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BEGIN:VEVENT
SUMMARY:Nattalie Tamam (UCSD)
DTSTART:20200423T210000Z
DTEND:20200423T223000Z
DTSTAMP:20260422T225726Z
UID:PacificDynamicsSeminar/1
DESCRIPTION:Title: Effective equidistribution of horospherical flows in infini
te volume\nby Nattalie Tamam (UCSD) as part of Pacific dynamics semina
r\n\n\nAbstract\nThe horospherical flow on finite-volume hyperbolic surfac
es is well-understood. In particular\, effective equidistribution of non-c
losed horospherical orbits is known. New difficulties arise when studying
the infinite-volume setting. We will discuss the setting in finite- and in
finite-volume manifolds\, and the measures that play a crucial role in the
latter. Joint work with Jacqueline Warren.\n\nThe first 45 minutes will
be targeted at beginning graduate students\; the second 45 minutes will be
more technical.\n
LOCATION:https://researchseminars.org/talk/PacificDynamicsSeminar/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lior Silberman (The University of British Columbia)
DTSTART:20200430T210000Z
DTEND:20200430T223000Z
DTSTAMP:20260422T225726Z
UID:PacificDynamicsSeminar/2
DESCRIPTION:Title: Quantum Unique Ergodicity\nby Lior Silberman (The Unive
rsity of British Columbia) as part of Pacific dynamics seminar\n\n\nAbstra
ct\nIn the first half I'll give a colloquium-style introduction to the equ
idistribution problem for Laplace eigenfucntions on Riemannian manifolds\,
with emphasis on the locally symmetric spaces. I will introduce positive
results for exact eigenfunctions (with and without reference to the numbe
r-theoretic symmetries of the manifold)\, and negative results for approxi
mate eigenfunctions. I will present results (independenlty) joint with A.
Venkatesh\, N. Anantharaman\, and S. Eswarathasan. In the second half I
'll answer questions and provide details as requested by the audience.\n\n
The first 45 minutes will be targeted at beginning graduate students\; the
second 45 minutes will be more technical.\n
LOCATION:https://researchseminars.org/talk/PacificDynamicsSeminar/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sophie MacDonald (The University of British Columbia)
DTSTART:20200507T210000Z
DTEND:20200507T223000Z
DTSTAMP:20260422T225726Z
UID:PacificDynamicsSeminar/3
DESCRIPTION:Title: Factors of Gibbs measures on subshifts\nby Sophie MacDo
nald (The University of British Columbia) as part of Pacific dynamics semi
nar\n\n\nAbstract\nClassical results of Dobrushin and Lanford-Ruelle estab
lish\, in rough terms\,\nthat for a local energy function on a subshift wi
thout too much long-range\norder\, the translation-invariant Gibbs measure
s are precisely the\nequilibrium measures. There are multiple definitions
of a Gibbs measure in\nthe literature\, which do not always coincide. We w
ill discuss two of these\ndefinitions\, one introduced by Capocaccia and t
he other used by\nDobrushin-Lanford-Ruelle\, and outline a proof (availabl
e at\nhttps://arxiv.org/abs/2003.05532) that they are equivalent.\n\nWe wi
ll also discuss forthcoming work\, in which we show that Gibbsianness is\n
preserved by pushforward through a certain kind of almost invertible facto
r\nmap. As an application in one dimension\, we show that for a sufficient
ly\nregular potential\, any equilibrium measure on an irreducible sofic sh
ift is\nGibbs. As far as we know\, this is the first reasonably general re
sult of the\nLanford-Ruelle type for a class of subshifts without the topo
logical Markov\nproperty.\n\nJoint work with Luísa Borsato\, with extensi
ve advice from Brian Marcus and\nTom Meyerovitch.\n\nParticipants should g
o over the slides or listen to the recorded presentation ahead of time (se
e links above). The meeting will be devoted to questions and discussion.\
n
LOCATION:https://researchseminars.org/talk/PacificDynamicsSeminar/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anthony Sanchez (University of Washington)
DTSTART:20200514T210000Z
DTEND:20200514T223000Z
DTSTAMP:20260422T225726Z
UID:PacificDynamicsSeminar/4
DESCRIPTION:Title: Gaps of saddle connection directions for some branched cove
rs of tori\nby Anthony Sanchez (University of Washington) as part of P
acific dynamics seminar\n\n\nAbstract\nTranslation surfaces given by gluin
g two identical tori along\na slit have genus two and two cone-type singul
arities of angle $4\\pi$.\nThere is a distinguished set of trajectories ca
lled saddle connections that\nare the straight lines trajectories between
cone points. We can\nassociate a *holonomy vector* in the plane to each sa
ddle connection whose components are the\nhorizontal and vertical displace
ment of the saddle connection. How random\nis the planar set of holonomy o
f saddle connections? We study this question\nby computing the *gap distri
bution* for slopes of saddle connections for\nthese and other related clas
ses of translation surfaces.\n\nThe first 45 minutes will be targeted at b
eginning graduate students\; the second 45 minutes will be more technical.
