BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Pranava Chaitanya Jayanti (University of Virginia) DTSTART:20250916T150000Z DTEND:20250916T160000Z DTSTAMP:20260404T094505Z UID:PotomacPDE/1 DESCRIPTION:Title: Avoiding vacuum in superfluidity\nby Pranava Chaitanya Jayan ti (University of Virginia) as part of Potomac region PDE seminar\n\nAbstr act: TBA\n LOCATION:https://stable.researchseminars.org/talk/PotomacPDE/1/ END:VEVENT BEGIN:VEVENT SUMMARY:Sanchit Chaturvedi (New York University) DTSTART:20250923T150000Z DTEND:20250923T160000Z DTSTAMP:20260404T094505Z UID:PotomacPDE/2 DESCRIPTION:Title: Zero viscosity limit of 1D viscous conservation laws at the poin t of first shock formation\nby Sanchit Chaturvedi (New York University ) as part of Potomac region PDE seminar\n\n\nAbstract\nDespite the small s cales involved\, the compressible Euler equations seem to be a good model even in the presence of shocks. Introducing viscosity is one way to resolv e some of these small-scale effects. In this talk\, we examine the vanishi ng viscosity limit near the formation of a generic shock in one spatial di mension for a class of viscous conservation laws which includes compressib le Navier Stokes. We provide an asymptotic expansion in viscosity of the v iscous solution via the help of matching approximate solutions constructed in regions where the viscosity is perturbative and where it is dominant. Furthermore\, we recover the inviscid (singular) solution in the limit\, a nd we uncover universal structure in the viscous correctors. This is joint work with John Anderson and Cole Graham.\n LOCATION:https://stable.researchseminars.org/talk/PotomacPDE/2/ END:VEVENT BEGIN:VEVENT SUMMARY:Vincent Martinez (Hunter College) DTSTART:20250930T150000Z DTEND:20250930T160000Z DTSTAMP:20260404T094505Z UID:PotomacPDE/3 DESCRIPTION:Title: Unique ergodicity for the damped-driven stochastic KdV equation< /a>\nby Vincent Martinez (Hunter College) as part of Potomac region PDE se minar\n\n\nAbstract\nWe discuss the existence\, uniqueness\, and regularit y of invariant measures for the damped-driven stochastic Korteweg-de Vries equation\, where the noise is additive and sufficiently non-degenerate. I t is shown that a simple\, but versatile control strategy\, typically empl oyed to establish exponential mixing for strongly dissipative systems such as the 2D Navier-Stokes equations\, can nevertheless be applied in this w eakly dissipative setting to establish elementary proofs of both unique er godicity\, albeit without mixing rates\, as well as regularity of the supp ort of the invariant measure. Under the assumption of large damping\, howe ver\, we are able to deduce the existence of a spectral gap with respect t o a Wasserstein distance-like function. This is joint work with Nathan Gla tt-Holtz (Indiana University) and Geordie Richards (Guelph University).\n LOCATION:https://stable.researchseminars.org/talk/PotomacPDE/3/ END:VEVENT BEGIN:VEVENT SUMMARY:Gavin Stewart (Arizona State University) DTSTART:20251007T150000Z DTEND:20251007T160000Z DTSTAMP:20260404T094505Z UID:PotomacPDE/4 DESCRIPTION:Title: Spatial decay for coherent states of the Benjamin-Ono equation\nby Gavin Stewart (Arizona State University) as part of Potomac region PDE seminar\n\n\nAbstract\nWe consider solutions to the Benjamin-Ono equat ion that are localized in a reference frame moving to the right with const ant speed. We show that any such solution that decays at least like $\\lan gle x \\rangle^{-1-\\epsilon}$ for some $\\epsilon > 0$ in a comoving coor dinate frame must in fact decay like $\\langle x \\rangle^{-2}$. In view o f the explicit soliton solutions\, this decay rate is sharp.\nOur proof ha s two main ingredients. The first is microlocal dispersive estimates for t he Benjamin-Ono equation in a moving frame\, which allow us to prove spati al decay of the solution provided the nonlinearity has sufficient decay. T he second is a careful normal form analysis\, which allows us to obtain ra pid decay of the nonlinearity for a transformed equation while assuming on ly modest decay of the solution. Our arguments are entirely time-dependent \, and do not require the solution to be an exact traveling wave.