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BEGIN:VEVENT
SUMMARY:Emmanuel Breuillard (University of Cambridge)
DTSTART:20200918T161500Z
DTEND:20200918T173000Z
DTSTAMP:20260422T225825Z
UID:NEDNT/1
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NEDNT/1/">A 
 subspace theorem for manifolds</a>\nby Emmanuel Breuillard (University of 
 Cambridge) as part of New England Dynamics and Number Theory Seminar\n\n\n
 Abstract\nSchmidt’s subspace theorem is a fundamental result in diophant
 ine approximation and a natural generalization of Roth’s celebrated theo
 rem. In this talk I will discuss a geometric understanding of this theorem
  that blends homogeneous dynamics and geometric invariant theory. Combined
  with the Kleinbock-Margulis quantitative non-divergence estimates this yi
 elds a natural generalization of the subspace theorem to systems of linear
  forms that depend nicely on a parameter. I will also present several appl
 ications and consequences of the main result. Joint work with Nicolas de S
 axcé.\n
LOCATION:https://researchseminars.org/talk/NEDNT/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yotam Smilansky (Rutgers University)
DTSTART:20200925T161500Z
DTEND:20200925T173000Z
DTSTAMP:20260422T225825Z
UID:NEDNT/2
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NEDNT/2/">Mu
 ltiscale substitution tilings</a>\nby Yotam Smilansky (Rutgers University)
  as part of New England Dynamics and Number Theory Seminar\n\n\nAbstract\n
 Multiscale substitution tilings are a new family of tilings of Euclidean s
 pace that are generated by multiscale substitution rules. Unlike the stand
 ard setup of substitution tilings\, which is a basic object of study withi
 n the aperiodic order community and includes examples such as the Penrose 
 and the pinwheel tilings\, multiple distinct scaling constants are allowed
 \, and the defining process of inflation and subdivision is a continuous o
 ne. Under a certain irrationality assumption on the scaling constants\, th
 is construction gives rise to a new class of tilings\, tiling spaces and t
 iling dynamical systems\, which are intrinsically different from those tha
 t arise in the standard setup. In the talk I will describe these new objec
 ts and discuss various structural\, geometrical\, statistical and dynamica
 l results. Based on joint work with Yaar Solomon.\n
LOCATION:https://researchseminars.org/talk/NEDNT/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Samantha Fairchild (University of Washington)
DTSTART:20201002T161500Z
DTEND:20201002T173000Z
DTSTAMP:20260422T225825Z
UID:NEDNT/3
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NEDNT/3/">Co
 unting social interactions for discrete subsets of the plane</a>\nby Saman
 tha Fairchild (University of Washington) as part of New England Dynamics a
 nd Number Theory Seminar\n\n\nAbstract\nGiven a discrete subset V in the p
 lane\, how many points would you expect there to be in a ball of radius 10
 0? What if the radius is 10\,000? Due to the results of Fairchild and fort
 hcoming work with Burrin\, when V arises as orbits of non-uniform lattice 
 subgroups of SL(2\,R)\, we can understand asymptotic growth rate with erro
 r 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 how to c
 ount pairs of saddle connections with certain properties determining the i
 nteractions between them\, like having a fixed determinant or having anoth
 er point in V nearby. We will focus on a concrete case used to state the t
 heorem and highlight the proof strategy. We will also discuss some ongoing
  work and ideas which advertise the generality and strength of this argume
 nt.\n
LOCATION:https://researchseminars.org/talk/NEDNT/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nattalie Tamam (University of California\, San Diego)
DTSTART:20201009T161500Z
DTEND:20201009T173000Z
DTSTAMP:20260422T225825Z
UID:NEDNT/4
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NEDNT/4/">Ef
 fective equidistribution of horospherical flows in infinite volume</a>\nby
  Nattalie Tamam (University of California\, San Diego) as part of New Engl
 and Dynamics and Number Theory Seminar\n\nLecture held in Online.\n\nAbstr
 act\nWe want to provide effective information about averages of orbits of 
 the horospherical subgroup acting on a hyperbolic manifold of infinite vol
 ume. We start by presenting the setting and results for manifolds with fin
 ite volume. Then\, discuss the difficulties that arise when studying the i
 nfinite volume setting\, and the measures that play a crucial role in it. 
 This is joint work with Jacqueline Warren.\n
LOCATION:https://researchseminars.org/talk/NEDNT/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Douglas Lind (University of Washington)
DTSTART:20201016T161500Z
DTEND:20201016T173000Z
DTSTAMP:20260422T225825Z
UID:NEDNT/5
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NEDNT/5/">De
 cimation limits of algebraic actions</a>\nby Douglas Lind (University of W
 ashington) as part of New England Dynamics and Number Theory Seminar\n\nLe
 cture held in Online.\n\nAbstract\nThis is intended to be an expository ta
 lk using simple examples to illustrate what’s going on\, and so will (ho
 pefully) be a gentle introduction to these topics. Given a polynomial in d
  commuting variables we can define an algebraic action of ℤ^d by commuti
 ng automorphisms of a compact subgroup of 𝕋^(ℤ^d). Restricting the co
 ordinates of points in this group to finite-index subgroups of ℤ^d gives
  other algebraic actions\, defined by polynomials whose support grows poly
 nomially and whose coefficients grow exponentially. But by “renormalizin
 g” we can obtain a limiting object that is a concave function on ℝ^d w
 ith interesting properties\, e.g. its maximum value is the entropy of the 
 action. For some polynomials this function also arises in statistical mech
 anics models as the “surface tension” of a random surface via a variat
 ional principle. In joint work with Arzhakova\, Schmidt\, and Verbitskiy\,
  we establish this limiting behavior\, and identify the limit in terms of 
 the Legendre transform of the Ronkin function of the polynomial. The 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 continu
 ous in the coefficients of the polynomial. Refinements of convergence ques
 tions involve diophantine issues that I will discuss\, together with some 
 open problems.\n
LOCATION:https://researchseminars.org/talk/NEDNT/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mishel Skenderi (Brandeis University)
DTSTART:20201023T161500Z
DTEND:20201023T173000Z
DTSTAMP:20260422T225825Z
UID:NEDNT/6
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NEDNT/6/">Sm
 all values at integer points of generic subhomogeneous functions</a>\nby M
 ishel Skenderi (Brandeis University) as part of New England Dynamics and N
 umber Theory Seminar\n\nLecture held in Online.\n\nAbstract\nThis talk wil
 l be based on joint work with Dmitry Kleinbock that has been motivated by 
 several recent papers (among them\, those of Athreya-Margulis\, Bourgain\,
  Ghosh-Gorodnik-Nevo\, Kelmer-Yu). Given a certain sort of group $G$ and c
 ertain sorts of functions $f: \\mathbb{R}^n \\to \\mathbb{R}$ and $\\psi :
  \\mathbb{R}^n \\to \\mathbb{R}_{>0}\,$ we obtain necessary and sufficient
  conditions so that for Haar-almost every $g \\in G\,$ there exist infinit
 ely many (respectively\, finitely many) $v \\in \\mathbb{Z}^n$ for which $
 |(f \\circ g)(v)| \\leq \\psi(\\|v\\|)\,$ where $\\|\\cdot\\|$ is an arbit
 rary norm on $\\mathbb{R}^n.$ We also give a sufficient condition in the s
 etting of uniform approximation. As a consequence of our methods\, we obta
 in generalizations to the case of vector-valued (simultaneous) approximati
 on with no additional effort. In our work\, we use probabilistic results i
 n the geometry of numbers that go back several decades to the work of Sieg
 el\, Rogers\, and W. Schmidt\; these results have recently found new life 
 thanks to a 2009 paper of Athreya-Margulis.\n
LOCATION:https://researchseminars.org/talk/NEDNT/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anthony Sanchez (University of Washington)
DTSTART:20201030T161500Z
DTEND:20201030T173000Z
DTSTAMP:20260422T225825Z
UID:NEDNT/7
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NEDNT/7/">Ga
 ps of saddle connection directions for some branched covers of tori</a>\nb
 y Anthony Sanchez (University of Washington) as part of New England Dynami
 cs and Number Theory Seminar\n\nLecture held in Online.\n\nAbstract\nConsi
 der the class of translation surfaces given by gluing two identical tori a
 long a slit. Every such surface has genus two and two cone-type singularit
 ies of angle $4\\pi$. There is a distinguished set of geodesics called sad
 dle connections that are the geodesics between cone points. We can recover
  a vector in the plane representing the saddle connection by keeping track
  of the amount that the saddle connection moves in the vertical and horizo
 ntal direction. How random is the set of saddle connections? \nWe motivate
  the gap distribution of slopes as a measure of randomness and compute the
  gap distribution of slopes of saddle connections for the class of transla
 tion surfaces given by gluing two identical tori along a slit.\n
LOCATION:https://researchseminars.org/talk/NEDNT/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Byungchul Cha (Muhlenberg College)
DTSTART:20201106T171500Z
DTEND:20201106T183000Z
DTSTAMP:20260422T225825Z
UID:NEDNT/8
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NEDNT/8/">In
 trinsic Diophantine Approximation of circles</a>\nby Byungchul Cha (Muhlen
 berg College) as part of New England Dynamics and Number Theory Seminar\n\
 nLecture held in Online.\n\nAbstract\nLet $S^1$ be the unit circle in $\\m
 athbb{R}^2$ 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 rational 
 points in $S^1$. We give a complete description of an initial discrete par
 t of the Lagrange spectrum of $S^1$ in the sense of intrinsic Diophantine 
 approximation. This is an analogue of the classical result of Markoff in 1
 879\, where he characterized the most badly approximable real numbers via 
 the periods of their continued fraction expansions. Additionally\, we pres
 ent similar results for a few different subsets $Z$ of $S^1$. This is join
 t work with Dong Han Kim.\n
LOCATION:https://researchseminars.org/talk/NEDNT/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jacqueline Warren (University of California\, San Diego)
DTSTART:20201113T171500Z
DTEND:20201113T183000Z
DTSTAMP:20260422T225825Z
UID:NEDNT/9
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NEDNT/9/">Jo
 ining classification and factor rigidity in infinite volume</a>\nby Jacque
 line Warren (University of California\, San Diego) as part of New England 
 Dynamics and Number Theory Seminar\n\nLecture held in Online.\n\nAbstract\
 nFor a group acting on two spaces\, a joining of these systems is a measur
 e on the product space that is invariant under the diagonal action and pro
 jects to the original measures on each space. As an important step towards
  her celebrated measure classification theorem\, Ratner proved an early la
 ndmark result classifying joinings for horocycle flows on finite volume qu
 otients of PSL(2\,R). In this talk\, I will discuss joining classification
  for horospherical flows in the infinite volume\, rank one setting\, as we
 ll as a key factor rigidity theorem that is used in the proof.\n
LOCATION:https://researchseminars.org/talk/NEDNT/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Shahriar Mirzadeh (Michigan State University)
DTSTART:20201120T171500Z
DTEND:20201120T183000Z
DTSTAMP:20260422T225825Z
UID:NEDNT/10
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NEDNT/10/">O
 n the dimension drop conjecture for diagonal flows on the space of lattice
 s</a>\nby Shahriar Mirzadeh (Michigan State University) as part of New Eng
 land Dynamics and Number Theory Seminar\n\nLecture held in Online.\n\nAbst
 ract\nConsider the set of points in a homogeneous space X=G/Gamma whose g_
 t orbit misses a fixed open set. It has measure zero if the flow is ergodi
 c. It has been conjectured that this set has Hausdorff dimension strictly 
 smaller than the dimension of X. This conjecture is proved when X is compa
 ct or when it has real rank 1. In this talk we will prove the conjecture f
 or probably the most important example of the higher rank case\, namely: G
 =SL(m+n\, R)\, Gamma=SL(m+n\,Z)\, and g_t = diag(exp(t/m)\, …\, exp(t/m)
 \, exp(-t/n)\, …\, exp(-t/n)). We can also use our main result to produc
 e new applications to Diophantine approximation. This project is joint wor
 k with Dmitry Kleinbock.\n
LOCATION:https://researchseminars.org/talk/NEDNT/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anthony Sanchez (University of Washington)
DTSTART:20201211T171500Z
DTEND:20201211T183000Z
DTSTAMP:20260422T225825Z
UID:NEDNT/12
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NEDNT/12/">G
 aps of saddle connection directions for some branched covers of tori</a>\n
 by Anthony Sanchez (University of Washington) as part of New England Dynam
 ics and Number Theory Seminar\n\nLecture held in Online.\n\nAbstract\nHolo
 nomy vectors of translation surfaces provide a geometric generalization fo
 r higher genus surfaces of (primitive) integer lattice points. The countin
 g and distribution properties of holonomy vectors on translation surfaces 
 have been studied extensively. In this talk\, we consider the following qu
 estion: How random are the holonomy vectors of a translation surface? We m
 otivate the gap distribution of slopes of holonomy vectors as a measure of
  randomness and compute the gap distribution for the class of translation 
 surfaces given by gluing two identical tori along a slit. No prior backgro
 und on translation surfaces or gap distributions will be assumed.\n
LOCATION:https://researchseminars.org/talk/NEDNT/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Osama Khalil (University of Utah)
DTSTART:20201204T171500Z
DTEND:20201204T183000Z
DTSTAMP:20260422T225825Z
UID:NEDNT/13
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NEDNT/13/">L
 arge centralizers and counting integral points on affine varieties</a>\nby
  Osama Khalil (University of Utah) as part of New England Dynamics and Num
 ber Theory Seminar\n\nLecture held in Online.\n\nAbstract\nDuke-Rudnick-Sa
 rnak and Eskin-McMullen initiated the use of ergodic methods to count inte
 gral points on affine homogeneous varieties. They reduced the problem to o
 ne of studying limiting distributions of translates of periods of reductiv
 e groups on homogeneous spaces. The breakthrough of Eskin\, Mozes and Shah
  provided a rather complete understanding of this question in the case the
  reductive group has a “small centralizer” inside the ambient group. I
 n this talk\, we describe work in progress giving new results on the equid
 istribution of generic translates of closed orbits of semisimple groups wi
 th “large centralizers”. The key new ingredient is an algebraic descri
 ption of a partial compactification (for lack of a better word) of the set
  of intermediate groups which act as obstructions to equidistribution. Thi
 s allows us to employ tools from geometric invariant theory to study the a
 voidance problem.\n
LOCATION:https://researchseminars.org/talk/NEDNT/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Cagri Sert (Universität Zürich)
DTSTART:20210201T171500Z
DTEND:20210201T183000Z
DTSTAMP:20260422T225825Z
UID:NEDNT/14
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NEDNT/14/">E
 xpanding measures and random walks on homogeneous spaces</a>\nby Cagri Ser
 t (Universität Zürich) as part of New England Dynamics and Number Theory
  Seminar\n\nLecture held in Online.\n\nAbstract\nWe will start by reviewin
 g some recent works on random walks on homogeneous spaces. We will continu
 e by discussing the notion of a H-expanding probability measure on a conne
 cted semisimple Lie group H\, that we introduce inspired by these developm
 ents. As we shall see\, for a H-expanding µ with H < G\, on the one hand\
 , one can obtain a description of µ-stationary probability measures on th
 e homogeneous space G/Λ using the measure classification results of Eskin
 – Lindenstrauss\, and on the other hand\, the recurrence techniques of B
 enoist–Quint can be generalized to this setting. As a result\, we will d
 educe equidistribution and orbit closure description results simultaneousl
 y for a class of subgroups which contains Zariski-dense subgroups and some
  epimorphic subgroups of H. If time allows\, we will see how\, using an id
 ea of Simmons–Weiss\, this allows also us to deduce Birkhoff genericity 
 of a class of fractal measures with respect to expanding diagonal actions.
