BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Nattalie Tamam (UCSD) DTSTART:20200423T210000Z DTEND:20200423T223000Z DTSTAMP:20260404T111007Z UID:PacificDynamicsSeminar/1 DESCRIPTION:Title: Effective equidistribution of horospherical flows in infinite volume\nby Nattalie Tamam (UCSD) as part of Pacific dynamics seminar\n\n\nAbstract\nThe horospherical flow on finite-volume hyperbolic surfaces is well-understood. In particular\, effective equidistribution o f non-closed horospherical orbits is known. New difficulties arise when st udying the infinite-volume setting. We will discuss the setting in finite- and infinite-volume manifolds\, and the measures that play a crucial role in the latter. Joint work with Jacqueline Warren.\n\nThe first 45 minute s will be targeted at beginning graduate students\; the second 45 minutes will be more technical.\n LOCATION:https://stable.researchseminars.org/talk/PacificDynamicsSeminar/1 / END:VEVENT BEGIN:VEVENT SUMMARY:Lior Silberman (The University of British Columbia) DTSTART:20200430T210000Z DTEND:20200430T223000Z DTSTAMP:20260404T111007Z UID:PacificDynamicsSeminar/2 DESCRIPTION:Title: Quantum Unique Ergodicity\nby Lior Silberman (Th e University of British Columbia) as part of Pacific dynamics seminar\n\n\ nAbstract\nIn the first half I'll give a colloquium-style introduction to the equidistribution problem for Laplace eigenfucntions on Riemannian mani folds\, with emphasis on the locally symmetric spaces. I will introduce p ositive results for exact eigenfunctions (with and without reference to th e number-theoretic symmetries of the manifold)\, and negative results for approximate 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 audien ce.\n\nThe first 45 minutes will be targeted at beginning graduate student s\; the second 45 minutes will be more technical.\n LOCATION:https://stable.researchseminars.org/talk/PacificDynamicsSeminar/2 / END:VEVENT BEGIN:VEVENT SUMMARY:Sophie MacDonald (The University of British Columbia) DTSTART:20200507T210000Z DTEND:20200507T223000Z DTSTAMP:20260404T111007Z UID:PacificDynamicsSeminar/3 DESCRIPTION:Title: Factors of Gibbs measures on subshifts\nby Sophi e MacDonald (The University of British Columbia) as part of Pacific dynami cs seminar\n\n\nAbstract\nClassical results of Dobrushin and Lanford-Ruell e establish\, in rough terms\,\nthat for a local energy function on a subs hift without too much long-range\norder\, the translation-invariant Gibbs measures are precisely the\nequilibrium measures. There are multiple defin itions of a Gibbs measure in\nthe literature\, which do not always coincid e. We will discuss two of these\ndefinitions\, one introduced by Capocacci a and the other used by\nDobrushin-Lanford-Ruelle\, and outline a proof (a vailable at\nhttps://arxiv.org/abs/2003.05532) that they are equivalent.\n \nWe will also discuss forthcoming work\, in which we show that Gibbsianne ss is\npreserved by pushforward through a certain kind of almost invertibl e factor\nmap. As an application in one dimension\, we show that for a suf ficiently\nregular potential\, any equilibrium measure on an irreducible s ofic shift is\nGibbs. As far as we know\, this is the first reasonably gen eral result of the\nLanford-Ruelle type for a class of subshifts without t he topological Markov\nproperty.\n\nJoint work with Luísa Borsato\, with extensive advice from Brian Marcus and\nTom Meyerovitch.\n\nParticipants s hould go over the slides or listen to the recorded presentation ahead of t ime (see links above). The meeting will be devoted to questions and discu ssion.\n LOCATION:https://stable.researchseminars.org/talk/PacificDynamicsSeminar/3 / END:VEVENT BEGIN:VEVENT SUMMARY:Anthony Sanchez (University of Washington) DTSTART:20200514T210000Z DTEND:20200514T223000Z DTSTAMP:20260404T111007Z UID:PacificDynamicsSeminar/4 DESCRIPTION:Title: Gaps of saddle connection directions for some branch ed covers of tori\nby Anthony Sanchez (University of Washington) as pa rt of Pacific dynamics seminar\n\n\nAbstract\nTranslation surfaces given b y gluing two identical tori along\na slit have genus two and two cone-type singularities of angle $4\\pi$.