties may be expressed in terms of Parametric Geometry of Numbers recentl
y developed by Schmidt\, Summerer\, Roy and the others. Also we discuss so
me properties of ratios under the consideration in accordance with the stu
dy of multidimensional Dirichlet spectra.\n
LOCATION:https://stable.researchseminars.org/talk/NEDNT/74/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alena Erchenko (Dartmouth College)
DTSTART:20240502T161500Z
DTEND:20240502T173000Z
DTSTAMP:20260404T111215Z
UID:NEDNT/75
DESCRIPTION:Title: Flexibility and rigidity for Cantor repellers\nby Alena Erchenko
(Dartmouth College) as part of New England Dynamics and Number Theory Sem
inar\n\nLecture held in Online.\n\nAbstract\nWe will consider dynamical sy
stems that we call Cantor repellers which are expanding maps on invariant
Cantor sets coming from iterated function systems. Cantor repellers have t
wo natural invariant measures: the measure of full dimension and the measu
re of maximal entropy. We show that dimensions and Lyapunov exponents of t
hose measures are flexible up to well understood restrictions. We will als
o discuss the boundary case for the range of values of the considered dyna
mical data. This is joint work with Jacob Mazor.\n
LOCATION:https://stable.researchseminars.org/talk/NEDNT/75/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sam Chow (Warwick)
DTSTART:20240924T161500Z
DTEND:20240924T173000Z
DTSTAMP:20260404T111215Z
UID:NEDNT/76
DESCRIPTION:Title: Smooth discrepancy and Littlewood’s conjecture\nby Sam Chow (W
arwick) as part of New England Dynamics and Number Theory Seminar\n\nLectu
re held in Online.\n\nAbstract\nGiven \\boldsymbol \\alpha \\in [0\,1]^d\,
we estimate the smooth discrepancy of the Kronecker sequence (n \\boldsym
bol \\alpha \\: \\mathrm{mod} \\: 1)_{n=1}^\\infty. We find that it can be
smaller than the classical discrepancy of any sequence when d \\le 2\, an
d can even be bounded in the case d=1. To achieve this\, we establish a no
vel deterministic analogue of Beck’s local-to-global principle (Annals 1
994)\, which relates the discrepancy of a Kronecker sequence to multiplica
tive diophantine approximation. This opens up a new avenue of attack for L
ittlewood’s conjecture.\n
LOCATION:https://stable.researchseminars.org/talk/NEDNT/76/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Manuel Hauke (NTNU Trondheim)
DTSTART:20241008T161500Z
DTEND:20241008T173000Z
DTSTAMP:20260404T111215Z
UID:NEDNT/77
DESCRIPTION:Title: Metric Diophantine approximation: Moving targets and inhomogeneous v
ariants\nby Manuel Hauke (NTNU Trondheim) as part of New England Dynam
ics and Number Theory Seminar\n\nLecture held in Online.\n\nAbstract\nKhin
tchine’s Theorem and its inhomogeneous and multidimensional variants pro
vide a satisfying answer about the quality of approximations for almost ev
ery number. In this talk\, I will discuss the (still open) question of all
owing a moving target (that is\, the inhomogeneous parameter changes for e
ach denominator) in Khintchine’s Theorem. Furthermore\, I will describe
Duffin–Schaeffer-type results and conjectures in these setups\, both in
dimension 1\, but also in higher dimensions. This is partially joint work
with Victor Beresnevich and Sanju Velani\, respectively with Felipe Ramír
ez.\n
LOCATION:https://stable.researchseminars.org/talk/NEDNT/77/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Shreyasi Datta (University of York)
DTSTART:20241105T171500Z
DTEND:20241105T183000Z
DTSTAMP:20260404T111215Z
UID:NEDNT/78
DESCRIPTION:Title: Fourier Asymptotics and Effective Equidistribution\nby Shreyasi
Datta (University of York) as part of New England Dynamics and Number Theo
ry Seminar\n\nLecture held in Online.\n\nAbstract\nWe talk about effective
equidistribution of the expanding horocycles on the unit cotangent bundle
of the modular surface with respect to various classes of Borel probabili
ty measures on the reals\, depending on their Fourier asymptotics. This i
s a joint work with Subhajit Jana.\n
LOCATION:https://stable.researchseminars.org/talk/NEDNT/78/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Keivan Mallahi-Karai (Constructor University)
DTSTART:20241119T171500Z
DTEND:20241119T183000Z
DTSTAMP:20260404T111215Z
UID:NEDNT/79
DESCRIPTION:Title: Spectral independence of compact groups\nby Keivan Mallahi-Karai
(Constructor University) as part of New England Dynamics and Number Theor
y Seminar\n\nLecture held in Online.\n\nAbstract\nLet $G_1$ and $G_2$ be
compact simple (real or $p$-adic) Lie groups\, and let $\\mu_1$ and $\\mu_
2$ be symmetric probability measures on $G_1$ and $G_2$. Under mild condit
ions on $\\mu_1$ and $\\mu_2$\, the distribution of $\\mu_i$ random walks
on $G_i$ converges to the uniform measure\, and the speed of convergence