\n
LOCATION:https://researchseminars.org/talk/PacificDynamicsSeminar/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ian Putnam (University of Victoria)
DTSTART:20200521T210000Z
DTEND:20200521T223000Z
DTSTAMP:20260422T225726Z
UID:PacificDynamicsSeminar/5
DESCRIPTION:Title: A Bratteli-Vershik model for $\\mathbb{Z}^2$ actions\, or h
ow cohomology can help us make dynamical systems\nby Ian Putnam (Unive
rsity of Victoria) as part of Pacific dynamics seminar\n\n\nAbstract\nThe
Bratteli-Vershik model is a method of producing minimal actions of the int
egers on a Cantor set. It was given by myself\, Rich Herman and Chris Skau
\, building on seminal ideas of Anatoly Vershik\, over 30 years ago. Rathe
r disappointingly and surprisingly\, there isn't a good version for $\\mat
hbb{Z}^2$ actions. I'll report on a new outlook on the problem and recent
progress with Thierry Giordano (Ottawa) and Christian Skau (Trondheim). Th
e new outlook focuses on the model as an answer to the question: which coh
omological invariants can arise from such actions? I will not assume any f
amiliarity with either the original model or the cohomology. The first hal
f of the talk will be a gentle introduction to the $\\mathbb{Z}$-case and
the second half will deal with how to adapt the question to get an answer
for $\\mathbb{Z}^2$.\n\nThe first 45 minutes are targeted at beginning gra
duate students\; the second 45 minutes may be more technical.\n
LOCATION:https://researchseminars.org/talk/PacificDynamicsSeminar/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jon Chaika (University of Utah)
DTSTART:20200611T210000Z
DTEND:20200611T223000Z
DTSTAMP:20260422T225726Z
UID:PacificDynamicsSeminar/6
DESCRIPTION:Title: There exists a weakly mixing billiard in a polygon\nby
Jon Chaika (University of Utah) as part of Pacific dynamics seminar\n\n\nA
bstract\nThis main result of this talk is that there exists a billiard flo
w in a polygon that is weakly mixing with respect to Lebesgue measure on t
he unit tangent bundle to the billiard. This strengthens Kerckhoff\, Masur
and Smillie's result that there exists ergodic billiard flows in polygons
. The existence of a weakly mixing billiard follows\, via a Baire category
argument\, from showing that for any translation surface the product of t
he flows in almost every pair of directions is ergodic with respect to Leb
esgue measure. This in turn is proven by showing that for every translatio
n surface the flows in almost every pair of directions do not share non-tr
ivial common eigenvalues. This talk will explain the problem\, related res
ults\, and approach. The talk will not assume familiarity with translation
surfaces. This is joint work with Giovanni Forni.\n
LOCATION:https://researchseminars.org/talk/PacificDynamicsSeminar/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Samantha Fairchild (University of Washington)
DTSTART:20200618T210000Z
DTEND:20200618T223000Z
DTSTAMP:20260422T225726Z
UID:PacificDynamicsSeminar/7
DESCRIPTION:Title: Counting social interactions for discrete subsets of the pl
ane\nby Samantha Fairchild (University of Washington) as part of Pacif
ic dynamics seminar\n\n\nAbstract\nGiven a discrete subset $V$ in the plan
e\, how many points would you expect there to be in a ball of radius $100$
? What if the radius is $10\,000$? Due to the results of Fairchild and for
thcoming work with Burrin\, when $V$ arises as orbits of non-uniform latti
ce subgroups of $\\mathrm{SL}(2\,\\mathbb{R})$\, we can understand asympto
tic growth rate with error terms of the number of points in $V$ for a broa
d family of sets. A crucial aspect of these arguments and similar argument
