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:20260404T110914Z UID:ONEPAS/1 DESCRIPTION:Title: Introduction to steady water waves\nby Walter Strauss (Brown Uni versity) as part of Online Northeast PDE and Analysis Seminar\n\n\nAbstrac t\nThis is a very basic introduction. No previous knowledge of water wave s is required. I will mention the high points of the history of water wave theory. Then the fundamental equations inside the water and on the free boundary will be discussed. Finally\, many important directions of current research will be briefly outlined.\n LOCATION:https://stable.researchseminars.org/talk/ONEPAS/1/ END:VEVENT BEGIN:VEVENT SUMMARY:John Toland (University of Bath) DTSTART:20200922T190000Z DTEND:20200922T200000Z DTSTAMP:20260404T110914Z UID:ONEPAS/2 DESCRIPTION:Title: Variational aspects of steady irrotational water wave theory\nby John Toland (University of Bath) as part of Online Northeast PDE and Anal ysis Seminar\n\n\nAbstract\nAmong the many modern approaches to abstract n onlinear problems\, those based on the implicit function theorem\, real-an alytic function theory\, Nash-Moser theory and topological degree theory h ave made significant contributions to water-wave theory in recent years. H owever\, the same cannot be said of variational methods (min/max\, mountai n-pass\, Morse index\, Lyusternik-Schnirelman genus etc) even though\, whe n the viscosity of water is ignored and the flow is assumed to be irrotati onal\, there are several attractive ways to formulate the equations of wav e motion variationally. On the 100th anniversary of the first proof that t he equations of motion have non-zero\, small-amplitude solutions\, this ta lk will briefly survey these issues and advocate variational methods for a nalyzing water waves that are 2π-periodic in space.\n LOCATION:https://stable.researchseminars.org/talk/ONEPAS/2/ END:VEVENT BEGIN:VEVENT SUMMARY:Susanna Haziot (University of Vienna) DTSTART:20200929T190000Z DTEND:20200929T200000Z DTSTAMP:20260404T110914Z UID:ONEPAS/3 DESCRIPTION:Title: Rotational water waves\nby Susanna Haziot (University of Vienna) as part of Online Northeast PDE and Analysis Seminar\n\n\nAbstract\nOne s ignificant difficulty of working with water waves is that the boundary of the fluid domain itself is an unknown. I will begin with a brief presentat ion of the steady water wave problem for waves with vorticity. Subsequentl y\, I will review some existence results as well as present recent researc h which involve different methods for transforming the fluid domain into a fixed domain.\n LOCATION:https://stable.researchseminars.org/talk/ONEPAS/3/ END:VEVENT BEGIN:VEVENT SUMMARY:Vera Mikyoung Hur (University of Illinois at Urbana-Champaign) DTSTART:20201013T190000Z DTEND:20201013T200000Z DTSTAMP:20260404T110914Z UID:ONEPAS/4 DESCRIPTION:Title: Stokes waves in constant vorticity flows\nby Vera Mikyoung Hur ( University of Illinois at Urbana-Champaign) as part of Online Northeast PD E and Analysis Seminar\n\n\nAbstract\nI will discuss recent progress on th e numerical computation of Stokes waves in constant vorticity flows. Based on a Babenko-kind equation\, our result improves those in the 1980s by Si mmen and Saffman\, Teles da Silva and Peregrine. Notably\, it reveals a pl ethora of new solutions: Crapper's exact solution (even though there is no surface tension)\, a fluid disk in rigid body rotation\, etc. I will also discuss the effects of vorticity on the extreme wave\, particularly\, the maximum slope for an almost extreme wave. I will discuss some open proble ms\, both analytical and numerical.