  Joint work with Roland Prohaska and Ronggang Shi.\n
LOCATION:https://researchseminars.org/talk/NEDNT/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Barak Weiss (Tel Aviv University)
DTSTART:20210208T171500Z
DTEND:20210208T183000Z
DTSTAMP:20260422T225825Z
UID:NEDNT/15
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NEDNT/15/">C
 lassification and statistics of cut-and-project sets</a>\nby Barak Weiss (
 Tel Aviv University) as part of New England Dynamics and Number Theory Sem
 inar\n\nLecture held in Online.\n\nAbstract\nWe introduce a class of so-ca
 lled “Ratner-Marklof-Strombergsson measures”. These are probability me
 asures supported on cut-and-project sets in Euclidean space of dimension d
 >1 which are invariant and ergodic for the action of the groups ASL_d(R) o
 r SL_d(R) (affine or linear maps preserving orientation and volume). We cl
 assify the measures that can arise in terms of algebraic groups and homoge
 neous dynamics. Using the classification\, we prove analogues of results o
 f Siegel\, Weil and Rogers about a Siegel summation formula and identities
  and bounds involving higher moments. We deduce results about asymptotics\
 , with error estimates\, of point-counting and patch-counting for typical 
 cut-and-project sets. Joint work with Rene Ruehr and Yotam Smilansky.\n
LOCATION:https://researchseminars.org/talk/NEDNT/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tsviqa Lakrec (The Hebrew University of Jerusalem)
DTSTART:20210222T171500Z
DTEND:20210222T183000Z
DTSTAMP:20260422T225825Z
UID:NEDNT/16
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NEDNT/16/">E
 quidistribution of affine random walks on some nilmanifolds</a>\nby Tsviqa
  Lakrec (The Hebrew University of Jerusalem) as part of New England Dynami
 cs and Number Theory Seminar\n\nLecture held in Online.\n\nAbstract\nWe co
 nsider the action of the group of affine transformations on a nilmanifold.
  Given a probability measure on this group and a starting point\, a random
  walk on the nilmanifold is defined. We study quantitative equidistributio
 n in law of such affine random walks on nilmanifolds. Under certain assump
 tions\, we show that a failure to have fast equidistribution on a nilmanif
 old is due to a failure on some factor nilmanifold. Combined with equidist
 ribution results on the torus\, this leads to an equidistribution statemen
 t on some nilmanifolds\, such as Heisenberg nilmanifolds.\nThis talk is ba
 sed on joint works with Weikun He and Elon Lindenstrauss.\n
LOCATION:https://researchseminars.org/talk/NEDNT/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Maxim Kirsebom (University of Hamburg)
DTSTART:20210315T161500Z
DTEND:20210315T173000Z
DTSTAMP:20260422T225825Z
UID:NEDNT/17
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NEDNT/17/">T
 owards an extreme value law for the deepest cusp excursions of the unipote
 nt flow</a>\nby Maxim Kirsebom (University of Hamburg) as part of New Engl
 and Dynamics and Number Theory Seminar\n\nLecture held in Online.\n\nAbstr
 act\nThe unipotent flow on the unit tangent bundle of the modular surface 
 is a classic example of a homogeneous flow when understood through the ide
 ntification with PSL_2(R)/PSL_2(Z). The ergodicity of the flow implies tha
 t almost every orbit is dense in the space and hence must eventually make 
 excursions deeper and deeper into the cusp. We are interested in understan
 ding the nature of these excursions. In the described setting\, and more g
 enerally\, Athreya and Margulis proved that the maximal excursions obey th
 e logarithm law almost surely\, meaning that their growth rate scales the 
 logarithm of the time. In this work we focus on a more precise description
  of this behaviour\, namely determining the probability that the deepest e
 xcursion fails to outperform the expected asymptotic behaviour by an addit
 ive 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 ge
 ometry of numbers. This is work in progress\, joint with Keivan Mallahi-Ka
 rai.\n
LOCATION:https://researchseminars.org/talk/NEDNT/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Peter Varju (University of Cambridge)
DTSTART:20210322T161500Z
DTEND:20210322T173000Z
DTSTAMP:20260422T225825Z
UID:NEDNT/18
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NEDNT/18/">O
 n the dimension of self-similar measures</a>\nby Peter Varju (University o
 f Cambridge) as part of New England Dynamics and Number Theory Seminar\n\n
 Lecture held in Online.\n\nAbstract\nLet $f_1$\,…\,$f_n$ be a collection
  of contracting similarities on $\\mathbb{R}$\, and let $p_1$\,…\,$p_n$ 
 be a probability vector. There is a unique probability measure mu on $\\ma
 thbb{R}$ 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 generate a fr
 ee semigroup (i.e. all compositions are distinct). Under this condition\, 
 the dimension of mu is conjectured to be the minimum of 1 and the ratio of
  the entropy of $p_1$\,…\,$p_n$ and the average logarithmic contraction 
 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 co
 ntraction factor. In the talk I will discuss recent progress by Ariel Rapa
 port and myself in the case $n=3$. In this case new difficulties arise as 
 was demonstrated by recent examples of Baker and Barany\, Kaenmaki of IFS
 ’s with arbitrarily weak separation properties.\n
LOCATION:https://researchseminars.org/talk/NEDNT/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tushar Das (University of Wisconsin - La Crosse)
DTSTART:20210419T161500Z
DTEND:20210419T173000Z
DTSTAMP:20260422T225825Z
UID:NEDNT/19
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NEDNT/19/">U
 sing templates to study problems in dynamics and number theory</a>\nby Tus
 har Das (University of Wisconsin - La Crosse) as part of New England Dynam
 ics and Number Theory Seminar\n\nLecture held in Online.\n\nAbstract\nTemp
 lates may be viewed as a combinatorial device that helps study\nasymptotic
  properties of lattice successive minima. This simple idea\,\nintroduced i
 n joint work with Lior Fishman\, David Simmons\, and Mariusz\nUrbanski\, p
 romises to be useful in several areas beyond our current\napplications. Th
 e latter lie at the fertile interface along Dani’s\ncorrespondence princ
 iple between Diophantine approximation and\nhomogeneous flows\, deepened b
 y Kleinbock & Margulis\; and Schmidt &\nSummerer’s parametric geometry o
 f numbers\, deepened by Roy. Templates\nare at the heart of our variationa
 l principle (arXiv:1901.06602)\,\nwhich provides a unified framework to co
 mpute the Hausdorff and\npacking dimensions of a variety of sets of dynami
 cal and\nnumber-theoretic interest. We will introduce and give some flavor
  for\nour project\, hint at a few new directions\, and hope to present sev
 eral\nopen problems of varying depth to reward participants of this\nwonde
 rful seminar!\n
LOCATION:https://researchseminars.org/talk/NEDNT/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Minju Lee (Yale University)
DTSTART:20210308T171500Z
DTEND:20210308T183000Z
DTSTAMP:20260422T225825Z
UID:NEDNT/20
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NEDNT/20/">O
 rbit closures of unipotent flows for hyperbolic manifolds with Fuchsian en
 ds</a>\nby Minju Lee (Yale University) as part of New England Dynamics and
  Number Theory Seminar\n\nLecture held in Online.\n\nAbstract\nThis is joi
 nt work with Hee Oh. We establish an analogue of Ratner’s orbit closure 
 theorem for any connected closed subgroup generated by unipotent elements 
 in $\\mathrm{SO}(d\,1)$ acting on the space $\\Gamma\\backslash\\mathrm{SO
 }(d\,1)$\, assuming that the associated hyperbolic manifold $M=\\Gamma\\ba
 ckslash\\mathbb{H}^d$ is a convex cocompact manifold with Fuchsian ends. F
 or $d = 3$\, 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 or
 bit closures of unipotent flows are relatively homogeneous. Our results im
 ply the following: for any $k\\geq 1$\,\n(1) the closure of any $k$-horosp
 here in $M$ is a properly immersed submanifold\;\n(2) the closure of any g
 eodesic $(k+1)$-plane in $M$ is a properly immersed submanifold\;\n(3) an 
 infinite sequence of maximal properly immersed geodesic $(k+1)$-planes int
 ersecting $\\mathrm{core} M$ becomes dense in $M$.\n
LOCATION:https://researchseminars.org/talk/NEDNT/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Han Yu (University of Cambridge)
DTSTART:20210412T161500Z
DTEND:20210412T173000Z
DTSTAMP:20260422T225825Z
UID:NEDNT/21
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NEDNT/21/">R
 ational numbers near self-similar sets</a>\nby Han Yu (University of Cambr
 idge) as part of New England Dynamics and Number Theory Seminar\n\nLecture
  held in Online.\n\nAbstract\nWe will discuss a problem on counting ration
 al numbers near\nself-similar sets. In particular\, we will show that the 
 set of rational\nnumbers is ‘reasonably well distributed’ around the m
 iddle $p$-th Cantor\nset when $p$ is a large integer. Our approach is via 
 Fourier analysis\nand we will also discuss some problems on Fourier transf
 orm of\nself-similar measures which are of independent interest. As a resu
 lt\, it\nis possible to show that $p=5$ satisfies the previous statement. 