is governed by the spectral gap. A coupling of $\\mu_1$ and $\\mu_2$ is an
y probability measure $\\mu$ on $G_1 \\times G_2$ whose marginal distrib
utions are $\\mu_1$ and $\\mu_2$\, respectively . A natural question is u
nder what conditions a spectral gap for all couplings depending on spectra
l gaps of $\\mu_1$ and $\\mu_2$ can be established. \nIn this talk\, I wil
l present results in this direction which are based on joint work with Ali
reza S. Golsefidy and Amir Mohammadi.\n
LOCATION:https://stable.researchseminars.org/talk/NEDNT/79/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Noy Soffer Aranov (University of Utah)
DTSTART:20241126T171500Z
DTEND:20241126T183000Z
DTSTAMP:20260404T111215Z
UID:NEDNT/80
DESCRIPTION:Title: Escape of Mass of Sequences\nby Noy Soffer Aranov (University of
Utah) as part of New England Dynamics and Number Theory Seminar\n\nLectur
e held in Online.\n\nAbstract\nOne way to study the distribution of nested
quadratic number fields satisfying fixed arithmetic relationships is thro
ugh the evolution of continued fraction expansions. In the function field
setting\, it was shown by de Mathan and Teullie that given a quadratic irr
ational $\\Theta$\, the degrees of the periodic part of the continued frac
tion of $t^n\\Theta$ are unbounded. Paulin and Shapira improved this by pr
oving that quadratic irrationals exhibit partial escape of mass. Moreover\
, they conjectured that they must exhibit full escape of mass. We construc
t counterexamples to their conjecture in every characteristic. In this tal
k we shall discuss the technique of proof as well as the connection betwee
n escape of mass in continued fractions\, Hecke trees\, and number walls.
This is part of ongoing works with Erez Nesharim and with Steven Robertson
.\n
LOCATION:https://stable.researchseminars.org/talk/NEDNT/80/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gaurav Aggarwal (TIFR)
DTSTART:20241203T171500Z
DTEND:20241203T183000Z
DTSTAMP:20260404T111215Z
UID:NEDNT/81
DESCRIPTION:Title: Singular matrices on fractals\nby Gaurav Aggarwal (TIFR) as part
of New England Dynamics and Number Theory Seminar\n\nLecture held in Onli
ne.\n\nAbstract\nSingular vectors are those for which Dirichlet’s Theore
m can be improved by arbitrarily small multiplicative constants. Recently\
, Kleinbock and Weiss showed that the set of singular vectors has measure
zero with respect to any friendly measure. However\, determining their Hau
sdorff dimension remains a subtle and challenging problem. Khalil addresse
d this by proving that the Hausdorff dimension of the set of singular vect
ors intersecting a self-similar fractal is strictly smaller than the fract
al’s dimension.\nIn this talk\, I will extend Khalil’s result in four
key directions. First\, we generalize the study from vectors to matrices.
Second\, we analyze intersections with products of fractals\, such as the
Cartesian product of the middle-third and middle-fifth Cantor sets. Third\
, we establish upper bounds for singular vectors in a generalized weighted
setting. Finally\, we derive an upper bound on the Hausdorff dimension of
$\\omega$-very singular matrices in these broader settings\, extending ea
rlier work of Das\, Fishman\, Simmons\, and Urbanski\, who studied the rea
l\, unweighted case.\nOur approach is dynamical in nature\, relying on the
construction of a height function inspired by the work of Kadyrov\, Klein
bock\, Lindenstrauss\, and Margulis. This is a joint work with Anish Ghosh
.\n
LOCATION:https://stable.researchseminars.org/talk/NEDNT/81/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Noy Soffer Aranov (University of Utah)
DTSTART:20241210T171500Z
DTEND:20241210T183000Z
DTSTAMP:20260404T111215Z
UID:NEDNT/82
DESCRIPTION:Title: Escape of Mass of Sequences\nby Noy Soffer Aranov (University of
Utah) as part of New England Dynamics and Number Theory Seminar\n\nLectur
e held in Online.\n\nAbstract\nOne way to study the distribution of nested
quadratic number fields satisfying fixed arithmetic relationships is thro
ugh the evolution of continued fraction expansions. In the function field
setting\, it was shown by de Mathan and Teullie that given a quadratic irr
ational $\\Theta$\, the degrees of the periodic part of the continued frac
tion of $t^n\\Theta$ are unbounded. Paulin and Shapira improved this by pr
oving that quadratic irrationals exhibit partial escape of mass. Moreover\
, they conjectured that they must exhibit full escape of mass. We construc
t counterexamples to their conjecture in every characteristic. In this tal
k we shall discuss the technique of proof as well as the connection betwee
n escape of mass in continued fractions\, Hecke trees\, and number walls.
