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BEGIN:VEVENT
SUMMARY:Jessica Striker
DTSTART:20201019T150000Z
DTEND:20201019T154500Z
DTSTAMP:20260404T041858Z
UID:BIRS_20w5164/1
DESCRIPTION:Title: Promotion and rowmotion – an ocean of notions\nby Jessic
a Striker as part of BIRS workshop: Dynamical Algebraic Combinatorics\n\n\
nAbstract\nIn this talk\, we introduce Dynamical Algebraic Combinatorics b
y investigating ever more general domains in which the actions of promotio
n on tableaux (or tableaux-like objects) and rowmotion on order ideals (or
generalizations of order ideals) correspond. These domains include: (1) p
romotion on $2\\times n$ standard Young tableaux and rowmotion on order id
eals of the Type A root poset\, (2) K-promotion on rectangular increasing
tableaux and rowmotion on order ideals of the product of three chains pose
t\, (3) generalized promotion on increasing labelings of a finite poset an
d 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 litt
le DAC background and of interest to those working in the field. It includ
es joint works with J. Bernstein\, K. Dilks\, O. Pechenik\, C. Vorland\, a
nd N. Williams.\n
LOCATION:https://stable.researchseminars.org/talk/BIRS_20w5164/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Corey Vorland
DTSTART:20201019T160000Z
DTEND:20201019T163000Z
DTSTAMP:20260404T041858Z
UID:BIRS_20w5164/2
DESCRIPTION:Title: An Introduction to Homomesy through Promotion and Rowmotion on
Order Ideals\nby Corey Vorland as part of BIRS workshop: Dynamical Al
gebraic Combinatorics\n\n\nAbstract\nHomomesy is a phenomenon in which a s
tatistic on a set under an action has the same average value over any orbi
t under as its global average. Homomesy results have been discovered among
many combinatorial objects\, such as order ideals of posets and various t
ableaux. In this talk\, I will give a brief introduction to homomesy and e
xplore 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 under r
owmotion and promotion\, along with my own results on order ideals of a pr
oduct of three chains.\n
LOCATION:https://stable.researchseminars.org/talk/BIRS_20w5164/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexander Garver
DTSTART:20201019T163000Z
DTEND:20201019T170000Z
DTSTAMP:20260404T041858Z
UID:BIRS_20w5164/3
DESCRIPTION:Title: Promotion via representations of quivers\nby Alexander Gar
ver as part of BIRS workshop: Dynamical Algebraic Combinatorics\n\n\nAbstr
act\nWe study promotion as a piecewise-linear operation on reverse plane p
artitions. We prove that this version of promotion is periodic by presenti
ng representation-theoretic incarnations of reverse plane partitions and p
romotion. This is joint work with Rebecca Patrias and Hugh Thomas.\n
LOCATION:https://stable.researchseminars.org/talk/BIRS_20w5164/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Oliver Pechenik
DTSTART:20201021T150000Z
DTEND:20201021T154500Z
DTSTAMP:20260404T041858Z
UID:BIRS_20w5164/4
DESCRIPTION:Title: Dynamics of plane partitions\nby Oliver Pechenik as part o
f BIRS workshop: Dynamical Algebraic Combinatorics\n\n\nAbstract\nConsider
a plane partition $P$ as an order ideal in the product $[a] \\times [b]
\\times [c]$ of three chain posets. The combinatorial rowmotion operator s
ends $P$ to the plane partition generated by the minimal elements of its c
omplement. What is the orbit structure of this action? I will attempt to s
urvey the state of this question. In particular\, I will describe my recen
t work with Becky Patrias\, showing that rowmotion exhibits a strong form
of resonance with frequency $a+b+c-1$\, in the sense that each orbit size
shares a prime divisor with $a+b+c-1$. This confirms a 1995 conjecture of
Peter Cameron and Dmitri Fon-Der-Flaass.\n
LOCATION:https://stable.researchseminars.org/talk/BIRS_20w5164/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Rebecca Patrias
DTSTART:20201021T160000Z
DTEND:20201021T163000Z
DTSTAMP:20260404T041858Z
UID:BIRS_20w5164/5
DESCRIPTION:Title: Promotion\, Webs\, and Kwebs\nby Rebecca Patrias as part o
f BIRS workshop: Dynamical Algebraic Combinatorics\n\n\nAbstract\nIn 2008\
, Petersen--Pylyavskyy--Rhoades proved that promotion on 2-row and 3-row r
ectangular standard Young tableaux can be realized as rotation of certain
planar graphs called webs\, which were introduced by Kuperberg. In this ta
lk\, we will introduce webs and their result. We will then generalize it t
o a larger family of webs---webs with both black and white boundary vertic
es. Lastly\, we discuss on-going work to generalize further to the setting
of K-theory combinatorics. This on-going work is joint with Oliver Pechen
ik\, Jessica Striker\, and Juliana Tymoczko.\n
LOCATION:https://stable.researchseminars.org/talk/BIRS_20w5164/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Emily Gunawan
DTSTART:20201021T163000Z
DTEND:20201021T170000Z
DTSTAMP:20260404T041858Z
UID:BIRS_20w5164/6
DESCRIPTION:Title: Infinite friezes and bracelets\nby Emily Gunawan as part o