 The\nmaterials come from various working-in-progress projects with D. Alle
 n\,\nS. Chow and P. Varju.\n
LOCATION:https://researchseminars.org/talk/NEDNT/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nicolas Chevallier (Université de Haute Alsace)
DTSTART:20210405T161500Z
DTEND:20210405T173000Z
DTSTAMP:20260422T225825Z
UID:NEDNT/22
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NEDNT/22/">M
 inimal vectors in $\\C^2$ and best constant for Dirichlet theorem over $\\
 C$</a>\nby Nicolas Chevallier (Université de Haute Alsace) as part of New
  England Dynamics and Number Theory Seminar\n\nLecture held in Online.\n\n
 Abstract\nWe study minimal vectors in lattices over Gaussian integers in $
 \\C^2$.We show that the index of the sub-lattice generated by two consecut
 ive minimal vectors in a lattice of $\\C^2$\, can be either $1$ or $2$.Nex
 t\, we describe the constraints on pairs of consecutive minimal vectors. T
 hese constraints  make it possible to find the best constant for Dirichlet
  theorem about approximations of complex numbers by quotient of Gaussian i
 ntegers.\n
LOCATION:https://researchseminars.org/talk/NEDNT/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Asaf Katz (University of Michigan)
DTSTART:20210426T161500Z
DTEND:20210426T173000Z
DTSTAMP:20260422T225825Z
UID:NEDNT/23
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NEDNT/23/">A
 n application of Margulis’ inequality to effective equidistribution</a>\
 nby Asaf Katz (University of Michigan) as part of New England Dynamics and
  Number Theory Seminar\n\nLecture held in Online.\n\nAbstract\nRatner’s 
 celebrated equidistribution theorem states that the trajectory of any poin
 t in a homogeneous space under a unipotent flow is getting equidistributed
  with respect to some algebraic measure. In the case where the action is h
 orospherical\, one can deduce an effective equidistribution result by mixi
 ng methods\, an idea that goes back to Margulis’ thesis. When the homoge
 neous space is non-compact\, one needs to impose further “diophantine co
 nditions” over the base point\, quantifying some recurrence rates\, in o
 rder to get a quantified equidistribution result. In the talk I will discu
 ss certain diophantine conditions\, and in particular I will show how a ne
 w Margulis’ type inequality for translates of horospherical orbits helps
  verify such conditions. This results in a quantified equidistribution res
 ult for a large class of points\, akin to the results of A. Strombreggson 
 dealing with the \\textrm{SL}_2 case. In particular we deduce a fully effe
 ctive quantitative equidistribution for horospherical trajectories of latt
 ices defined over number fields\, without pertaining to the strong subspac
 e theorem.\n
LOCATION:https://researchseminars.org/talk/NEDNT/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:No Talk
DTSTART:20210329T161500Z
DTEND:20210329T173000Z
DTSTAMP:20260422T225825Z
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://researchseminars.org/talk/NEDNT/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pratyush Sarkar (Yale University)
DTSTART:20210503T161500Z
DTEND:20210503T173000Z
DTSTAMP:20260422T225825Z
UID:NEDNT/25
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NEDNT/25/">G
 eneralization of Selberg’s 3⁄16 theorem for convex cocompact thin subg
 roups of SO(n\, 1)</a>\nby Pratyush Sarkar (Yale University) as part of Ne
 w England Dynamics and Number Theory Seminar\n\nLecture held in Online.\n\
 nAbstract\nSelberg’s 3/16 theorem for congruence covers of the modular s
 urface is a beautiful theorem which has a natural dynamical interpretation
  as uniform exponential mixing. Bourgain-Gamburd-Sarnak’s breakthrough w
 orks initiated many recent developments to generalize Selberg’s theorem 
 for infinite volume hyperbolic manifolds. One such result is by Oh-Winter 
 establishing uniform exponential mixing for convex cocompact hyperbolic su
 rfaces. These are not only interesting in and of itself but can also be us
 ed for a wide range of applications including uniform resonance free regio
 ns for the resolvent of the Laplacian\, affine sieve\, and prime geodesic 
 theorems. I will present a further generalization to higher dimensions and
  some of these immediate consequences.\n
LOCATION:https://researchseminars.org/talk/NEDNT/25/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Seungki Kim (University of Cincinnati)
DTSTART:20210510T161500Z
DTEND:20210510T173000Z
DTSTAMP:20260422T225825Z
UID:NEDNT/26
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NEDNT/26/">C
 ounting problems on a random lattice</a>\nby Seungki Kim (University of Ci
 ncinnati) as part of New England Dynamics and Number Theory Seminar\n\nLec
 ture held in Online.\n\nAbstract\nA random lattice is a random element of 
 SL(n\,Z) \\ SL(n\,R) equipped with the probability measure inherited from 
 the Haar measure of SL(n\,R). Analogous to the usual lattice point-countin
 g\, one tries to “count” — more precisely\, study the statistics 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 their app
 lications.\n
LOCATION:https://researchseminars.org/talk/NEDNT/26/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jayadev Athreya (University of Washington)
DTSTART:20210923T161500Z
DTEND:20210923T173000Z
DTSTAMP:20260422T225825Z
UID:NEDNT/28
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NEDNT/28/">G
 eometric Structures and Point Processes</a>\nby Jayadev Athreya (Universit
 y of Washington) as part of New England Dynamics and Number Theory Seminar
 \n\nLecture held in Online.\n\nAbstract\nIn this talk\, we will prove the 
 convergence part of Khitchine’s theorem on non-degenerate manifolds. Thi
 s confirms a conjecture of Kleinbock and Margulis in 1998. Our approach us
 es geometric and dynamical ideas together with a new technique of `major a
 nd minor arcs’. In particular\, we establish sharp upper bounds for 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://researchseminars.org/talk/NEDNT/28/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sebastian Hurtado (University of Chicago)
DTSTART:20210930T161500Z
DTEND:20210930T173000Z
DTSTAMP:20260422T225825Z
UID:NEDNT/29
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NEDNT/29/">H
 eight Gap\, an Arithmetic Margulis Lemma and Almost Laws</a>\nby Sebastian
  Hurtado (University of Chicago) as part of New England Dynamics and Numbe
 r 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 solvable
  group has a positive lower bound in its arithmetic height (we will explai
 n this notion)\, this is a non-abelian version of Lehmer’s problem. We a
 lso show that in arithmetic locally symmetric spaces\, short geodesics ten
 d to be far from each other if the degree of the trace field is large. Thi
 s lemma allows us to prove new results about growth of cohomology of seque
 nces of locally symmetric spaces and to give a proof of a conjecture of Ge
 lander. These results are works in progress with Joe Chen and Homin Lee\, 
 and with Mikolaj Fraczyk and Jean Raimbault.\n
LOCATION:https://researchseminars.org/talk/NEDNT/29/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dubi Kelmer (Boston College)
DTSTART:20211021T161500Z
DTEND:20211021T173000Z
DTSTAMP:20260422T225825Z
UID:NEDNT/30
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NEDNT/30/">T
 he light cone Siegel transform\, its moment formulas\, and their applicati
 ons</a>\nby Dubi Kelmer (Boston College) as part of New England Dynamics a
 nd Number Theory Seminar\n\nLecture held in Online.\n\nAbstract\nIn this t
 alk I will describe an analogue of the Siegel transform where the role of 
 Euclidean space is replaced by a light cone corresponding to an indefinite
  quadratic form.In this case one can use results on the spectral theory of
  incomplete Eisenstein series to establish moment formulas analogous to th
 e classical formulas of Siegel\, Rogers\, and Schmidt.I will then describe
  several applications of these formulas to counting lattice points on the 
 light cone\, as well as for the distribution of rational points on the sph
 ere.   All new results are based on joint work with Shucheng Yu.\n
LOCATION:https://researchseminars.org/talk/NEDNT/30/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lei Yang (Sichuan University)
DTSTART:20211007T161500Z
DTEND:20211007T173000Z
DTSTAMP:20260422T225825Z
UID:NEDNT/31
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NEDNT/31/">K
 hintchine’s theorem on manifolds</a>\nby Lei Yang (Sichuan University) a
 s part of New England Dynamics and Number Theory Seminar\n\nLecture held i
 n Online.\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/NEDNT/31/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pengyu Yang (ETH)
DTSTART:20211014T161500Z
DTEND:20211014T173000Z
DTSTAMP:20260422T225825Z
UID:NEDNT/32
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NEDNT/32/">E
 quidistribution of degenerate curves and Dirichlet improvability</a>\nby P
 engyu 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 s
 tudy the translates of a line segment under a diagonal flow. Sharp conditi
 ons for non-divergence and equidistribution will be given. As an applicati
 on\, we will show that Lebesgue-almost every point on a planar line is Dir
 ichlet non-improvable if and only if the line is irrational. This is joint
  work with Kleinbock\, de Saxcé and Shah. Generalizations to higher dimen
 sions will also be discussed (work in progress with Shah).\n
LOCATION:https://researchseminars.org/talk/NEDNT/32/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Demi Allen (University of Warwick)
DTSTART:20211028T161500Z
DTEND:20211028T173000Z
DTSTAMP:20260422T225825Z
UID:NEDNT/33
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NEDNT/33/">A
 n inhomogeneous Khintchine-Groshev Theorem without monotonicity</a>\nby De
 mi Allen (University of Warwick) as part of New England Dynamics and Numbe
 r Theory Seminar\n\nLecture held in Online.\n\nAbstract\nThe classical (in
 homogeneous) Khintchine-Groshev Theorem tells us that for a monotonic appr
 oximating function $\\psi: \\mathbb{N} \\to [0\,\\infty)$ the Lebesgue mea
 sure of the set of (inhomogeneously) $\\psi$-well-approximable points in $
 \\mathbb{R}^{nm}$ is zero or full depending on\, respectively\, the conver
 gence 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 $\\p
 si$ can be removed whenever $nm>1$ and cannot be removed when $nm=1$. In t
 his talk I will discuss recent work with Felipe A. Ramírez (Wesleyan\, US
 ) in which we show that the inhomogeneous Khintchine-Groshev Theorem is tr
 ue without the monotonicity assumption on $\\psi$ whenever $nm>2$. This re
 sult brings the inhomogeneous theory almost in line with the completed hom
 ogeneous theory. I will survey previous results towards removing monotonic
 ity from the homogeneous and inhomogeneous Khintchine-Groshev Theorem befo
 re discussing the main ideas behind the proof our recent result.\n
LOCATION:https://researchseminars.org/talk/NEDNT/33/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexander Gorodnik (University of Zurich)
DTSTART:20211104T161500Z
DTEND:20211104T173000Z
DTSTAMP:20260422T225825Z
UID:NEDNT/34
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NEDNT/34/">Q
 uantitative equidistribution and Randomness</a>\nby Alexander Gorodnik (Un
 iversity of Zurich) as part of New England Dynamics and Number Theory Semi
 nar\n\nLecture held in Online.\n\nAbstract\nWe discuss some results on qua
 ntitative equidistribution on homogeneous spaces and related problems abou
 t behaviour of arithmetic counting functions. This is a joint work with Bj
 örklund and Fregoli.\n
LOCATION:https://researchseminars.org/talk/NEDNT/34/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Chris Lutsko (Rutgers University)
DTSTART:20211111T171500Z
DTEND:20211111T183000Z
DTSTAMP:20260422T225825Z
UID:NEDNT/35
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NEDNT/35/">P
 air correlation of monomial sequences modulo 1</a>\nby Chris Lutsko (Rutge
 rs University) as part of New England Dynamics and Number Theory Seminar\n
 \nLecture held in Online.\n\nAbstract\nFix $\\alpha\, \\theta > 0$\, and c
 onsider the sequence $(\\alpha n^\\theta \\mod 1)_{n>0}$. Since the semina
 l work of Rudnick-Sarnak (1998)\, and due to the Berry-Tabor conjecture in
  quantum chaos\, the fine-scale properties of these dilated mononomial seq
 uences have been intensively studied. In this talk\, I will briefly survey
  what is known about these sequences and present a recent result (joint wi
 th Sourmelidis and Technau) showing that for $\\theta \\le 1/3$\, and $\\a
 lpha > 0$\, the pair correlation function is Poissonian. While the techniq
 ues 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://researchseminars.org/talk/NEDNT/35/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ilya Khayutin (Northwestern University)
DTSTART:20211202T171500Z
DTEND:20211202T183000Z
DTSTAMP:20260422T225825Z
UID:NEDNT/36
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NEDNT/36/">T
 wo-step equidistribution for bi-quadratic torus packets</a>\nby Ilya Khayu
 tin (Northwestern University) as part of New England Dynamics and Number T
 heory Seminar\n\nLecture held in Online.\n\nAbstract\nA major challenge to
  the asymptotic analysis of a sequence of probability measures on a homoge
 neous space\, invariant under diagonalizable groups\, is the possibility o
 f accumulation on intermediate homogeneous subspaces. In this aspect highe
 r rank homogeneous flows cannot be expected to share the rigidity properti
 es of unipotent ones. In particular\, the linearization technique fails fo
 r diagonalizable flows. \n\nIn a joint work in progress with A. Wieser we 
 show how in favorable situations one can actually use the existence of int
 ermediate homogeneous spaces in our benefit. We show that periodic measure
 s on some packets of periodic torus orbits on PGL4(Z)\\PGL4(R) converge in
  the limit to a measure with a non-trivial Haar component. The proof goes 
 by establishing high entropy for the limit measure. The method utilizes th
 e intermediate homogeneous space to split the analysis into two more tract
 able steps.\n
LOCATION:https://researchseminars.org/talk/NEDNT/36/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Michael Bersudsky (Technion)
DTSTART:20211209T171500Z
DTEND:20211209T183000Z
DTSTAMP:20260422T225825Z
UID:NEDNT/37
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NEDNT/37/">O
 n the image in the torus of sparse points on expanding analytic curves</a>
 \nby Michael Bersudsky (Technion) as part of New England Dynamics and Numb
 er Theory Seminar\n\nLecture held in Online.\n\nAbstract\nIt is known that
  the projection to the 2-torus of the normalised parameter measure on a ci
 rcle of radius $R$ in the plane becomes uniformly distributed as $R$ grows
  to infinity. I will discuss the following natural discrete analogue for t
 his problem. Starting from an angle and a sequence of radii {$R_n$} which 
 diverges to infinity\, I will consider the projection to the 2-torus of th
 e n’th roots of unity rotated by this angle and dilated by a factor 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 dilated c
 ircle.I will discuss 3 types of results:\n\nValidity of equidistribution f
 or all angles when the sparsity is polynomial.\nFailure of equidistributio
 n for some super polynomial dilations.\nEquidistribution for almost all an
 gles for arbitrary dilations.\nI will discuss the above type of results in
  greater generality and I will try to explain how the theory of o-minimal 
 structures is related to the proof.\n
LOCATION:https://researchseminars.org/talk/NEDNT/37/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Akshat Das (University of Houston)
DTSTART:20220203T171500Z
DTEND:20220203T183000Z
DTSTAMP:20260422T225825Z
UID:NEDNT/38
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NEDNT/38/">A
 n adelic version of the three gap theorem</a>\nby Akshat Das (University o
 f Houston) as part of New England Dynamics and Number Theory Seminar\n\nLe
 cture held in Online.\n\nAbstract\nIn order to understand problems in dyna
 mics which are sensitive to arithmetic properties of return times to regio
 ns\, it is desirable to generalize classical results about rotations on th
 e circle to the setting of rotations on adelic tori. One such result is th
 e classical three gap theorem\, which is also referred to as the three dis
 tance theorem and as the Steinhaus problem. It states that\, for any 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 ha
 ving one of at most three distinct lengths. Since the 1950s\, when this th
 eorem was first proved independently by multiple authors\, it has been rep
 roved 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 talk\, we 
 use an adaptation of this approach to the adeles to prove a natural genera
 lization of the classical three gap theorem for rotations on adelic tori. 
