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:20260422T225703Z UID:Dynamics/1 DESCRIPTION:Title: Thresholds in Complexity\nby Aimee Johnson (Swarthmore) as part of Li ttle school dynamics\n\n\nAbstract\nA celebrated result of Morse and Hedlu nd in 1938 established a link between the complexity function associated t o a bi-infinite sequence of symbols and the periodicity of that sequence. In this talk we will continue this investigation\, looking at when comple xity can yield information about a symbolic system. Spoiler alert: it tur ns out that it can tell us something about the property of loosely Bernoul li.\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 Va n Cyr\, Bryna Kra\, and Ayse Sahin.\n LOCATION:https://researchseminars.org/talk/Dynamics/1/ END:VEVENT BEGIN:VEVENT SUMMARY:Jim Wiseman (Agnes Scott College) DTSTART:20210814T180000Z DTEND:20210814T190000Z DTSTAMP:20260422T225703Z UID:Dynamics/2 DESCRIPTION:Title: Persistence for finite-resolution dynamics\nby Jim Wiseman (Agnes Sco tt College) as part of Little school dynamics\n\n\nAbstract\nTo study 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 approximation depend on the choice of resolution. We study the persistence -- a notion from topological data analysis -- of the dynamics as the resolution change s\, in particular of the Morse decomposition of the recurrent set.\n LOCATION:https://researchseminars.org/talk/Dynamics/2/ END:VEVENT BEGIN:VEVENT SUMMARY:Arek Goetz (SFSU) DTSTART:20210911T180000Z DTEND:20210911T190000Z DTSTAMP:20260422T225703Z UID:Dynamics/3 DESCRIPTION:Title: The microscopic world of piecewise isometries\nby Arek Goetz (SFSU) a s part of Little school dynamics\n\n\nAbstract\nIn this talk we invite the audience to witness how a rigid\nexchange of two or more regions leads to strikingly complicated and\nbeautiful dynamics in the plane. A rich lands cape of phenomena is due\nto the presence of discontinuities that propagat e forming patterns\nthat appear to be self similar. We present examples fo r which the\nlocal dynamics is not well understood as well as major open q uestions\nin this field some of which may be of interest to students in\np rimarily undergraduate institutions.\n\nExamples of such maps are dual bil liards and invertible rotations of\ntwo half-planes.\n\nThe presentation w ill be accessible to an audience without familiarity\nwith advanced dynami cal tools.\n LOCATION:https://researchseminars.org/talk/Dynamics/3/ END:VEVENT BEGIN:VEVENT SUMMARY:Dave Constantine (Wesleyan) DTSTART:20211009T180000Z DTEND:20211009T190000Z DTSTAMP:20260422T225703Z UID:Dynamics/4 DESCRIPTION:Title: Geodesic flows on locally CAT(-1) spaces\nby Dave Constantine (Wesley an) as part of Little school dynamics\n\n\nAbstract\nGeodesic flows on com pact\, negatively curved Riemannian manifolds famously have lots of extrem ely nice dynamical properties. To what extent do those properties hold fo r geodesic flows on metric spaces that are negatively curved? In this 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\, locall y CAT(-1) space. It turns out that the CAT(-1) condition is sufficient fo r us to recover many nice properties. This is joint work with Jean-Francoi s Lafont and Daniel Thompson.\n LOCATION:https://researchseminars.org/talk/Dynamics/4/ END:VEVENT BEGIN:VEVENT SUMMARY:Cesar Silva (Williams College) DTSTART:20211113T190000Z DTEND:20211113T200000Z DTSTAMP:20260422T225703Z UID:Dynamics/5 DESCRIPTION:Title: "Characterizations of rank-one transformations that factor onto an odomet er\, or are isomorphic to an odometer\nby Cesar Silva (Williams Colleg e) as part of Little school dynamics\n\n\nAbstract\nWe will start by discu ssing rank-one transformations and odometer transformations\, and review t he isomorphism problem in ergodic theory. We will then present explicit c haracterizations\, based on the cutting and spacer parameters of the rank- one transformation\, of (a) which rank-one transformations factor onto a g iven finite cyclic permutation\, (b) which rank-one transformations factor onto a given odometer\, and (c) which rank-one transformations are isomor phic to a given odometer. These naturally yield characterizations of (d) w hich rank-one transformations factor onto some (unspecified) finite cyclic permutation\, (e) which rank-one transformations factor onto some (unspe cified) odometer\, and (f) which rank-one transformations are isomorphic t o some (unspecified) odometer. This is joint work with Matthew Foreman\, Su Gao\, Aaron Hill\, and Benjamin Weiss.