f BIRS workshop: Dynamical Algebraic Combinatorics\n\n\nAbstract\nFrieze p
atterns were studied by Conway and Coxeter in the 1970s. More recently\, i
n 2015\, Baur\, Parsons\, and Tschabold introduced infinite friezes and re
lated them to the once-punctured disk and annulus. In this talk\, we will
explain the connection between periodic infinite friezes and cluster algeb
ras of type D and affine A (modeled by once-punctured disks and annuli\, r
espectively). We will discuss an invariant called growth coefficients whic
h correspond to bracelets on the surface. These growth coefficients may or
may not be homomesy-like.\n
LOCATION:https://stable.researchseminars.org/talk/BIRS_20w5164/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tom Roby
DTSTART:20201023T150000Z
DTEND:20201023T154500Z
DTSTAMP:20260404T041858Z
UID:BIRS_20w5164/7
DESCRIPTION:Title: Let's birational: Lifting periodicity and homomesy to higher r
ealms\nby Tom Roby as part of BIRS workshop: Dynamical Algebraic Combi
natorics\n\n\nAbstract\nMaps and actions on sets of combinatorial objects
often have interesting extensions to the piecewise-linear realm of order a
nd chain polytopes These can be further lifted to the birational realm via
detropicalization/geometricization\, and even to a setting with noncommut
ing variables. Surprisingly often\, properties shown at the "combinatorial
shadow" level\, such as homomesy and low-order periodicity\, lift all the
way up to these higher realms.\n
LOCATION:https://stable.researchseminars.org/talk/BIRS_20w5164/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Soichi Okada
DTSTART:20201023T160000Z
DTEND:20201023T163000Z
DTSTAMP:20260404T041858Z
UID:BIRS_20w5164/8
DESCRIPTION:Title: Proof of birational file homomesy for minuscule posets\nby
Soichi Okada as part of BIRS workshop: Dynamical Algebraic Combinatorics\
n\n\nAbstract\nMusiker and Roby used an explicit formula for iterated acti
ons 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 fi
le homomesy. In this talk\, we extend the file homomesy result to biration
al rowmotion on arbitrary minuscule posets and give an almost uniform proo
f. Also we discuss a similar result for Coxeter-motion\, which is a genera
lization of promotion on a product of two chains.\n
LOCATION:https://stable.researchseminars.org/talk/BIRS_20w5164/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nathan Williams
DTSTART:20201026T150000Z
DTEND:20201026T154500Z
DTSTAMP:20260404T041858Z
UID:BIRS_20w5164/9
DESCRIPTION:Title: Independence Posets\nby Nathan Williams as part of BIRS wo
rkshop: Dynamical Algebraic Combinatorics\n\n\nAbstract\nLet G be an acycl
ic directed graph. For each vertex of G\, we define an involution on the i
ndependent sets of G. We call these involutions flips\, and use them to de
fine the independence poset for G--a new partial order on independent sets
of G. Our independence posets are a generalization of distributive lattic
es\, eliminating the lattice requirement: an independence poset that is a
graded lattice is always a distributive lattice. Many well-known posets tu
rn out to be special cases of our construction.\n
LOCATION:https://stable.researchseminars.org/talk/BIRS_20w5164/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Emily Barnard
DTSTART:20201026T160000Z
DTEND:20201026T163000Z
DTSTAMP:20260404T041858Z
UID:BIRS_20w5164/10
DESCRIPTION:Title: The Kreweras Complement\nby Emily Barnard as part of BIRS
workshop: Dynamical Algebraic Combinatorics\n\n\nAbstract\nFor a certain
class of finite lattices called semidistributive\, there exists a map k wh
ich gives a bijection between the set of join-irreducible elements and mee
t-irreducible elements. In this talk\, we begin by connecting the map k an
d the Kreweras complement defined on noncrossing partitions. Our goal is t
o describe the map k in the context of torsion classes and the Kreweras co
mplement in the context of wide subcategories. Experience with torsion cla
sses and wide subcategories will not be assumed\, and many examples will b
e given.\n
LOCATION:https://stable.researchseminars.org/talk/BIRS_20w5164/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Emine Yıldırım
DTSTART:20201026T163000Z
DTEND:20201026T170000Z
DTSTAMP:20260404T041858Z
UID:BIRS_20w5164/11
DESCRIPTION:Title: The orbits of the Coxeter Transformation and Rowmotion for co
minuscule posets\nby Emine Yıldırım as part of BIRS workshop: Dynam
ical Algebraic Combinatorics\n\n\nAbstract\nLet h to be the Coxeter number
of a root system. We show that the Coxeter transformation of the incidenc
e algebra coming from the order ideals in a cominuscule poset is periodic
of order 'h+1' (up to a sign) in most cases using tools from representatio
n theory of algebras. On the other hand\, there is a combinatorial action\
, called the Rowmotion\, defined on cominuscule posets. It is well-known t
hat this action has order 'h' on the order ideals of a cominuscule poset.
