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BEGIN:VEVENT
SUMMARY:Jessica Striker
DTSTART;VALUE=DATE-TIME:20201019T150000Z
DTEND;VALUE=DATE-TIME:20201019T154500Z
DTSTAMP;VALUE=DATE-TIME:20201031T051052Z
UID:BIRS_20w5164/1
DESCRIPTION:Title: Promotion and rowmotion – an ocean of notions\nby Jes
sica Striker as part of BIRS workshop: Dynamical Algebraic Combinatorics\n
\n\nAbstract\nIn this talk\, we introduce Dynamical Algebraic Combinatoric
s by investigating ever more general domains in which the actions of promo
tion on tableaux (or tableaux-like objects) and rowmotion on order ideals
(or generalizations of order ideals) correspond. These domains include: (1
) promotion on $2\\times n$ standard Young tableaux and rowmotion on order
ideals of the Type A root poset\, (2) K-promotion on rectangular increasi
ng tableaux and rowmotion on order ideals of the product of three chains p
oset\, (3) generalized promotion on increasing labelings of a finite poset
and rowmotion on order ideals of a corresponding poset\, and\, finally\,
(4) promotion on new objects we call P-strict labelings (named in analogy
to column-strict tableaux) and piecewise-linear rowmotion on P-partitions
of a corresponding poset.\n \nThis talk will be accessible to those with l
ittle DAC background and of interest to those working in the field. It inc
ludes joint works with J. Bernstein\, K. Dilks\, O. Pechenik\, C. Vorland\
, and N. Williams.\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Corey Vorland
DTSTART;VALUE=DATE-TIME:20201019T160000Z
DTEND;VALUE=DATE-TIME:20201019T163000Z
DTSTAMP;VALUE=DATE-TIME:20201031T051052Z
UID:BIRS_20w5164/2
DESCRIPTION:Title: An Introduction to Homomesy through Promotion and Rowmo
tion on Order Ideals\nby Corey Vorland as part of BIRS workshop: Dynamical
Algebraic Combinatorics\n\n\nAbstract\nHomomesy is a phenomenon in which
a statistic on a set under an action has the same average value over any o
rbit under as its global average. Homomesy results have been discovered am
ong many combinatorial objects\, such as order ideals of posets and variou
s tableaux. In this talk\, I will give a brief introduction to homomesy an
d explore some of these results. The main emphasis will be Propp and Roby
’s homomesy results on order ideals of a product of two chains poset und
er rowmotion and promotion\, along with my own results on order ideals of
a product of three chains.\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexander Garver
DTSTART;VALUE=DATE-TIME:20201019T163000Z
DTEND;VALUE=DATE-TIME:20201019T170000Z
DTSTAMP;VALUE=DATE-TIME:20201031T051052Z
UID:BIRS_20w5164/3
DESCRIPTION:Title: Promotion via representations of quivers\nby Alexander
Garver as part of BIRS workshop: Dynamical Algebraic Combinatorics\n\n\nAb
stract\nWe study promotion as a piecewise-linear operation on reverse plan
e partitions. We prove that this version of promotion is periodic by prese
nting representation-theoretic incarnations of reverse plane partitions an
d promotion. This is joint work with Rebecca Patrias and Hugh Thomas.\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Oliver Pechenik
DTSTART;VALUE=DATE-TIME:20201021T150000Z
DTEND;VALUE=DATE-TIME:20201021T154500Z
DTSTAMP;VALUE=DATE-TIME:20201031T051052Z
UID:BIRS_20w5164/4
DESCRIPTION:Title: Dynamics of plane partitions\nby Oliver Pechenik as par
t of BIRS workshop: Dynamical Algebraic Combinatorics\n\n\nAbstract\nConsi
der a plane partition $P$ as an order ideal in the product $[a] \\times [
b] \\times [c]$ of three chain posets. The combinatorial rowmotion operato
r sends $P$ to the plane partition generated by the minimal elements of it
s complement. What is the orbit structure of this action? I will attempt t
o survey the state of this question. In particular\, I will describe my re
cent work with Becky Patrias\, showing that rowmotion exhibits a strong fo
rm of resonance with frequency $a+b+c-1$\, in the sense that each orbit si
ze shares a prime divisor with $a+b+c-1$. This confirms a 1995 conjecture
of Peter Cameron and Dmitri Fon-Der-Flaass.\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Rebecca Patrias
DTSTART;VALUE=DATE-TIME:20201021T160000Z
DTEND;VALUE=DATE-TIME:20201021T163000Z
DTSTAMP;VALUE=DATE-TIME:20201031T051052Z
UID:BIRS_20w5164/5
DESCRIPTION:Title: Promotion\, Webs\, and Kwebs\nby Rebecca Patrias as par
t of BIRS workshop: Dynamical Algebraic Combinatorics\n\n\nAbstract\nIn 20
08\, Petersen--Pylyavskyy--Rhoades proved that promotion on 2-row and 3-ro