 This is joint work with Alan Haynes.\n
LOCATION:https://researchseminars.org/talk/NEDNT/38/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jiyoung Han (TIFR)
DTSTART:20220210T171500Z
DTEND:20220210T183000Z
DTSTAMP:20260422T225825Z
UID:NEDNT/39
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NEDNT/39/">T
 he asymptotic distribution of the joint values of the integral lattice poi
 nts for a system of a quadratic form and a linear form</a>\nby Jiyoung Han
  (TIFR) as part of New England Dynamics and Number Theory Seminar\n\nLectu
 re held in Online.\n\nAbstract\nLet Q be a quadratic form and let L be a l
 inear form on the n-dimensional real vector space. We are interested in th
 e 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 the numbe
 r of integral vectors in the ball of radius T whose joint values are conta
 ined 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. This cond
 ition is introduced by Gorodnik in 2004.\nFor this\, we need to classify a
 ll intermediate subgroups between the special orthogonal group preserving 
 Q and L and the special linear group. Among them\, only two closed subgrou
 ps are of our concern. We will introduce Siegel integral formulas and equi
 distribution theorems for each subgroup\, and show how to reach our main t
 heorem. This is joint work with Seonhee Lim and Keivan Mallahi-Karai.\n
LOCATION:https://researchseminars.org/talk/NEDNT/39/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Julien Trevisan (Institut de Mathématiques de Jussieu)
DTSTART:20220217T171500Z
DTEND:20220217T183000Z
DTSTAMP:20260422T225825Z
UID:NEDNT/40
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NEDNT/40/">L
 imit laws in the lattice counting problem. The case of ellipses.</a>\nby J
 ulien Trevisan (Institut de Mathématiques de Jussieu) as part of New Engl
 and Dynamics and Number Theory Seminar\n\nLecture held in Online.\n\nAbstr
 act\nLet E be an ellipse centered around 0. We are interested in the asymp
 totic distribution\nof the error of the number of unimodular lattice point
 s that fall into tE when the lattice is random\nand when t goes to infinit
 y.\nBuilding on previous works by Bleher and by Fayad and Dolgopyat\, we s
 how that the error term\, when normalized by the square root of t\, conver
 ges in distribution towards an explicit distribution.\nFor this\, we 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 Si
 egel transform behaves in distribution as\, what we call\, a modified Sieg
 el transform with random weights. Such objects often appear in average cou
 nting problems.\nFinally\, we show that this last quantity converges almos
 t surely\, and we study the existence of the moments of its law.\nThis wor
 k was supervised by Bassam Fayad.\n
LOCATION:https://researchseminars.org/talk/NEDNT/40/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Irving Calderón (Université Paris-Saclay)
DTSTART:20220303T171500Z
DTEND:20220303T183000Z
DTSTAMP:20260422T225825Z
UID:NEDNT/41
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NEDNT/41/">S
 -adic quadratic forms and Homogeneous Dynamics</a>\nby Irving Calderón (U
 niversité Paris-Saclay) as part of New England Dynamics and Number Theory
  Seminar\n\nLecture held in Online.\n\nAbstract\nWe present two new quanti
 tative 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 of decid
 ing if any given integral quadratic forms $Q_1$ and $Q_2$ are $Z_S$-equiva
 lent. 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 clo
 sed orbits in X{d\,S}. As an application we obtain\, for any S-integral or
 thogonal group\, polynomial bounds on the S-norms of the elements of a fin
 ite 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://researchseminars.org/talk/NEDNT/41/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nattalie Tamam (University of Michigan)
DTSTART:20220310T171500Z
DTEND:20220310T183000Z
DTSTAMP:20260422T225825Z
UID:NEDNT/42
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NEDNT/42/">C
 lassification of divergence of trajectories</a>\nby Nattalie Tamam (Univer
 sity of Michigan) as part of New England Dynamics and Number Theory Semina
 r\n\nLecture held in Online.\n\nAbstract\nAs shown by Dani\, diophantine a
 pproximations are in direct correspondence to the behavior of orbits in ce
 rtain homogeneous spaces. We will discuss the interpretation of the diverg
 ent trajectories and the obvious ones\, the ones diverging due to a purely
  algebraic reason. As conjectured by Barak Weiss\, there is a complete cla
 ssification of divergent trajectories when considering the action of subgr
 oups of the diagonal group. We will discuss the last part of this conjectu
 re\, showing that for a ‘large enough’ such subgroup\, every divergent
  trajectory diverges obviously. This is a joint work with Omri Solan.\n
LOCATION:https://researchseminars.org/talk/NEDNT/42/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nate Hughes (University of Exeter)
DTSTART:20220317T161500Z
DTEND:20220317T173000Z
DTSTAMP:20260422T225825Z
UID:NEDNT/43
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NEDNT/43/">E
 ffective Counting and Spiralling of Lattice Approximates</a>\nby Nate Hugh
 es (University of Exeter) as part of New England Dynamics and Number Theor
 y Seminar\n\nLecture held in Online.\n\nAbstract\nWe will prove an effecti
 ve version of Dirichlet’s approximation theorem\, giving the error betwe
 en the number of rational approximations to a real vector with denominator
  less than some real number T and the asymptotic growth of this count. Add
 itional results for linear forms can be obtained\, as well as results meas
 uring the direction of these approximates\, known as ‘spiralling of latt
 ice approximates’. These results are obtained by reformulating the numbe
 r-theoretic problem to the context of homogeneous spaces of unimodular lat
 tices. The advantage of this reformulation is that we have more tools to d
 eal with the problem\, such as Siegel’s mean value theorem and Rogers’
  higher moment formula. The proof involves using the ergodic properties of
  diagonal flows on this homogeneous space to calculate the number of latti
 ce approximates\, bounding the second moment of the count\, then applying 
 an effective ergodic theorem due to Gaposhkin. Particular attention is pai
 d to the case of primitive lattices in two-dimensions\, where Rogers’ th
 eorem 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://researchseminars.org/talk/NEDNT/43/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Simon Machado (the University of Cambridge)
DTSTART:20220324T161500Z
DTEND:20220324T173000Z
DTSTAMP:20260422T225825Z
UID:NEDNT/44
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NEDNT/44/">S
 uperrigidity and arithmeticity for some aperiodic subsets in higher-rank s
 imple Lie groups</a>\nby Simon Machado (the University of Cambridge) as pa
 rt of New England Dynamics and Number Theory Seminar\n\nLecture held in On
 line.\n\nAbstract\nMeyer sets are fascinating objects: they are aperiodic 
 subsets of Euclidean spaces that nonetheless exhibit long-range aperiodic 
 order. Sets of vertices of the Penrose tiling (P3) and Pisot-Vijarayaghava
 n numbers of a real number field are some of the most well-known examples.
  In his pioneering work\, Meyer provided a powerful and elegant characteri
 sation of Meyer sets. Years later\, Lagarias proved a similar characterisa
 tion starting from what seemed to be considerably weaker assumptions.\nA f
 ascinating question asks whether Meyer’s and Lagarias’ results may be 
 extended to more general ambient groups. In fact\, a first result in that 
 direction was already obtained in Meyer’s work: he proved a sum-product 
 phenomenon which\, implicitly\, boiled down to a classification of Meyer s
 ets in the group of affine transformations of the line.\nI will talk about
  a generalisation of both Meyer’s and Lagarias’ theorems to discrete s
 ubsets of higher-rank simple Lie groups. I will explain how this result ca
 n be seen as a generalisation of Margulis’ arithmeticity theorem and how
  it can be deduced from Zimmer’s cocycle superrigidity. We will see that
 \, surprisingly\, Pisot-Vijarayaghavan numbers appear naturally in this co
 ntext too.\n
LOCATION:https://researchseminars.org/talk/NEDNT/44/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Johannes Schleischitz (Middle East Technical University)
DTSTART:20220331T161500Z
DTEND:20220331T173000Z
DTSTAMP:20260422T225825Z
UID:NEDNT/45
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NEDNT/45/">E
 xact uniform approximation and Dirichlet spectrum</a>\nby Johannes Schleis
 chitz (Middle East Technical University) as part of New England Dynamics a
 nd Number Theory Seminar\n\nLecture held in Online.\n\nAbstract\nWe consid
 er the Dirichlet spectrum\, with respect to maximum norm and simultaneous 
 approximation. It is basically the analogue of the famous (multi-dimension
 al) Lagrange spectrum with respect to uniform approximation. By Dirichlet
 ’s Theorem it is contained in [0\,1]. The central new result is that it 
 equals the entire interval [0\,1] when the number of variables is two or m
 ore. We thereby get a new\, constructive proof of a recent result by Beres
 nevich\, Guan\, Marnat\, Ramirez and Velani that there are Dirichlet impro
 vable vectors that are neither bad nor singular\, in any dimension. We pro
 vide several generalizations\, including metrical claims.\n
LOCATION:https://researchseminars.org/talk/NEDNT/45/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Emilio Corso (ETH)
DTSTART:20220407T161500Z
DTEND:20220407T173000Z
DTSTAMP:20260422T225825Z
UID:NEDNT/46
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NEDNT/46/">A
 symptotics of the equidistribution rate of expanding circles on compact hy
 perbolic quotients and applications</a>\nby Emilio Corso (ETH) as part of 
 New England Dynamics and Number Theory Seminar\n\nLecture held in Online.\
 n\nAbstract\nEquidistribution properties of translates of orbits for subgr
 oup actions on homogeneous spaces are intimately linked to the mixing feat
 ures of the global action of the ambient group. The connection appears alr
 eady in Margulis’ thesis (1969)\, displaying its full potential in the w
 ork of Eskin and McMullen during the nineties. On a quantitative level\, t
 he philosophy underpinning this linkage allows to transfer mixing rates to
  effective estimates for the rate of equidistribution\, albeit at the cost
  of a sizeable loss in the exponent. In joint work with Ravotti\, we inste
 ad resort to a spectral method\, pioneered by Ratner in her study of quant
 itative mixing of geodesic and horocycle flows\, in order to obtain the pr
 ecise asymptotic behaviour of averages of regular observables along expand
 ing circles on compact hyperbolic surfaces. The primary goal of the talk i
 s to outline the salient traits of this method\, illustrating how it leads
  to the relevant asymptotic expansion. In addition\, we shall also present
  applications of the main result to distributional limit theorems and to q
 uantitative error estimates on the corresponding hyperbolic lattice point 
 counting problem\, the latter having been examined\, to date\, only throug
 h number-theoretical methods in works of Selberg\, Lax-Phillips and Philli
 ps-Rudnick.\n
LOCATION:https://researchseminars.org/talk/NEDNT/46/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mikolaj Fraczyk (University of Chicago)
DTSTART:20220414T161500Z
DTEND:20220414T173000Z
DTSTAMP:20260422T225825Z
UID:NEDNT/47
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NEDNT/47/">T
 hin part of the arithmetic orbifolds</a>\nby Mikolaj Fraczyk (University o
 f Chicago) as part of New England Dynamics and Number Theory Seminar\n\nLe
 cture held in Online.\n\nAbstract\nLet X be a symmetric space. The collar 
 lemma\, also known as the Margulis lemma\, says that there exists an epsil
 on=epsilon(X)\, such that the epsilon-thin part of a locally symmetric spa
 ce X/\\Gamma looks locally like a quotient by a virtually unipotent subgro
 up. 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 filed gene
 rated 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 t
 hat an arithmetic locally symmetric manifold M is homotopy equivalent to a
  simplicial complex of size bounded linearly in the volume of M and degree
 s of all vertices bounded uniformly in terms of X. Based on a joint work w
 ith Sebastian Hurtado and Jean Raimbault.\n
LOCATION:https://researchseminars.org/talk/NEDNT/47/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ian Hoover (Boston College)
DTSTART:20220428T161500Z
DTEND:20220428T173000Z
DTSTAMP:20260422T225825Z
UID:NEDNT/48
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NEDNT/48/">E
 ffective Equidistribution on Hilbert Modular Surfaces</a>\nby Ian Hoover (
 Boston College) as part of New England Dynamics and Number Theory Seminar\
 n\nLecture held in Online.\n\nAbstract\nWhile ineffective equidistribution
  has been understood much more generally\, effective results for non-compa
 ct orbits have been more scarce. I will give effective (polynomial) error 
 rates for the translates of diagonal orbits on Hilbert modular surfaces. T
 his work follows as a higher dimensional extension of the work of Kelmer a
 nd Kontorovich.\n
LOCATION:https://researchseminars.org/talk/NEDNT/48/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jiajie Zheng (Brandeis University)
DTSTART:20220505T161500Z
DTEND:20220505T173000Z
DTSTAMP:20260422T225825Z
UID:NEDNT/49
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NEDNT/49/">D
 ynamical Borel–Cantelli Lemma for Lipschitz Twists</a>\nby Jiajie Zheng 
 (Brandeis University) as part of New England Dynamics and Number Theory Se
 minar\n\nLecture held in Online.\n\nAbstract\nIn the study of some dynamic
 al systems\, the limit superior of a sequence of measurable sets is often 
 of interest. The shrinking targets and recurrence are two of the most comm
 only studied problems that concern limit superior sets. However\, the zero
 -one laws for the shrinking targets and recurrence are usually treated sep
 arately and proved differently. In this talk\, we construct a generalized 
 definition that can specialize into the shrinking targets and recurrence a
 nd our approach gives a unified proof to the zero-one laws for the two pro
 blems.\n
LOCATION:https://researchseminars.org/talk/NEDNT/49/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Simon Baker (University of Birmingham)
DTSTART:20220922T161500Z
DTEND:20220922T173000Z
DTSTAMP:20260422T225825Z
UID:NEDNT/50
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NEDNT/50/">O
 verlapping iterated function systems from the perspective of Metric Number
  Theory</a>\nby Simon Baker (University of Birmingham) as part of New Engl
 and Dynamics and Number Theory Seminar\n\nLecture held in Online.\n\nAbstr
 act\nKhintchine’s theorem is a classical result from metric number theor
 y which relates the Lebesgue measure of certain limsup sets with the diver
 gence of naturally occurring volume sums. Importantly this result provides
  a quantitative description of how the rationals are distributed within th
 e reals. In this talk I will discuss some recent work where I prove that a
  similar Khintchine like phenomenon occurs typically within many families 
 of overlapping iterated function systems. Families of iterated function sy
 stems these results apply to include those arising from Bernoulli convolut
 ions\, the 0\,1\,3 problem\, and affine contractions with varying translat
 ion parameters. \nTime permitting I also will discuss a particular family 
 of iterated function systems for which we can be more precise. Our analysi
 s of this family shows that by studying the metric properties of limsup se
 ts\, we can distinguish between the overlapping behaviour of iterated func
 tion systems in a way that is not available to us by simply studying prope
 rties of self-similar measures.\n
LOCATION:https://researchseminars.org/talk/NEDNT/50/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Juno Seong (UC San Diego)
DTSTART:20221006T161500Z
DTEND:20221006T173000Z
DTSTAMP:20260422T225825Z
UID:NEDNT/51
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NEDNT/51/">A
 n avoidance principle and Margulis functions for expanding translates of u
 nipotent orbits</a>\nby Juno Seong (UC San Diego) as part of New England D
 ynamics and Number Theory Seminar\n\nLecture held in Online.\n\nAbstract\n
 Avoidance principles — quantifying how much time trajectories avoid cert
 ain subsets of the ambient space — have been fruitful in the study of dy
 namical systems. We prove an avoidance principle for expanding translates 
 of unipotent orbits for some semisimple homogeneous spaces. In addition\, 
 we prove a quantitative isolation result of closed orbits and give an uppe
 r 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. This is jo
 int work with Anthony Sanchez.\n
LOCATION:https://researchseminars.org/talk/NEDNT/51/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Chris Lutsko (Rutgers University)
DTSTART:20221013T161500Z
DTEND:20221013T173000Z
DTSTAMP:20260422T225825Z
UID:NEDNT/52
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NEDNT/52/">A
  Spectral Approach to Counting and Equidistribution</a>\nby Chris Lutsko (
 Rutgers University) as part of New England Dynamics and Number Theory Semi
 nar\n\nLecture held in Online.\n\nAbstract\nSince the early 20th century\,
  spectral methods have been used to obtain effective counting theorems for
  various objects of interest in number theory\, geometry and group theory.