This is part of ongoing works with Erez Nesharim and with Steven Robertson
.\n
LOCATION:https://stable.researchseminars.org/talk/NEDNT/82/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Han Zhang (Souchow University)
DTSTART:20250211T171500Z
DTEND:20250211T183000Z
DTSTAMP:20260404T111215Z
UID:NEDNT/83
DESCRIPTION:Title: Khintchine’s theorem on self-similar measures on the real line
\nby Han Zhang (Souchow University) as part of New England Dynamics and Nu
mber Theory Seminar\n\nLecture held in Online.\n\nAbstract\nIn 1984\, Mahl
er proposed the following question on Diophantine approximation : How clos
e can irrational numbers in the middle-thirds Cantor set be approximated b
y rational numbers? One way to reformulate Mahler’s question is to ask
if Khintchine’s theorem extends to the middle-thirds Cantor set. In a jo
int work with Timothée Bénard and Weikun He\, we prove that Khintchine
’s theorem holds for any self-similar measures on the real line. In part
icular this applies to the Hausdorff measure on the middle-thirds Cantor s
et. Our result generalizes the recent breakthrough work of Khalil-Luethi i
n dimension one. Our proof is inspired by the work of Bénard-He regarding
the semisimple random walks on homogeneous spaces.\n
LOCATION:https://stable.researchseminars.org/talk/NEDNT/83/
END:VEVENT
BEGIN:VEVENT
SUMMARY:JinCheng Wang (Tufts University)
DTSTART:20250225T171500Z
DTEND:20250225T183000Z
DTSTAMP:20260404T111215Z
UID:NEDNT/84
DESCRIPTION:by JinCheng Wang (Tufts University) as part of New England Dyn
amics and Number Theory Seminar\n\nLecture held in Online.\nAbstract: TBA\
n
LOCATION:https://stable.researchseminars.org/talk/NEDNT/84/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Michael Bersudsky (Ohio State University)
DTSTART:20250311T161500Z
DTEND:20250311T173000Z
DTSTAMP:20260404T111215Z
UID:NEDNT/85
DESCRIPTION:by Michael Bersudsky (Ohio State University) as part of New En
gland Dynamics and Number Theory Seminar\n\nLecture held in Online.\n\nAbs
tract\nAs a generalization of geodesic flows\, magnetic flows trace unit-s
peed curves with constant geodesic curvature. We consider the magnetic flo
ws of surfaces with negative Gaussian curvature that are nonuniformly hype
rbolic. By studying its geometry on the universal covering of the surface\
, we show the uniqueness of the measure of maximal entropy via the Bowen-C
limenhaga-Thompson machinery. This is a joint work with Boris Hasselblatt.
