BEGIN:VCALENDAR VERSION:2.0 PRODID:-//wp-events-plugin.com//7.2.3.1//EN TZID:Europe/Paris X-WR-TIMEZONE:Europe/Paris BEGIN:VEVENT UID:8128@i2m.univ-amu.fr DTSTART;TZID=Europe/Paris:20150323T000000 DTEND;TZID=Europe/Paris:20150327T000000 DTSTAMP:20241211T153001Z URL:https://www.i2m.univ-amu.fr/evenements/artin-approximation-and-infinit e-dimensional-geometry-morlet-chair-herwig-hauser/ SUMMARY:Conference (CIRM\, Luminy\, Marseille): Artin Approximation and Inf inite Dimensional Geometry (Morlet Chair - Herwig Hauser) DESCRIPTION:Conference: \n\n\n\n\n CIRM - Jean-Morlet Chair \n Herwig Hause r &\; Guillaume Rond\n\nSingularities and Artin Approximation​\n\nSin gularités et approximation de Artin\n\n\n 2015-Semester 1 \n\n\n\n\n\n\n\ n\n\n\n\n\n\n\n\n\n\n\nMAIN CONFERENCE\nArtin Approximation and Infinite D imensional Geometry (1255)\nApproximation de Artin et géométrie dimensio nnelle infinie\nDates: 23-27 March 2015 at CIRM (Marseille\, France)\nPlac e : CIRM (Marseille Luminy\, France)\n\n\n\n\n \n\n\n\n\n\n\n\n\n\n\n\n\n \n\n\n\n\n\n\n\n SCHEDULE \n\n\n\n\n\n PARTICIPANTS \n\n\n\n\n\n ABSTRACTS \n\n\n\n\n\n\n \n\n\n\n\n\n\n\n \n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\nDES CRIPTION\n​\nSymplectic topology can be considered as the mathematical v ersant of String theory. They were discovered independently at the same ti me in the 80's. The second one is a fantastic enterprise to unify low-scal e and highscale physics\, while the first one was born as a tool to resol ve the extraordinarily difficult problems of closed orbits in non-integra ble generic Hamiltonian systems (the famous Arnold and Weinstein conjectur es). Since that time\, both theories have developed into a far reaching ma thematical endeavour and much of today's attention from the geometers acro ss the world is directed towards the many conjectures of Symplectic Topolo gy. Symplectic Topology is\, together with Number Theory\, the only field that seems able to produce very simple conjectures that are notoriously h ard to prove. It is also the only theory\, to our knowledge\, that produce s deep and rich moduli spaces at such a pace! This workshop will bring tog ether the best specialists in the world around the problems of moduli spac es in Symplectic topology and Gauge theory. These rich moduli spaces are a lways set up to de fine functors or morphisms depending on pertinent non-l inear elliptic PDE's configurations \, often coupled with trees of Morse f lows. Our understanding of these moduli spaces is based on (1) the appropr iate setting for these moduli spaces to get the right compactifi cation ne eded (of which Uhlenbeck's and the Gromov's compacti fication theorems are just the very first basic blocks)\, and (2) the construction of the alge braic structures that prevail in these moduli spaces and that\, ultimately \, govern the whole Floer-SFT-like theory. So the workshop was divided alo ng these lines in the following way:\n1. Analytic foundations and applica tions to dynamics.\nThat part of the workshop focused on the following thr ee subjects that are in fast development:\na. Analytical foundations of Sy mplectic Field Theory. The main development in this direction is that the monumental work of Hofer-Wisocki-Zehnder is now reaching cruising speed an d is now starting to be understood and applied by more and more researcher s. In particular\, it is expected that in a few years the foundations of t he various symplectic fi eld theories will become solid.\nb. Closed orbits of Hamiltonian flows\, symplectic dynamics and Seiberg-Witten Floer homol ogy. A number of spectacular results have been obtained recently in this d irection. For instance\, Taubes' proof of the Weinstein conjecture is rela ted to the embedded contact homology of Hutchings\, and extensions of his proof of this conjecture yielded the famous isomorphism between embedded c ontact homology and Seiberg-Witten Floer homology.\nAnother application of the theory is Ginzburg's proof of the Conley conjecture. In a di fferent direction\, we mentioned the dynamical perspective on the study of groups of Hamiltonian   di ffeomorphisms provided by the "quasi-morphisms" work of Entov-Polterovich.