\n LOCATION:https://stable.researchseminars.org/talk/ONEPAS/4/ END:VEVENT BEGIN:VEVENT SUMMARY:Samuel Walsh (University of Missouri) DTSTART:20201027T190000Z DTEND:20201027T200000Z DTSTAMP:20260404T110914Z UID:ONEPAS/5 DESCRIPTION:Title: Water waves with density stratification or localized vorticity\n by Samuel Walsh (University of Missouri) as part of Online Northeast PDE a nd Analysis Seminar\n\n\nAbstract\nThis talk will serve as a general intro duction to two areas of active research in water waves. In the ocean\, the presence of salt and temperature gradients can lead to substantial strati fication of the density. This phenomenon is well-known to have significant physical implications. Indeed\, it makes possible enormous ``internal wav es'' that can dwarf even the largest waves seen on the surface. We will pr esent an overview of the mathematical work on this subject\, focusing prim arily on recent results regarding the existence of large-amplitude solitar y stratified waves.\n\nThe second part of the talk will discuss waves with localized distributions of vorticity. These include water waves with subm erged point vortices\, dipoles\, vortex patches\, and those exhibiting a v ortex spike.\n\nThis is joint work with Robin Ming Chen\, Mats Ehrnström\ , Jalal Shatah\, Kristoffer Varholm\, Erik Wahlén\, Miles H. Wheeler\, a nd Chongchun Zeng.\n LOCATION:https://stable.researchseminars.org/talk/ONEPAS/5/ END:VEVENT BEGIN:VEVENT SUMMARY:Miles Wheeler (University of Bath) DTSTART:20201020T190000Z DTEND:20201020T200000Z DTSTAMP:20260404T110914Z UID:ONEPAS/6 DESCRIPTION:Title: Solitary waves and fronts\nby Miles Wheeler (University of Bath) as part of Online Northeast PDE and Analysis Seminar\n\n\nAbstract\nI wil l give a general introduction to the theory of solitary water waves\, that is traveling waves whose surfaces converge to some asymptotic height at i nfinity. In many respects\, the theory for solitary waves is more difficul t and more subtle than that for periodic waves. Yet in other ways the prob lem is much simpler\, and indeed many results for solitary waves are stron ger than their periodic counterparts. \n\nBeginning with the linear theory \, or perhaps more accurately the lack of a linear theory\, I wil l explain how small-amplitude waves can be rigorously constructed via a ce nter manifold reduction. Next I will collect a series of results which tog ether guarantee that any solitary wave\, regardless of amplitude\, is symm etric and decreasing about a central crest and travels at a “supercritic al” speed $c>\\sqrt{gd}$. Finally\, I will explain how the significant o bstacles to applying global bifurcation techniques can be overcome by taki ng advantage of the above properties together with the nonexistence of front-type solutions. This approach is surprisingly robust\, and has recently been generalized to apply to front-type solutions in addition to solitary waves.\n LOCATION:https://stable.researchseminars.org/talk/ONEPAS/6/ END:VEVENT BEGIN:VEVENT SUMMARY:Erik Wahlén (Lund University) DTSTART:20201103T200000Z DTEND:20201103T210000Z DTSTAMP:20260404T110914Z UID:ONEPAS/7 DESCRIPTION:Title: Three-dimensional water waves\nby Erik Wahlén (Lund University) as part of Online Northeast PDE and Analysis Seminar\n\n\nAbstract\nThe o ther talks in the series have concentrated on two-dimensional water waves. In my talk I will give an overview of the considerably younger three-dime nsional theory. In the irrotational case\, there is by now a rich existenc e theory for small-amplitude solutions. These can have different behaviour s in different horizontal directions\, e.g. periodic or solitary. In the t alk I will mainly focus on waves which are "doubly periodic"\, that is\, p eriodic in two different horizontal directions\, or "fully localised"\, th at is\, solitary in all horizontal directions. As we will see\, surface te nsion plays a much more crucial role than in 2D. I will also discuss some recent work on 3D water waves with vorticity.