\n
LOCATION:https://stable.researchseminars.org/talk/NEDNT/85/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alon Agin (Tel Aviv University)
DTSTART:20250318T161500Z
DTEND:20250318T173000Z
DTSTAMP:20260404T111215Z
UID:NEDNT/86
DESCRIPTION:Title: The Dirichlet spectrum\nby Alon Agin (Tel Aviv University) as pa
rt of New England Dynamics and Number Theory Seminar\n\nLecture held in On
line.\n\nAbstract\nAkhunzhanov and Shatskov defined the Dirichlet spectrum
\, corresponding to mxn matrices and to norms on R^m and R^n. In case (m\,
n) = (2\,1) and using the Euclidean norm on R^2\, they showed that the spe
ctrum is an interval. We generalize this result to arbitrary (m\,n) with m
ax(m\,n)>1 and arbitrary norms\, improving previous works from recent year
s. We also define some related spectra and show that they too are interval
s. We also prove the existence of matrices exhibiting special properties w
ith respect to their uniform exponent. Our argument is a modification of a
n argument of Khintchine from 1926.\n
LOCATION:https://stable.researchseminars.org/talk/NEDNT/86/
END:VEVENT
BEGIN:VEVENT
SUMMARY:JinCheng Wang (Tufts University)
DTSTART:20250304T171500Z
DTEND:20250304T183000Z
DTSTAMP:20260404T111215Z
UID:NEDNT/87
DESCRIPTION:Title: Some geometric and dynamical properties of hyperbolic magnetic flows
\nby JinCheng Wang (Tufts University) as part of New England Dynamics
and Number Theory Seminar\n\nLecture held in Online.\n\nAbstract\nAs a gen
eralization of geodesic flows\, magnetic flows trace unit-speed curves wit
h constant geodesic curvature. We consider the magnetic flows of surfaces
with negative Gaussian curvature that are non-uniformly hyperbolic. By stu
dying its geometry on the universal covering of the surface\, we show the
uniqueness of the measure of maximal entropy via the Bowen-Climenhaga-Thom
pson machinery. This is a joint work with Boris Hasselblatt.\n
LOCATION:https://stable.researchseminars.org/talk/NEDNT/87/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Liyang Shao (UC Berkeley)
DTSTART:20250422T161500Z
DTEND:20250422T173000Z
DTSTAMP:20260404T111215Z
UID:NEDNT/88
DESCRIPTION:Title: Weighted Inhomogeneous Bad is Winning and Null\nby Liyang Shao (
UC Berkeley) as part of New England Dynamics and Number Theory Seminar\n\n
Lecture held in Online.\n\nAbstract\nWe will introduce the notion of inhom
ogeneous weighted badly approximable vectors. We discuss that this set can
be very large (winning) in a sense and in some other sense it is very sma
ll (measure wise). In particular\, we talk about such largeness and smalln
ess via studying weighted inhomogeneous bad intersected with manifolds and
support of certain measures. This is a joint work with Shreyasi Datta.\n
LOCATION:https://stable.researchseminars.org/talk/NEDNT/88/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Srivatsa Srinivas (UC San Diego)
DTSTART:20250429T161500Z
DTEND:20250429T173000Z
DTSTAMP:20260404T111215Z
UID:NEDNT/89
DESCRIPTION:Title: Random Walks on SL_2(F_p) x SL_2(F_p)\nby Srivatsa Srinivas (UC
San Diego) as part of New England Dynamics and Number Theory Seminar\n\nLe
cture held in Online.\n\nAbstract\nWe will give a taste of the flavors of
math that constitute the study of random walks on compact groups\, followe
d by which we will describe the author’s work with Prof. Golsefidy in so
lving a question of Lindenstrauss and Varju. Namely\, can the spectral gap
of a random walk on a product of groups be related to those of the projec
tions onto its factors\n
LOCATION:https://stable.researchseminars.org/talk/NEDNT/89/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Emilio Corso (Penn State)
DTSTART:20250506T161500Z
DTEND:20250506T173000Z
DTSTAMP:20260404T111215Z
UID:NEDNT/90
DESCRIPTION:by Emilio Corso (Penn State) as part of New England Dynamics a
nd Number Theory Seminar\n\nLecture held in Online.\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/NEDNT/90/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vasiliy Neckrasov (Brandeis University)
DTSTART:20250930T164500Z
DTEND:20250930T174500Z
DTSTAMP:20260404T111215Z
UID:NEDNT/91
DESCRIPTION:Title: Zero-one laws for uniform inhomogeneous Diophantine approximations\nby Vasiliy Neckrasov (Brandeis University) as part of New England Dyna
mics and Number Theory Seminar\n\nLecture held in Online.\n\nAbstract\nIn
[Compositio Math. 155 (2019)] Kleinbock and Wadleigh proved a “zero-one
law” for uniform Diophantine approximations to pairs (\\Theta\, \\eta) o
f a matrix \\Theta and vector \\eta by using dynamics on the space of grid
s. We will show how the classical Diophantine transference principle provi