  In this talk I’ll start by introducing two classical problems: the Gaus
 s circle problem\, and the Apollonian counting problem. By surveying resul
 ts on these problems (and some generalizations)\, I’ll demonstrate how t
 o use spectral methods to obtain effective asymptotics for some very class
 ical problems. Then I will try and explain how to generalize this method t
 o apply to certain horospherical equidistribution theorems.\n
LOCATION:https://researchseminars.org/talk/NEDNT/52/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lam Pham (Brandeis University)
DTSTART:20221020T161500Z
DTEND:20221020T173000Z
DTSTAMP:20260422T225825Z
UID:NEDNT/53
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NEDNT/53/">S
 hort closed geodesics in higher rank arithmetic locally symmetric spaces</
 a>\nby Lam Pham (Brandeis University) as part of New England Dynamics and 
 Number Theory Seminar\n\nLecture held in Online.\n\nAbstract\nA well-known
  conjecture of Margulis predicts that there is a uniform lower bound on th
 e systole of any irreducible arithmetic locally symmetric space. Recently\
 , in joint work with Mikolaj Fraczyk\, we show that for simple Lie groups 
 of higher rank\, this conjecture is equivalent to a well-known conjecture 
 in number theory: that Salem numbers are uniformly bounded away from 1. I 
 will discuss our proof and some tools used\, and some additional results w
 hich hold unconditionally and highlight the structure of the bottom of the
  length spectrum.\n
LOCATION:https://researchseminars.org/talk/NEDNT/53/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Shreyasi Datta (University of Michigan)
DTSTART:20221103T161500Z
DTEND:20221103T173000Z
DTSTAMP:20260422T225825Z
UID:NEDNT/54
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NEDNT/54/">p
 -Adic Diophantine approximation with respect to fractal measures</a>\nby S
 hreyasi Datta (University of Michigan) as part of New England Dynamics and
  Number Theory Seminar\n\nLecture held in Online.\n\nAbstract\nI will give
  an introduction to Diophantine approximation problems starting with the f
 amous Sprindzuk Conjecture (which is now a theorem by Kleinbock and Margul
 is\, who solved this using homogeneous dynamics).\nNext\, I will talk abou
 t p-adic Diophantine approximation and how it is different than the real c
 ase. In a very recent work with Anish Ghosh and Victor Beresnevich we solv
 ed a conjecture of Kleinbock and Tomanov\, which shows pushforward of a fr
 actal measure by ‘nice’ functions exhibits ‘nice’ Diophantine prop
 erties. In particular\, we prove p-adic analogue of a result by Kleinbock\
 , Lindenstrauss and Weiss on friendly measures. I will talk about how lack
  of the mean value theorem makes life difficult in the p-adic fields. (No 
 prior knowledge on this subject will be assumed!)\n
LOCATION:https://researchseminars.org/talk/NEDNT/54/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nikolay Moshchevitin (Lomonosov Moscow State University)
DTSTART:20221110T171500Z
DTEND:20221110T183000Z
DTSTAMP:20260422T225825Z
UID:NEDNT/55
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NEDNT/55/">O
 n inhomogeneous Diophantine approximation</a>\nby Nikolay Moshchevitin (Lo
 monosov Moscow State University) as part of New England Dynamics and Numbe
 r Theory Seminar\n\nLecture held in Online.\n\nAbstract\nWe will discuss s
 ome classical and modern results related to systems of inhomogeneous linea
 r forms. We  will begin with Kronecker approximation theorem and famous re
 sults by Khintchine and continue with rather modern problems\, in particul
 ar related to weighted setting and coprime approximation.\n
LOCATION:https://researchseminars.org/talk/NEDNT/55/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nicolas de Saxce (Université Paris-Nord)
DTSTART:20221117T171500Z
DTEND:20221117T183000Z
DTSTAMP:20260422T225825Z
UID:NEDNT/56
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NEDNT/56/">R
 ational approximations to linear subspaces</a>\nby Nicolas de Saxce (Unive
 rsité Paris-Nord) as part of New England Dynamics and Number Theory Semin
 ar\n\nLecture held in Online.\n\nAbstract\nUsing diagonal orbits on the sp
 ace of lattices\, we revisit some old questions of Schmidt concerning diop
 hantine approximation on Grassmann varieties\, and in particular\, we prov
 e a version of Dirichlet’s principle in that setting.\n
LOCATION:https://researchseminars.org/talk/NEDNT/56/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tariq Osman (Brandeis University)
DTSTART:20221201T171500Z
DTEND:20221201T183000Z
DTSTAMP:20260422T225825Z
UID:NEDNT/57
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NEDNT/57/">T
 ail Asymptotics for Generalised Theta Sums with Rational Parameters</a>\nb
 y Tariq Osman (Brandeis University) as part of New England Dynamics and Nu
 mber Theory Seminar\n\nLecture held in Online.\n\nAbstract\nWe define gene
 ralised theta sums as exponential sums of the form S^f_N(x\; \\alpha\, \\b
 eta) := \\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 nu
 mbers\, and x is chosen randomly from the unit interval\, we may use homog
 eneous dynamics to show that N^{-1/2} S^f_N$ possesses a limiting distribu
 tion as N goes to infinity\, provided f is sufficiently regular. In joint 
 work with F. Cellarosi\, we prove that for specific rational pairs (\\alph
 a\, \\beta) this limiting distribution is compactly supported and that all
  other rational pairs lead to a limiting distribution with heavy tails. Th
 is complements the existing work of F. Cellarosi and J. Marklof where at l
 east one of \\alpha or \\beta is irrational.\n
LOCATION:https://researchseminars.org/talk/NEDNT/57/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sam Chow (University of Warwick)
DTSTART:20221208T171500Z
DTEND:20221208T183000Z
DTSTAMP:20260422T225825Z
UID:NEDNT/58
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NEDNT/58/">C
 ounting rationals and diophantine approximation on fractals</a>\nby Sam Ch
 ow (University of Warwick) as part of New England Dynamics and Number Theo
 ry Seminar\n\nLecture held in Online.\n\nAbstract\nWe count rationals in m
 issing-digit sets\, with applications to diophantine approximation. In the
  process\, we develop the theory of Fourier \\ell^1 dimension\, including 
 the computational aspect.\n
LOCATION:https://researchseminars.org/talk/NEDNT/58/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Omri Solan (Hebrew University of Jerusalem)
DTSTART:20230921T161500Z
DTEND:20230921T173000Z
DTSTAMP:20260422T225825Z
UID:NEDNT/59
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NEDNT/59/">B
 irkhoff generic points on curves</a>\nby Omri Solan (Hebrew University of 
 Jerusalem) as part of New England Dynamics and Number Theory Seminar\n\nLe
 cture held in Online.\n\nAbstract\nLet $a_t$ be a diagonal flow on the spa
 ce X of unimodular lattices in R^n. A point x in X is called Birkhoff gene
 ric if a_t.x equidistributes in X as t\\to \\infty. By Birkhoff ergodic th
 eorem\, 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 measure singu
 lar to Lebesgue. \nIn a joint work with Andreas Wieser\, we discuss the ca
 se of a generic point x in an analytic curve in X\, and show that under ce
 rtain conditions\, it must be Birkhoff generic. This Birkhoff genericity r
 esult has various applications in Diophantine approximation. In this talk 
 we will relate Birkhoff genericity to approximations of real numbers by al
 gebraic numbers of degree at most n.\n
LOCATION:https://researchseminars.org/talk/NEDNT/59/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Zach Selk (Queen’s University)
DTSTART:20230928T161500Z
DTEND:20230928T173000Z
DTSTAMP:20260422T225825Z
UID:NEDNT/60
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NEDNT/60/">S
 tochastic Calculus for the Theta Process</a>\nby Zach Selk (Queen’s Univ
 ersity) as part of New England Dynamics and Number Theory Seminar\n\nLectu
 re held in Online.\n\nAbstract\nThe Theta process\, $X(t)$\, is a complex 
 valued stochastic process of number theoretical origin arising as a scalin
 g 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 $(\\alpha\,\\beta)\\in \\mat
 hbb R^2 \\setminus \\mathbb Q^2$ and $x\\in \\mathbb R$ is chosen at rando
 m according to any law absolutely continuous with respect to Lebesgue meas
 ure. The Theta process can be explicitly represented as $X(t)=\\sqrt{t} \\
 Theta(\\Gamma g \\Phi^{2 \\log t})$ where $\\Theta$ is an automorphic func
 tion defined on Lie group $G$\, invariant under left multiplication under 
 lattice $\\Gamma$. Additionally\, $g\\in \\Gamma \\setminus G$ is chosen H
 aar uniformly at random and $\\Phi$ is the geodesic flow on $\\Gamma \\set
 minus G$. The Theta process shares several similar properties with the Bro
 wnian motion. In particular\, both lack differentiability and have the sam
 e $p$ variation and H\\”older properties.\nSimilarly to Brownian motion\
 , standard calculus and even Young/Riemann-Stieltjes calculus techniques d
 o not work. However\, Brownian motion is what is known as a martingale all
 owing for a classical theory of It\\^o calculus which makes use of cancell
 ations “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\, absolutely cont
 inuous changes in measure and much more. \nUnfortunately\, we show that th
 e Theta process $X$ is not a (semi)martingale\, therefore It\\^o technique
 s don’t work. However\, a new theory introduced in 1998 by Terry Lyons c
 alled rough paths theory handles processes with the same analytic regulari
 ty as $X$. The key idea in rough paths theory is that constructing stochas
 tic calculus for a signal can be reduced to constructing the “iterated i
 ntegrals” of the signal. In this talk\, we will show the construction of
  the iterated integrals – the “rough path” – above the process $X$
 . Joint with Francesco Cellarosi.\n
LOCATION:https://researchseminars.org/talk/NEDNT/60/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yuval Yifrach (Technion)
DTSTART:20231005T161500Z
DTEND:20231005T173000Z
DTSTAMP:20260422T225825Z
UID:NEDNT/61
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NEDNT/61/">A
  variation on the p-adic Littlewood Conjecture</a>\nby Yuval Yifrach (Tech
 nion) as part of New England Dynamics and Number Theory Seminar\n\nLecture
  held in Online.\n\nAbstract\nWe consider a variation on the p-adic Little
 wood Conjecture where instead of using powers of one prime\, we use arbitr
 arily large primes. We examine this conjecture from two viewpoints: the Di
 ophantine-approximation one and the dynamical one. Using the dynamical vie
 wpoint\, we rephrase the conjecture using Hecke neighbors and prove a part
 ial statement towards the conjecture. Namely\, we prove that the Hausdorff
  dimension of the exception set is strictly smaller than 1. Our tools for 
 the proof are mainly the effective equidistribution of Hecke neighbors due
  to Oh et al and to expander properties of $SL_2(Z/pZ)$ due to Bourgain-Ga
 mburd. This talk is based on an ongoing joint work with Erez Nesharim.\n
LOCATION:https://researchseminars.org/talk/NEDNT/61/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hao Xing (Ohio State University)
DTSTART:20231019T161500Z
DTEND:20231019T173000Z
DTSTAMP:20260422T225825Z
UID:NEDNT/62
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NEDNT/62/">E
 quidistribution problem in the space of Euclidean sublattices</a>\nby Hao 
 Xing (Ohio State University) as part of New England Dynamics and Number Th
 eory Seminar\n\nLecture held in Online.\n\nAbstract\nConsider the space of
  covolume-one sublattices of a fixed rank m in the Euclidean space ℝd. H
 ow do the orbits behave under the action of the lattice subgroups of SL(d\
 ,ℝ)  (e.g. SL(d\,ℤ))?  In a recent joint work with Michael Bersudsky\,
  we established an equidistribution phenomenon of such orbits when d=m+1. 
