BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Aimee Johnson (Swarthmore) DTSTART:20210220T190000Z DTEND:20210220T200000Z DTSTAMP:20260404T110824Z UID:Dynamics/1 DESCRIPTION:Title: Thresholds in Complexity\nby Aimee Johnson (Swarthmore) as par t of Little school dynamics\n\n\nAbstract\nA celebrated result of Morse an d Hedlund in 1938 established a link between the complexity function assoc iated to a bi-infinite sequence of symbols and the periodicity of that seq uence. In this talk we will continue this investigation\, looking at when complexity can yield information about a symbolic system. Spoiler alert: it turns out that it can tell us something about the property of loosely Bernoulli.\n\nWe will review notation and definitions\, go over some past results in this area\, and then culminate in a recent result done jointly with Van Cyr\, Bryna Kra\, and Ayse Sahin.\n LOCATION:https://stable.researchseminars.org/talk/Dynamics/1/ END:VEVENT BEGIN:VEVENT SUMMARY:Jim Wiseman (Agnes Scott College) DTSTART:20210814T180000Z DTEND:20210814T190000Z DTSTAMP:20260404T110824Z UID:Dynamics/2 DESCRIPTION:Title: Persistence for finite-resolution dynamics\nby Jim Wiseman (Ag nes Scott College) as part of Little school dynamics\n\n\nAbstract\nTo stu dy the dynamics of a continuous self-map on a metric space\, we can use a finite-resolution approximation of the map. But the dynamics of the approx imation depend on the choice of resolution. We study the persistence -- a notion from topological data analysis -- of the dynamics as the resolution changes\, in particular of the Morse decomposition of the recurrent set.\ n LOCATION:https://stable.researchseminars.org/talk/Dynamics/2/ END:VEVENT BEGIN:VEVENT SUMMARY:Arek Goetz (SFSU) DTSTART:20210911T180000Z DTEND:20210911T190000Z DTSTAMP:20260404T110824Z UID:Dynamics/3 DESCRIPTION:Title: The microscopic world of piecewise isometries\nby Arek Goetz ( SFSU) as part of Little school dynamics\n\n\nAbstract\nIn this talk we inv ite the audience to witness how a rigid\nexchange of two or more regions l eads to strikingly complicated and\nbeautiful dynamics in the plane. A ric h landscape of phenomena is due\nto the presence of discontinuities that p ropagate forming patterns\nthat appear to be self similar. We present exam ples for which the\nlocal dynamics is not well understood as well as major open questions\nin this field some of which may be of interest to student s in\nprimarily undergraduate institutions.\n\nExamples of such maps are d ual billiards and invertible rotations of\ntwo half-planes.\n\nThe present ation will be accessible to an audience without familiarity\nwith advanced dynamical tools.\n LOCATION:https://stable.researchseminars.org/talk/Dynamics/3/ END:VEVENT BEGIN:VEVENT SUMMARY:Dave Constantine (Wesleyan) DTSTART:20211009T180000Z DTEND:20211009T190000Z DTSTAMP:20260404T110824Z UID:Dynamics/4 DESCRIPTION:Title: Geodesic flows on locally CAT(-1) spaces\nby Dave Constantine (Wesleyan) as part of Little school dynamics\n\n\nAbstract\nGeodesic flows on compact\, negatively curved Riemannian manifolds famously have lots of extremely nice dynamical properties. To what extent do those properties hold for geodesic flows on metric spaces that are negatively curved? In th is talk I'll discuss how we can consider geodesic flows on general metric spaces\, and then discuss some results on the geodesic flow of a compact\, locally CAT(-1) space. It turns out that the CAT(-1) condition is suffic ient for us to recover many nice properties. This is joint work with Jean- Francois Lafont and Daniel Thompson.\n LOCATION:https://stable.researchseminars.org/talk/Dynamics/4/ END:VEVENT BEGIN:VEVENT SUMMARY:Cesar Silva (Williams College) DTSTART:20211113T190000Z DTEND:20211113T200000Z DTSTAMP:20260404T110824Z UID:Dynamics/5 DESCRIPTION:Title: "Characterizations of rank-one transformations that factor onto an odometer\, or are isomorphic to an odometer\nby Cesar Silva (Williams College) as part of Little school dynamics\n\n\nAbstract\nWe will start b y discussing rank-one transformations and odometer transformations\, and r eview the isomorphism problem in ergodic theory. We will then present exp licit characterizations\, based on the cutting and spacer parameters of th e rank-one transformation\, of (a) which rank-one transformations factor o nto a given finite cyclic permutation\, (b) which rank-one transformations factor onto a given odometer\, and (c) which rank-one transformations are isomorphic to a given odometer. These naturally yield characterizations o f (d) which rank-one transformations factor onto some (unspecified) finite cyclic permutation\, (e) which rank-one transformations factor onto some (unspecified) odometer\, and (f) which rank-one transformations are isomo rphic to some (unspecified) odometer. This is joint work with Matthew For eman\, Su Gao\, Aaron Hill\, and Benjamin Weiss.