des an alternative approach to this problem and allows us to prove some ge
neralizations. Namely\, we will reduce the statement for pairs to the twis
ted (“fixed matrix”) case and show zero-one laws for twisted uniform a
pproximations.\nAll the proofs are made in weighted case and\, more genera
lly\, in the setup of approximations with arbitrary weight functions\, whi
ch will also be discussed.\nThis talk is based on arXiv:2508.01912 and arX
iv:2503.21180.\n
LOCATION:https://stable.researchseminars.org/talk/NEDNT/91/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Chengyang Wu (Peking University)
DTSTART:20251014T164500Z
DTEND:20251014T174500Z
DTSTAMP:20260404T111215Z
UID:NEDNT/92
DESCRIPTION:Title: Simultaneously bounded and dense orbits for commuting Cartan actions
\nby Chengyang Wu (Peking University) as part of New England Dynamics
and Number Theory Seminar\n\nLecture held in Online.\n\nAbstract\nWith the
goal to attack Uniform Littlewood’s Conjecture proposed in [BFK25]\, we
introduced the concept of “fiberwise nondivergence” for the action of
a cone inside the full diagonal subgroup of SL_3(R). Then it is proved in
our paper that there exists a dense subset of SL_3(R)/SL_3(Z) in which ea
ch point has a fiberwise non-divergent orbit under a cone inside the full
diagonal subgroup and an unbounded orbit under every diagonal flow. Our pr
oof also presented the first instance of results concerning simultaneously
bounded and dense orbits for commuting actions on noncompact spaces. This
is a joint work with Dmitry Kleinbock.\n
LOCATION:https://stable.researchseminars.org/talk/NEDNT/92/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pratyush Sarkar (ETHZ)
DTSTART:20251021T164500Z
DTEND:20251021T174500Z
DTSTAMP:20260404T111215Z
UID:NEDNT/93
DESCRIPTION:Title: Effective equidistribution of translates of tori in arithmetic homog
eneous spaces and applications\nby Pratyush Sarkar (ETHZ) as part of N
ew England Dynamics and Number Theory Seminar\n\nLecture held in Online.\n
\nAbstract\nA celebrated theorem of Eskin–Mozes–Shah gives an asymptot
ic counting formula for the number of integral (n x n)-matrices with a pre
scribed irreducible (over the integers/rationals) integral characteristic
polynomial. We obtain a power saving error term for the counting problem f
or (3 x 3)-matrices. We do this by using the connection to homogeneous dyn
amics and proving effective equidistribution of translates of tori in SL_3
(R)/SL_3(Z). A key tool is that the limiting Lie algebra corresponding to
the translates of tori is a certain nilpotent Lie algebra. This allows us
to use the recent breakthrough work of Lindenstrauss–Mohammadi–Wang–
Yang on effective versions of Shah’s/Ratner’s theorems. We actually st
udy the phenomenon more generally for any semisimple Lie group which we ma
y discuss if time permits.\n
LOCATION:https://stable.researchseminars.org/talk/NEDNT/93/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Suxuan Chen (Ohio State)
DTSTART:20251028T164500Z
DTEND:20251028T174500Z
DTSTAMP:20260404T111215Z
UID:NEDNT/94
DESCRIPTION:Title: The Hausdorff dimension of the intersection of \\psi-well approximab
le numbers and self-similar sets\nby Suxuan Chen (Ohio State) as part
of New England Dynamics and Number Theory Seminar\n\nLecture held in Onlin
e.\n\nAbstract\nLet \\psi be a monotonically non-increasing function from
N to R\, and let \\psi_v be defined by \\psi_v(q)=1/q^v. Here\, we conside
r self-similar sets whose iterated function systems satisfy the open set c
ondition. For functions \\psi that do not decrease too rapidly\, we give a
conjecturally sharp upper bound on the Hausdorff dimension of the interse
ction of \\psi-well approximable numbers and such self-similar sets. When
\\psi=\\psi_v for some v greater than 1 and sufficiently close to 1\, we g
ive a lower bound for this Hausdorff dimension\, which asymptotically matc
hes the upper bound as v approaches 1. In particular\, we show that the se
t of very well approximable numbers has full Hausdorff dimension within se
lf-similar sets.\n
LOCATION:https://stable.researchseminars.org/talk/NEDNT/94/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Reynold Fregoli (University of Michigan)
DTSTART:20251104T174500Z
DTEND:20251104T184500Z
DTSTAMP:20260404T111215Z
UID:NEDNT/95
DESCRIPTION:Title: Ergodic theorems for dilates of submanifolds in R^d actions\nby
Reynold Fregoli (University of Michigan) as part of New England Dynamics a
nd Number Theory Seminar\n\nLecture held in Online.\n\nAbstract\nI will di
scuss the validity of pointwise ergodic theorems for dilates of submanifol
