BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Jessica Striker DTSTART:20201019T150000Z DTEND:20201019T154500Z DTSTAMP:20260422T185537Z UID:BIRS_20w5164/1 DESCRIPTION:Title: Promotion and rowmotion – an ocean of notions\nby Jessica Strik er as part of BIRS workshop: Dynamical Algebraic Combinatorics\n\n\nAbstra ct\nIn this talk\, we introduce Dynamical Algebraic Combinatorics by inves tigating ever more general domains in which the actions of promotion on ta bleaux (or tableaux-like objects) and rowmotion on order ideals (or genera lizations of order ideals) correspond. These domains include: (1) promotio n on $2\\times n$ standard Young tableaux and rowmotion on order ideals of the Type A root poset\, (2) K-promotion on rectangular increasing tableau x and rowmotion on order ideals of the product of three chains poset\, (3) generalized promotion on increasing labelings of a finite poset and rowmo tion on order ideals of a corresponding poset\, and\, finally\, (4) promot ion on new objects we call P-strict labelings (named in analogy to column- strict tableaux) and piecewise-linear rowmotion on P-partitions of a corre sponding poset.\n \nThis talk will be accessible to those with little DAC background and of interest to those working in the field. It includes join t works with J. Bernstein\, K. Dilks\, O. Pechenik\, C. Vorland\, and N. W illiams.\n LOCATION:https://researchseminars.org/talk/BIRS_20w5164/1/ END:VEVENT BEGIN:VEVENT SUMMARY:Corey Vorland DTSTART:20201019T160000Z DTEND:20201019T163000Z DTSTAMP:20260422T185537Z 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 Algebraic Combinatorics\n\n\nAbstract\nHomomesy is a phenomenon in which a statisti c on a set under an action has the same average value over any orbit under as its global average. Homomesy results have been discovered among many c ombinatorial objects\, such as order ideals of posets and various tableaux . In this talk\, I will give a brief introduction to homomesy and explore some of these results. The main emphasis will be Propp and Roby’s homome sy results on order ideals of a product of two chains poset under rowmotio n and promotion\, along with my own results on order ideals of a product o f three chains.\n LOCATION:https://researchseminars.org/talk/BIRS_20w5164/2/ END:VEVENT BEGIN:VEVENT SUMMARY:Alexander Garver DTSTART:20201019T163000Z DTEND:20201019T170000Z DTSTAMP:20260422T185537Z UID:BIRS_20w5164/3 DESCRIPTION:Title: Promotion via representations of quivers\nby Alexander Garver as part of BIRS workshop: Dynamical Algebraic Combinatorics\n\n\nAbstract\nWe study promotion as a piecewise-linear operation on reverse plane partitio ns. We prove that this version of promotion is periodic by presenting repr esentation-theoretic incarnations of reverse plane partitions and promotio n. This is joint work with Rebecca Patrias and Hugh Thomas.\n LOCATION:https://researchseminars.org/talk/BIRS_20w5164/3/ END:VEVENT BEGIN:VEVENT SUMMARY:Oliver Pechenik DTSTART:20201021T150000Z DTEND:20201021T154500Z DTSTAMP:20260422T185537Z UID:BIRS_20w5164/4 DESCRIPTION:Title: Dynamics of plane partitions\nby Oliver Pechenik as part of BIRS workshop: Dynamical Algebraic Combinatorics\n\n\nAbstract\nConsider a plan e partition $P$ as an order ideal in the product $[a] \\times [b] \\times [c]$ of three chain posets. The combinatorial rowmotion operator sends $P $ to the plane partition generated by the minimal elements of its compleme nt. What is the orbit structure of this action? I will attempt to survey t he state of this question. In particular\, I will describe my recent work with Becky Patrias\, showing that rowmotion exhibits a strong form of reso nance 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 C ameron and Dmitri Fon-Der-Flaass.\n LOCATION:https://researchseminars.org/talk/BIRS_20w5164/4/ END:VEVENT BEGIN:VEVENT SUMMARY:Rebecca Patrias DTSTART:20201021T160000Z DTEND:20201021T163000Z DTSTAMP:20260422T185537Z UID:BIRS_20w5164/5 DESCRIPTION:Title: Promotion\, Webs\, and Kwebs\nby Rebecca Patrias as part of BIRS workshop: Dynamical Algebraic Combinatorics\n\n\nAbstract\nIn 2008\, Peter sen--Pylyavskyy--Rhoades proved that promotion on 2-row and 3-row rectangu lar standard Young tableaux can be realized as rotation of certain planar graphs called webs\, which were introduced by Kuperberg. In this talk\, we will introduce webs and their result. We will then generalize it to a lar ger family of webs---webs with both black and white boundary vertices. Las tly\, we discuss on-going work to generalize further to the setting of K-t heory combinatorics. This on-going work is joint with Oliver Pechenik\, Je ssica Striker\, and Juliana Tymoczko.