BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Walter Strauss (Brown University) DTSTART:20200915T190000Z DTEND:20200915T200000Z DTSTAMP:20260422T225719Z UID:ONEPAS/1 DESCRIPTION:Title: I ntroduction to steady water waves\nby Walter Strauss (Brown University ) as part of Online Northeast PDE and Analysis Seminar\n\n\nAbstract\nThis is a very basic introduction. No previous knowledge of water waves is re quired. I will mention the high points of the history of water wave theory . Then the fundamental equations inside the water and on the free boundar y will be discussed. Finally\, many important directions of current resear ch will be briefly outlined.\n LOCATION:https://researchseminars.org/talk/ONEPAS/1/ END:VEVENT BEGIN:VEVENT SUMMARY:John Toland (University of Bath) DTSTART:20200922T190000Z DTEND:20200922T200000Z DTSTAMP:20260422T225719Z UID:ONEPAS/2 DESCRIPTION:Title: V ariational aspects of steady irrotational water wave theory\nby John T oland (University of Bath) as part of Online Northeast PDE and Analysis Se minar\n\n\nAbstract\nAmong the many modern approaches to abstract nonlinea r problems\, those based on the implicit function theorem\, real-analytic function theory\, Nash-Moser theory and topological degree theory have mad e significant contributions to water-wave theory in recent years. However\ , the same cannot be said of variational methods (min/max\, mountain-pass\ , Morse index\, Lyusternik-Schnirelman genus etc) even though\, when the v iscosity of water is ignored and the flow is assumed to be irrotational\, there are several attractive ways to formulate the equations of wave motio n variationally. On the 100th anniversary of the first proof that the equa tions of motion have non-zero\, small-amplitude solutions\, this talk will briefly survey these issues and advocate variational methods for analyzin g water waves that are 2π-periodic in space.\n LOCATION:https://researchseminars.org/talk/ONEPAS/2/ END:VEVENT BEGIN:VEVENT SUMMARY:Susanna Haziot (University of Vienna) DTSTART:20200929T190000Z DTEND:20200929T200000Z DTSTAMP:20260422T225719Z UID:ONEPAS/3 DESCRIPTION:Title: R otational water waves\nby Susanna Haziot (University of Vienna) as par t of Online Northeast PDE and Analysis Seminar\n\n\nAbstract\nOne signific ant difficulty of working with water waves is that the boundary of the flu id domain itself is an unknown. I will begin with a brief presentation of the steady water wave problem for waves with vorticity. Subsequently\, I w ill review some existence results as well as present recent research which involve different methods for transforming the fluid domain into a fixed domain.\n LOCATION:https://researchseminars.org/talk/ONEPAS/3/ END:VEVENT BEGIN:VEVENT SUMMARY:Vera Mikyoung Hur (University of Illinois at Urbana-Champaign) DTSTART:20201013T190000Z DTEND:20201013T200000Z DTSTAMP:20260422T225719Z UID:ONEPAS/4 DESCRIPTION:Title: S tokes waves in constant vorticity flows\nby Vera Mikyoung Hur (Univers ity of Illinois at Urbana-Champaign) as part of Online Northeast PDE and A nalysis Seminar\n\n\nAbstract\nI will discuss recent progress on the numer ical computation of Stokes waves in constant vorticity flows. Based on a B abenko-kind equation\, our result improves those in the 1980s by Simmen an d Saffman\, Teles da Silva and Peregrine. Notably\, it reveals a plethora of new solutions: Crapper's exact solution (even though there is no surfac e tension)\, a fluid disk in rigid body rotation\, etc. I will also discus s the effects of vorticity on the extreme wave\, particularly\, the maximu m slope for an almost extreme wave. I will discuss some open problems\, bo th analytical and numerical.