ds in R^d-actions. In particular\, I will present two recent results in th
is direction. The first\, joint work with P. Bandi and D. Kleinbock\, prov
ides a positive result for continuous test functions in mixing R^d-actions
. The second\, joint work with J. Cheng and B. Guo\, shows that if the reg
ularity assumption on the test function is removed\, a pointwise theorem m
ay fail to hold.\n
LOCATION:https://stable.researchseminars.org/talk/NEDNT/95/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Manuel Hauke (TU Graz)
DTSTART:20251118T174500Z
DTEND:20251118T184500Z
DTSTAMP:20260404T111215Z
UID:NEDNT/96
DESCRIPTION:Title: Pseudo-random sequences\, twin primes\, and twisted diophantine appr
oximation\nby Manuel Hauke (TU Graz) as part of New England Dynamics a
nd Number Theory Seminar\n\nLecture held in Online.\n\nAbstract\nIn this t
alk\, I will speak about dynamics of $(a_n\\alpha)_{n} \\mod 1$ for intege
r sequences $(a_n)_n$ and fixed irrational rotations $\\alpha$. The focus
will be on the sequence of primes and other multiplicatively defined seque
nces\, where gap statistics as well as twisted diophantine approximation w
ill be considered. If time permits\, I will outline the proof that include
s a sieve coming from the twin prime counting problem\, and establishing v
ia random walks on Ostrowski digits an equidistribution result on diophant
ine Bohr sets mod d. This talk is partially based on https://arxiv.org/abs
/2506.01736 and joint work with E. Kowalski \nhttps://arxiv.org/abs/2502.0
8335.\n
LOCATION:https://stable.researchseminars.org/talk/NEDNT/96/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Zuo Lin (UC Berkeley)
DTSTART:20251202T174500Z
DTEND:20251202T184500Z
DTSTAMP:20260404T111215Z
UID:NEDNT/97
DESCRIPTION:Title: Polynomial effective equidistribution for some higher dimensional un
ipotent subgroups\nby Zuo Lin (UC Berkeley) as part of New England Dyn
amics and Number Theory Seminar\n\nLecture held in Online.\n\nAbstract\nLe
t G be a semisimple Lie group\, Γ be a lattice in G and U be a unipotent
subgroup of G. A celebrated theorem of Ratner says that for any x in G/Γ
the orbit U.x is equidistributed in a periodic orbit of some subgroup U
≤ L ≤ G. Establishing a quantitative version of Ratner’s theorem has
been long sought after. If U is a horospherical subgroup of G\, the quest
ion is well-studied. If U is not a horospherical subgroup\, this question
is far less understood. Recently\, Lindenstrauss\, Mohammadi\, Wang and Ya
ng established a fully quantitative and effective equidistribution result
for orbits of one-parameter (non-horospherical) unipotent groups in some c
ases. In this talk\, we will discuss a recent equidistribution theorem for
some unipotent subgroups in higher dimension. Our results in particular p
rovide equidistribution theorems for orbits of the isometry group of a non
-degenerate bilinear form on R^n in SL_n(R)/SL_n(Z).\n
LOCATION:https://stable.researchseminars.org/talk/NEDNT/97/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Demi Allen (University of Exeter)
DTSTART:20251209T150000Z
DTEND:20251209T160000Z
DTSTAMP:20260404T111215Z
UID:NEDNT/98
DESCRIPTION:Title: Rectangular Shrinking Targets on Self-Similar Carpets\nby Demi A
llen (University of Exeter) as part of New England Dynamics and Number The
ory Seminar\n\nLecture held in Online.\n\nAbstract\nSuppose $(X\,d)$ is a
metric space equipped with a Borel probability measure\, and suppose $(B_i
)_{i \\in \n}$ is a sequence of measurable sets in $X$. Suppose $T: X \\to
X$ is a measure preserving transformation\, and consider the set \n$\\{x
\\in X: T^n x \\in B_n \\text{ for infinitely many } n\\in\n\\}$. \nThis i
s a shrinking target set. The terminology of "shrinking targets" was first
introduced by Hill and Velani in 1995. Since then\, shrinking target prob
lems have received a great deal of interest\, especially with regards to s
tudying the measure-theoretic and dimension-theoretic properties of shrink
ing target sets. In this talk\, I will discuss some recent work with Thoma
s Jordan (Bristol\, UK) and Ben Ward (York\, UK) where we establish the Ha
usdorff dimension of a shrinking target set where our "targets" (the $B_n$
) are rectangles and $X$ is a self-similar carpet.\n
LOCATION:https://stable.researchseminars.org/talk/NEDNT/98/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexander Smith (Northwestern University)
DTSTART:20260129T171500Z
DTEND:20260129T183000Z
DTSTAMP:20260404T111215Z
UID:NEDNT/99
DESCRIPTION:Title: Diophantine approximation for hypersurfaces\nby Alexander Smith