\n LOCATION:https://stable.researchseminars.org/talk/ONEPAS/7/ END:VEVENT BEGIN:VEVENT SUMMARY:Rafael de la Llave (Georgia Tech) DTSTART:20201111T200000Z DTEND:20201111T210000Z DTSTAMP:20260404T110914Z UID:ONEPAS/8 DESCRIPTION:Title: Constructive methods for the long term analysis of dynamics\nby Rafael de la Llave (Georgia Tech) as part of Online Northeast PDE and Anal ysis Seminar\n\n\nAbstract\nThe long term behavior of dynamical systems is an important practical problem in technology and a deep challenge for ma thematics. In this set of lectures\, we plan to present some ide as of a concrete methodology that can be used to study the long term dynam ics of some given systems. The key idea is to: \n We can only cover some generalities and some vignettes that illustrate these program both in finite dimensional problems and in infinite dimensional s ystems. This first lecture will present some of the main tools from analy sis and topology.\n LOCATION:https://stable.researchseminars.org/talk/ONEPAS/8/ END:VEVENT BEGIN:VEVENT SUMMARY:Rafael de la Llave (Georgia Tech) DTSTART:20201118T200000Z DTEND:20201118T210000Z DTSTAMP:20260404T110914Z UID:ONEPAS/9 DESCRIPTION:Title: Hard implicit function theorems\nby Rafael de la Llave (Georgia Tech) as part of Online Northeast PDE and Analysis Seminar\n\n\nAbstract\n The main idea is the Newton method with iteration. We will discuss the c onjugacy of circle maps\, following Moser's Pisa Lectures. A proof of the theorem will be given along with numerical implementation.\n LOCATION:https://stable.researchseminars.org/talk/ONEPAS/9/ END:VEVENT BEGIN:VEVENT SUMMARY:Alex Haro (University of Barcelona) DTSTART:20201202T200000Z DTEND:20201202T210000Z DTSTAMP:20260404T110914Z UID:ONEPAS/10 DESCRIPTION:Title: Computer-assisted applications of KAM theory\nby Alex Haro (Uni versity of Barcelona) as part of Online Northeast PDE and Analysis Seminar \n\n\nAbstract\nStability of Hamiltonian systems is relevant to problems f rom celestial mechanics\, particle accelerators\, plasma confinement\, qua sigeostrophic flows\, etc. Motivated by such applications\, one is interes ted in detecting mechanisms of stability in concrete models\, and in provi ding quantitative information on the stable trajectories. KAM theory conce rns the existence of quasi-periodic solutions\, that are geometrically des cribed as orbits lying inside invariant tori.\n

\n In this lect ure we will overview a methodology for rigorously detecting quasi-periodi c orbits in Hamiltonian systems. The methodology involves analytical\, geo metrical and computational methods and covers from pen and paper rigorous results to computer-assisted rigorous results\, passing through algorithms (and the study of their convergence) and implementations. We will prese nt some ideas for performing computer assisted proofs in this context. In particular\, we will see FFT-methods for representing rigorously real-anal ytic periodic functions\, that are used to parameterize tori in phase spac e. We will see some applications in this context. We will finish the lect ure with some other applications and further topics.