  However\, there are many more unsolved problems along this direction whic
 h might be of interest not only to homogeneous dynamicists\, but also to n
 umber theorists and analysts as well. In this talk\, I will explain the pr
 oblem\, our result\, an overview of methods and further directions of rese
 arch in a user-friendly way.\n
LOCATION:https://researchseminars.org/talk/NEDNT/62/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Noy Soffer Aranov (Technion)
DTSTART:20231026T161500Z
DTEND:20231026T173000Z
DTSTAMP:20260422T225825Z
UID:NEDNT/63
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NEDNT/63/">C
 overing Radii in Positive Characteristic</a>\nby Noy Soffer Aranov (Techni
 on) as part of New England Dynamics and Number Theory Seminar\n\nLecture h
 eld in Online.\n\nAbstract\nA fascinating question in geometry of number p
 ertains to the covering radius of lattice with respect to an interesting f
 unction. For example\, given a convex body C and a lattice L in R^d\, it i
 s interesting to ask what is the infimal r ≥ 0 such that L + rC = R^d. A
 nother interesting covering radius is the multiplicative covering radius\,
  which connects to dynamics due to its invariance under the diagonal group
 . It was conjectured by Minkowski that the multiplicative covering radius 
 is bounded above by 2^{-d} and that this upper bound is obtained only on A
 Z^d. In this talk I will discuss surprising results pertaining to covering
  radii in the positive characteristic setting and discover several surpris
 ing results. Some of my results include explicitly connecting between the 
 covering radii with respect to convex bodies and successive minima and pro
 ving a positive characteristic analogue of Minkowski’s function.\n
LOCATION:https://researchseminars.org/talk/NEDNT/63/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alon Agin (Tel Aviv University)
DTSTART:20231102T161500Z
DTEND:20231102T173000Z
DTSTAMP:20260422T225825Z
UID:NEDNT/64
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NEDNT/64/">C
 onstructing best approximation vectors</a>\nby Alon Agin (Tel Aviv Univers
 ity) as part of New England Dynamics and Number Theory Seminar\n\nLecture 
 held in Online.\n\nAbstract\nFor v in R^d and arbitrary norm\, we define t
 he best approximation sequence of v and the displacement vectors sequence 
 of v. We will discuss classical and recent works in Diophantine approximat
 ions in the language of these objects – focusing on their length\, direc
 tion and congruence class.\n
LOCATION:https://researchseminars.org/talk/NEDNT/64/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sam Chow (Warwick)
DTSTART:20231109T171500Z
DTEND:20231109T183000Z
DTSTAMP:20260422T225825Z
UID:NEDNT/65
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NEDNT/65/">D
 ispersion and Littlewood’s conjecture</a>\nby Sam Chow (Warwick) as part
  of New England Dynamics and Number Theory Seminar\n\nLecture held in Onli
 ne.\n\nAbstract\nI’ll discuss some problems related to Littlewood’s co
 njecture in diophantine approximation\, and the role hitherto played by di
 screpancy theory. I’ll explain why our new dispersion-theoretic approach
  should\, and does\, deliver stronger results. Our dispersion estimate is 
 proved using Poisson summation and diophantine inequalities. Joint with Ni
 clas Technau.\n
LOCATION:https://researchseminars.org/talk/NEDNT/65/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mikey Chow (Mikey Chow)
DTSTART:20231116T171500Z
DTEND:20231116T183000Z
DTSTAMP:20260422T225825Z
UID:NEDNT/66
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NEDNT/66/">J
 ordan and Cartan spectra in higher rank with applications to correlations<
 /a>\nby Mikey Chow (Mikey Chow) as part of New England Dynamics and Number
  Theory Seminar\n\nLecture held in Online.\n\nAbstract\nThe celebrated pri
 me geodesic theorem for a closed hyperbolic surface says that the number o
 f closed geodesics of length at most t is asymptotically e^t/t. For a clos
 ed surface equipped with two different hyperbolic structures\, Schwartz an
 d Sharp (’93) showed that the number of free homotopy classes of length 
 about t in both hyperbolic structures is asymptotically a constant multipl
 e of e^{ct} /t^{3/2} for some 0<c<1. \nWe will discuss the asymptotic corr
 elations of the length spectra of convex cocompact manifolds\, generalizin
 g Schwartz-Sharp’s results. Surprisingly\, it is helpful for us to relat
 e this problem with understanding the Jordan spectrum of a discrete subgro
 up in higher rank. In particular\, we will explain the source of the expon
 ential and polynomial factors in Schwartz-Sharp’s asymptotics from a hig
 her rank viewpoint. \nWe will also discuss the asymptotic correlations of 
 the displacement spectra and the ratio law between the asymptotic correlat
 ions of the length and displacement spectra.   \nThis is joint work with H
 ee Oh.\n
LOCATION:https://researchseminars.org/talk/NEDNT/66/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Daniel El-Baz (TU Graz)
DTSTART:20231130T171500Z
DTEND:20231130T183000Z
DTSTAMP:20260422T225825Z
UID:NEDNT/67
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NEDNT/67/">P
 rimitive rational points on expanding horospheres: effective joint equidis
 tribution</a>\nby Daniel El-Baz (TU Graz) as part of New England Dynamics 
 and Number Theory Seminar\n\nLecture held in Online.\n\nAbstract\nI will p
 resent joint work with Min Lee and Andreas Strömbergsson. Using technique
 s from analytic number theory\, spectral theory\, geometry of numbers as w
 ell 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 th
 eorem by Einsiedler\, Mozes\, Shah and Shapira. That theorem concerns the 
 equidistribution of primitive rational points on certain homogeneous space
 s and our proof has the added benefit of yielding a rate of convergence. I
 t turns out to have several (perhaps surprising) applications to number th
 eory and combinatorics\, which I shall also discuss.\n
LOCATION:https://researchseminars.org/talk/NEDNT/67/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Florian Richter (EPFL)
DTSTART:20231207T171500Z
DTEND:20231207T183000Z
DTSTAMP:20260422T225825Z
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://researchseminars.org/talk/NEDNT/68/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Oleksiy Klurman (University of Bristol)
DTSTART:20231214T171500Z
DTEND:20231214T183000Z
DTSTAMP:20260422T225825Z
UID:NEDNT/69
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NEDNT/69/">F
 inding Infinite arithmetic structures in sets of positive density</a>\nby 
 Oleksiy Klurman (University of Bristol) as part of New England Dynamics an
 d Number Theory Seminar\n\nLecture held in Online.\n\nAbstract\nIs there a
  partition of the natural numbers into finitely many pieces\, none of whic
 h 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 arithmetic R
 amsey theory which is still widely open. I will talk about a recent partia
 l result\, showing that “Pythagorean pairs” are partition regular\, th
 at 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 so
 me integer z (which may be coloured differently). The proof is a blend of 
 ideas from ergodic theory and multiplicative number theory. Based on a joi
 nt work with N. Frantzikinakis and J. Moreira.\n
LOCATION:https://researchseminars.org/talk/NEDNT/69/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lei Yang (IAS)
DTSTART:20240229T171500Z
DTEND:20240229T183000Z
DTSTAMP:20260422T225825Z
UID:NEDNT/70
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NEDNT/70/">I
 ncidence geometry and effective equidistribution in homogeneous dynamics</
 a>\nby Lei Yang (IAS) as part of New England Dynamics and Number Theory Se
 minar\n\nLecture held in Online.\n\nAbstract\nI will explain my proof of a
 n effective version of Ratner’s equidistribution theorem for unipotent o
 rbits in SL(3\,R)/SL(3\,Z). The proof combines new ideas from harmonic ana
 lysis and incidence geometry. In particular\, the proof is based on a boot
 strapping argument improving the local dimension of measures generated by 
 unipotent orbits. The key is to relate the behavior of the unipotent orbit
 s to a Kakeya model.\n
LOCATION:https://researchseminars.org/talk/NEDNT/70/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gaurav Aggarwal (TIFR)
DTSTART:20240307T171500Z
DTEND:20240307T183000Z
DTSTAMP:20260422T225825Z
UID:NEDNT/71
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NEDNT/71/">J
 oint Equidistribution of Approximates</a>\nby Gaurav Aggarwal (TIFR) as pa
 rt of New England Dynamics and Number Theory Seminar\n\nLecture held in On
 line.\n\nAbstract\nThe distribution of integer points on varieties has occ
 upied mathematicians for centuries. In the 1950’s Linnik used an “ergo
 dic method” to prove the equidistribution of integer points on large sph
 eres under a congruence condition. As shown by Maaß\, this problem is clo
 sely related to modular forms. Subsequently\, there were spectacular devel
 opments both from the analytic as well as ergodic side. I will discuss a m
 ore refined problem\, namely the joint distribution of lattice points in c
 onjunction with other arithmetic data. An example of such data is the “s
 hape” of an associated lattice\, or in number theoretic language\, a Hee
 gner point. In a completely different direction\, a “Poincaré section
 ” is a classical and useful tool in ergodic theory and dynamical systems
 . Recently\, Shapira and Weiss\, constructed a Poincaré section for the g
 eodesic flow on the moduli space of lattices to study joint equidistributi
 on properties. Their work in fact is very general but crucially uses the f
 act that the acting group has rank one. In joint work with Anish Ghosh\, w
 e develop a new method to deal with actions of higher rank groups. I will 
 explain this and\, if time permits\, some corollaries in Diophantine analy
 sis.\n
LOCATION:https://researchseminars.org/talk/NEDNT/71/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Shreyasi Datta (Uppsala University)
DTSTART:20240314T161500Z
DTEND:20240314T173000Z
DTSTAMP:20260422T225825Z
UID:NEDNT/72
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NEDNT/72/">B
 ad is null via constant invariance</a>\nby Shreyasi Datta (Uppsala Univers
 ity) as part of New England Dynamics and Number Theory Seminar\n\nLecture 
 held in Online.\n\nAbstract\nThe set of badly approximable vectors in Diop
 hantine approximation plays a significant role. In a recent work with Vict
 or Beresnevich\, Anish Ghosh\, and Ben Ward\, we developed a general frame
 work to show a `constant invariance’ property for a large class of limsu
 p sets of neighbourhoods of subsets of a metric measure space. As a conseq
 uence\, we get that the set of badly approximable points has measure zero 
 in a metric space equipped with certain natural measures. In particular\, 
 given any C^2 manifold\, we show almost every point is not badly approxima
 ble.\n
LOCATION:https://researchseminars.org/talk/NEDNT/72/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Carsten Peterson (Paderborn University)
DTSTART:20240411T161500Z
DTEND:20240411T173000Z
DTSTAMP:20260422T225825Z
UID:NEDNT/73
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NEDNT/73/">Q
 uantum ergodicity on the Bruhat-Tits building for PGL(3) in the Benjamini-
 Schramm limit</a>\nby Carsten Peterson (Paderborn University) as part of N
 ew England Dynamics and Number Theory Seminar\n\nLecture held in Online.\n
 \nAbstract\nOriginally\, quantum ergodicity concerned equidistribution pro
 perties of Laplacian eigenfunctions with large eigenvalue on manifolds for
  which the geodesic flow is ergodic. More recently\, several authors have 
 investigated quantum ergodicity for sequences of spaces which “converge
 ” to their common universal cover and when one restricts to eigenfunctio
 ns with eigenvalues in a fixed range. Previous authors have considered thi
 s type of quantum ergodicity in the settings of regular graphs\, rank one 
 symmetric spaces\, and some higher rank symmetric spaces. We prove analogo
 us results in the case when the underlying common universal cover is the B
 ruhat-Tits building associated to \\textrm{PGL}(3\, F) where F is a non-ar
 chimedean local field. This may be seen as both a higher rank analogue of 
 the regular graphs setting as well as a non-archimedean analogue of the sy
 mmetric space setting\n
LOCATION:https://researchseminars.org/talk/NEDNT/73/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nikolay Moshchevitin (Technion)
DTSTART:20240418T161500Z
DTEND:20240418T173000Z
DTSTAMP:20260422T225825Z
UID:NEDNT/74
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NEDNT/74/">B
 ounded ratios and badly approximability</a>\nby Nikolay Moshchevitin (Tech
 nion) as part of New England Dynamics and Number Theory Seminar\n\nLecture
  held in Online.\n\nAbstract\nWe will discuss relatively new criteria of b
 adly approximability in terms of ratios of best approximations. Let qν be
  convergents of continued fractions to real irrational α. It is well know
 n that\n\nα is badly approximable   iff   supν qν+1/qν is finite 
   iff   infν||qν+1α||/||qνα||>0.\n\nWe will discuss how this prop
 erty may be generalised to Diophantine Approximation in higher dimensions.
  The answer seems to be rather non-trivial. Some of the related properties
  may be expressed in terms of Parametric Geometry of Numbers recently deve
 loped by Schmidt\, Summerer\, Roy and the others. Also we discuss some pro
 perties of ratios under the consideration in accordance with the study of 
 multidimensional Dirichlet spectra.\n
LOCATION:https://researchseminars.org/talk/NEDNT/74/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alena Erchenko (Dartmouth College)
DTSTART:20240502T161500Z
DTEND:20240502T173000Z
DTSTAMP:20260422T225825Z
UID:NEDNT/75
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NEDNT/75/">F
 lexibility and rigidity for Cantor repellers</a>\nby Alena Erchenko (Dartm
 outh College) as part of New England Dynamics and Number Theory Seminar\n\
 nLecture held in Online.\n\nAbstract\nWe will consider dynamical systems t
 hat we call Cantor repellers which are expanding maps on invariant Cantor 
 sets coming from iterated function systems. Cantor repellers have two natu
 ral invariant measures: the measure of full dimension and the measure of m
 aximal entropy. We show that dimensions and Lyapunov exponents of those me
 asures are flexible up to well understood restrictions. We will also discu
 ss the boundary case for the range of values of the considered dynamical d
 ata. This is joint work with Jacob Mazor.\n
LOCATION:https://researchseminars.org/talk/NEDNT/75/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sam Chow (Warwick)
DTSTART:20240924T161500Z
DTEND:20240924T173000Z
DTSTAMP:20260422T225825Z
UID:NEDNT/76
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NEDNT/76/">S
 mooth discrepancy and Littlewood’s conjecture</a>\nby Sam Chow (Warwick)
  as part of New England Dynamics and Number Theory Seminar\n\nLecture held
  in Online.\n\nAbstract\nGiven \\boldsymbol \\alpha \\in [0\,1]^d\, we est
 imate the smooth discrepancy of the Kronecker sequence (n \\boldsymbol \\a
 lpha \\: \\mathrm{mod} \\: 1)_{n=1}^\\infty. We find that it can be smalle
 r than the classical discrepancy of any sequence when d \\le 2\, and can e
 ven be bounded in the case d=1. To achieve this\, we establish a novel det
 erministic analogue of Beck’s local-to-global principle (Annals 1994)\, 
 which relates the discrepancy of a Kronecker sequence to multiplicative di
 ophantine approximation. This opens up a new avenue of attack for Littlewo
 od’s conjecture.\n
LOCATION:https://researchseminars.org/talk/NEDNT/76/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Manuel Hauke (NTNU Trondheim)
DTSTART:20241008T161500Z
DTEND:20241008T173000Z
DTSTAMP:20260422T225825Z
UID:NEDNT/77
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NEDNT/77/">M
 etric Diophantine approximation: Moving targets and inhomogeneous variants
 </a>\nby Manuel Hauke (NTNU Trondheim) as part of New England Dynamics and
  Number Theory Seminar\n\nLecture held in Online.\n\nAbstract\nKhintchine
 ’s Theorem and its inhomogeneous and multidimensional variants provide a
  satisfying answer about the quality of approximations for almost every nu
 mber. In this talk\, I will discuss the (still open) question of allowing 
 a moving target (that is\, the inhomogeneous parameter changes for each de
 nominator) in Khintchine’s Theorem. Furthermore\, I will describe Duffin
 –Schaeffer-type results and conjectures in these setups\, both in dimens
 ion 1\, but also in higher dimensions. This is partially joint work with V
 ictor Beresnevich and Sanju Velani\, respectively with Felipe Ramírez.\n
LOCATION:https://researchseminars.org/talk/NEDNT/77/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Shreyasi Datta (University of York)
DTSTART:20241105T171500Z
DTEND:20241105T183000Z
DTSTAMP:20260422T225825Z
UID:NEDNT/78
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NEDNT/78/">F
 ourier Asymptotics and Effective Equidistribution</a>\nby Shreyasi Datta (
 University of York) as part of New England Dynamics and Number Theory Semi
 nar\n\nLecture held in Online.\n\nAbstract\nWe talk about effective equidi
 stribution of the expanding horocycles on the unit cotangent bundle of the
  modular surface with respect to various classes of Borel probability meas
 ures on the reals\, depending on their Fourier asymptotics.  This is a joi
 nt work with Subhajit Jana.\n
LOCATION:https://researchseminars.org/talk/NEDNT/78/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Keivan Mallahi-Karai (Constructor University)
DTSTART:20241119T171500Z
DTEND:20241119T183000Z
DTSTAMP:20260422T225825Z
UID:NEDNT/79
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NEDNT/79/">S
 pectral independence of compact groups</a>\nby Keivan Mallahi-Karai (Const
 ructor University) as part of New England Dynamics and Number Theory Semin
 ar\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 s
 ymmetric probability measures on $G_1$ and $G_2$. Under mild conditions 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 gove
 rned by the spectral gap. A coupling of $\\mu_1$ and $\\mu_2$ is any proba
 bility measure $\\mu$ on $G_1 \\times G_2$  whose  marginal distributions 
  are $\\mu_1$ and $\\mu_2$\, respectively . A natural question is under wh
 at conditions a spectral gap for all couplings depending on spectral gaps 
 of $\\mu_1$ and $\\mu_2$ can be established. \nIn this talk\, I will prese
 nt results in this direction which are based on joint work with Alireza S.