\n LOCATION:https://researchseminars.org/talk/BIRS_20w5164/5/ END:VEVENT BEGIN:VEVENT SUMMARY:Emily Gunawan DTSTART:20201021T163000Z DTEND:20201021T170000Z DTSTAMP:20260422T185537Z UID:BIRS_20w5164/6 DESCRIPTION:Title: Infinite friezes and bracelets\nby Emily Gunawan as part of BIRS workshop: Dynamical Algebraic Combinatorics\n\n\nAbstract\nFrieze patterns were studied by Conway and Coxeter in the 1970s. More recently\, in 2015\ , Baur\, Parsons\, and Tschabold introduced infinite friezes and related t hem to the once-punctured disk and annulus. In this talk\, we will explain the connection between periodic infinite friezes and cluster algebras of type D and affine A (modeled by once-punctured disks and annuli\, respecti vely). We will discuss an invariant called growth coefficients which corre spond to bracelets on the surface. These growth coefficients may or may no t be homomesy-like.\n LOCATION:https://researchseminars.org/talk/BIRS_20w5164/6/ END:VEVENT BEGIN:VEVENT SUMMARY:Tom Roby DTSTART:20201023T150000Z DTEND:20201023T154500Z DTSTAMP:20260422T185537Z UID:BIRS_20w5164/7 DESCRIPTION:Title: Let's birational: Lifting periodicity and homomesy to higher realms\nby Tom Roby as part of BIRS workshop: Dynamical Algebraic Combinatoric s\n\n\nAbstract\nMaps and actions on sets of combinatorial objects often h ave interesting extensions to the piecewise-linear realm of order and chai n polytopes These can be further lifted to the birational realm via detrop icalization/geometricization\, and even to a setting with noncommuting var iables. 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://researchseminars.org/talk/BIRS_20w5164/7/ END:VEVENT BEGIN:VEVENT SUMMARY:Soichi Okada DTSTART:20201023T160000Z DTEND:20201023T163000Z DTSTAMP:20260422T185537Z 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\nAb stract\nMusiker and Roby used an explicit formula for iterated actions of the birational rowmotion map on a product of two chains\, a type A minuscu le poset\, to gave the first proof of the birational analogue of file homo mesy. In this talk\, we extend the file homomesy result to birational rowm otion on arbitrary minuscule posets and give an almost uniform proof. Also we discuss a similar result for Coxeter-motion\, which is a generalizatio n of promotion on a product of two chains.\n LOCATION:https://researchseminars.org/talk/BIRS_20w5164/8/ END:VEVENT BEGIN:VEVENT SUMMARY:Nathan Williams DTSTART:20201026T150000Z DTEND:20201026T154500Z DTSTAMP:20260422T185537Z 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 acyclic dire cted graph. For each vertex of G\, we define an involution on the independ ent sets of G. We call these involutions flips\, and use them to define th e independence poset for G--a new partial order on independent sets of G. Our independence posets are a generalization of distributive lattices\, el iminating 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 LOCATION:https://researchseminars.org/talk/BIRS_20w5164/9/ END:VEVENT BEGIN:VEVENT SUMMARY:Emily Barnard DTSTART:20201026T160000Z DTEND:20201026T163000Z DTSTAMP:20260422T185537Z UID:BIRS_20w5164/10 DESCRIPTION:Title: The Kreweras Complement\nby Emily Barnard as part of BIRS worksh op: Dynamical Algebraic Combinatorics\n\n\nAbstract\nFor a certain class o f finite lattices called semidistributive\, there exists a map k which giv es a bijection between the set of join-irreducible elements and meet-irred ucible elements. In this talk\, we begin by connecting the map k and the K reweras complement defined on noncrossing partitions. Our goal is to descr ibe the map k in the context of torsion classes and the Kreweras complemen t in the context of wide subcategories. Experience with torsion classes an d wide subcategories will not be assumed\, and many examples will be given .