BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Irina Bobrova DTSTART:20240307T080000Z DTEND:20240307T090000Z DTSTAMP:20260404T095717Z UID:NIS2024/4 DESCRIPTION:Title: Non-Abelian ODEs and O∆Es\nby Irina Bobrova as part of Semina r-Type Workshop on Noncommutative Integrable Systems\n\n\nAbstract\nSome s olutions of important integrable systems can be expressed in terms of ordi nary differential or difference equations. The famous Painlevé equations are a good example of this phenomenon. Since the theory of integrable syst ems has been developing intensively towards the non-commutative case\, the question of defining and deriving non-abelian ODEs and O∆Es becomes nat ural. \n\nIn this series of lectures\, we will discuss some methods for th e deriving and classification of such equations as well as investigation t heir integrability.\n LOCATION:https://stable.researchseminars.org/talk/NIS2024/4/ END:VEVENT BEGIN:VEVENT SUMMARY:Vladimir Retakh DTSTART:20240308T003000Z DTEND:20240308T013000Z DTSTAMP:20260404T095717Z UID:NIS2024/5 DESCRIPTION:Title: Quasideterminants and their applications. An introduction III\n by Vladimir Retakh as part of Seminar-Type Workshop on Noncommutative Inte grable Systems\n\nAbstract: TBA\n LOCATION:https://stable.researchseminars.org/talk/NIS2024/5/ END:VEVENT BEGIN:VEVENT SUMMARY:Vladimir Retakh DTSTART:20240305T003000Z DTEND:20240305T013000Z DTSTAMP:20260404T095717Z UID:NIS2024/6 DESCRIPTION:Title: Quasideterminants and their applications. An introduction I\nby Vladimir Retakh as part of Seminar-Type Workshop on Noncommutative Integr able Systems\n\nAbstract: TBA\n LOCATION:https://stable.researchseminars.org/talk/NIS2024/6/ END:VEVENT BEGIN:VEVENT SUMMARY:Irina Bobrova DTSTART:20240305T080000Z DTEND:20240305T090000Z DTSTAMP:20260404T095717Z UID:NIS2024/7 DESCRIPTION:Title: Non-Abelian ODEs and O∆Es\nby Irina Bobrova as part of Semina r-Type Workshop on Noncommutative Integrable Systems\n\nAbstract: TBA\n LOCATION:https://stable.researchseminars.org/talk/NIS2024/7/ END:VEVENT BEGIN:VEVENT SUMMARY:Vladimir Retakh DTSTART:20240307T003000Z DTEND:20240307T013000Z DTSTAMP:20260404T095717Z UID:NIS2024/8 DESCRIPTION:Title: Quasideterminants and their applications. An introduction II\nb y Vladimir Retakh as part of Seminar-Type Workshop on Noncommutative Integ rable Systems\n\nAbstract: TBA\n LOCATION:https://stable.researchseminars.org/talk/NIS2024/8/ END:VEVENT BEGIN:VEVENT SUMMARY:Volodya Roubtsov DTSTART:20240308T080000Z DTEND:20240308T090000Z DTSTAMP:20260404T095717Z UID:NIS2024/11 DESCRIPTION:Title: Painlevé equations – different facets of non-commutativity\ nby Volodya Roubtsov as part of Seminar-Type Workshop on Noncommutative In tegrable Systems\n\n\nAbstract\nI propose an overview my results on differ ent «non–commutative aspects» Painlevé equations and some related sys tems. \nI shall describe various non–commutative models associated with different Painlevé and corresponding toolbox and resulted properties and applications. \nOur methodology includes Gelfand–Retakh quasidetrminant technics for Painlevé II and IV\, isomonodrtomy representations for the matrix Takasaki Hamiltonian Calogero–Painlevé systems and some analogue s of Ruijsenaars duality.\n LOCATION:https://stable.researchseminars.org/talk/NIS2024/11/ END:VEVENT BEGIN:VEVENT SUMMARY:Sandra Carillo DTSTART:20240311T080000Z DTEND:20240311T084500Z DTSTAMP:20260404T095717Z UID:NIS2024/12 DESCRIPTION:Title: Bäcklund transformations and non-Abelian nonlinear evolution equa tions\nby Sandra Carillo as part of Seminar-Type Workshop on Noncommut ative Integrable Systems\n\n\nAbstract\nBäcklund transformations are well known to represent a powerful tool in investigating nonlinear differentia l equations. In particular\, we are concerned about so-called soliton equa tions since they admit soliton type solutions. The aim of the present stud y is twofold since\, on one side\, we consider the connections which can b e established and the induced structural properties\; on the other side\, we consider Bäcklund transformations as a tool to construct solutions\, a dmitted by nonlinear evolution equations. Hence\, first of all\, we consid er the links which can be established among different nonlinear evolution equations via Bäcklund transformations. Accordingly\, a net of connection s among different nonlinear evolution equations is depicted in a Bäcklund Chart\, as we term such a net of links. The attention is focussed on thir d order\, nonlinear evolution questions in particular\, the comparison be tween the commutative (Abelian) and the non-commutative cases is analyzed. Notably\, a richer structure can be observed when the commutativity condi tion is removed. Then\, via Bäcklund transformations\, solutions of matri x modified KdV equation can be constructed. Finally\, some new results as well as some problems\, currently under investigation\, concerning fifth order nonlinear evolution equations are mentioned. \nMost of the presented results are part of a joint research project with Cornelia Schiebold\, Su ndsvall University\, Sweden which involves also\, in alphabetical order\, M. Lo Schiavo\, Rome\, E. Porten\, Sundsvall\, and F. Zullo\, Brescia.