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:20260422T214955Z UID:NIS2024/4 DESCRIPTION:Title: Non-Abelian ODEs and O∆Es\nby Irina Bobrova as part of Seminar-Type Workshop on Noncommutative Integrable Systems\n\n\nAbstract\nSome solution s of important integrable systems can be expressed in terms of ordinary di fferential or difference equations. The famous Painlevé equations are a g ood example of this phenomenon. Since the theory of integrable systems has been developing intensively towards the non-commutative case\, the questi on of defining and deriving non-abelian ODEs and O∆Es becomes natural. \ n\nIn this series of lectures\, we will discuss some methods for the deriv ing and classification of such equations as well as investigation their in tegrability.\n LOCATION:https://researchseminars.org/talk/NIS2024/4/ END:VEVENT BEGIN:VEVENT SUMMARY:Vladimir Retakh DTSTART:20240308T003000Z DTEND:20240308T013000Z DTSTAMP:20260422T214955Z UID:NIS2024/5 DESCRIPTION:Title: Quasideterminants and their applications. An introduction III\nby Vlad imir Retakh as part of Seminar-Type Workshop on Noncommutative Integrable Systems\n\nAbstract: TBA\n LOCATION:https://researchseminars.org/talk/NIS2024/5/ END:VEVENT BEGIN:VEVENT SUMMARY:Vladimir Retakh DTSTART:20240305T003000Z DTEND:20240305T013000Z DTSTAMP:20260422T214955Z UID:NIS2024/6 DESCRIPTION:Title: Quasideterminants and their applications. An introduction I\nby Vladim ir Retakh as part of Seminar-Type Workshop on Noncommutative Integrable Sy stems\n\nAbstract: TBA\n LOCATION:https://researchseminars.org/talk/NIS2024/6/ END:VEVENT BEGIN:VEVENT SUMMARY:Irina Bobrova DTSTART:20240305T080000Z DTEND:20240305T090000Z DTSTAMP:20260422T214955Z UID:NIS2024/7 DESCRIPTION:Title: Non-Abelian ODEs and O∆Es\nby Irina Bobrova as part of Seminar-Type Workshop on Noncommutative Integrable Systems\n\nAbstract: TBA\n LOCATION:https://researchseminars.org/talk/NIS2024/7/ END:VEVENT BEGIN:VEVENT SUMMARY:Vladimir Retakh DTSTART:20240307T003000Z DTEND:20240307T013000Z DTSTAMP:20260422T214955Z UID:NIS2024/8 DESCRIPTION:Title: Quasideterminants and their applications. An introduction II\nby Vladi mir Retakh as part of Seminar-Type Workshop on Noncommutative Integrable S ystems\n\nAbstract: TBA\n LOCATION:https://researchseminars.org/talk/NIS2024/8/ END:VEVENT BEGIN:VEVENT SUMMARY:Volodya Roubtsov DTSTART:20240308T080000Z DTEND:20240308T090000Z DTSTAMP:20260422T214955Z UID:NIS2024/11 DESCRIPTION:Title: Painlevé equations – different facets of non-commutativity\nby Vol odya Roubtsov as part of Seminar-Type Workshop on Noncommutative Integrabl e Systems\n\n\nAbstract\nI propose an overview my results on different «n on–commutative aspects» Painlevé equations and some related systems. \ nI shall describe various non–commutative models associated with differe nt Painlevé and corresponding toolbox and resulted properties and applic ations. \nOur methodology includes Gelfand–Retakh quasidetrminant techni cs for Painlevé II and IV\, isomonodrtomy representations for the matrix Takasaki Hamiltonian Calogero–Painlevé systems and some analogues of Ru ijsenaars duality.\n LOCATION:https://researchseminars.org/talk/NIS2024/11/ END:VEVENT BEGIN:VEVENT SUMMARY:Sandra Carillo DTSTART:20240311T080000Z DTEND:20240311T084500Z DTSTAMP:20260422T214955Z UID:NIS2024/12 DESCRIPTION:Title: Bäcklund transformations and non-Abelian nonlinear evolution equations\nby Sandra Carillo as part of Seminar-Type Workshop on Noncommutative I ntegrable Systems\n\n\nAbstract\nBäcklund transformations are well known to represent a powerful tool in investigating nonlinear differential equat ions. In particular\, we are concerned about so-called soliton equations s ince they admit soliton type solutions. The aim of the present study is tw ofold since\, on one side\, we consider the connections which can be estab lished and the induced structural properties\; on the other side\, we cons ider Bäcklund transformations as a tool to construct solutions\, admitted by nonlinear evolution equations. Hence\, first of all\, we consider the links which can be established among different nonlinear evolution equatio ns via Bäcklund transformations. Accordingly\, a net of connections among different nonlinear evolution equations is depicted in a Bäcklund Chart\ , as we term such a net of links. The attention is focussed on third order \, nonlinear evolution questions in particular\, the comparison between t he commutative (Abelian) and the non-commutative cases is analyzed. Notabl y\, a richer structure can be observed when the commutativity condition is removed. Then\, via Bäcklund transformations\, solutions of matrix modif ied KdV equation can be constructed. Finally\, some new results as well a s some problems\, currently under investigation\, concerning fifth order n onlinear evolution equations are mentioned. \nMost of the presented result s are part of a joint research project with Cornelia Schiebold\, Sundsvall University\, Sweden which involves also\, in alphabetical order\, M. Lo Schiavo\, Rome\, E. Porten\, Sundsvall\, and F. Zullo\, Brescia.