\n LOCATION:https://researchseminars.org/talk/ONEPAS/4/ END:VEVENT BEGIN:VEVENT SUMMARY:Samuel Walsh (University of Missouri) DTSTART:20201027T190000Z DTEND:20201027T200000Z DTSTAMP:20260422T225719Z UID:ONEPAS/5 DESCRIPTION:Title: W ater waves with density stratification or localized vorticity\nby Samu el Walsh (University of Missouri) as part of Online Northeast PDE and Anal ysis Seminar\n\n\nAbstract\nThis talk will serve as a general introduction to two areas of active research in water waves. In the ocean\, the presen ce of salt and temperature gradients can lead to substantial stratificatio n of the density. This phenomenon is well-known to have significant physic al implications. Indeed\, it makes possible enormous ``internal waves'' th at can dwarf even the largest waves seen on the surface. We will present a n overview of the mathematical work on this subject\, focusing primarily o n recent results regarding the existence of large-amplitude solitary strat ified waves.\n\nThe second part of the talk will discuss waves with locali zed distributions of vorticity. These include water waves with submerged p oint vortices\, dipoles\, vortex patches\, and those exhibiting a vortex s pike.\n\nThis is joint work with Robin Ming Chen\, Mats Ehrnström\, Jalal Shatah\, Kristoffer Varholm\, Erik Wahlén\, Miles H. Wheeler\, and Chon gchun Zeng.\n LOCATION:https://researchseminars.org/talk/ONEPAS/5/ END:VEVENT BEGIN:VEVENT SUMMARY:Miles Wheeler (University of Bath) DTSTART:20201020T190000Z DTEND:20201020T200000Z DTSTAMP:20260422T225719Z UID:ONEPAS/6 DESCRIPTION:Title: S olitary waves and fronts\nby Miles Wheeler (University of Bath) as par t of Online Northeast PDE and Analysis Seminar\n\n\nAbstract\nI will give a general introduction to the theory of solitary water waves\, that is tra veling waves whose surfaces converge to some asymptotic height at infinity . In many respects\, the theory for solitary waves is more difficult and m ore subtle than that for periodic waves. Yet in other ways the problem is much simpler\, and indeed many results for solitary waves are stronger tha n their periodic counterparts. \n\nBeginning with the linear theory\, or p erhaps more accurately the lack of a linear theory\, I will expla in how small-amplitude waves can be rigorously constructed via a center ma nifold reduction. Next I will collect a series of results which together g uarantee that any solitary wave\, regardless of amplitude\, is symmetric a nd decreasing about a central crest and travels at a “supercritical” s peed $c>\\sqrt{gd}$. Finally\, I will explain how the significant obstacle s to applying global bifurcation techniques can be overcome by taking adva ntage of the above properties together with the nonexistence of f ront-type solutions. This approach is surprisingly robust\, and has recent ly been generalized to apply to front-type solutions in addition to solita ry waves.\n LOCATION:https://researchseminars.org/talk/ONEPAS/6/ END:VEVENT BEGIN:VEVENT SUMMARY:Erik Wahlén (Lund University) DTSTART:20201103T200000Z DTEND:20201103T210000Z DTSTAMP:20260422T225719Z UID:ONEPAS/7 DESCRIPTION:Title: T hree-dimensional water waves\nby Erik Wahlén (Lund University) as par t of Online Northeast PDE and Analysis Seminar\n\n\nAbstract\nThe other ta lks in the series have concentrated on two-dimensional water waves. In my talk I will give an overview of the considerably younger three-dimensional theory. In the irrotational case\, there is by now a rich existence theor y for small-amplitude solutions. These can have different behaviours in di fferent horizontal directions\, e.g. periodic or solitary. In the talk I w ill mainly focus on waves which are "doubly periodic"\, that is\, periodic in two different horizontal directions\, or "fully localised"\, that is\, solitary in all horizontal directions. As we will see\, surface tension p lays a much more crucial role than in 2D. I will also discuss some recent work on 3D water waves with vorticity.