w rectangular standard Young tableaux can be realized as rotation of certa
in planar graphs called webs\, which were introduced by Kuperberg. In this
talk\, we will introduce webs and their result. We will then generalize i
t to a larger family of webs---webs with both black and white boundary ver
tices. Lastly\, we discuss on-going work to generalize further to the sett
ing of K-theory combinatorics. This on-going work is joint with Oliver Pec
henik\, Jessica Striker\, and Juliana Tymoczko.\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Emily Gunawan
DTSTART;VALUE=DATE-TIME:20201021T163000Z
DTEND;VALUE=DATE-TIME:20201021T170000Z
DTSTAMP;VALUE=DATE-TIME:20201031T051052Z
UID:BIRS_20w5164/6
DESCRIPTION:Title: Infinite friezes and bracelets\nby Emily Gunawan as par
t of BIRS workshop: Dynamical Algebraic Combinatorics\n\n\nAbstract\nFriez
e patterns were studied by Conway and Coxeter in the 1970s. More recently\
, in 2015\, Baur\, Parsons\, and Tschabold introduced infinite friezes and
related them to the once-punctured disk and annulus. In this talk\, we wi
ll explain the connection between periodic infinite friezes and cluster al
gebras of type D and affine A (modeled by once-punctured disks and annuli\
, respectively). We will discuss an invariant called growth coefficients w
hich correspond to bracelets on the surface. These growth coefficients may
or may not be homomesy-like.\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tom Roby
DTSTART;VALUE=DATE-TIME:20201023T150000Z
DTEND;VALUE=DATE-TIME:20201023T154500Z
DTSTAMP;VALUE=DATE-TIME:20201031T051052Z
UID:BIRS_20w5164/7
DESCRIPTION:Title: Let's birational: Lifting periodicity and homomesy to h
igher realms\nby Tom Roby as part of BIRS workshop: Dynamical Algebraic Co
mbinatorics\n\n\nAbstract\nMaps and actions on sets of combinatorial objec
ts often have interesting extensions to the piecewise-linear realm of orde
r and chain polytopes These can be further lifted to the birational realm
via detropicalization/geometricization\, and even to a setting with noncom
muting variables. Surprisingly often\, properties shown at the "combinator
ial shadow" level\, such as homomesy and low-order periodicity\, lift all
the way up to these higher realms.\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Soichi Okada
DTSTART;VALUE=DATE-TIME:20201023T160000Z
DTEND;VALUE=DATE-TIME:20201023T163000Z
DTSTAMP;VALUE=DATE-TIME:20201031T051052Z
UID:BIRS_20w5164/8
DESCRIPTION:Title: Proof of birational file homomesy for minuscule posets\
nby Soichi Okada as part of BIRS workshop: Dynamical Algebraic Combinatori
cs\n\n\nAbstract\nMusiker and Roby used an explicit formula for iterated a
ctions of the birational rowmotion map on a product of two chains\, a type
A minuscule poset\, to gave the first proof of the birational analogue of
file homomesy. In this talk\, we extend the file homomesy result to birat
ional rowmotion on arbitrary minuscule posets and give an almost uniform p
roof. Also we discuss a similar result for Coxeter-motion\, which is a gen
eralization of promotion on a product of two chains.\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nathan Williams
DTSTART;VALUE=DATE-TIME:20201026T150000Z
DTEND;VALUE=DATE-TIME:20201026T154500Z
DTSTAMP;VALUE=DATE-TIME:20201031T051052Z
UID:BIRS_20w5164/9
DESCRIPTION:Title: Independence Posets\nby Nathan Williams as part of BIRS
workshop: Dynamical Algebraic Combinatorics\n\n\nAbstract\nLet G be an ac
yclic directed graph. For each vertex of G\, we define an involution on th
e independent sets of G. We call these involutions flips\, and use them to
define the independence poset for G--a new partial order on independent s
ets of G. Our independence posets are a generalization of distributive lat
tices\, eliminating the lattice requirement: an independence poset that is
a graded lattice is always a distributive lattice. Many well-known posets
turn out to be special cases of our construction.\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Emily Barnard
DTSTART;VALUE=DATE-TIME:20201026T160000Z
DTEND;VALUE=DATE-TIME:20201026T163000Z
DTSTAMP;VALUE=DATE-TIME:20201031T051052Z
UID:BIRS_20w5164/10
DESCRIPTION:Title: The Kreweras Complement\nby Emily Barnard as part of BI
RS workshop: Dynamical Algebraic Combinatorics\n\n\nAbstract\nFor a certai
n class of finite lattices called semidistributive\, there exists a map k
which gives a bijection between the set of join-irreducible elements and m
eet-irreducible elements. In this talk\, we begin by connecting the map k
and the Kreweras complement defined on noncrossing partitions. Our goal is