\nThere is a distinguished set of trajecto ries called saddle connections that\nare the straight lines trajectories b etween cone points. We can\nassociate a *holonomy vector* in the plane to each saddle connection whose components are the\nhorizontal and vertical d isplacement of the saddle connection. How random\nis the planar set of hol onomy of saddle connections? We study this question\nby computing the *gap distribution* for slopes of saddle connections for\nthese and other relat ed classes of translation surfaces.\n\nThe first 45 minutes will be target ed at beginning graduate students\; the second 45 minutes will be more tec hnical.\n LOCATION:https://stable.researchseminars.org/talk/PacificDynamicsSeminar/4 / END:VEVENT BEGIN:VEVENT SUMMARY:Ian Putnam (University of Victoria) DTSTART:20200521T210000Z DTEND:20200521T223000Z DTSTAMP:20260404T111007Z UID:PacificDynamicsSeminar/5 DESCRIPTION:Title: A Bratteli-Vershik model for $\\mathbb{Z}^2$ actions \, or how cohomology can help us make dynamical systems\nby Ian Putnam (University of Victoria) as part of Pacific dynamics seminar\n\n\nAbstrac t\nThe Bratteli-Vershik model is a method of producing minimal actions of the integers on a Cantor set. It was given by myself\, Rich Herman and Chr is Skau\, building on seminal ideas of Anatoly Vershik\, over 30 years ago . Rather disappointingly and surprisingly\, there isn't a good version for $\\mathbb{Z}^2$ actions. I'll report on a new outlook on the problem and recent progress with Thierry Giordano (Ottawa) and Christian Skau (Trondhe im). The new outlook focuses on the model as an answer to the question: wh ich cohomological invariants can arise from such actions? I will not assum e any familiarity with either the original model or the cohomology. The fi rst half of the talk will be a gentle introduction to the $\\mathbb{Z}$-ca se 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 beginn ing graduate students\; the second 45 minutes may be more technical.\n LOCATION:https://stable.researchseminars.org/talk/PacificDynamicsSeminar/5 / END:VEVENT BEGIN:VEVENT SUMMARY:Jon Chaika (University of Utah) DTSTART:20200611T210000Z DTEND:20200611T223000Z DTSTAMP:20260404T111007Z 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\nAbstract\nThis main result of this talk is that there exists a billi ard flow in a polygon that is weakly mixing with respect to Lebesgue measu re on the unit tangent bundle to the billiard. This strengthens Kerckhoff\ , Masur and Smillie's result that there exists ergodic billiard flows in p olygons. The existence of a weakly mixing billiard follows\, via a Baire c ategory argument\, from showing that for any translation surface the produ ct of the flows in almost every pair of directions is ergodic with respect to Lebesgue measure. This in turn is proven by showing that for every tra nslation surface the flows in almost every pair of directions do not share non-trivial common eigenvalues. This talk will explain the problem\, rela ted results\, and approach. The talk will not assume familiarity with tran slation surfaces. This is joint work with Giovanni Forni.\n LOCATION:https://stable.researchseminars.org/talk/PacificDynamicsSeminar/6 / END:VEVENT BEGIN:VEVENT SUMMARY:Samantha Fairchild (University of Washington) DTSTART:20200618T210000Z DTEND:20200618T223000Z DTSTAMP:20260404T111007Z UID:PacificDynamicsSeminar/7 DESCRIPTION:Title: Counting social interactions for discrete subsets of the plane\nby Samantha Fairchild (University of Washington) as part o f Pacific dynamics seminar\n\n\nAbstract\nGiven a discrete subset $V$ in t he plane\, how many points would you expect there to be in a ball of radiu s $100$? What if the radius is $10\,000$? Due to the results of Fairchild and forthcoming work with Burrin\, when $V$ arises as orbits of non-unifor m lattice subgroups of $\\mathrm{SL}(2\,\\mathbb{R})$\, we can understand asymptotic growth rate with error terms of the number of points in $V$ for a broad family of sets. A crucial aspect of these arguments and similar a rguments is understanding how to count pairs of saddle connections with ce rtain properties determining the interactions between them\, like having a fixed determinant or having another point in $V$ nearby.\n\nWe will spend the first 40 minutes discussing how these sets arise and counting results arise from the study of concrete translation surfaces. The following 40 m inutes will be spent highlighting the proof strategy used to obtain these results\, and advertising the generality and strength of this argument tha t arises from the computation of all higher moments of the Siegel--Veech t ransform over quotients of $\\mathrm{SL}(2\,\\mathbb{R})$ by non-uniform l attices.