\n LOCATION:https://stable.researchseminars.org/talk/Dynamics/5/ END:VEVENT BEGIN:VEVENT SUMMARY:Heather Zinn-Brooks (Harvey Mudd) DTSTART:20211211T190000Z DTEND:20211211T200000Z DTSTAMP:20260404T110824Z UID:Dynamics/6 DESCRIPTION:Title: Bounded-confidence models for opinion dynamics on networks\nby Heather Zinn-Brooks (Harvey Mudd) as part of Little school dynamics\n\n\n Abstract\nOnline social media networks have become extremely influential s ources of news and information. Given the large audience and the ease of s haring content online\, the content that spreads on online social networks can have important consequences on public opinion\, policy\, and voting. To better understand the online content spread\, mathematical modeling of opinion dynamics is becoming an increasingly popular field of study. In th is talk\, I will introduce you to a special class of models of opinion dyn amics on networks called bounded-confidence models. I will then discuss so me of the applications and theory that my collaborators and I have been de veloping with these models\, including the impact of media\, opinion disse mination\, mean-field dynamics\, and extensions to hypergraphs and multila yer networks. This talk will also include some unsolved questions for futu re work.\n LOCATION:https://stable.researchseminars.org/talk/Dynamics/6/ END:VEVENT BEGIN:VEVENT SUMMARY:Jasper Weinburd (Harvey Mudd College) DTSTART:20220312T190000Z DTEND:20220312T200000Z DTSTAMP:20260404T110824Z UID:Dynamics/7 DESCRIPTION:Title: Collective Behavior in Locust Swarms from Differential Equations t o Data\nby Jasper Weinburd (Harvey Mudd College) as part of Little sch ool dynamics\n\n\nAbstract\nLocusts are devastating pests that infest and destroy crops. Locusts forage and migrate in\nlarge swarms which exhibit d istinctive shapes that improve efficiency on the group level\, a\nphenomen on known as collective behavior. One of the difficulties in understanding and preventing\nthese collective behaviors has been a lack of biological d ata for individual interactions between\nlocusts. In this talk\, I’ll fi rst describe mathematical models for these phenomena on both the\ncollecti ve and individual levels. I’ll then discuss a collaboration with undergr aduate students that\nuse field data derived from video footage of locust swarms. We digitized nearly 20\,000 locust\ntrajectories and revealed indi vidual behaviors that depend on a locust’s motion and the relative\nposi tion of its nearby neighbors. Finally\, I will illustrate the challenges a nd potential benefits of\nincorporating these field observations into our models of locust swarms.\n LOCATION:https://stable.researchseminars.org/talk/Dynamics/7/ END:VEVENT BEGIN:VEVENT SUMMARY:Andy Parrish (Eastern Illinois University) DTSTART:20220514T180000Z DTEND:20220514T190000Z DTSTAMP:20260404T110824Z UID:Dynamics/8 DESCRIPTION:Title: Good and Bad Functions for Translates\nby Andy Parrish (Easter n Illinois University) as part of Little school dynamics\n\n\nAbstract\nWe say that a set of functions is good for a sequence of\noperators if the s equence converges for every function in the set\; the\nset is bad if there is a function in the set for which the sequence of\noperators does not co nverge. For example\, given a fixed sequence\ntending to zero\, the contin uous functions are pointwise good for\ntranslations by this sequence-- yet bounded Lebesgue-measurable\nfunctions are pointwise bad. We'll discuss h ow the set of functions\nthat are pointwise good for translation by any se quence is precisely\nthe set of functions locally equal a.e. to a Riemann- integrable\nfunction. Time permitting\, we will also explore some new pers pectives\non a well-known conjecture due to Erdos. This is joint work with \nJoseph Rosenblatt (UIUC).\n LOCATION:https://stable.researchseminars.org/talk/Dynamics/8/ END:VEVENT BEGIN:VEVENT SUMMARY:May Mei (Denison) DTSTART:20220813T180000Z DTEND:20220813T190000Z DTSTAMP:20260404T110824Z UID:Dynamics/9 DESCRIPTION:Title: Adventures in Mutual Local Derivability\nby May Mei (Denison) as part of Little school dynamics\n\n\nAbstract\nTwo tilings are said to b e mutually locally derivable (MLD)\nif each can be obtained from the other using local rules. From many\nperspective\, two MLD tilings can be though t of as "the same."\nHowever\, local derivability greatly impacts the adja cency relationship\nbetween tiles\, which leads to the potential for adven ture. Put on your\nexplorer hats\, in this talk we present results on eige nfunctions of\nthe discrete Laplace operator and on playing the Game of Li fe on\ndifferent manifestations of the Penrose tiling.