\n LOCATION:https://stable.researchseminars.org/talk/NIS2024/12/ END:VEVENT BEGIN:VEVENT SUMMARY:Claire Gilson DTSTART:20240311T090000Z DTEND:20240311T100000Z DTSTAMP:20260404T095717Z UID:NIS2024/13 DESCRIPTION:Title: Pfaffian Solutions to Non-Commutative Integrable Systems\nby C laire Gilson as part of Seminar-Type Workshop on Noncommutative Integrable Systems\n\n\nAbstract\nSolutions to a number of integrable systems an be expressed in the form of Pfaffians. In this talk we shall investigate for ms for non-commutative Pfaffians via the quasi-determinant formalism. We shall explore the possibility of constructing new integrable systems emplo ying these non-commutative Pfaffians. Among the equations we shall explor e are the BKP equation\, the Novikov-Veselov equation and the Hirota-Ohta coupled soliton equations.\n LOCATION:https://stable.researchseminars.org/talk/NIS2024/13/ END:VEVENT BEGIN:VEVENT SUMMARY:Arkady Berenstein DTSTART:20240313T003000Z DTEND:20240313T013000Z DTSTAMP:20260404T095717Z UID:NIS2024/14 DESCRIPTION:Title: Noncommutative surfaces\, clusters\, and their symmetries\nby Arkady Berenstein as part of Seminar-Type Workshop on Noncommutative Integ rable Systems\n\n\nAbstract\nThe aim of my talk (based on joint work in pr ogress with Min Huang and Vladimir Retakh) is to introduce and study certa in noncommutative algebras $A$ for any marked surface. These algebras admi t noncommutative clusters\, i.e.\, embeddings of a given group $G$ which i s either free or one-relator (we call it triangle group) into the multipli cative monoid $A^\\times$. The clusters are parametrized by triangulations of the surface and exhibit a noncommutative Laurent Phenomenon\, which as serts that generators of the algebra can be written as sums of the images of elements of $G$ for any noncommutative cluster. If the surface is unpun ctured\, then our algebra $A$ can be specialized to the ordinary quantum c luster algebra\, and the noncommutative Laurent Phenomenon becomes the (po sitive) quantum one. \n\n It turns out that there is a natural action of a certain braid-like group $Br_A$ by automorphisms of $G$ on each cluster i n a compatible way (this is\, indeed\, the braid group $Br_n$ if the surfa ce is an unpunctured disk with n+2 marked boundary points). If surface is punctured\, the algebra $A$ admits a family of commuting automorphisms whi ch will give new clusters and new "tagged" noncommutative Laurent Phenomen a. \n\nThere are important elements in $A$ assigned to each marked point\ , which we refer to as noncommutative angles (or h-lengths). They belong t o the group algebra of each cluster group and are invariant under all nonc ommutative cluster mutations. This eventually gives rise to noncommutative integrable systems on unpunctured cylinders and other surfaces which\, in particular\, recover the ones introduced by Kontsevich in 2011 together w ith their Laurentness and positivity.\n LOCATION:https://stable.researchseminars.org/talk/NIS2024/14/ END:VEVENT BEGIN:VEVENT SUMMARY:Chun-Xia Li DTSTART:20240315T080000Z DTEND:20240315T090000Z DTSTAMP:20260404T095717Z UID:NIS2024/15 DESCRIPTION:Title: On construction and integrability of the noncommutative extended K P equation and the noncommutative extended mKP equation\nby Chun-Xia L i as part of Seminar-Type Workshop on Noncommutative Integrable Systems\n\ n\nAbstract\nGeneralization of soliton theory and integrable systems to th eir noncommutative counterparts is an interesting topic. Some classical in tegrable systems have been generalized to their noncommutative versions an d their integrability has been investigated. Moreover\, as is known that i ntegrable systems are closely related to other topcis such as orthogonal p olynomials and combinatorics. Their noncommutative generalization is of gr eat research interest too. KP equation is one of the most fundamental amon g many soliton equations. Its generalizations and extensions have been pai d much attention to. In this talk\, I will talk about how to construct the noncommutative extended KP equation and the noncommutative extended modif ied KP equation by using variation of parameter. As a consequence\, two ty pes of quasideterminant solutions are presented for the two noncommutative extended integrable systems respectively. In addition\, Miura transformat ions between them are established successfully as well.\n LOCATION:https://stable.researchseminars.org/talk/NIS2024/15/ END:VEVENT END:VCALENDAR