to describe the map k in the context of torsion classes and the Kreweras
complement in the context of wide subcategories. Experience with torsion c
lasses and wide subcategories will not be assumed\, and many examples will
be given.\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Emine Yıldırım
DTSTART;VALUE=DATE-TIME:20201026T163000Z
DTEND;VALUE=DATE-TIME:20201026T170000Z
DTSTAMP;VALUE=DATE-TIME:20201031T051052Z
UID:BIRS_20w5164/11
DESCRIPTION:Title: The orbits of the Coxeter Transformation and Rowmotion
for cominuscule posets\nby Emine Yıldırım as part of BIRS workshop: Dyn
amical Algebraic Combinatorics\n\n\nAbstract\nLet h to be the Coxeter numb
er of a root system. We show that the Coxeter transformation of the incide
nce algebra coming from the order ideals in a cominuscule poset is periodi
c of order 'h+1' (up to a sign) in most cases using tools from representat
ion theory of algebras. On the other hand\, there is a combinatorial actio
n\, called the Rowmotion\, defined on cominuscule posets. It is well-known
that this action has order 'h' on the order ideals of a cominuscule poset
. In this talk\, we will demonstrate combinatorial similarities of the orb
its of these two actions.\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Darij Grinberg
DTSTART;VALUE=DATE-TIME:20201028T150000Z
DTEND;VALUE=DATE-TIME:20201028T153000Z
DTSTAMP;VALUE=DATE-TIME:20201031T051052Z
UID:BIRS_20w5164/12
DESCRIPTION:Title: Littlewood-Richardson coefficients and birational combi
natorics\nby Darij Grinberg as part of BIRS workshop: Dynamical Algebraic
Combinatorics\n\n\nAbstract\nI will discuss a novel (partial) symmetry of
Littlewood-Richardson coefficients conjectured by Pelletier and Ressayre (
arXiv:2005.09877)\, and its proof (arXiv:2008.06128). The proof proceeds b
y constructing a birational involution and applying it to the tropical sem
ifield\, making for a particularly wieldly example of how (de)tropicalizat
ion can be used to prove combinatorial results.\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Michael Joseph
DTSTART;VALUE=DATE-TIME:20201028T153000Z
DTEND;VALUE=DATE-TIME:20201028T160000Z
DTSTAMP;VALUE=DATE-TIME:20201031T051052Z
UID:BIRS_20w5164/13
DESCRIPTION:Title: A birational lifting of the Lalanne–Kreweras involuti
on on Dyck paths\nby Michael Joseph as part of BIRS workshop: Dynamical Al
gebraic Combinatorics\n\n\nAbstract\nThe Lalanne–Kreweras involution (LK
) on Dyck paths yields a bijective proof of the symmetry of two statistics
: the number of valleys and the major index. Equivalently\, this involutio
n can be considered on the set of antichains of the type A root poset\, on
which rowmotion and LK together generate a dihedral action (as first disc
overed by Panyushev). Piecewise-linear and birational rowmotion were first
defined by Einstein and Propp. Moving further in this direction\, we defi
ne an analogue of the LK involution to the piecewise-linear and birational
realms. In fact\, LK is a special case of a more general action\, rowvacu
ation\, an involution that can be defined on any finite graded poset where
it forms a dihedral action with rowmotion. We will explain that the symme
try properties of the number of valleys and the major index also lift to t
he higher realms. In this process\, we have discovered more refined homome
sies for LK\, and we will explain how certain statistics which are homomes
ic under rowvacuation are also homomesic under rowmotion. This is joint wo
rk with Sam Hopkins.\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Samuel Hopkins (University of Minnesota)
DTSTART;VALUE=DATE-TIME:20201028T161500Z
DTEND;VALUE=DATE-TIME:20201028T170000Z
DTSTAMP;VALUE=DATE-TIME:20201031T051052Z
UID:BIRS_20w5164/14
DESCRIPTION:Title: Symmetry of Narayana numbers and rowvacuation of root p
osets\nby Samuel Hopkins (University of Minnesota) as part of BIRS worksho
p: Dynamical Algebraic Combinatorics\n\n\nAbstract\nI will present a conje
ctural way that ideas from Dynamical Algebraic Combinatorics could be used
to resolve a fundamental problem in Coxeter-Catalan combinatorics: biject
ively demonstrating the symmetry of the nonnesting W-Narayana numbers. Thi
s continues a project of Panyushev\, whose interest in this problem led hi
m to study rowmotion for root posets\, and thus initiated a lot of the rec
ent activity in DAC. I hope that others will become interested in this pro
blem\, and that we can "bring DAC full circle."\n
END:VEVENT
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