\n LOCATION:https://stable.researchseminars.org/talk/Dynamics/9/ END:VEVENT BEGIN:VEVENT SUMMARY:Joanna Furno (University of South Alabama) DTSTART:20220910T180000Z DTEND:20220910T190000Z DTSTAMP:20260404T110824Z UID:Dynamics/10 DESCRIPTION:Title: Polynomial Families Converging to a Family with an Exponential Ma p\nby Joanna Furno (University of South Alabama) as part of Little sch ool dynamics\n\n\nAbstract\nIn joint work with Devin Becker and Lorelei Ko ss\, we explore\nthe convergence of polynomial families to families that a re a product\nof a power map and the exponential. This exploration encompa sses the\nconvergence of Julia sets in dynamical space and convergence in\ nhyperbolic components of parameter space.\n LOCATION:https://stable.researchseminars.org/talk/Dynamics/10/ END:VEVENT BEGIN:VEVENT SUMMARY:Drew Ash (Albion College) DTSTART:20221008T180000Z DTEND:20221008T190000Z DTSTAMP:20260404T110824Z UID:Dynamics/11 DESCRIPTION:Title: Introduction to Bratteli Diagrams and Bounded Topological Speedup s\nby Drew Ash (Albion College) as part of Little school dynamics\n\n\ nAbstract\nGiven a dynamical system $(X\,T)$\, one can define a speedup\no f $(X\,T)$ as another dynamical system $S: X → X$ where $S= T^{p(·)}$\n for some $p: X → Z^+$. In this talk\, we will focus on bounded\ntopologi cal speedups of minimal Cantor systems. Specifically\, we\nrequire that ou r “jump function” $p$ be bounded and hence continuous.\nOur motivating question is: What\, if anything\, can be preserved with\nthe added struct ure of p being bounded? To do so\, we introduce\nKakutani-Rokhlin towers a nd Bratteli diagrams as ways of visualizing\nthe dynamics of minimal Canto r systems. Then we will illustrate a\nnovel construction of a Bratteli dia gram for $(X\,S)$ given a Bratteli\ndiagram for $(X\,T)$. We will conclude the talk with an brief\napplication of this constructions as well as disc uss various open\nproblems inspired by this construction. The work present ed is joint\nwork with Andrew Dykstra and Michelle LeMasurier\, both of Ha milton\nCollege.\n LOCATION:https://stable.researchseminars.org/talk/Dynamics/11/ END:VEVENT BEGIN:VEVENT SUMMARY:E. Cabral Balreira (Trinity University) DTSTART:20221112T190000Z DTEND:20221112T200000Z DTSTAMP:20260404T110824Z UID:Dynamics/12 DESCRIPTION:Title: Geometric ideas on global stability and monotonicity for discrete systems\nby E. Cabral Balreira (Trinity University) as part of Little school dynamics\n\n\nAbstract\nIt is an important problem in discrete dyn amics to\ndetermine when local stability of fixed points implies global\ns tability. We will focus on the planar Ricker competition model and\nintrod uce ideas from singularity theory to describe the dynamics of\nthe images of the critical curves to show that local stability of the\ncoexistence (p ositive) fixed point implies global stability. The\nintroduction of geomet ric methods will allow us to revisit the notion\nof monotonicity and devel op a geometric generalization for the notion\nof monotonicity (or competit ive) maps in higher dimensions. We show\nthat this definition is equivalen t for known results for planar maps\nand provide analytic conditions to ch eck for geometric monotonicity\nand global stability. We illustrate our re sults with the Beverton-Holt\nand Ricker competition map.\n LOCATION:https://stable.researchseminars.org/talk/Dynamics/12/ END:VEVENT BEGIN:VEVENT SUMMARY:James Kelly (Christopher Newport University) DTSTART:20221210T190000Z DTEND:20221210T200000Z DTSTAMP:20260404T110824Z UID:Dynamics/13 DESCRIPTION:Title: Chaos and entropy in linear dynamical system\nby James Kelly (Christopher Newport University) as part of Little school dynamics\n\n\nAb stract\nWe discuss various notions of chaos in the context of linear\ndyna mics. Many types of chaos (for linear operators) can only occur\nwithin in finite dimensional vector spaces. Two specific categories of\nthese spaces on which we focus are weighted sequence spaces and\nfunction spaces\, and the natural operators on these spaces are\nbackward shifts and translatio ns (respectively). We discuss\nrelationships between the types of chaos fo r these operators and\ncharacterizations for them in terms of the weight s equence/function.\nMore generally\, we examine how chaos and entropy relat e to the\neigenvalues of the operator. Throughout\, we highlight recent an d\ncurrent projects completed with undergraduate students.\n LOCATION:https://stable.researchseminars.org/talk/Dynamics/13/ END:VEVENT END:VCALENDAR