\n LOCATION:https://stable.researchseminars.org/talk/PacificDynamicsSeminar/7 / END:VEVENT BEGIN:VEVENT SUMMARY:Taylor McAdam (Yale University) DTSTART:20200528T210000Z DTEND:20200528T223000Z DTSTAMP:20260404T111007Z UID:PacificDynamicsSeminar/8 DESCRIPTION:Title: Almost-prime times in horospherical flows\nby Ta ylor McAdam (Yale University) as part of Pacific dynamics seminar\n\n\nAbs tract\nThere is a rich connection between homogeneous dynamics and number theory. Often in such applications it is desirable for dynamical results t o be effective (i.e. the rate of convergence for dynamical phenomena are k nown). In the first part of this talk\, I will provide the necessary backg round and relevant history to state an effective equidistribution result f or horospherical flows on the space of unimodular lattices in $\\mathbb{R} ^n$. I will then describe an application to studying the distribution of a lmost-prime times (integer times having fewer than a fixed number of prime factors) in horospherical orbits and discuss connections of this work to Sarnak’s Möbius disjointness conjecture. In the second part of the talk I will describe some of the ingredients and key steps that go into provin g these results.\n\nThe first 45 minutes are targeted at beginning graduat e students\; the second 45 minutes may be more technical.\n LOCATION:https://stable.researchseminars.org/talk/PacificDynamicsSeminar/8 / END:VEVENT BEGIN:VEVENT SUMMARY:Pablo Shmerkin (T. Di Tella University and Conicet) DTSTART:20200604T200000Z DTEND:20200604T213000Z DTSTAMP:20260404T111007Z UID:PacificDynamicsSeminar/9 DESCRIPTION:Title: Arithmetic and geometric properties of planar self-s imilar sets\nby Pablo Shmerkin (T. Di Tella University and Conicet) as part of Pacific dynamics seminar\n\n\nAbstract\nFurstenberg's conjecture on the dimension of the intersection of $\\times2\,\\times3$-invariant Can tor sets can be restated as a bound on the dimension of linear slices of t he product of $\\times2\,\\times3$-Cantor sets\, which is a self-affine se t in the plane. I will discuss some older and newer variants of this\, whe re the self-affine set is replaced by a self-similar set such as the Sierp inski triangle\, Sierpinski carpet or (support of) a complex Bernoulli con volution. Among other things\, I will show that the intersection of the Si erpinski carpet with circles has small dimension\, but on the other hand t he Sierpinski carpet can be covered very efficiently by linear tubes (neig hborhoods of lines). The latter fact is a recent result joint with A. Pyö rälä\, 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://stable.researchseminars.org/talk/PacificDynamicsSeminar/9 / END:VEVENT BEGIN:VEVENT SUMMARY:Rodrigo Treviño (University of Maryland) DTSTART:20200702T210000Z DTEND:20200702T223000Z DTSTAMP:20260404T111007Z UID:PacificDynamicsSeminar/10 DESCRIPTION:Title: Quantitative weak mixing for random substitution ti lings\nby Rodrigo Treviño (University of Maryland) as part of Pacific dynamics seminar\n\n\nAbstract\n"Quantitative weak mixing" is the term us ed to bound the dimensions of spectral measures of a measure-preserving sy stem. This type of study has gained popularity over the last decade\, led by a series of results of Bufetov and Solomyak for a large class of flows which include general one-dimensional tiling spaces as well as translation flows on flat surfaces\, as well as results on quantitative weak mixing b y Forni. In this talk I will present results which extend the results for flows to higher rank parabolic actions\, focusing on quantitative results for a broad class of tilings in any dimension. The talk won't assume famil iarity with almost anything\, so I will define all objects in consideratio n.