In this talk\, we will demonstrate combinatorial similarities of the orbit
s of these two actions.\n
LOCATION:https://stable.researchseminars.org/talk/BIRS_20w5164/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Darij Grinberg
DTSTART:20201028T150000Z
DTEND:20201028T153000Z
DTSTAMP:20260404T041858Z
UID:BIRS_20w5164/12
DESCRIPTION:Title: Littlewood-Richardson coefficients and birational combinatori
cs\nby Darij Grinberg as part of BIRS workshop: Dynamical Algebraic Co
mbinatorics\n\n\nAbstract\nI will discuss a novel (partial) symmetry of Li
ttlewood-Richardson coefficients conjectured by Pelletier and Ressayre (ar
Xiv:2005.09877)\, and its proof (arXiv:2008.06128). The proof proceeds by
constructing a birational involution and applying it to the tropical semif
ield\, making for a particularly wieldly example of how (de)tropicalizatio
n can be used to prove combinatorial results.\n
LOCATION:https://stable.researchseminars.org/talk/BIRS_20w5164/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Michael Joseph
DTSTART:20201028T153000Z
DTEND:20201028T160000Z
DTSTAMP:20260404T041858Z
UID:BIRS_20w5164/13
DESCRIPTION:Title: A birational lifting of the Lalanne–Kreweras involution on
Dyck paths\nby Michael Joseph as part of BIRS workshop: Dynamical Alge
braic 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 involution
can be considered on the set of antichains of the type A root poset\, on w
hich rowmotion and LK together generate a dihedral action (as first discov
ered by Panyushev). Piecewise-linear and birational rowmotion were first d
efined by Einstein and Propp. Moving further in this direction\, we define
an analogue of the LK involution to the piecewise-linear and birational r
ealms. In fact\, LK is a special case of a more general action\, rowvacuat
ion\, an involution that can be defined on any finite graded poset where i
t forms a dihedral action with rowmotion. We will explain that the symmetr
y properties of the number of valleys and the major index also lift to the
higher realms. In this process\, we have discovered more refined homomesi
es for LK\, and we will explain how certain statistics which are homomesic
under rowvacuation are also homomesic under rowmotion. This is joint work
with Sam Hopkins.\n
LOCATION:https://stable.researchseminars.org/talk/BIRS_20w5164/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Samuel Hopkins (University of Minnesota)
DTSTART:20201028T161500Z
DTEND:20201028T170000Z
DTSTAMP:20260404T041858Z
UID:BIRS_20w5164/14
DESCRIPTION:Title: Symmetry of Narayana numbers and rowvacuation of root posets<
/a>\nby Samuel Hopkins (University of Minnesota) as part of BIRS workshop:
Dynamical Algebraic Combinatorics\n\n\nAbstract\nI will present a conject
ural way that ideas from Dynamical Algebraic Combinatorics could be used t
o resolve a fundamental problem in Coxeter-Catalan combinatorics: bijectiv
ely demonstrating the symmetry of the nonnesting W-Narayana numbers. This
continues a project of Panyushev\, whose interest in this problem led him
to study rowmotion for root posets\, and thus initiated a lot of the recen
t activity in DAC. I hope that others will become interested in this probl
em\, and that we can "bring DAC full circle."\n
LOCATION:https://stable.researchseminars.org/talk/BIRS_20w5164/14/
END:VEVENT
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