s is understanding how to count pairs of saddle connections with certain p
roperties determining the interactions between them\, like having a fixed
determinant or having another point in $V$ nearby.\n\nWe will spend the fi
rst 40 minutes discussing how these sets arise and counting results arise
from the study of concrete translation surfaces. The following 40 minutes
will be spent highlighting the proof strategy used to obtain these results
\, and advertising the generality and strength of this argument that arise
s from the computation of all higher moments of the Siegel--Veech transfor
m over quotients of $\\mathrm{SL}(2\,\\mathbb{R})$ by non-uniform lattices
.\n
LOCATION:https://researchseminars.org/talk/PacificDynamicsSeminar/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Taylor McAdam (Yale University)
DTSTART:20200528T210000Z
DTEND:20200528T223000Z
DTSTAMP:20260422T225726Z
UID:PacificDynamicsSeminar/8
DESCRIPTION:Title: Almost-prime times in horospherical flows\nby Taylor Mc
Adam (Yale University) as part of Pacific dynamics seminar\n\n\nAbstract\n
There is a rich connection between homogeneous dynamics and number theory.
Often in such applications it is desirable for dynamical results to be ef
fective (i.e. the rate of convergence for dynamical phenomena are known).
In the first part of this talk\, I will provide the necessary background a
nd relevant history to state an effective equidistribution result for horo
spherical flows on the space of unimodular lattices in $\\mathbb{R}^n$. I
will then describe an application to studying the distribution of almost-p
rime times (integer times having fewer than a fixed number of prime factor
s) in horospherical orbits and discuss connections of this work to Sarnak
’s Möbius disjointness conjecture. In the second part of the talk I wil
l describe some of the ingredients and key steps that go into proving thes
e results.\n\nThe first 45 minutes are targeted at beginning graduate stud
ents\; the second 45 minutes may be more technical.\n
LOCATION:https://researchseminars.org/talk/PacificDynamicsSeminar/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pablo Shmerkin (T. Di Tella University and Conicet)
DTSTART:20200604T200000Z
DTEND:20200604T213000Z
DTSTAMP:20260422T225726Z
UID:PacificDynamicsSeminar/9
DESCRIPTION:Title: Arithmetic and geometric properties of planar self-similar
sets\nby Pablo Shmerkin (T. Di Tella University and Conicet) as part o
f Pacific dynamics seminar\n\n\nAbstract\nFurstenberg's conjecture on the
dimension of the intersection of $\\times2\,\\times3$-invariant Cantor set
s can be restated as a bound on the dimension of linear slices of the prod
uct of $\\times2\,\\times3$-Cantor sets\, which is a self-affine set in th
e plane. I will discuss some older and newer variants of this\, where the
self-affine set is replaced by a self-similar set such as the Sierpinski t
riangle\, Sierpinski carpet or (support of) a complex Bernoulli convolutio
n. Among other things\, I will show that the intersection of the Sierpinsk
i carpet with circles has small dimension\, but on the other hand the Sier
pinski carpet can be covered very efficiently by linear tubes (neighborhoo
ds of lines). The latter fact is a recent result joint with A. Pyörälä\
, V. Suomala and M. Wu.\n\nNote special time: 1 hours earlier than usual.\
n\nThe first 45 minutes are targeted at beginning graduate students\; the
second 45 minutes may be more technical.\n
LOCATION:https://researchseminars.org/talk/PacificDynamicsSeminar/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Rodrigo Treviño (University of Maryland)
DTSTART:20200702T210000Z
DTEND:20200702T223000Z