  Golsefidy and Amir Mohammadi.\n
LOCATION:https://researchseminars.org/talk/NEDNT/79/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Noy Soffer Aranov (University of Utah)
DTSTART:20241126T171500Z
DTEND:20241126T183000Z
DTSTAMP:20260422T225825Z
UID:NEDNT/80
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NEDNT/80/">E
 scape of Mass of Sequences</a>\nby Noy Soffer Aranov (University of Utah) 
 as part of New England Dynamics and Number Theory Seminar\n\nLecture held 
 in Online.\n\nAbstract\nOne way to study the distribution of nested quadra
 tic number fields satisfying fixed arithmetic relationships is through the
  evolution of continued fraction expansions. In the function field setting
 \, it was shown by de Mathan and Teullie that given a quadratic irrational
  $\\Theta$\, the degrees of the periodic part of the continued fraction of
  $t^n\\Theta$ are unbounded. Paulin and Shapira improved this by proving t
 hat quadratic irrationals exhibit partial escape of mass. Moreover\, they 
 conjectured that they must exhibit full escape of mass. We construct count
 erexamples to their conjecture in every characteristic. In this talk we sh
 all discuss the technique of proof as well as the connection between escap
 e 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://researchseminars.org/talk/NEDNT/80/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gaurav Aggarwal (TIFR)
DTSTART:20241203T171500Z
DTEND:20241203T183000Z
DTSTAMP:20260422T225825Z
UID:NEDNT/81
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NEDNT/81/">S
 ingular matrices on fractals</a>\nby Gaurav Aggarwal (TIFR) as part of New
  England Dynamics and Number Theory Seminar\n\nLecture held in Online.\n\n
 Abstract\nSingular vectors are those for which Dirichlet’s Theorem can b
 e improved by arbitrarily small multiplicative constants. Recently\, Klein
 bock and Weiss showed that the set of singular vectors has measure zero wi
 th respect to any friendly measure. However\, determining their Hausdorff 
 dimension remains a subtle and challenging problem. Khalil addressed this 
 by proving that the Hausdorff dimension of the set of singular vectors int
 ersecting a self-similar fractal is strictly smaller than the fractal’s 
 dimension.\nIn this talk\, I will extend Khalil’s result in four key dir
 ections. First\, we generalize the study from vectors to matrices. Second\
 , we analyze intersections with products of fractals\, such as the Cartesi
 an product of the middle-third and middle-fifth Cantor sets. Third\, we es
 tablish upper bounds for singular vectors in a generalized weighted settin
 g. Finally\, we derive an upper bound on the Hausdorff dimension of $\\ome
 ga$-very singular matrices in these broader settings\, extending earlier w
 ork of Das\, Fishman\, Simmons\, and Urbanski\, who studied the real\, unw
 eighted case.\nOur approach is dynamical in nature\, relying on the constr
 uction of a height function inspired by the work of Kadyrov\, Kleinbock\, 
 Lindenstrauss\, and Margulis. This is a joint work with Anish Ghosh.\n
LOCATION:https://researchseminars.org/talk/NEDNT/81/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Noy Soffer Aranov (University of Utah)
DTSTART:20241210T171500Z
DTEND:20241210T183000Z
DTSTAMP:20260422T225825Z
UID:NEDNT/82
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NEDNT/82/">E
 scape of Mass of Sequences</a>\nby Noy Soffer Aranov (University of Utah) 
 as part of New England Dynamics and Number Theory Seminar\n\nLecture held 
 in Online.\n\nAbstract\nOne way to study the distribution of nested quadra
 tic number fields satisfying fixed arithmetic relationships is through the
  evolution of continued fraction expansions. In the function field setting
 \, it was shown by de Mathan and Teullie that given a quadratic irrational
  $\\Theta$\, the degrees of the periodic part of the continued fraction of
  $t^n\\Theta$ are unbounded. Paulin and Shapira improved this by proving t
 hat quadratic irrationals exhibit partial escape of mass. Moreover\, they 
 conjectured that they must exhibit full escape of mass. We construct count
 erexamples to their conjecture in every characteristic. In this talk we sh
 all discuss the technique of proof as well as the connection between escap
 e 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://researchseminars.org/talk/NEDNT/82/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Han Zhang (Souchow University)
DTSTART:20250211T171500Z
DTEND:20250211T183000Z
DTSTAMP:20260422T225825Z
UID:NEDNT/83
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NEDNT/83/">K
 hintchine’s theorem on self-similar measures on the real line</a>\nby Ha
 n Zhang (Souchow University) as part of New England Dynamics and Number Th
 eory Seminar\n\nLecture held in Online.\n\nAbstract\nIn 1984\, Mahler prop
 osed the following question on Diophantine approximation : How close can i
 rrational numbers in the middle-thirds Cantor set be approximated by ratio
 nal numbers?  One way to reformulate Mahler’s question is to ask if Khin
 tchine’s theorem extends to the middle-thirds Cantor set. In a joint wor
 k with Timothée Bénard and Weikun He\, we prove that Khintchine’s theo
 rem holds for any self-similar measures on the real line. In particular th
 is applies to the Hausdorff measure on the middle-thirds Cantor set. Our r
 esult generalizes the recent breakthrough work of Khalil-Luethi in dimensi
 on one. Our proof is inspired by the work of Bénard-He regarding the semi
 simple random walks on homogeneous spaces.\n
LOCATION:https://researchseminars.org/talk/NEDNT/83/
END:VEVENT
BEGIN:VEVENT
SUMMARY:JinCheng Wang (Tufts University)
DTSTART:20250225T171500Z
DTEND:20250225T183000Z
DTSTAMP:20260422T225825Z
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://researchseminars.org/talk/NEDNT/84/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Michael Bersudsky (Ohio State University)
DTSTART:20250311T161500Z
DTEND:20250311T173000Z
DTSTAMP:20260422T225825Z
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://researchseminars.org/talk/NEDNT/85/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alon Agin (Tel Aviv University)
DTSTART:20250318T161500Z
DTEND:20250318T173000Z
DTSTAMP:20260422T225825Z
UID:NEDNT/86
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NEDNT/86/">T
 he Dirichlet spectrum</a>\nby Alon Agin (Tel Aviv University) as part of N
 ew England Dynamics and Number Theory Seminar\n\nLecture held in Online.\n
 \nAbstract\nAkhunzhanov and Shatskov defined the Dirichlet spectrum\, corr
 esponding 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 spectrum i
 s an interval. We generalize this result to arbitrary (m\,n) with max(m\,n
 )>1 and arbitrary norms\, improving previous works from recent years. We a
 lso define some related spectra and show that they too are intervals. We a
 lso prove the existence of matrices exhibiting special properties with res
 pect to their uniform exponent. Our argument is a modification of an argum
 ent of Khintchine from 1926.\n
LOCATION:https://researchseminars.org/talk/NEDNT/86/
END:VEVENT
BEGIN:VEVENT
SUMMARY:JinCheng Wang (Tufts University)
DTSTART:20250304T171500Z
DTEND:20250304T183000Z
DTSTAMP:20260422T225825Z
UID:NEDNT/87
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NEDNT/87/">S
 ome geometric and dynamical properties of hyperbolic magnetic flows</a>\nb
 y JinCheng Wang (Tufts University) as part of New England Dynamics and Num
 ber Theory Seminar\n\nLecture held in Online.\n\nAbstract\nAs a generaliza
 tion of geodesic flows\, magnetic flows trace unit-speed curves with const
 ant geodesic curvature. We consider the magnetic flows of surfaces with ne
 gative Gaussian curvature that are non-uniformly hyperbolic. By studying i
 ts geometry on the universal covering of the surface\, we show the uniquen
 ess of the measure of maximal entropy via the Bowen-Climenhaga-Thompson ma
 chinery. This is a joint work with Boris Hasselblatt.\n
LOCATION:https://researchseminars.org/talk/NEDNT/87/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Liyang Shao (UC Berkeley)
DTSTART:20250422T161500Z
DTEND:20250422T173000Z
DTSTAMP:20260422T225825Z
UID:NEDNT/88
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NEDNT/88/">W
 eighted Inhomogeneous Bad is Winning and Null</a>\nby Liyang Shao (UC Berk
 eley) as part of New England Dynamics and Number Theory Seminar\n\nLecture
  held in Online.\n\nAbstract\nWe will introduce the notion of inhomogeneou
 s weighted badly approximable vectors. We discuss that this set can be ver
 y large (winning) in a sense and in some other sense it is very small (mea
 sure wise). In particular\, we talk about such largeness and smallness via
  studying weighted inhomogeneous bad intersected with manifolds and suppor
 t of certain measures. This is a joint work with Shreyasi Datta.\n
LOCATION:https://researchseminars.org/talk/NEDNT/88/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Srivatsa Srinivas (UC San Diego)
DTSTART:20250429T161500Z
DTEND:20250429T173000Z
DTSTAMP:20260422T225825Z
UID:NEDNT/89
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NEDNT/89/">R
 andom Walks on SL_2(F_p) x SL_2(F_p)</a>\nby Srivatsa Srinivas (UC San Die
 go) as part of New England Dynamics and Number Theory Seminar\n\nLecture h
 eld in Online.\n\nAbstract\nWe will give a taste of the flavors of math th
 at constitute the study of random walks on compact groups\, followed by wh
 ich we will describe the author’s work with Prof. Golsefidy in solving a
  question of Lindenstrauss and Varju. Namely\, can the spectral gap of a r
 andom walk on a product of groups be related to those of the projections o
 nto its factors\n
LOCATION:https://researchseminars.org/talk/NEDNT/89/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Emilio Corso (Penn State)
DTSTART:20250506T161500Z
DTEND:20250506T173000Z
DTSTAMP:20260422T225825Z
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://researchseminars.org/talk/NEDNT/90/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vasiliy Neckrasov (Brandeis University)
DTSTART:20250930T164500Z
DTEND:20250930T174500Z
DTSTAMP:20260422T225825Z
UID:NEDNT/91
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NEDNT/91/">Z
 ero-one laws for uniform inhomogeneous Diophantine approximations</a>\nby 
 Vasiliy Neckrasov (Brandeis University) as part of New England Dynamics an
 d Number Theory Seminar\n\nLecture held in Online.\n\nAbstract\nIn [Compos
 itio Math. 155 (2019)] Kleinbock and Wadleigh proved a “zero-one law” 
 for uniform Diophantine approximations to pairs (\\Theta\, \\eta) of a mat
 rix \\Theta and vector \\eta by using dynamics on the space of grids. We w
 ill show how the classical Diophantine transference principle provides an 
 alternative approach to this problem and allows us to prove some generaliz
 ations. Namely\, we will reduce the statement for pairs to the twisted (
 “fixed matrix”) case and show zero-one laws for twisted uniform approx
 imations.\nAll the proofs are made in weighted case and\, more generally\,
  in the setup of approximations with arbitrary weight functions\, which wi
 ll also be discussed.\nThis talk is based on arXiv:2508.01912 and arXiv:25
 03.21180.\n
LOCATION:https://researchseminars.org/talk/NEDNT/91/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Chengyang Wu (Peking University)
DTSTART:20251014T164500Z
DTEND:20251014T174500Z
DTSTAMP:20260422T225825Z
UID:NEDNT/92
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NEDNT/92/">S
 imultaneously bounded and dense orbits for commuting Cartan actions</a>\nb
 y Chengyang Wu (Peking University) as part of New England Dynamics and Num
 ber Theory Seminar\n\nLecture held in Online.\n\nAbstract\nWith the goal t
 o attack Uniform Littlewood’s Conjecture proposed in [BFK25]\, we introd
 uced 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 pa
 per that there exists a dense subset of SL_3(R)/SL_3(Z) in which each poin
 t has a fiberwise non-divergent orbit under a cone inside the full diagona
 l subgroup and an unbounded orbit under every diagonal flow. Our proof als
 o presented the first instance of results concerning simultaneously bounde
 d and dense orbits for commuting actions on noncompact spaces. This is a j
 oint work with Dmitry Kleinbock.\n
LOCATION:https://researchseminars.org/talk/NEDNT/92/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pratyush Sarkar (ETHZ)
DTSTART:20251021T164500Z
DTEND:20251021T174500Z
DTSTAMP:20260422T225825Z
UID:NEDNT/93
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NEDNT/93/">E
 ffective equidistribution of translates of tori in arithmetic homogeneous 
 spaces and applications</a>\nby Pratyush Sarkar (ETHZ) as part of New Engl
 and Dynamics and Number Theory Seminar\n\nLecture held in Online.\n\nAbstr
 act\nA celebrated theorem of Eskin–Mozes–Shah gives an asymptotic coun
 ting formula for the number of integral (n x n)-matrices with a prescribed
  irreducible (over the integers/rationals) integral characteristic polynom
 ial. We obtain a power saving error term for the counting problem for (3 x
  3)-matrices. We do this by using the connection to homogeneous dynamics a
 nd 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 tra
 nslates 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 study the
  phenomenon more generally for any semisimple Lie group which we may discu
 ss if time permits.\n
LOCATION:https://researchseminars.org/talk/NEDNT/93/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Suxuan Chen (Ohio State)
DTSTART:20251028T164500Z
DTEND:20251028T174500Z
DTSTAMP:20260422T225825Z
UID:NEDNT/94
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NEDNT/94/">T
 he Hausdorff dimension of the intersection of \\psi-well approximable numb
 ers and self-similar sets</a>\nby Suxuan Chen (Ohio State) as part of New 
 England Dynamics and Number Theory Seminar\n\nLecture held in Online.\n\nA
 bstract\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 consider self-
 similar sets whose iterated function systems satisfy the open set conditio
 n. For functions \\psi that do not decrease too rapidly\, we give a conjec
 turally sharp upper bound on the Hausdorff dimension of the intersection o
 f \\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 give a l
 ower bound for this Hausdorff dimension\, which asymptotically matches the
  upper bound as v approaches 1. In particular\, we show that the set of ve
 ry well approximable numbers has full Hausdorff dimension within self-simi
 lar sets.\n
