BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Valentin Lychagin DTSTART:20261007T162000Z DTEND:20261007T180000Z DTSTAMP:20261004T235242Z UID:GDEq/160 DESCRIPTION:Title: T hermodynamics\, jets geometry and phase transitions\nby Valentin Lycha gin as part of Geometry of differential equations seminar\n\nLecture held in room 303 of the Independent University of Moscow.\n\nAbstract\nIn this talk\, we will discuss equations of state and phase transitions in thermod ynamics\, as well as their relationship to the geometry of jet spaces and differential equations.\n\nThe equations of state give a description of th e thermodynamic media under consideration and\, in the simplest case\, are geometrically realized as Legendre manifolds in the contact space. This c orresponds to first-order thermodynamics\, and phase transitions of the 1s t order correspond to the singularities of their projection onto the space of intensive quantities\, and thus their study is based on Arnold's theor y of the singularities of projections of Legendre and Lagrangian manifolds .\n\nIn practice\, it is sometimes more convenient to set equations of sta te by thermodynamic quantities of the second and higher orders\, which mea ns a transition from contact geometry to the geometry of the spaces of jet s of the second and higher order. This will be discussed in the talk\, and the relationship of the equations of state with overdetermined systems of partial differential equations and with integral manifolds of the Cartan distribution is shown.\n\nIf time allows\, the relationship between second - and higher-order phase transitions and the singularities given by integr al manifolds of the Cartan distribution will be considered.\n\nThe propose d approach will also be illustrated by examples from thermodynamics.\n LOCATION:https://researchseminars.org/talk/GDEq/160/ END:VEVENT END:VCALENDAR