\n LOCATION:https://stable.researchseminars.org/talk/PotomacPDE/4/ END:VEVENT BEGIN:VEVENT SUMMARY:Juraj Foldes (University of Virginia) DTSTART:20251028T150000Z DTEND:20251028T160000Z DTSTAMP:20260404T094505Z UID:PotomacPDE/5 DESCRIPTION:Title: Almost sure local well-posedness of Nonlinear Schrödinger equat ion\nby Juraj Foldes (University of Virginia) as part of Potomac regio n PDE seminar\n\n\nAbstract\nDuring the talk\, we will discuss the local s olutions of the super-critical cubic Schrödinger equation (NLS) on the wh ole space with general differential operator. Although such a problem is k nown to be ill-posed\, we show that the random initial data yield almost s ure local well-posedness. Using estimates in directional spaces\, we impro ve and extend known results for the standard Schrödinger equation in vari ous directions: higher dimensions\, more general operators\, weaker regula rity assumptions on the initial conditions. In particular\, we show that i n 3D\, the classical cubic NLS is stochastically\, locally well-posed for any initial data with regularity in $H^\\varepsilon$ for any $\\varepsilon > 0$\, compared to the known results $\\varepsilon > 1/6$ . The proofs ar e based on precise estimates in frequency space using various tools from H armonic analysis. This is a joint project with Jean-Baptise Casteras (Lisb on University)\, Itamar Oliviera (University of Birmingham)\, and Gennady Uraltsev (University of Virginia\, University of Arkansas).\n LOCATION:https://stable.researchseminars.org/talk/PotomacPDE/5/ END:VEVENT BEGIN:VEVENT SUMMARY:Jose Madrid Padilla (Virginia Tech) DTSTART:20251202T160000Z DTEND:20251202T170000Z DTSTAMP:20260404T094505Z UID:PotomacPDE/6 DESCRIPTION:by Jose Madrid Padilla (Virginia Tech) as part of Potomac regi on PDE seminar\n\nAbstract: TBA\n LOCATION:https://stable.researchseminars.org/talk/PotomacPDE/6/ END:VEVENT BEGIN:VEVENT SUMMARY:Tai Melcher (University of Virginia) DTSTART:20251118T160000Z DTEND:20251118T170000Z DTSTAMP:20260404T094505Z UID:PotomacPDE/7 DESCRIPTION:by Tai Melcher (University of Virginia) as part of Potomac reg ion PDE seminar\n\nAbstract: TBA\n LOCATION:https://stable.researchseminars.org/talk/PotomacPDE/7/ END:VEVENT BEGIN:VEVENT SUMMARY:Bjoern Bringmann (Princeton University) DTSTART:20260310T150000Z DTEND:20260310T160000Z DTSTAMP:20260404T094505Z UID:PotomacPDE/8 DESCRIPTION:Title: Global well-posedness of the stochastic Abelian-Higgs equations in two dimensions\nby Bjoern Bringmann (Princeton University) as part of Potomac region PDE seminar\n\n\nAbstract\nThere has been much recent pr ogress on the local solution theory for geometric singular SPDEs. However\ , the global theory is still largely open. In this talk\, we discuss the g lobal well-posedness of the stochastic Abelian-Higgs model in two dimensio n\, which is a geometric singular SPDE arising from gauge theory. The proo f is based on a new covariant approach\, which consists of two parts: Firs t\, we introduce covariant stochastic objects\, which are controlled using covariant heat kernel estimates. Second\, we control nonlinear remainders using a covariant monotonicity formula\, which is inspired by earlier wor k of Hamilton. \n\nThis is joint work with S. Cao.\n LOCATION:https://stable.researchseminars.org/talk/PotomacPDE/8/ END:VEVENT BEGIN:VEVENT SUMMARY:Jeffrey Galkowski (University College London) DTSTART:20251111T160000Z DTEND:20251111T170000Z DTSTAMP:20260404T094505Z UID:PotomacPDE/9 DESCRIPTION:Title: Spectral asymptotics for the Schrödinger equation with bounded\ , unstructured potentials\nby Jeffrey Galkowski (University College Lo ndon) as part of Potomac region PDE seminar\n\n\nAbstract\nHigh energy spe ctral asymptotics for Schrödinger operators on compact manifolds have bee n well studied since the early 1900s and it is now well known that they ar e intimately related to the structure of periodic geodesics. In this talk\ , we discuss analogous questions for Schrödinger operators\, $-\\Delta +V $ on $\\mathbb{R}^d$\, where $V$ is bounded together with all of its deriv atives. Since the geodesic flow on $\\mathbb{R}^d$ has no periodic traject ories (or indeed looping trajectories) one might guess that the spectral p rojector has a full asymptotic expansion. Indeed\, for (quasi) periodic $V $ this has been known since the work of Parnovski–Shterenberg in 2016. W e show that when $d=1$\, full asymptotic expansions continue to hold for a ny such $V$. When $d=2$\, we give a large class of potentials whose spectr al projectors have full asymptotics. Nevertheless\, in \n$d\\geq 2$\, we c onstruct examples where full asymptotics fail. Based on joint work with L. Parnovski and R. Shterenberg.