\n LOCATION:https://researchseminars.org/talk/Dynamics/5/ END:VEVENT BEGIN:VEVENT SUMMARY:Heather Zinn-Brooks (Harvey Mudd) DTSTART:20211211T190000Z DTEND:20211211T200000Z DTSTAMP:20260422T225703Z UID:Dynamics/6 DESCRIPTION:Title: Bounded-confidence models for opinion dynamics on networks\nby Heathe r Zinn-Brooks (Harvey Mudd) as part of Little school dynamics\n\n\nAbstrac t\nOnline social media networks have become extremely influential sources of news and information. Given the large audience and the ease of sharing content online\, the content that spreads on online social networks can ha ve important consequences on public opinion\, policy\, and voting. To bett er understand the online content spread\, mathematical modeling of opinion dynamics is becoming an increasingly popular field of study. In this talk \, I will introduce you to a special class of models of opinion dynamics o n networks called bounded-confidence models. I will then discuss some of t he applications and theory that my collaborators and I have been developin g with these models\, including the impact of media\, opinion disseminatio n\, mean-field dynamics\, and extensions to hypergraphs and multilayer net works. This talk will also include some unsolved questions for future work .\n LOCATION:https://researchseminars.org/talk/Dynamics/6/ END:VEVENT BEGIN:VEVENT SUMMARY:Jasper Weinburd (Harvey Mudd College) DTSTART:20220312T190000Z DTEND:20220312T200000Z DTSTAMP:20260422T225703Z UID:Dynamics/7 DESCRIPTION:Title: Collective Behavior in Locust Swarms from Differential Equations to Data< /a>\nby Jasper Weinburd (Harvey Mudd College) as part of Little school dyn amics\n\n\nAbstract\nLocusts are devastating pests that infest and destroy crops. Locusts forage and migrate in\nlarge swarms which exhibit distinct ive shapes that improve efficiency on the group level\, a\nphenomenon know n as collective behavior. One of the difficulties in understanding and pre venting\nthese collective behaviors has been a lack of biological data for individual interactions between\nlocusts. In this talk\, I’ll first des cribe mathematical models for these phenomena on both the\ncollective and individual levels. I’ll then discuss a collaboration with undergraduate students that\nuse field data derived from video footage of locust swarms. We digitized nearly 20\,000 locust\ntrajectories and revealed individual behaviors that depend on a locust’s motion and the relative\nposition of its nearby neighbors. Finally\, I will illustrate the challenges and pote ntial benefits of\nincorporating these field observations into our models of locust swarms.\n LOCATION:https://researchseminars.org/talk/Dynamics/7/ END:VEVENT BEGIN:VEVENT SUMMARY:Andy Parrish (Eastern Illinois University) DTSTART:20220514T180000Z DTEND:20220514T190000Z DTSTAMP:20260422T225703Z UID:Dynamics/8 DESCRIPTION:Title: Good and Bad Functions for Translates\nby Andy Parrish (Eastern Illin ois University) as part of Little school dynamics\n\n\nAbstract\nWe say th at a set of functions is good for a sequence of\noperators if the sequence converges for every function in the set\; the\nset is bad if there is a f unction in the set for which the sequence of\noperators does not converge. For example\, given a fixed sequence\ntending to zero\, the continuous fu nctions are pointwise good for\ntranslations by this sequence-- yet bounde d Lebesgue-measurable\nfunctions are pointwise bad. We'll discuss how the set of functions\nthat are pointwise good for translation by any sequence is precisely\nthe set of functions locally equal a.e. to a Riemann-integra ble\nfunction. Time permitting\, we will also explore some new perspective s\non a well-known conjecture due to Erdos. This is joint work with\nJosep h Rosenblatt (UIUC).\n LOCATION:https://researchseminars.org/talk/Dynamics/8/ END:VEVENT BEGIN:VEVENT SUMMARY:May Mei (Denison) DTSTART:20220813T180000Z DTEND:20220813T190000Z DTSTAMP:20260422T225703Z 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 be mutua lly locally derivable (MLD)\nif each can be obtained from the other using local rules. From many\nperspective\, two MLD tilings can be thought of as "the same."\nHowever\, local derivability greatly impacts the adjacency r elationship\nbetween tiles\, which leads to the potential for adventure. P ut on your\nexplorer hats\, in this talk we present results on eigenfuncti ons of\nthe discrete Laplace operator and on playing the Game of Life on\n different manifestations of the Penrose tiling.