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SUMMARY:Aimee Johnson (Swarthmore)
DTSTART;VALUE=DATE-TIME:20210220T190000Z
DTEND;VALUE=DATE-TIME:20210220T200000Z
DTSTAMP;VALUE=DATE-TIME:20220528T201514Z
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;VALUE=DATE-TIME:20210814T180000Z
DTEND;VALUE=DATE-TIME:20210814T190000Z
DTSTAMP;VALUE=DATE-TIME:20220528T201514Z
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;VALUE=DATE-TIME:20210911T180000Z
DTEND;VALUE=DATE-TIME:20210911T190000Z
DTSTAMP;VALUE=DATE-TIME:20220528T201514Z
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/
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SUMMARY:Dave Constantine (Wesleyan)
DTSTART;VALUE=DATE-TIME:20211009T180000Z
DTEND;VALUE=DATE-TIME:20211009T190000Z
DTSTAMP;VALUE=DATE-TIME:20220528T201514Z
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;VALUE=DATE-TIME:20211113T190000Z
DTEND;VALUE=DATE-TIME:20211113T200000Z
DTSTAMP;VALUE=DATE-TIME:20220528T201514Z
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;VALUE=DATE-TIME:20211211T190000Z
DTEND;VALUE=DATE-TIME:20211211T200000Z
DTSTAMP;VALUE=DATE-TIME:20220528T201514Z
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/
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SUMMARY:Jasper Weinburd (Harvey Mudd College)
DTSTART;VALUE=DATE-TIME:20220312T190000Z
DTEND;VALUE=DATE-TIME:20220312T200000Z
DTSTAMP;VALUE=DATE-TIME:20220528T201514Z
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;VALUE=DATE-TIME:20220514T180000Z
DTEND;VALUE=DATE-TIME:20220514T190000Z
DTSTAMP;VALUE=DATE-TIME:20220528T201514Z
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/
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