\n LOCATION:https://researchseminars.org/talk/NIS2024/12/ END:VEVENT BEGIN:VEVENT SUMMARY:Claire Gilson DTSTART:20240311T090000Z DTEND:20240311T100000Z DTSTAMP:20260422T214955Z UID:NIS2024/13 DESCRIPTION:Title: Pfaffian Solutions to Non-Commutative Integrable Systems\nby Claire G ilson as part of Seminar-Type Workshop on Noncommutative Integrable System s\n\n\nAbstract\nSolutions to a number of integrable systems an be express ed in the form of Pfaffians. In this talk we shall investigate forms for non-commutative Pfaffians via the quasi-determinant formalism. We shall e xplore the possibility of constructing new integrable systems employing th ese non-commutative Pfaffians. Among the equations we shall explore are t he BKP equation\, the Novikov-Veselov equation and the Hirota-Ohta coupled soliton equations.\n LOCATION:https://researchseminars.org/talk/NIS2024/13/ END:VEVENT BEGIN:VEVENT SUMMARY:Arkady Berenstein DTSTART:20240313T003000Z DTEND:20240313T013000Z DTSTAMP:20260422T214955Z UID:NIS2024/14 DESCRIPTION:Title: Noncommutative surfaces\, clusters\, and their symmetries\nby Arkady Berenstein as part of Seminar-Type Workshop on Noncommutative Integrable S ystems\n\n\nAbstract\nThe aim of my talk (based on joint work in progress with Min Huang and Vladimir Retakh) is to introduce and study certain nonc ommutative algebras $A$ for any marked surface. These algebras admit nonco mmutative clusters\, i.e.\, embeddings of a given group $G$ which is eithe r free or one-relator (we call it triangle group) into the multiplicative monoid $A^\\times$. The clusters are parametrized by triangulations of the surface and exhibit a noncommutative Laurent Phenomenon\, which asserts t hat generators of the algebra can be written as sums of the images of elem ents of $G$ for any noncommutative cluster. If the surface is unpunctured\ , then our algebra $A$ can be specialized to the ordinary quantum cluster algebra\, and the noncommutative Laurent Phenomenon becomes the (positive) quantum one. \n\n It turns out that there is a natural action of a certai n braid-like group $Br_A$ by automorphisms of $G$ on each cluster in a com patible way (this is\, indeed\, the braid group $Br_n$ if the surface is a n unpunctured disk with n+2 marked boundary points). If surface is punctur ed\, the algebra $A$ admits a family of commuting automorphisms which will give new clusters and new "tagged" noncommutative Laurent Phenomena. \n\ nThere are important elements in $A$ assigned to each marked point\, which we refer to as noncommutative angles (or h-lengths). They belong to the g roup algebra of each cluster group and are invariant under all noncommutat ive cluster mutations. This eventually gives rise to noncommutative integr able systems on unpunctured cylinders and other surfaces which\, in partic ular\, recover the ones introduced by Kontsevich in 2011 together with the ir Laurentness and positivity.\n LOCATION:https://researchseminars.org/talk/NIS2024/14/ END:VEVENT BEGIN:VEVENT SUMMARY:Chun-Xia Li DTSTART:20240315T080000Z DTEND:20240315T090000Z DTSTAMP:20260422T214955Z UID:NIS2024/15 DESCRIPTION:Title: On construction and integrability of the noncommutative extended KP equat ion and the noncommutative extended mKP equation\nby Chun-Xia Li as pa rt of Seminar-Type Workshop on Noncommutative Integrable Systems\n\n\nAbst ract\nGeneralization of soliton theory and integrable systems to their non commutative counterparts is an interesting topic. Some classical integrabl e systems have been generalized to their noncommutative versions and their integrability has been investigated. Moreover\, as is known that integrab le systems are closely related to other topcis such as orthogonal polynomi als and combinatorics. Their noncommutative generalization is of great res earch interest too. KP equation is one of the most fundamental among many soliton equations. Its generalizations and extensions have been paid much attention to. In this talk\, I will talk about how to construct the noncom mutative extended KP equation and the noncommutative extended modified KP equation by using variation of parameter. As a consequence\, two types of quasideterminant solutions are presented for the two noncommutative extend ed integrable systems respectively. In addition\, Miura transformations be tween them are established successfully as well.\n LOCATION:https://researchseminars.org/talk/NIS2024/15/ END:VEVENT END:VCALENDAR