\n LOCATION:https://researchseminars.org/talk/BIRS_20w5164/10/ END:VEVENT BEGIN:VEVENT SUMMARY:Emine Yıldırım DTSTART:20201026T163000Z DTEND:20201026T170000Z DTSTAMP:20260422T185537Z UID:BIRS_20w5164/11 DESCRIPTION:Title: The orbits of the Coxeter Transformation and Rowmotion for cominuscu le posets\nby Emine Yıldırım as part of BIRS workshop: Dynamical Al gebraic Combinatorics\n\n\nAbstract\nLet h to be the Coxeter number of a r oot system. We show that the Coxeter transformation of the incidence algeb ra coming from the order ideals in a cominuscule poset is periodic of orde r 'h+1' (up to a sign) in most cases using tools from representation theor y of algebras. On the other hand\, there is a combinatorial action\, calle d the Rowmotion\, defined on cominuscule posets. It is well-known that thi s action has order 'h' on the order ideals of a cominuscule poset. In this talk\, we will demonstrate combinatorial similarities of the orbits of th ese two actions.\n LOCATION:https://researchseminars.org/talk/BIRS_20w5164/11/ END:VEVENT BEGIN:VEVENT SUMMARY:Darij Grinberg DTSTART:20201028T150000Z DTEND:20201028T153000Z DTSTAMP:20260422T185537Z UID:BIRS_20w5164/12 DESCRIPTION:Title: Littlewood-Richardson coefficients and birational combinatorics\ nby Darij Grinberg as part of BIRS workshop: Dynamical Algebraic Combinato rics\n\n\nAbstract\nI will discuss a novel (partial) symmetry of Littlewoo d-Richardson coefficients conjectured by Pelletier and Ressayre (arXiv:200 5.09877)\, and its proof (arXiv:2008.06128). The proof proceeds by constru cting a birational involution and applying it to the tropical semifield\, making for a particularly wieldly example of how (de)tropicalization can b e used to prove combinatorial results.\n LOCATION:https://researchseminars.org/talk/BIRS_20w5164/12/ END:VEVENT BEGIN:VEVENT SUMMARY:Michael Joseph DTSTART:20201028T153000Z DTEND:20201028T160000Z DTSTAMP:20260422T185537Z UID:BIRS_20w5164/13 DESCRIPTION:Title: A birational lifting of the Lalanne–Kreweras involution on Dyck pa ths\nby Michael Joseph as part of BIRS workshop: Dynamical Algebraic C ombinatorics\n\n\nAbstract\nThe Lalanne–Kreweras involution (LK) on Dyck paths yields a bijective proof of the symmetry of two statistics: the num ber of valleys and the major index. Equivalently\, this involution can be considered on the set of antichains of the type A root poset\, on which ro wmotion and LK together generate a dihedral action (as first discovered by Panyushev). Piecewise-linear and birational rowmotion were first defined by Einstein and Propp. Moving further in this direction\, we define an ana logue of the LK involution to the piecewise-linear and birational realms. In fact\, LK is a special case of a more general action\, rowvacuation\, a n involution that can be defined on any finite graded poset where it forms a dihedral action with rowmotion. We will explain that the symmetry prope rties of the number of valleys and the major index also lift to the higher realms. In this process\, we have discovered more refined homomesies for LK\, and we will explain how certain statistics which are homomesic under rowvacuation are also homomesic under rowmotion. This is joint work with S am Hopkins.\n LOCATION:https://researchseminars.org/talk/BIRS_20w5164/13/ END:VEVENT BEGIN:VEVENT SUMMARY:Samuel Hopkins (University of Minnesota) DTSTART:20201028T161500Z DTEND:20201028T170000Z DTSTAMP:20260422T185537Z UID:BIRS_20w5164/14 DESCRIPTION:Title: Symmetry of Narayana numbers and rowvacuation of root posets\nby Samuel Hopkins (University of Minnesota) as part of BIRS workshop: Dynami cal Algebraic Combinatorics\n\n\nAbstract\nI will present a conjectural wa y that ideas from Dynamical Algebraic Combinatorics could be used to resol ve a fundamental problem in Coxeter-Catalan combinatorics: bijectively dem onstrating the symmetry of the nonnesting W-Narayana numbers. This continu es a project of Panyushev\, whose interest in this problem led him to stud y rowmotion for root posets\, and thus initiated a lot of the recent activ ity in DAC. I hope that others will become interested in this problem\, an d that we can "bring DAC full circle."\n LOCATION:https://researchseminars.org/talk/BIRS_20w5164/14/ END:VEVENT END:VCALENDAR