DTSTAMP:20260422T225726Z
UID:PacificDynamicsSeminar/10
DESCRIPTION:Title: Quantitative weak mixing for random substitution tilings\nby Rodrigo Treviño (University of Maryland) as part of Pacific dynami
cs seminar\n\n\nAbstract\n"Quantitative weak mixing" is the term used to b
ound the dimensions of spectral measures of a measure-preserving system. T
his type of study has gained popularity over the last decade\, led by a se
ries of results of Bufetov and Solomyak for a large class of flows which i
nclude general one-dimensional tiling spaces as well as translation flows
on flat surfaces\, as well as results on quantitative weak mixing by Forni
. In this talk I will present results which extend the results for flows t
o higher rank parabolic actions\, focusing on quantitative results for a b
road class of tilings in any dimension. The talk won't assume familiarity
with almost anything\, so I will define all objects in consideration.\n
LOCATION:https://researchseminars.org/talk/PacificDynamicsSeminar/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ping Ngai (Brian) Chung (University of Chicago)
DTSTART:20200709T210000Z
DTEND:20200709T223000Z
DTSTAMP:20260422T225726Z
UID:PacificDynamicsSeminar/11
DESCRIPTION:Title: Stationary measure and orbit closure classification for ra
ndom walks on surfaces\nby Ping Ngai (Brian) Chung (University of Chic
ago) as part of Pacific dynamics seminar\n\n\nAbstract\nWe study the probl
em of classifying stationary measures and orbit closures for non-abelian a
ction on surfaces. Using a result of Brown and Rodriguez Hertz\, we show t
hat under a certain average growth condition\, the orbit closures are eith
er finite or dense. Moreover\, every infinite orbit equidistributes on the
surface. This is analogous to the results of Benoist-Quint and Eskin-Lind
enstrauss in the homogeneous setting\, and the result of Eskin-Mirzakhani
in the setting of moduli spaces of translation surfaces.\n\nWe then consid
er the problem of verifying this growth condition in concrete settings. In
particular\, we apply the theorem to two settings\, namely discrete pertu
rbations of the standard map and the $\\mathrm{Out}(F_2)$-action on a cert
ain character variety. We verify the growth condition analytically in the
former setting\, and verify numerically in the latter setting.\n
LOCATION:https://researchseminars.org/talk/PacificDynamicsSeminar/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Paul Apisa\, Alex Wright (University of Michigan)
DTSTART:20210121T223000Z
DTEND:20210121T233000Z
DTSTAMP:20260422T225726Z
UID:PacificDynamicsSeminar/12
DESCRIPTION:Title: Large orbit closures of translation surfaces are strata or
loci of double covers\, Lecture 1/5\nby Paul Apisa\, Alex Wright (Uni
versity of Michigan) as part of Pacific dynamics seminar\n\n\nAbstract\nAn
y translation surface can be presented as a collection of polygons in the
plane with sides identified. By acting linearly on the polygons\, we obtai
n an action of GL(2\,R) on moduli spaces of translation surfaces. Recent w
ork of Eskin\, Mirzakhani\, and Mohammadi showed that $\\mathrm{GL}(2\,\\m
athbb{R})$ orbit closures are locally described by linear equations on the
edges of the polygons. However\, which linear manifolds arise this way is
mysterious.\n\nIn this lecture series\, we will describe new joint work t
hat shows that when an orbit closure is sufficiently large it must be a wh
ole moduli space\, called a stratum in this context\, or a locus defined b
y rotation by $\\pi$ symmetry.\n\nWe define "sufficiently large" in terms
of rank\, which is the most important numerical invariant of an orbit clos