\n LOCATION:https://stable.researchseminars.org/talk/ONEPAS/10/ END:VEVENT BEGIN:VEVENT SUMMARY:Marian Gidea (Yeshiva University) DTSTART:20201209T200000Z DTEND:20201209T210000Z DTSTAMP:20260404T110914Z UID:ONEPAS/11 DESCRIPTION:Title: Topological methods and Hamiltonian instability\nby Marian Gide a (Yeshiva University) as part of Online Northeast PDE and Analysis Semina r\n\n\nAbstract\nInstability of Hamiltonian systems is relevant to problem s from celestial mechanics\, particle accelerators\, plasma confinement\, quasigeostrophic flows\, etc. Motivated by such applications\, one is int erested in detecting mechanisms of instability in concrete models\, and in providing 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 behavior of dynamical systems. In particular\, this method enables one to detect topological horseshoes. The method can be implemented in compute r assisted proofs\, via validated numerical computations. We will show ap plication of this method to Hamiltonian instability. Concrete examples wi ll include mechanical systems consisting of rotators and penduli\, and t he three-body problem in celestial mechanics.\n LOCATION:https://stable.researchseminars.org/talk/ONEPAS/11/ END:VEVENT BEGIN:VEVENT SUMMARY:Jiaqi Yang (Georgia Tech) DTSTART:20201216T200000Z DTEND:20201216T210000Z DTSTAMP:20260404T110914Z UID:ONEPAS/12 DESCRIPTION:Title: Invariant objects of infinite dimensional systems\nby Jiaqi Yan g (Georgia Tech) as part of Online Northeast PDE and Analysis Seminar\n\n\ nAbstract\nTo find invariant objects with specified dynamics (e.g. periodi c\, quasi-periodic\, etc.)\, we consider the space of functions in the cor responding class and impose that they are solutions. This leads to solving functional equations. One advantage of this method is that it does not n eed to study the evolution\, which in some infinite dimensional problems i s problematic. We will present some examples of solutions of special kinds in state dependent delay equations\, for which even the natural phase spa ce is debatable.\n LOCATION:https://stable.researchseminars.org/talk/ONEPAS/12/ END:VEVENT BEGIN:VEVENT SUMMARY:Patrick Flynn\, Milen Ivanov\, and Stefano Pasquali DTSTART:20201217T190000Z DTEND:20201217T210000Z DTSTAMP:20260404T110914Z UID:ONEPAS/13 DESCRIPTION:Title: ONEPAS Young Researcher Showcase\nby Patrick Flynn\, Milen Ivan ov\, and Stefano Pasquali as part of Online Northeast PDE and Analysis Sem inar\n\nAbstract: TBA\n LOCATION:https://stable.researchseminars.org/talk/ONEPAS/13/ END:VEVENT BEGIN:VEVENT SUMMARY:Israel Michael Sigal (University of Toronto) DTSTART:20210211T200000Z DTEND:20210211T210000Z DTSTAMP:20260404T110914Z UID:ONEPAS/14 DESCRIPTION:Title: The partial differential equations of quantum mechanics\nby Isr ael Michael Sigal (University of Toronto) as part of Online Northeast PDE and Analysis Seminar\n\nAbstract: TBA\n LOCATION:https://stable.researchseminars.org/talk/ONEPAS/14/ END:VEVENT BEGIN:VEVENT SUMMARY:Stephen Gustafson (University of British Columbia) DTSTART:20210218T190000Z DTEND:20210218T200000Z DTSTAMP:20260404T110914Z UID:ONEPAS/15 DESCRIPTION:Title: Solitons and dynamics of Landau-Lifshitz equations in 2D\nby St ephen Gustafson (University of British Columbia) as part of Online Northea st PDE and Analysis Seminar\n\nAbstract: TBA\n LOCATION:https://stable.researchseminars.org/talk/ONEPAS/15/ END:VEVENT BEGIN:VEVENT SUMMARY:Avy Soffer (Rutgers University) DTSTART:20210225T200000Z DTEND:20210225T210000Z DTSTAMP:20260404T110914Z UID:ONEPAS/16 DESCRIPTION:Title: Evolution of NLS with bounded data\nby Avy Soffer (Rutgers Univ ersity) as part of Online Northeast PDE and Analysis Seminar\n\nAbstract: TBA\n LOCATION:https://stable.researchseminars.org/talk/ONEPAS/16/ END:VEVENT BEGIN:VEVENT SUMMARY:Michael Loss (Georgia Tech) DTSTART:20210304T200000Z DTEND:20210304T210000Z DTSTAMP:20260404T110914Z UID:ONEPAS/17 DESCRIPTION:Title: Symmetry and symmetry breaking in functional inequalities\nby M ichael Loss (Georgia Tech) as part of Online Northeast PDE and Analysis Se minar\n\nAbstract: TBA\n