- \n
- Identify some geometr ic structures that imply interesting long term behaviors. \n
- Devel op rigorous methods that\, with a finite computations can establish the ex istence of these objects in concrete systems. \n

\n In this lecture we will overview a methodology for rigorously detecting quasi-periodic orbit s in Hamiltonian systems. The methodology involves analytical\, geometrica l and computational methods and covers from pen and paper rigorous results to computer-assisted rigorous results\, passing through algorithms (and t he study of their convergence) and implementations. We will present some ideas for performing computer assisted proofs in this context. In particu lar\, we will see FFT-methods for representing rigorously real-analytic pe riodic functions\, that are used to parameterize tori in phase space. We w ill see some applications in this context. We will finish the lecture wit h some other applications and further topics.\n LOCATION:https://researchseminars.org/talk/ONEPAS/10/ END:VEVENT BEGIN:VEVENT SUMMARY:Marian Gidea (Yeshiva University) DTSTART;VALUE=DATE-TIME:20201209T200000Z DTEND;VALUE=DATE-TIME:20201209T210000Z DTSTAMP;VALUE=DATE-TIME:20211128T084110Z UID:ONEPAS/11 DESCRIPTION:Title: Topological methods and Hamiltonian instability\nby Marian Gidea (Yesh iva University) as part of Online Northeast PDE and Analysis Seminar\n\n\n Abstract\nInstability of Hamiltonian systems is relevant to problems from celestial mechanics\, particle accelerators\, plasma confinement\, quasige ostrophic flows\, etc. Motivated by such applications\, one is interested in detecting mechanisms of instability in concrete models\, and in provid ing quantitative information on the unstable trajectories.\n

\n We will describe a topological method based on `correctly aligned windows '\, which can be used to derive properties concerning the long-term behavi or of dynamical systems. In particular\, this method enables one to dete ct topological horseshoes. The method can be implemented in computer assis ted proofs\, via validated numerical computations. We will show applicati on of this method to Hamiltonian instability. Concrete examples will incl ude mechanical systems consisting of rotators and penduli\, and the thre e-body problem in celestial mechanics.\n LOCATION:https://researchseminars.org/talk/ONEPAS/11/ END:VEVENT BEGIN:VEVENT SUMMARY:Jiaqi Yang (Georgia Tech) DTSTART;VALUE=DATE-TIME:20201216T200000Z DTEND;VALUE=DATE-TIME:20201216T210000Z DTSTAMP;VALUE=DATE-TIME:20211128T084110Z UID:ONEPAS/12 DESCRIPTION:Title: Invariant objects of infinite dimensional systems\nby Jiaqi Yang (Geor gia Tech) as part of Online Northeast PDE and Analysis Seminar\n\n\nAbstra ct\nTo find invariant objects with specified dynamics (e.g. periodic\, qua si-periodic\, etc.)\, we consider the space of functions in the correspond ing class and impose that they are solutions. This leads to solving functi onal equations. One advantage of this method is that it does not need to study the evolution\, which in some infinite dimensional problems is probl ematic. We will present some examples of solutions of special kinds in sta te dependent delay equations\, for which even the natural phase space is d ebatable.