ure\, and is an integer between $1$ and the genus $g$. Our result applies
when the rank is at least $1+g/2$\, and so handles roughly half of the pos
sible values of rank.\n\nLecture 1: An introduction to orbit closures\, th
eir rank\, their boundary in the WYSIWYG partial compactification\, and cy
linder deformations.\n\nFor the other lectures see https://www.math.ubc.ca/~lior/sem/WC
DS.html#talk12\n
LOCATION:https://researchseminars.org/talk/PacificDynamicsSeminar/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Paul Apisa\, Alex Wright (University of Michigan)
DTSTART:20210128T220000Z
DTEND:20210128T233000Z
DTSTAMP:20260422T225726Z
UID:PacificDynamicsSeminar/13
DESCRIPTION:Title: Large orbit closures of translation surfaces are strata or
loci of double covers\, Lecture 2/5\nby Paul Apisa\, Alex Wright (Uni
versity of Michigan) as part of Pacific dynamics seminar\n\n\nAbstract\nAn
y translation surface can be presented as a collection of polygons in the
plane with sides identified. By acting linearly on the polygons\, we obtai
n an action of GL(2\,R) on moduli spaces of translation surfaces. Recent w
ork of Eskin\, Mirzakhani\, and Mohammadi showed that $\\mathrm{GL}(2\,\\m
athbb{R})$ orbit closures are locally described by linear equations on the
edges of the polygons. However\, which linear manifolds arise this way is
mysterious.\n\nIn this lecture series\, we will describe new joint work t
hat shows that when an orbit closure is sufficiently large it must be a wh
ole moduli space\, called a stratum in this context\, or a locus defined b
y rotation by $\\pi$ symmetry.\n\nWe define "sufficiently large" in terms
of rank\, which is the most important numerical invariant of an orbit clos
ure\, and is an integer between $1$ and the genus $g$. Our result applies
when the rank is at least $1+g/2$\, and so handles roughly half of the pos
sible values of rank.\n\nLecture 2: Reconstructing orbit closures from the
ir boundaries (this talk will explicate a preprint of the same name).\n\nF
or the other lectures see https://www.math.ubc.ca/~lior/sem/WCDS.html#talk12\n
LOCATION:https://researchseminars.org/talk/PacificDynamicsSeminar/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Paul Apisa\, Alex Wright (University of Michigan)
DTSTART:20210204T220000Z
DTEND:20210204T233000Z
DTSTAMP:20260422T225726Z
UID:PacificDynamicsSeminar/14
DESCRIPTION:Title: Large orbit closures of translation surfaces are strata or
loci of double covers\, Lecture 3/5\nby Paul Apisa\, Alex Wright (Uni
versity of Michigan) as part of Pacific dynamics seminar\n\n\nAbstract\nAn
y translation surface can be presented as a collection of polygons in the
plane with sides identified. By acting linearly on the polygons\, we obtai
n an action of GL(2\,R) on moduli spaces of translation surfaces. Recent w
ork of Eskin\, Mirzakhani\, and Mohammadi showed that $\\mathrm{GL}(2\,\\m
athbb{R})$ orbit closures are locally described by linear equations on the
edges of the polygons. However\, which linear manifolds arise this way is
mysterious.\n\nIn this lecture series\, we will describe new joint work t
hat shows that when an orbit closure is sufficiently large it must be a wh
ole moduli space\, called a stratum in this context\, or a locus defined b
y rotation by $\\pi$ symmetry.\n\nWe define "sufficiently large" in terms
of rank\, which is the most important numerical invariant of an orbit clos
ure\, and is an integer between $1$ and the genus $g$. Our result applies
when the rank is at least $1+g/2$\, and so handles roughly half of the pos
sible values of rank.\n\nLecture 3: Recognizing loci of covers using cylin
ders (this talk will follow a preprint titled “Generalizations of the Ei