(Northwestern University) as part of New England Dynamics and Number Theor
y Seminar\n\nLecture held in Online.\n\nAbstract\nAmong the nondegenerate
C^4 hypersurfaces\, we characterize the rational quadrics as the hypersurf
aces that are the least well approximated by rational points. For all othe
r hypersurfaces\, we give a heuristically sharp lower bound for the number
of rational points near them\, improving the sensitivity of prior results
of Beresnevich and Huang. Our methods are dynamical\, involving the appli
cation of Ratner’s theorems for unipotent orbits\, and we will show how
our work relates to the dynamical resolution of the Oppenheim conjecture b
y Margulis.\n
LOCATION:https://stable.researchseminars.org/talk/NEDNT/99/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexander Skenderi (UW Madison)
DTSTART:20260205T171500Z
DTEND:20260205T183000Z
DTSTAMP:20260404T111215Z
UID:NEDNT/100
DESCRIPTION:Title: Asymptotically large free semigroups in Zariski dense discrete subg
roups of Lie groups\nby Alexander Skenderi (UW Madison) as part of New
England Dynamics and Number Theory Seminar\n\nLecture held in Online.\n\n
Abstract\nAn important quantity in the study of discrete groups of isometr
ies of Riemannian manifolds\, Gromov hyperbolic spaces\, and other interes
ting geometric objects is the critical exponent. For a discrete subgroup o
f isometries of the quaternionic hyperbolic space or octonionic projective
plane\, Kevin Corlette established in 1990 that the critical exponent det
ects whether a discrete subgroup is a lattice or has infinite covolume. Pr
ecisely\, either the critical exponent equals the volume entropy\, in whic
h case the discrete subgroup is a lattice\, or the critical exponent is le
ss than the volume entropy by some definite amount\, in which case the dis
crete subgroup has infinite covolume. In 2003\, Leuzinger extended this ga
p theorem for the critical exponent to any discrete subgroup of a Lie grou
p having Kazhdan’s property (T) (for instance\, a discrete subgroup of S
L(n\,R)\, where n is at least 3).\nIn this talk\, I will present a result
which shows that no such gap phenomenon holds for discrete semigroups of L
ie groups. More precisely\, for any Zariski dense discrete subgroup of a L
ie group\, there exist free\, finitely generated\, Zariski dense subsemigr
oups whose critical exponents are arbitrarily close to that of the ambient
discrete subgroup.\nAs an application\, we show that the critical exponen
t is lower semicontinuous in the Chabauty topology whenever the Chabauty l
imit of a sequence of Zariski dense discrete subgroups is itself a Zariski
dense discrete subgroup.\n
LOCATION:https://stable.researchseminars.org/talk/NEDNT/100/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kecheng Li (Tufts University)
DTSTART:20260226T171500Z
DTEND:20260226T183000Z
DTSTAMP:20260404T111215Z
UID:NEDNT/101
DESCRIPTION:Title: Unique Equilibrium States for Viana Maps for Small Potentials\n
by Kecheng Li (Tufts University) as part of New England Dynamics and Numbe
r Theory Seminar\n\nLecture held in Online.\n\nAbstract\nWe study the ther
modynamic formalism for Viana maps (skew products that couple an expanding
circle map with a small perturbation of a quadratic map on the fibers). W
orking within the Climenhaga–-Thompson framework\, we show that for ever
y Hölder potential whose oscillation is below an explicit threshold\, the
re is a unique equilibrium state. The main step is a uniform control of re
currence to the critical region in the fibers\, where the derivative degen
erates. This yields the pressure gap and the specification estimates neede
d to apply the method and removes the principal obstruction. These conclus
ions are robust under sufficiently small perturbations of the reference ma
p.\n
LOCATION:https://stable.researchseminars.org/talk/NEDNT/101/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kavita Dhanda (University of Houston)
DTSTART:20260305T171500Z
DTEND:20260305T183000Z
DTSTAMP:20260404T111215Z
UID:NEDNT/102
DESCRIPTION:Title: Accumulation points of normalized approximations\nby Kavita Dha
nda (University of Houston) as part of New England Dynamics and Number The
ory Seminar\n\nLecture held in Online.\n\nAbstract\nConsider the collectio
n of all accumulation points of normalized integer vector translates of po
ints qα with α ∈ R^d and q ∈ Z. For each normalization factor\, We f
ind the lebesgue measure of the set of α whose accumulation points are al
l of R^d and of the complement set. In cases\, where the lebesgue measure
is zero\, we seek finer information about Hausdorff dimensions of the corr