\nc. Mean curvature flows for Lagrangian submanifold s. This is a direction that only is starting to get on the "screen" these days but will become quite signi cant in the years to come. It is concerne d with properties of the mean curvature flows applied to Lagrangian subman ifolds as discussed in the work of Yau\, Joyce\, Smoczyk\, Schwarz\, Neves \, Tian and others.2. Algebraic structures and ramifi cations.\nThere are three subjects in this direction that were discussed:\na. Further algebra ic structures. The complexity of algebraic structures used today in symple ctic topology is quite high but even more sophisticated constructions are attempted these days by various authors\, especially Fukaya et al.\, Elias hberg and collaborators\, Seidel\, Abouzaid\, Auroux in particular. This i s sometimes done in relation to Mirror Symmetry (Seidel\, Abouzaid\, Aurou x ) or in relation to Lagrangian topology (for instance by Cornea-Lalonde\ , Biran-Cornea\, Hu-Lalonde).\nb. Enumerative invariants for Lagrangian su bmanifolds. A topic of much interest these days\, these constructions are reflected in work on "real" symplectic topology as pursued by Welschinger\ , Solomon and others. There are also other developments in the Calabi-Yau case (by Yau\, Fukaya\, Iacovino) as well as in the monotone Lagrangian ca se by Biran-Cornea.\nc. Rami fications. This concerns a number of exciting relations with a number of different other subjects which are in the proc ess of being understood today. For instance\, relations with number theory as exempli fied by recent work of McDuff -Schlenk as well as Biran-Cornea . Relations with toric geometry as described in the work of Fukaya-Oh-Ohta -Ono.\n\n\n \n\nSCIENTIFIC COMMITTEE\n\n\n Javier Fernández de Bobadill a (Madrid)\n Herwig Hauser (Vienna)\n Melvin Hochster (Michigan)\n Leon ard Lipshitz (Purdue)\n François Loeser (Paris)\n\n\n\nORGANIZING COMMIT TEE\n\n\n Herwig Hauser (Vienna)\n Guillaume Rond (Marseille)\n\n\n\nSPE AKERS\n\n\n Janusz Adamus (London - Ontario)\n\nOn relative Nash approxi mation of complex analytic sets (pdf)\n\n Matthias Aschenbrenner (Los An geles)\n\nThe algebra and model theory of transseries (pdf)\n\n Raf Cluck ers (CNRS Lille/Leuven)\n\nPfaffian functions: real and non-archimedean\, and an application to counting rational points (pdf)\n\n Jan Draisma (E indhoven) \n\nStabilisation in algebraic geometry (pdf)\n\n Jack Hall (C anberra)\n\nTannaka duality and formal glueings (pdf)\n\n Shuzo Izumi (Os aka)\n\nZero-estimates from geometric point of view (pdf)\n\n Pierre Lai rez (Berlin)\n\nDiagonals of rational functions (pdf)\n\n Leonard Lipshi tz (Purdue)\n\nArtin Approximation\, recursion relations\, decidability an d definability in local rings and fields (pdf)\n\n Henri Lombardi (Franc he-Comté)\n\nConstructive steps towards Popescu desingularization theorem (pdf)\n\n Nordine Mir (Doha)\n\nArtin approximation and Cauchy-Riemann g eometry (pdf)\n\n Laurent Moret-Bailly (Rennes)\n\nTopological aspects of  strong approximation: the case of torsors over valued fields (pdf)\n\n Hussein Mourtada (Paris Diderot)\n\nArc spaces and Rogers-Ramanujan ident ities (pdf)\n\n Maria Pé Pereira (Madrid) \n\nAbout the arc space of C2 and adjacencies of plane curves (tba)\n\n Dorin Popescu (Bucarest)\n\nOn the regular local rings (pdf)\n\n Ana Reguera (Valladolid)\n\nHow to obt ain finiteness properties in the infinite dimensional scheme of the space of arcs (pdf)\n\n David Rydh (Stockholm)\n\nEquivariant Artin algebraiz ation (pdf)\n\n Hans Schoutens (New York)\n\nThe synergy between Artin Ap proximation and Ultraproducts (pdf)\n\n Julien Sebag (Rennes)\n\nThe Grot hendieck ring of varieties (pdf)\n\n Mark Spivakovsky (CNRS Toulouse)\n\n Popescu's theorem and (nested) Artin approximation (pdf)\n\n Sebastian Wo blistin (Vienna)\n\nGeometry of analytic subset of power series spaces (pd f)\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\nSPONSORS\n\n\n\n \n\n\n\n\n\n\n\n\n \n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n CATEGORIES:Colloque,Morlet Chair Semester END:VEVENT BEGIN:VTIMEZONE TZID:Europe/Paris X-LIC-LOCATION:Europe/Paris BEGIN:STANDARD DTSTART:20141026T020000 TZOFFSETFROM:+0200 TZOFFSETTO:+0100 TZNAME:CET END:STANDARD END:VTIMEZONE END:VCALENDAR