erlegende-Wollmilchsau”).\n\nFor the other lectures see https://www.math.ubc.ca/~lior
/sem/WCDS.html#talk12\n
LOCATION:https://researchseminars.org/talk/PacificDynamicsSeminar/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Paul Apisa\, Alex Wright (University of Michigan)
DTSTART:20210211T223000Z
DTEND:20210211T233000Z
DTSTAMP:20260422T225726Z
UID:PacificDynamicsSeminar/15
DESCRIPTION:Title: Large orbit closures of translation surfaces are strata or
loci of double covers\, Lecture 4/5\nby Paul Apisa\, Alex Wright (Uni
versity of Michigan) as part of Pacific dynamics seminar\n\n\nAbstract\nAn
y translation surface can be presented as a collection of polygons in the
plane with sides identified. By acting linearly on the polygons\, we obtai
n an action of GL(2\,R) on moduli spaces of translation surfaces. Recent w
ork of Eskin\, Mirzakhani\, and Mohammadi showed that $\\mathrm{GL}(2\,\\m
athbb{R})$ orbit closures are locally described by linear equations on the
edges of the polygons. However\, which linear manifolds arise this way is
mysterious.\n\nIn this lecture series\, we will describe new joint work t
hat shows that when an orbit closure is sufficiently large it must be a wh
ole moduli space\, called a stratum in this context\, or a locus defined b
y rotation by $\\pi$ symmetry.\n\nWe define "sufficiently large" in terms
of rank\, which is the most important numerical invariant of an orbit clos
ure\, and is an integer between $1$ and the genus $g$. Our result applies
when the rank is at least $1+g/2$\, and so handles roughly half of the pos
sible values of rank.\n\nLecture 4: An overview of the proof of the main t
heorem\; marked points (following the preprint “Marked Points on Transla
tion Surfaces”)\; and a dichotomy for cylinder degenerations.\n\nFor the
other lectures see https://www.math.ubc.ca/~lior/sem/WCDS.html#talk12\n
LOCATION:https://researchseminars.org/talk/PacificDynamicsSeminar/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Paul Apisa\, Alex Wright (University of Michigan)
DTSTART:20210218T220000Z
DTEND:20210218T233000Z
DTSTAMP:20260422T225726Z
UID:PacificDynamicsSeminar/16
DESCRIPTION:Title: Large orbit closures of translation surfaces are strata or
loci of double covers: Lecture 5/5\nby Paul Apisa\, Alex Wright (Univ
ersity of Michigan) as part of Pacific dynamics seminar\n\n\nAbstract\nAny
translation surface can be presented as a collection of polygons in the p
lane with sides identified. By acting linearly on the polygons\, we obtain
an action of GL(2\,R) on moduli spaces of translation surfaces. Recent wo
rk of Eskin\, Mirzakhani\, and Mohammadi showed that $\\mathrm{GL}(2\,\\ma
thbb{R})$ orbit closures are locally described by linear equations on the
edges of the polygons. However\, which linear manifolds arise this way is
mysterious.\n\nIn this lecture series\, we will describe new joint work th
at shows that when an orbit closure is sufficiently large it must be a who
le moduli space\, called a stratum in this context\, or a locus defined by
rotation by $\\pi$ symmetry.\n\nWe define "sufficiently large" in terms o
f rank\, which is the most important numerical invariant of an orbit closu
re\, and is an integer between $1$ and the genus $g$. Our result applies w
hen the rank is at least $1+g/2$\, and so handles roughly half of the poss
ible values of rank.\n\nLecture 5: Completion of the proof of the main the
orem.\n\nFor the other lectures see https://www.math.ubc.ca/~lior/sem/WCDS.html#talk12<
/a>\n
LOCATION:https://researchseminars.org/talk/PacificDynamicsSeminar/16/
END:VEVENT
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