\n LOCATION:https://researchseminars.org/talk/Dynamics/9/ END:VEVENT BEGIN:VEVENT SUMMARY:Joanna Furno (University of South Alabama) DTSTART:20220910T180000Z DTEND:20220910T190000Z DTSTAMP:20260422T225703Z UID:Dynamics/10 DESCRIPTION:Title: Polynomial Families Converging to a Family with an Exponential Map\n by Joanna Furno (University of South Alabama) as part of Little school dyn amics\n\n\nAbstract\nIn joint work with Devin Becker and Lorelei Koss\, we explore\nthe convergence of polynomial families to families that are a pr oduct\nof a power map and the exponential. This exploration encompasses th e\nconvergence of Julia sets in dynamical space and convergence in\nhyperb olic components of parameter space.\n LOCATION:https://researchseminars.org/talk/Dynamics/10/ END:VEVENT BEGIN:VEVENT SUMMARY:Drew Ash (Albion College) DTSTART:20221008T180000Z DTEND:20221008T190000Z DTSTAMP:20260422T225703Z UID:Dynamics/11 DESCRIPTION:Title: Introduction to Bratteli Diagrams and Bounded Topological Speedups\n by Drew Ash (Albion College) as part of Little school dynamics\n\n\nAbstra ct\nGiven a dynamical system $(X\,T)$\, one can define a speedup\nof $(X\, T)$ as another dynamical system $S: X → X$ where $S= T^{p(·)}$\nfor som e $p: X → Z^+$. In this talk\, we will focus on bounded\ntopological spe edups of minimal Cantor systems. Specifically\, we\nrequire that our “ju mp function” $p$ be bounded and hence continuous.\nOur motivating questi on is: What\, if anything\, can be preserved with\nthe added structure of p being bounded? To do so\, we introduce\nKakutani-Rokhlin towers and Brat teli diagrams as ways of visualizing\nthe dynamics of minimal Cantor syste ms. Then we will illustrate a\nnovel construction of a Bratteli diagram fo r $(X\,S)$ given a Bratteli\ndiagram for $(X\,T)$. We will conclude the ta lk with an brief\napplication of this constructions as well as discuss var ious open\nproblems inspired by this construction. The work presented is j oint\nwork with Andrew Dykstra and Michelle LeMasurier\, both of Hamilton\ nCollege.\n LOCATION:https://researchseminars.org/talk/Dynamics/11/ END:VEVENT BEGIN:VEVENT SUMMARY:E. Cabral Balreira (Trinity University) DTSTART:20221112T190000Z DTEND:20221112T200000Z DTSTAMP:20260422T225703Z UID:Dynamics/12 DESCRIPTION:Title: Geometric ideas on global stability and monotonicity for discrete system s\nby E. Cabral Balreira (Trinity University) as part of Little school dynamics\n\n\nAbstract\nIt is an important problem in discrete dynamics t o\ndetermine when local stability of fixed points implies global\nstabilit y. We will focus on the planar Ricker competition model and\nintroduce ide as from singularity theory to describe the dynamics of\nthe images of the critical curves to show that local stability of the\ncoexistence (positive ) fixed point implies global stability. The\nintroduction of geometric met hods will allow us to revisit the notion\nof monotonicity and develop a ge ometric generalization for the notion\nof monotonicity (or competitive) ma ps in higher dimensions. We show\nthat this definition is equivalent for k nown results for planar maps\nand provide analytic conditions to check for geometric monotonicity\nand global stability. We illustrate our results w ith the Beverton-Holt\nand Ricker competition map.\n LOCATION:https://researchseminars.org/talk/Dynamics/12/ END:VEVENT BEGIN:VEVENT SUMMARY:James Kelly (Christopher Newport University) DTSTART:20221210T190000Z DTEND:20221210T200000Z DTSTAMP:20260422T225703Z UID:Dynamics/13 DESCRIPTION:Title: Chaos and entropy in linear dynamical system\nby James Kelly (Christ opher Newport University) as part of Little school dynamics\n\n\nAbstract\ nWe discuss various notions of chaos in the context of linear\ndynamics. M any types of chaos (for linear operators) can only occur\nwithin infinite dimensional vector spaces. Two specific categories of\nthese spaces on whi ch we focus are weighted sequence spaces and\nfunction spaces\, and the na tural operators on these spaces are\nbackward shifts and translations (res pectively). We discuss\nrelationships between the types of chaos for these operators and\ncharacterizations for them in terms of the weight sequence /function.\nMore generally\, we examine how chaos and entropy relate to th e\neigenvalues of the operator. Throughout\, we highlight recent and\ncurr ent projects completed with undergraduate students.\n LOCATION:https://researchseminars.org/talk/Dynamics/13/ END:VEVENT END:VCALENDAR