LOCATION:https://researchseminars.org/talk/NEDNT/94/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Reynold Fregoli (University of Michigan)
DTSTART:20251104T174500Z
DTEND:20251104T184500Z
DTSTAMP:20260422T225825Z
UID:NEDNT/95
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NEDNT/95/">E
 rgodic theorems for dilates of submanifolds in R^d actions</a>\nby Reynold
  Fregoli (University of Michigan) as part of New England Dynamics and Numb
 er Theory Seminar\n\nLecture held in Online.\n\nAbstract\nI will discuss t
 he validity of pointwise ergodic theorems for dilates of submanifolds in R
 ^d-actions. In particular\, I will present two recent results in this dire
 ction. The first\, joint work with P. Bandi and D. Kleinbock\, provides a 
 positive result for continuous test functions in mixing R^d-actions. The s
 econd\, joint work with J. Cheng and B. Guo\, shows that if the regularity
  assumption on the test function is removed\, a pointwise theorem may fail
  to hold.\n
LOCATION:https://researchseminars.org/talk/NEDNT/95/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Manuel Hauke (TU Graz)
DTSTART:20251118T174500Z
DTEND:20251118T184500Z
DTSTAMP:20260422T225825Z
UID:NEDNT/96
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NEDNT/96/">P
 seudo-random sequences\, twin primes\, and twisted diophantine approximati
 on</a>\nby Manuel Hauke (TU Graz) as part of New England Dynamics and Numb
 er Theory Seminar\n\nLecture held in Online.\n\nAbstract\nIn this talk\, I
  will speak about dynamics of $(a_n\\alpha)_{n} \\mod 1$ for integer seque
 nces $(a_n)_n$ and fixed irrational rotations $\\alpha$. The focus will be
  on the sequence of primes and other multiplicatively defined sequences\, 
 where gap statistics as well as twisted diophantine approximation will be 
 considered. If time permits\, I will outline the proof that includes a sie
 ve coming from the twin prime counting problem\, and establishing via rand
 om walks on Ostrowski digits an equidistribution result on diophantine Boh
 r sets mod d. This talk is partially based on https://arxiv.org/abs/2506.0
 1736 and joint work with E. Kowalski \nhttps://arxiv.org/abs/2502.08335.\n
LOCATION:https://researchseminars.org/talk/NEDNT/96/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Zuo Lin (UC Berkeley)
DTSTART:20251202T174500Z
DTEND:20251202T184500Z
DTSTAMP:20260422T225825Z
UID:NEDNT/97
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NEDNT/97/">P
 olynomial effective equidistribution for some higher dimensional unipotent
  subgroups</a>\nby Zuo Lin (UC Berkeley) as part of New England Dynamics a
 nd Number Theory Seminar\n\nLecture held in Online.\n\nAbstract\nLet G be 
 a semisimple Lie group\, Γ be a lattice in G and U be a unipotent subgrou
 p of G. A celebrated theorem of Ratner says that for any x in G/Γ the orb
 it U.x is equidistributed in a periodic orbit of some subgroup U ≤ L ≤
  G. Establishing a quantitative version of Ratner’s theorem has been lon
 g sought after. If U is a horospherical subgroup of G\, the question is we
 ll-studied. If U is not a horospherical subgroup\, this question is far le
 ss understood. Recently\, Lindenstrauss\, Mohammadi\, Wang and Yang establ
 ished a fully quantitative and effective equidistribution result for orbit
 s of one-parameter (non-horospherical) unipotent groups in some cases. In 
 this talk\, we will discuss a recent equidistribution theorem for some uni
 potent subgroups in higher dimension. Our results in particular provide eq
 uidistribution theorems for orbits of the isometry group of a non-degenera
 te bilinear form on R^n in SL_n(R)/SL_n(Z).\n
LOCATION:https://researchseminars.org/talk/NEDNT/97/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Demi Allen (University of Exeter)
DTSTART:20251209T150000Z
DTEND:20251209T160000Z
DTSTAMP:20260422T225825Z
UID:NEDNT/98
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NEDNT/98/">R
 ectangular Shrinking Targets on Self-Similar Carpets</a>\nby Demi Allen (U
 niversity of Exeter) as part of New England Dynamics and Number Theory Sem
 inar\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 is a shr
 inking target set. The terminology of "shrinking targets" was first introd
 uced by Hill and Velani in 1995. Since then\, shrinking target problems ha
 ve received a great deal of interest\, especially with regards to studying
  the measure-theoretic and dimension-theoretic properties of shrinking tar
 get sets. In this talk\, I will discuss some recent work with Thomas Jorda
 n (Bristol\, UK) and Ben Ward (York\, UK) where we establish the Hausdorff
  dimension of a shrinking target set where our "targets" (the $B_n$) are r
 ectangles and $X$ is a self-similar carpet.\n
LOCATION:https://researchseminars.org/talk/NEDNT/98/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexander Smith (Northwestern University)
DTSTART:20260129T171500Z
DTEND:20260129T183000Z
DTSTAMP:20260422T225825Z
UID:NEDNT/99
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NEDNT/99/">D
 iophantine approximation for hypersurfaces</a>\nby Alexander Smith (Northw
 estern University) as part of New England Dynamics and Number Theory Semin
 ar\n\nLecture held in Online.\n\nAbstract\nAmong the nondegenerate C^4 hyp
 ersurfaces\, we characterize the rational quadrics as the hypersurfaces th
 at are the least well approximated by rational points. For all other hyper
 surfaces\, we give a heuristically sharp lower bound for the number of rat
 ional points near them\, improving the sensitivity of prior results of Ber
 esnevich and Huang. Our methods are dynamical\, involving the application 
 of Ratner’s theorems for unipotent orbits\, and we will show how our wor
 k relates to the dynamical resolution of the Oppenheim conjecture by Margu
 lis.\n
LOCATION:https://researchseminars.org/talk/NEDNT/99/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexander Skenderi (UW Madison)
DTSTART:20260205T171500Z
DTEND:20260205T183000Z
DTSTAMP:20260422T225825Z
UID:NEDNT/100
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NEDNT/100/">
 Asymptotically large free semigroups in Zariski dense discrete subgroups o
 f Lie groups</a>\nby Alexander Skenderi (UW Madison) as part of New Englan
 d Dynamics and Number Theory Seminar\n\nLecture held in Online.\n\nAbstrac
 t\nAn important quantity in the study of discrete groups of isometries of 
 Riemannian manifolds\, Gromov hyperbolic spaces\, and other interesting ge
 ometric objects is the critical exponent. For a discrete subgroup of isome
 tries of the quaternionic hyperbolic space or octonionic projective plane\
 , Kevin Corlette established in 1990 that the critical exponent detects wh
 ether a discrete subgroup is a lattice or has infinite covolume. Precisely
 \, either the critical exponent equals the volume entropy\, in which case 
 the discrete subgroup is a lattice\, or the critical exponent is less than
  the volume entropy by some definite amount\, in which case the discrete s
 ubgroup has infinite covolume. In 2003\, Leuzinger extended this gap theor
 em for the critical exponent to any discrete subgroup of a Lie group havin
 g Kazhdan’s property (T) (for instance\, a discrete subgroup of SL(n\,R)
 \, where n is at least 3).\nIn this talk\, I will present a result which s
 hows that no such gap phenomenon holds for discrete semigroups of Lie grou
 ps. More precisely\, for any Zariski dense discrete subgroup of a Lie grou
 p\, there exist free\, finitely generated\, Zariski dense subsemigroups wh
 ose critical exponents are arbitrarily close to that of the ambient discre
 te subgroup.\nAs an application\, we show that the critical exponent is lo
 wer semicontinuous in the Chabauty topology whenever the Chabauty limit of
  a sequence of Zariski dense discrete subgroups is itself a Zariski dense 
 discrete subgroup.\n
LOCATION:https://researchseminars.org/talk/NEDNT/100/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kecheng Li (Tufts University)
DTSTART:20260226T171500Z
DTEND:20260226T183000Z
DTSTAMP:20260422T225825Z
UID:NEDNT/101
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NEDNT/101/">
 Unique Equilibrium States for Viana Maps for Small Potentials</a>\nby Kech
 eng Li (Tufts University) as part of New England Dynamics and Number Theor
 y Seminar\n\nLecture held in Online.\n\nAbstract\nWe study the thermodynam
 ic formalism for Viana maps (skew products that couple an expanding circle
  map with a small perturbation of a quadratic map on the fibers). Working 
 within the Climenhaga–-Thompson framework\, we show that for every Höld
 er potential whose oscillation is below an explicit threshold\, there is a
  unique equilibrium state. The main step is a uniform control of recurrenc
 e to the critical region in the fibers\, where the derivative degenerates.
  This yields the pressure gap and the specification estimates needed to ap
 ply the method and removes the principal obstruction. These conclusions ar
 e robust under sufficiently small perturbations of the reference map.\n
LOCATION:https://researchseminars.org/talk/NEDNT/101/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kavita Dhanda (University of Houston)
DTSTART:20260305T171500Z
DTEND:20260305T183000Z
DTSTAMP:20260422T225825Z
UID:NEDNT/102
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NEDNT/102/">
 Accumulation points of normalized approximations</a>\nby Kavita Dhanda (Un
 iversity of Houston) as part of New England Dynamics and Number Theory Sem
 inar\n\nLecture held in Online.\n\nAbstract\nConsider the collection of al
 l accumulation points of normalized integer vector translates of points q
 α with α ∈ R^d and q ∈ Z. For each normalization factor\, We find th
 e lebesgue measure of the set of α whose accumulation points are all of R
 ^d and of the complement set. In cases\, where the lebesgue measure is zer
 o\, we seek finer information about Hausdorff dimensions of the correspond
 ing sets.\n
LOCATION:https://researchseminars.org/talk/NEDNT/102/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Rishi Kumar (Tel Aviv University)
DTSTART:20260312T161500Z
DTEND:20260312T173000Z
DTSTAMP:20260422T225825Z
UID:NEDNT/103
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NEDNT/103/">
 On the error bounds for visible points in some cut-and-project sets</a>\nb
 y Rishi Kumar (Tel Aviv University) as part of New England Dynamics and Nu
 mber Theory Seminar\n\nLecture held in Online.\n\nAbstract\nThe density of
  points visible from the origin in sets such as the Ammann–Beenker point
  set has recently attracted attention. These sets can also be viewed as a 
 cut-and-project set. In this talk\, we will present an error estimate for 
 the density of visible points for some class of cut-and-project sets\, alo
 ng with related results. Joint work with Ilya and Barak.\n
LOCATION:https://researchseminars.org/talk/NEDNT/103/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jiajie Zheng (University of North Texas)
DTSTART:20260319T161500Z
DTEND:20260319T173000Z
DTSTAMP:20260422T225825Z
UID:NEDNT/104
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NEDNT/104/">
 Absolute-winning properties of equicontinuously-twisted badly approximable
  points in continued fractions and beta-transformations</a>\nby Jiajie Zhe
 ng (University of North Texas) as part of New England Dynamics and Number 
 Theory Seminar\n\nLecture held in Online.\n\nAbstract\nIt is well know tha
 t in a $\\beta$-transformation system for an integer $\\beta>0$\, the set 
 ${x: \\liminf_{n\\to\\infty}|T^nx-y_n|>0}$ has full Hausdorff dimension fo
 r all sequences $(y_n)$ in $[0\,1)$ and in the Gauss map system ${x: \\lim
 inf_{n\\to\\infty}|T^nx-0|>0}$ also has full Hausdorff dimension. In this 
 talk\, I will introduce a dynamical approach to understanding these sets\,
  and the new technique will allow us to strengthen the results so that the
  “targets’’ can be generalized to any equicontinuous sequence of fun
 ctions\, enabling the targets to vary by trajectories. In particular\, not
 ably this will imply the full dimension of non-recurrent points\, bridging
  the problems of shrinking targets and Poincare recurrence.\n
LOCATION:https://researchseminars.org/talk/NEDNT/104/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alex Maldague (Rice University)
DTSTART:20260416T161500Z
DTEND:20260416T173000Z
DTSTAMP:20260422T225825Z
UID:NEDNT/105
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NEDNT/105/">
 Superrigidity of rich representations</a>\nby Alex Maldague (Rice Universi
 ty) as part of New England Dynamics and Number Theory Seminar\n\nLecture h
 eld in Online.\n\nAbstract\nIn this talk\, I will introduce the class of g
 eodesically rich representations. These are representations of (real or co
 mplex) hyperbolic lattices that preserve a significant amount of the geome
 tric structure of the associated quotient manifold. When the quotient mani
 fold has robust geometric structure\, these representations exhibit rigidi
 ty phenomena. In particular\, a recent superrigidity theorem for rich repr
 esentations was used to prove that finite-volume hyperbolic manifolds with
  infinitely many maximal totally geodesic submanifolds are arithmetic (Bad
 er-Fisher-Miller-Stover). I will discuss a new superrigidity theorem for r
 ich representations that efficiently recovers existing results and address
 es target groups that were previously inaccessible.\n
LOCATION:https://researchseminars.org/talk/NEDNT/105/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ingrid Vukusic (University of York)
DTSTART:20260402T161500Z
DTEND:20260402T173000Z
DTSTAMP:20260422T225825Z
UID:NEDNT/106
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NEDNT/106/">
 Some bounds related to the 2-adic Littlewood conjecture</a>\nby Ingrid Vuk
 usic (University of York) as part of New England Dynamics and Number Theor
 y Seminar\n\nLecture held in Online.\n\nAbstract\nConsider alpha = (sqrt(1
 7)-1)/8. One can check that all partial quotients in the continued fractio
 n 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 the same 
 is true for 4*alpha. Might this go on forever as we keep multiplying by 2 
 (mod 1)? Of course\, the answer is “no”\, as the 2-adic Littlewood con
 jecture is known to be true for quadratic irrationals.\nIn this talk\, we 
 will use Hurwitz’s algorithm for multiplication by 2 to approach the 2-a
 dic Littlewood conjecture in a completely naive way\, and we will (im)prov
 e some bounds related to the 2-adic Littlewood conjecture and a variant of
  it.\nJoint work with Dinis Vitorino.\n
LOCATION:https://researchseminars.org/talk/NEDNT/106/
END:VEVENT
END:VCALENDAR