\n LOCATION:https://stable.researchseminars.org/talk/PacificDynamicsSeminar/1 0/ END:VEVENT BEGIN:VEVENT SUMMARY:Ping Ngai (Brian) Chung (University of Chicago) DTSTART:20200709T210000Z DTEND:20200709T223000Z DTSTAMP:20260404T111007Z UID:PacificDynamicsSeminar/11 DESCRIPTION:Title: Stationary measure and orbit closure classification for random walks on surfaces\nby Ping Ngai (Brian) Chung (University of Chicago) as part of Pacific dynamics seminar\n\n\nAbstract\nWe study th e problem of classifying stationary measures and orbit closures for non-ab elian action on surfaces. Using a result of Brown and Rodriguez Hertz\, we show that under a certain average growth condition\, the orbit closures a re either finite or dense. Moreover\, every infinite orbit equidistributes on the surface. This is analogous to the results of Benoist-Quint and Esk in-Lindenstrauss in the homogeneous setting\, and the result of Eskin-Mirz akhani in the setting of moduli spaces of translation surfaces.\n\nWe then consider the problem of verifying this growth condition in concrete setti ngs. In particular\, we apply the theorem to two settings\, namely discret e perturbations of the standard map and the $\\mathrm{Out}(F_2)$-action on a certain character variety. We verify the growth condition analytically in the former setting\, and verify numerically in the latter setting.\n LOCATION:https://stable.researchseminars.org/talk/PacificDynamicsSeminar/1 1/ END:VEVENT BEGIN:VEVENT SUMMARY:Paul Apisa\, Alex Wright (University of Michigan) DTSTART:20210121T223000Z DTEND:20210121T233000Z DTSTAMP:20260404T111007Z UID:PacificDynamicsSeminar/12 DESCRIPTION:Title: Large orbit closures of translation surfaces are st rata or loci of double covers\, Lecture 1/5\nby Paul Apisa\, Alex Wrig ht (University of Michigan) as part of Pacific dynamics seminar\n\n\nAbstr act\nAny translation surface can be presented as a collection of polygons in the plane with sides identified. By acting linearly on the polygons\, w e obtain an action of GL(2\,R) on moduli spaces of translation surfaces. R ecent work of Eskin\, Mirzakhani\, and Mohammadi showed that $\\mathrm{GL} (2\,\\mathbb{R})$ 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 that shows that when an orbit closure is sufficiently large it must be a whole moduli space\, called a stratum in this context\, or a locus de fined by rotation by $\\pi$ symmetry.\n\nWe define "sufficiently large" in terms of rank\, which is the most important numerical invariant of an orb it closure\, and is an integer between $1$ and the genus $g$. Our result a pplies when the rank is at least $1+g/2$\, and so handles roughly half of the possible values of rank.\n\nLecture 1: An introduction to orbit closur es\, their rank\, their boundary in the WYSIWYG partial compactification\, and cylinder deformations.\n\nFor the other lectures see https://www.math.ubc.ca/~lior /sem/WCDS.html#talk12\n LOCATION:https://stable.researchseminars.org/talk/PacificDynamicsSeminar/1 2/ END:VEVENT BEGIN:VEVENT SUMMARY:Paul Apisa\, Alex Wright (University of Michigan) DTSTART:20210128T220000Z DTEND:20210128T233000Z DTSTAMP:20260404T111007Z UID:PacificDynamicsSeminar/13 DESCRIPTION:Title: Large orbit closures of translation surfaces are st rata or loci of double covers\, Lecture 2/5\nby Paul Apisa\, Alex Wrig ht (University of Michigan) as part of Pacific dynamics seminar\n\n\nAbstr act\nAny translation surface can be presented as a collection of polygons in the plane with sides identified. By acting linearly on the polygons\, w e obtain an action of GL(2\,R) on moduli spaces of translation surfaces. R ecent work of Eskin\, Mirzakhani\, and Mohammadi showed that $\\mathrm{GL} (2\,\\mathbb{R})$ 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 that shows that when an orbit closure is sufficiently large it must be a whole moduli space\, called a stratum in this context\, or a locus de fined by rotation by $\\pi$ symmetry.\n\nWe define "sufficiently large" in terms of rank\, which is the most important numerical invariant of an orb it closure\, and is an integer between $1$ and the genus $g$. Our result a pplies when the rank is at least $1+g/2$\, and so handles roughly half of the possible values of rank.\n\nLecture 2: Reconstructing orbit closures f rom their boundaries (this talk will explicate a preprint of the same name ).