esponding sets.\n
LOCATION:https://stable.researchseminars.org/talk/NEDNT/102/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Rishi Kumar (Tel Aviv University)
DTSTART:20260312T161500Z
DTEND:20260312T173000Z
DTSTAMP:20260404T111215Z
UID:NEDNT/103
DESCRIPTION:Title: On the error bounds for visible points in some cut-and-project sets
\nby Rishi Kumar (Tel Aviv University) as part of New England Dynamics
and Number Theory Seminar\n\nLecture held in Online.\n\nAbstract\nThe den
sity of points visible from the origin in sets such as the Ammann–Beenke
r point set has recently attracted attention. These sets can also be viewe
d as a cut-and-project set. In this talk\, we will present an error estima
te for the density of visible points for some class of cut-and-project set
s\, along with related results. Joint work with Ilya and Barak.\n
LOCATION:https://stable.researchseminars.org/talk/NEDNT/103/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jiajie Zheng (University of North Texas)
DTSTART:20260319T161500Z
DTEND:20260319T173000Z
DTSTAMP:20260404T111215Z
UID:NEDNT/104
DESCRIPTION:Title: Absolute-winning properties of equicontinuously-twisted badly appro
ximable points in continued fractions and beta-transformations\nby Jia
jie Zheng (University of North Texas) as part of New England Dynamics and
Number Theory Seminar\n\nLecture held in Online.\n\nAbstract\nIt is well k
now that in a $\\beta$-transformation system for an integer $\\beta>0$\, t
he set ${x: \\liminf_{n\\to\\infty}|T^nx-y_n|>0}$ has full Hausdorff dimen
sion for all sequences $(y_n)$ in $[0\,1)$ and in the Gauss map system ${x
: \\liminf_{n\\to\\infty}|T^nx-0|>0}$ also has full Hausdorff dimension. I
n this talk\, I will introduce a dynamical approach to understanding these
sets\, and the new technique will allow us to strengthen the results so t
hat the “targets’’ can be generalized to any equicontinuous sequence
of functions\, enabling the targets to vary by trajectories. In particula
r\, notably this will imply the full dimension of non-recurrent points\, b
ridging the problems of shrinking targets and Poincare recurrence.\n
LOCATION:https://stable.researchseminars.org/talk/NEDNT/104/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alex Maldague (Rice University)
DTSTART:20260416T161500Z
DTEND:20260416T173000Z
DTSTAMP:20260404T111215Z
UID:NEDNT/105
DESCRIPTION:Title: Superrigidity of rich representations\nby Alex Maldague (Rice U
niversity) as part of New England Dynamics and Number Theory Seminar\n\nLe
cture held in Online.\n\nAbstract\nIn this talk\, I will introduce the cla
ss of geodesically rich representations. These are representations of (rea
l or complex) hyperbolic lattices that preserve a significant amount of th
e geometric structure of the associated quotient manifold. When the quotie
nt manifold has robust geometric structure\, these representations exhibit
rigidity phenomena. In particular\, a recent superrigidity theorem for ri
ch representations was used to prove that finite-volume hyperbolic manifol
ds with infinitely many maximal totally geodesic submanifolds are arithmet
ic (Bader-Fisher-Miller-Stover). I will discuss a new superrigidity theore
m for rich representations that efficiently recovers existing results and
addresses target groups that were previously inaccessible.\n
LOCATION:https://stable.researchseminars.org/talk/NEDNT/105/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ingrid Vukusic (University of York)
DTSTART:20260402T161500Z
DTEND:20260402T173000Z
DTSTAMP:20260404T111215Z
UID:NEDNT/106
DESCRIPTION:Title: Some bounds related to the 2-adic Littlewood conjecture\nby Ing
rid Vukusic (University of York) as part of New England Dynamics and Numbe
r Theory Seminar\n\nLecture held in Online.\n\nAbstract\nConsider alpha =
(sqrt(17)-1)/8. One can check that all partial quotients in the continued
fraction expansion of alpha are bounded by 3. If we multiply alpha by 2\,
we get a number where again all partial quotients are bounded by 3. And th
e same is true for 4*alpha. Might this go on forever as we keep multiplyin
g by 2 (mod 1)? Of course\, the answer is “no”\, as the 2-adic Littlew
ood conjecture is known to be true for quadratic irrationals.\nIn this tal
k\, we will use Hurwitz’s algorithm for multiplication by 2 to approach
the 2-adic Littlewood conjecture in a completely naive way\, and we will (
im)prove some bounds related to the 2-adic Littlewood conjecture and a var
iant of it.\nJoint work with Dinis Vitorino.\n
LOCATION:https://stable.researchseminars.org/talk/NEDNT/106/
END:VEVENT
END:VCALENDAR