\n LOCATION:https://researchseminars.org/talk/ONEPAS/12/ END:VEVENT BEGIN:VEVENT SUMMARY:Patrick Flynn\, Milen Ivanov\, and Stefano Pasquali DTSTART;VALUE=DATE-TIME:20201217T190000Z DTEND;VALUE=DATE-TIME:20201217T210000Z DTSTAMP;VALUE=DATE-TIME:20211128T084110Z UID:ONEPAS/13 DESCRIPTION:Title: ONEPAS Young Researcher Showcase\nby Patrick Flynn\, Milen Ivanov\, an d Stefano Pasquali as part of Online Northeast PDE and Analysis Seminar\n\ nAbstract: TBA\n LOCATION:https://researchseminars.org/talk/ONEPAS/13/ END:VEVENT BEGIN:VEVENT SUMMARY:Israel Michael Sigal (University of Toronto) DTSTART;VALUE=DATE-TIME:20210211T200000Z DTEND;VALUE=DATE-TIME:20210211T210000Z DTSTAMP;VALUE=DATE-TIME:20211128T084110Z UID:ONEPAS/14 DESCRIPTION:Title: The partial differential equations of quantum mechanics\nby Israel Mic hael Sigal (University of Toronto) as part of Online Northeast PDE and Ana lysis Seminar\n\nAbstract: TBA\n LOCATION:https://researchseminars.org/talk/ONEPAS/14/ END:VEVENT BEGIN:VEVENT SUMMARY:Stephen Gustafson (University of British Columbia) DTSTART;VALUE=DATE-TIME:20210218T190000Z DTEND;VALUE=DATE-TIME:20210218T200000Z DTSTAMP;VALUE=DATE-TIME:20211128T084110Z UID:ONEPAS/15 DESCRIPTION:Title: Solitons and dynamics of Landau-Lifshitz equations in 2D\nby Stephen G ustafson (University of British Columbia) as part of Online Northeast PDE and Analysis Seminar\n\nAbstract: TBA\n LOCATION:https://researchseminars.org/talk/ONEPAS/15/ END:VEVENT BEGIN:VEVENT SUMMARY:Avy Soffer (Rutgers University) DTSTART;VALUE=DATE-TIME:20210225T200000Z DTEND;VALUE=DATE-TIME:20210225T210000Z DTSTAMP;VALUE=DATE-TIME:20211128T084110Z UID:ONEPAS/16 DESCRIPTION:Title: Evolution of NLS with bounded data\nby Avy Soffer (Rutgers University) as part of Online Northeast PDE and Analysis Seminar\n\nAbstract: TBA\n LOCATION:https://researchseminars.org/talk/ONEPAS/16/ END:VEVENT BEGIN:VEVENT SUMMARY:Michael Loss (Georgia Tech) DTSTART;VALUE=DATE-TIME:20210304T200000Z DTEND;VALUE=DATE-TIME:20210304T210000Z DTSTAMP;VALUE=DATE-TIME:20211128T084110Z UID:ONEPAS/17 DESCRIPTION:Title: Symmetry and symmetry breaking in functional inequalities\nby Michael Loss (Georgia Tech) as part of Online Northeast PDE and Analysis Seminar\n \nAbstract: TBA\n LOCATION:https://researchseminars.org/talk/ONEPAS/17/ END:VEVENT BEGIN:VEVENT SUMMARY:Ákos Nagy (University of California\, Santa Barbara) DTSTART;VALUE=DATE-TIME:20210311T200000Z DTEND;VALUE=DATE-TIME:20210311T210000Z DTSTAMP;VALUE=DATE-TIME:20211128T084110Z UID:ONEPAS/18 DESCRIPTION:Title: Novel solutions in Ginzburg–Landau theory\nby Ákos Nagy (University of California\, Santa Barbara) as part of Online Northeast PDE and Analys is Seminar\n\nAbstract: TBA\n LOCATION:https://researchseminars.org/talk/ONEPAS/18/ END:VEVENT BEGIN:VEVENT SUMMARY:Peter Hislop (University of Kentucky) DTSTART;VALUE=DATE-TIME:20210318T190000Z DTEND;VALUE=DATE-TIME:20210318T200000Z DTSTAMP;VALUE=DATE-TIME:20211128T084110Z UID:ONEPAS/19 DESCRIPTION:Title: Eigenvalue statistics for some random Schrödinger operators and random ba nd matrices\nby Peter Hislop (University of Kentucky) as part of Onlin e Northeast PDE and Analysis Seminar\n\nAbstract: TBA\n LOCATION:https://researchseminars.org/talk/ONEPAS/19/ END:VEVENT BEGIN:VEVENT SUMMARY:Jacob Shapiro (Princeton) DTSTART;VALUE=DATE-TIME:20210325T190000Z DTEND;VALUE=DATE-TIME:20210325T200000Z DTSTAMP;VALUE=DATE-TIME:20211128T084110Z UID:ONEPAS/20 DESCRIPTION:Title: Tight-binding limits in strong magnetic fields and the integer quantum Hal l effect\nby Jacob Shapiro (Princeton) as part of Online Northeast PDE and Analysis Seminar\n\nAbstract: TBA\n LOCATION:https://researchseminars.org/talk/ONEPAS/20/ END:VEVENT BEGIN:VEVENT SUMMARY:Irene Fonseca (Carnegie Mellon) DTSTART;VALUE=DATE-TIME:20210401T163000Z DTEND;VALUE=DATE-TIME:20210401T173000Z DTSTAMP;VALUE=DATE-TIME:20211128T084110Z UID:ONEPAS/21 DESCRIPTION:Title: The mathematics of thin structures\nby Irene Fonseca (Carnegie Mellon) as part of Online Northeast PDE and Analysis Seminar\n\nAbstract: TBA\n LOCATION:https://researchseminars.org/talk/ONEPAS/21/ END:VEVENT BEGIN:VEVENT SUMMARY:Gilles Francfort (Université Paris XIII) DTSTART;VALUE=DATE-TIME:20210408T163000Z DTEND;VALUE=DATE-TIME:20210408T173000Z DTSTAMP;VALUE=DATE-TIME:20211128T084110Z UID:ONEPAS/22 DESCRIPTION:Title: Beyond membranes\nby Gilles Francfort (Université Paris XIII) as part of Online Northeast PDE and Analysis Seminar\n\nAbstract: TBA\n LOCATION:https://researchseminars.org/talk/ONEPAS/22/ END:VEVENT BEGIN:VEVENT SUMMARY:Marta Lewicka (University of Pittsburgh) DTSTART;VALUE=DATE-TIME:20210415T163000Z DTEND;VALUE=DATE-TIME:20210415T173000Z DTSTAMP;VALUE=DATE-TIME:20211128T084110Z UID:ONEPAS/23 DESCRIPTION:Title: Geometry and morphogenesis: problems and prospects\nby Marta Lewicka ( University of Pittsburgh) as part of Online Northeast PDE and Analysis Sem inar\n\nAbstract: TBA\n LOCATION:https://researchseminars.org/talk/ONEPAS/23/ END:VEVENT BEGIN:VEVENT SUMMARY:Giovanni Di Fratta (TU Wien) DTSTART;VALUE=DATE-TIME:20210422T163000Z DTEND;VALUE=DATE-TIME:20210422T173000Z DTSTAMP;VALUE=DATE-TIME:20211128T084110Z UID:ONEPAS/24 DESCRIPTION:Title: Micromagnetics of curved thin films\nby Giovanni Di Fratta (TU Wien) a s part of Online Northeast PDE and Analysis Seminar\n\nAbstract: TBA\n LOCATION:https://researchseminars.org/talk/ONEPAS/24/ END:VEVENT BEGIN:VEVENT SUMMARY:Maria Giovanna Mora (University of Pavia) DTSTART;VALUE=DATE-TIME:20210429T163000Z DTEND;VALUE=DATE-TIME:20210429T173000Z DTSTAMP;VALUE=DATE-TIME:20211128T084110Z UID:ONEPAS/25 DESCRIPTION:Title: The energy of a Möbius strip\nby Maria Giovanna Mora (University of P avia) as part of Online Northeast PDE and Analysis Seminar\n\nAbstract: TB A\n LOCATION:https://researchseminars.org/talk/ONEPAS/25/ END:VEVENT BEGIN:VEVENT SUMMARY:Jean-François Babadjian (Université Paris Saclay) DTSTART;VALUE=DATE-TIME:20210506T163000Z DTEND;VALUE=DATE-TIME:20210506T173000Z DTSTAMP;VALUE=DATE-TIME:20211128T084110Z UID:ONEPAS/26 DESCRIPTION:Title: Reduced models for linearly elastic thin films allowing for fracture\, deb onding or delamination\nby Jean-François Babadjian (Université Paris Saclay) as part of Online Northeast PDE and Analysis Seminar\n\nAbstract: TBA\n LOCATION:https://researchseminars.org/talk/ONEPAS/26/ END:VEVENT BEGIN:VEVENT SUMMARY:Cyrill Muratov (New Jersey Institute of Technology) DTSTART;VALUE=DATE-TIME:20210513T163000Z DTEND;VALUE=DATE-TIME:20210513T173000Z DTSTAMP;VALUE=DATE-TIME:20211128T084110Z UID:ONEPAS/27 DESCRIPTION:by Cyrill Muratov (New Jersey Institute of Technology) as part of Online Northeast PDE and Analysis Seminar\n\nAbstract: TBA\n LOCATION:https://researchseminars.org/talk/ONEPAS/27/ END:VEVENT 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