\n\nFor the other lectures see https://www.math.ubc.ca/~lior/sem/WCDS.html#talk12 \n LOCATION:https://stable.researchseminars.org/talk/PacificDynamicsSeminar/1 3/ END:VEVENT BEGIN:VEVENT SUMMARY:Paul Apisa\, Alex Wright (University of Michigan) DTSTART:20210204T220000Z DTEND:20210204T233000Z DTSTAMP:20260404T111007Z UID:PacificDynamicsSeminar/14 DESCRIPTION:Title: Large orbit closures of translation surfaces are st rata or loci of double covers\, Lecture 3/5\nby Paul Apisa\, Alex Wrig ht (University of Michigan) as part of Pacific dynamics seminar\n\n\nAbstr act\nAny translation surface can be presented as a collection of polygons in the plane with sides identified. By acting linearly on the polygons\, w e obtain an action of GL(2\,R) on moduli spaces of translation surfaces. R ecent work of Eskin\, Mirzakhani\, and Mohammadi showed that $\\mathrm{GL} (2\,\\mathbb{R})$ 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 that shows that when an orbit closure is sufficiently large it must be a whole moduli space\, called a stratum in this context\, or a locus de fined by rotation by $\\pi$ symmetry.\n\nWe define "sufficiently large" in terms of rank\, which is the most important numerical invariant of an orb it closure\, and is an integer between $1$ and the genus $g$. Our result a pplies when the rank is at least $1+g/2$\, and so handles roughly half of the possible values of rank.\n\nLecture 3: Recognizing loci of covers usin g cylinders (this talk will follow a preprint titled “Generalizations of the Eierlegende-Wollmilchsau”).\n\nFor the other lectures see https://www.math.ubc.c a/~lior/sem/WCDS.html#talk12\n LOCATION:https://stable.researchseminars.org/talk/PacificDynamicsSeminar/1 4/ END:VEVENT BEGIN:VEVENT SUMMARY:Paul Apisa\, Alex Wright (University of Michigan) DTSTART:20210211T223000Z DTEND:20210211T233000Z DTSTAMP:20260404T111007Z UID:PacificDynamicsSeminar/15 DESCRIPTION:Title: Large orbit closures of translation surfaces are st rata or loci of double covers\, Lecture 4/5\nby Paul Apisa\, Alex Wrig ht (University of Michigan) as part of Pacific dynamics seminar\n\n\nAbstr act\nAny translation surface can be presented as a collection of polygons in the plane with sides identified. By acting linearly on the polygons\, w e obtain an action of GL(2\,R) on moduli spaces of translation surfaces. R ecent work of Eskin\, Mirzakhani\, and Mohammadi showed that $\\mathrm{GL} (2\,\\mathbb{R})$ 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 that shows that when an orbit closure is sufficiently large it must be a whole moduli space\, called a stratum in this context\, or a locus de fined by rotation by $\\pi$ symmetry.\n\nWe define "sufficiently large" in terms of rank\, which is the most important numerical invariant of an orb it closure\, and is an integer between $1$ and the genus $g$. Our result a pplies when the rank is at least $1+g/2$\, and so handles roughly half of the possible values of rank.\n\nLecture 4: An overview of the proof of the main theorem\; marked points (following the preprint “Marked Points on Translation Surfaces”)\; and a dichotomy for cylinder degenerations.\n\n For the other lectures see https://www.math.ubc.ca/~lior/sem/WCDS.html#talk12\n LOCATION:https://stable.researchseminars.org/talk/PacificDynamicsSeminar/1 5/ END:VEVENT BEGIN:VEVENT SUMMARY:Paul Apisa\, Alex Wright (University of Michigan) DTSTART:20210218T220000Z DTEND:20210218T233000Z DTSTAMP:20260404T111007Z UID:PacificDynamicsSeminar/16 DESCRIPTION:Title: Large orbit closures of translation surfaces are st rata or loci of double covers: Lecture 5/5\nby Paul Apisa\, Alex Wrigh t (University of Michigan) as part of Pacific dynamics seminar\n\n\nAbstra ct\nAny translation surface can be presented as a collection of polygons i n the plane with sides identified. By acting linearly on the polygons\, we obtain an action of GL(2\,R) on moduli spaces of translation surfaces. Re cent work of Eskin\, Mirzakhani\, and Mohammadi showed that $\\mathrm{GL}( 2\,\\mathbb{R})$ 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 that shows that when an orbit closure is sufficiently large it must b e a whole moduli space\, called a stratum in this context\, or a locus def ined by rotation by $\\pi$ symmetry.\n\nWe define "sufficiently large" in terms of rank\, which is the most important numerical invariant of an orbi t closure\, and is an integer between $1$ and the genus $g$. Our result ap plies when the rank is at least $1+g/2$\, and so handles roughly half of t he possible values of rank.\n\nLecture 5: Completion of the proof of the m ain theorem.\n\nFor the other lectures see https://www.math.ubc.ca/~lior/sem/WCDS.html# talk12\n LOCATION:https://stable.researchseminars.org/talk/PacificDynamicsSeminar/1 6/ END:VEVENT END:VCALENDAR