LOCATION:https://stable.researchseminars.org/talk/ONEPAS/17/ END:VEVENT BEGIN:VEVENT SUMMARY:Ákos Nagy (University of California\, Santa Barbara) DTSTART:20210311T200000Z DTEND:20210311T210000Z DTSTAMP:20260404T110914Z UID:ONEPAS/18 DESCRIPTION:Title: Novel solutions in Ginzburg–Landau theory\nby Ákos Nagy (Uni versity of California\, Santa Barbara) as part of Online Northeast PDE and Analysis Seminar\n\nAbstract: TBA\n LOCATION:https://stable.researchseminars.org/talk/ONEPAS/18/ END:VEVENT BEGIN:VEVENT SUMMARY:Peter Hislop (University of Kentucky) DTSTART:20210318T190000Z DTEND:20210318T200000Z DTSTAMP:20260404T110914Z UID:ONEPAS/19 DESCRIPTION:Title: Eigenvalue statistics for some random Schrödinger operators and ra ndom band matrices\nby Peter Hislop (University of Kentucky) as part o f Online Northeast PDE and Analysis Seminar\n\nAbstract: TBA\n LOCATION:https://stable.researchseminars.org/talk/ONEPAS/19/ END:VEVENT BEGIN:VEVENT SUMMARY:Jacob Shapiro (Princeton) DTSTART:20210325T190000Z DTEND:20210325T200000Z DTSTAMP:20260404T110914Z UID:ONEPAS/20 DESCRIPTION:Title: Tight-binding limits in strong magnetic fields and the integer quan tum Hall effect\nby Jacob Shapiro (Princeton) as part of Online Northe ast PDE and Analysis Seminar\n\nAbstract: TBA\n LOCATION:https://stable.researchseminars.org/talk/ONEPAS/20/ END:VEVENT BEGIN:VEVENT SUMMARY:Irene Fonseca (Carnegie Mellon) DTSTART:20210401T163000Z DTEND:20210401T173000Z DTSTAMP:20260404T110914Z 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://stable.researchseminars.org/talk/ONEPAS/21/ END:VEVENT BEGIN:VEVENT SUMMARY:Gilles Francfort (Université Paris XIII) DTSTART:20210408T163000Z DTEND:20210408T173000Z DTSTAMP:20260404T110914Z 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://stable.researchseminars.org/talk/ONEPAS/22/ END:VEVENT BEGIN:VEVENT SUMMARY:Marta Lewicka (University of Pittsburgh) DTSTART:20210415T163000Z DTEND:20210415T173000Z DTSTAMP:20260404T110914Z UID:ONEPAS/23 DESCRIPTION:Title: Geometry and morphogenesis: problems and prospects\nby Marta Le wicka (University of Pittsburgh) as part of Online Northeast PDE and Analy sis Seminar\n\nAbstract: TBA\n LOCATION:https://stable.researchseminars.org/talk/ONEPAS/23/ END:VEVENT BEGIN:VEVENT SUMMARY:Giovanni Di Fratta (TU Wien) DTSTART:20210422T163000Z DTEND:20210422T173000Z DTSTAMP:20260404T110914Z UID:ONEPAS/24 DESCRIPTION:Title: Micromagnetics of curved thin films\nby Giovanni Di Fratta (TU Wien) as part of Online Northeast PDE and Analysis Seminar\n\nAbstract: TB A\n LOCATION:https://stable.researchseminars.org/talk/ONEPAS/24/ END:VEVENT BEGIN:VEVENT SUMMARY:Maria Giovanna Mora (University of Pavia) DTSTART:20210429T163000Z DTEND:20210429T173000Z DTSTAMP:20260404T110914Z UID:ONEPAS/25 DESCRIPTION:Title: The energy of a Möbius strip\nby Maria Giovanna Mora (Universi ty of Pavia) as part of Online Northeast PDE and Analysis Seminar\n\nAbstr act: TBA\n LOCATION:https://stable.researchseminars.org/talk/ONEPAS/25/ END:VEVENT BEGIN:VEVENT SUMMARY:Jean-François Babadjian (Université Paris Saclay) DTSTART:20210506T163000Z DTEND:20210506T173000Z DTSTAMP:20260404T110914Z UID:ONEPAS/26 DESCRIPTION:Title: Reduced models for linearly elastic thin films allowing for fractur e\, debonding or delamination\nby Jean-François Babadjian (Universit é Paris Saclay) as part of Online Northeast PDE and Analysis Seminar\n\nA bstract: TBA\n LOCATION:https://stable.researchseminars.org/talk/ONEPAS/26/ END:VEVENT BEGIN:VEVENT SUMMARY:Cyrill Muratov (New Jersey Institute of Technology) DTSTART:20210513T163000Z DTEND:20210513T173000Z DTSTAMP:20260404T110914Z 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://stable.researchseminars.org/talk/ONEPAS/27/ END:VEVENT END:VCALENDAR