\n LOCATION:https://researchseminars.org/talk/ONEPAS/7/ END:VEVENT BEGIN:VEVENT SUMMARY:Rafael de la Llave (Georgia Tech) DTSTART:20201111T200000Z DTEND:20201111T210000Z DTSTAMP:20260422T225719Z UID:ONEPAS/8 DESCRIPTION:Title: C onstructive methods for the long term analysis of dynamics\nby Rafael de la Llave (Georgia Tech) as part of Online Northeast PDE and Analysis Se minar\n\n\nAbstract\nThe long term behavior of dynamical systems is an imp ortant practical problem in technology and a deep challenge for mathemati cs. In this set of lectures\, we plan to present some ideas of a concrete methodology that can be used to study the long term dynamics of some given systems. The key idea is to: \n We can on ly cover some generalities and some vignettes that illustrate these progra m both in finite dimensional problems and in infinite dimensional systems. This first lecture will present some of the main tools from analysis and topology.\n LOCATION:https://researchseminars.org/talk/ONEPAS/8/ END:VEVENT BEGIN:VEVENT SUMMARY:Rafael de la Llave (Georgia Tech) DTSTART:20201118T200000Z DTEND:20201118T210000Z DTSTAMP:20260422T225719Z UID:ONEPAS/9 DESCRIPTION:Title: H ard implicit function theorems\nby Rafael de la Llave (Georgia Tech) a s part of Online Northeast PDE and Analysis Seminar\n\n\nAbstract\nThe mai n idea is the Newton method with iteration. We will discuss the conjugac y of circle maps\, following Moser's Pisa Lectures. A proof of the theore m will be given along with numerical implementation.\n LOCATION:https://researchseminars.org/talk/ONEPAS/9/ END:VEVENT BEGIN:VEVENT SUMMARY:Alex Haro (University of Barcelona) DTSTART:20201202T200000Z DTEND:20201202T210000Z DTSTAMP:20260422T225719Z UID:ONEPAS/10 DESCRIPTION:Title: Computer-assisted applications of KAM theory\nby Alex Haro (University of Barcelona) as part of Online Northeast PDE and Analysis Seminar\n\n\nA bstract\nStability of Hamiltonian systems is relevant to problems from cel estial mechanics\, particle accelerators\, plasma confinement\, quasigeost rophic flows\, etc. Motivated by such applications\, one is interested in detecting mechanisms of stability in concrete models\, and in providing qu antitative information on the stable trajectories. KAM theory concerns the existence of quasi-periodic solutions\, that are geometrically described as orbits lying inside invariant tori.\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:20201209T200000Z DTEND:20201209T210000Z DTSTAMP:20260422T225719Z 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:20201216T200000Z DTEND:20201216T210000Z DTSTAMP:20260422T225719Z 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:20201217T190000Z DTEND:20201217T210000Z DTSTAMP:20260422T225719Z 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:20210211T200000Z DTEND:20210211T210000Z DTSTAMP:20260422T225719Z 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:20210218T190000Z DTEND:20210218T200000Z DTSTAMP:20260422T225719Z 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:20210225T200000Z DTEND:20210225T210000Z DTSTAMP:20260422T225719Z 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:20210304T200000Z DTEND:20210304T210000Z DTSTAMP:20260422T225719Z 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:20210311T200000Z DTEND:20210311T210000Z DTSTAMP:20260422T225719Z 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:20210318T190000Z DTEND:20210318T200000Z DTSTAMP:20260422T225719Z 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:20210325T190000Z DTEND:20210325T200000Z DTSTAMP:20260422T225719Z 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:20210401T163000Z DTEND:20210401T173000Z DTSTAMP:20260422T225719Z 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:20210408T163000Z DTEND:20210408T173000Z DTSTAMP:20260422T225719Z 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:20210415T163000Z DTEND:20210415T173000Z DTSTAMP:20260422T225719Z 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:20210422T163000Z DTEND:20210422T173000Z DTSTAMP:20260422T225719Z 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:20210429T163000Z DTEND:20210429T173000Z DTSTAMP:20260422T225719Z 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:20210506T163000Z DTEND:20210506T173000Z DTSTAMP:20260422T225719Z 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:20210513T163000Z DTEND:20210513T173000Z DTSTAMP:20260422T225719Z 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 END:VCALENDAR