\n LOCATION:https://stable.researchseminars.org/talk/PotomacPDE/9/ END:VEVENT BEGIN:VEVENT SUMMARY:Anping Pan (Penn State University) DTSTART:20260120T160000Z DTEND:20260120T170000Z DTSTAMP:20260404T094505Z UID:PotomacPDE/10 DESCRIPTION:Title: Variational principle and Lagrangian formulations of hydrodynam ic equations\nby Anping Pan (Penn State University) as part of Potomac region PDE seminar\n\n\nAbstract\nThe seminal work by Arnold and Ebin-Mar sden back in 60-70s uncovered the geodesic interpretation of incompressibl e Euler equation. This geometric framework has since been extensively deve loped\, and the variational nature of inviscid incompressible hydrodynamic models are now well understood. However\, existing frame work fails to ex tend to viscous hydrodynamics. Based on Hamilton-Pontryagin action princip le in geometric mechanics\, we developed a framework to realize many visco us hydrodynamic models as critical points of stochastic action functionals . This variational principle also echoes Constantin-Iyer's stochastic Lagr angian formulation of Navier-Stokes equation. We'll also discuss analysis of local well-posedness and Lagrangian analyticity of fluid PDEs in this L agrangian framework. This talk is based on joint work with A.Mazzucato.\n LOCATION:https://stable.researchseminars.org/talk/PotomacPDE/10/ END:VEVENT BEGIN:VEVENT SUMMARY:Sathyanarayanan Chandramouli (University of Massachusetts Amherst) DTSTART:20260127T160000Z DTEND:20260127T170000Z DTSTAMP:20260404T094505Z UID:PotomacPDE/11 DESCRIPTION:Title: Dispersive shock waves in the discrete nonlinear Schrödinger e quation\nby Sathyanarayanan Chandramouli (University of Massachusetts Amherst) as part of Potomac region PDE seminar\n\n\nAbstract\nIn conservat ive media\, the dispersive regularization of gradient catastrophe gives ri se to dispersive shock waves (DSWs). Unlike classical viscous shocks\, a D SW is a highly oscillatory nonlinear wavetrain whose leading edge propagat es faster than the long-wave speed\, while the entire structure expands ov er time. A powerful framework for describing DSWs is Whitham modulation th eory (WMT)\, a nonlinear WKB-type approach that captures the slow evolutio n of wave parameters such as amplitude\, wavelength\, and frequency.\n\nIn this talk\, we study DSWs in the one-dimensional discrete\, defocusing no nlinear Schrödinger equation (DNLS)\, with a particular focus on strongly discrete regimes approaching the anti-continuum limit (ACL)\, as well as intermediate regimes bridging the ACL and the continuum limit. Using WMT i n combination with asymptotic reductions\, we analyze the long-time evolut ion of step initial data and elucidate how lattice-induced dispersion alte rs shock structure. Our analysis reveals a sharp discretization threshold beyond which continuum DSW dynamics are recovered\, as well as a rich vari ety of intermediate shock morphologies unique to the discrete setting. Fin ally\, we apply these results to shock wave formation in ultracold atomic gases confined in optical lattices\, within the framework of the tight-bin ding approximation.\n LOCATION:https://stable.researchseminars.org/talk/PotomacPDE/11/ END:VEVENT BEGIN:VEVENT SUMMARY:Henok Mawi (Howard University) DTSTART:20260324T150000Z DTEND:20260324T160000Z DTSTAMP:20260404T094505Z UID:PotomacPDE/12 DESCRIPTION:Title: Optimal transport and Monge-Ampère type equations in the desig n of freeform optical surfaces\nby Henok Mawi (Howard University) as p art of Potomac region PDE seminar\n\n\nAbstract\nA freeform optical surfac e\, simply stated\, refers to an optical surface (lens or mirror) whose sh ape lacks rotational symmetry. The use of such surfaces allows generation of complex\, compact and highly efficient imaging systems. Mathematically\ , the design of freeform optical surfaces is an inverse problem that can b e studied by using variational technique of optimal transportation theory and nonlinear partial differential equations of Monge-Ampère type. In thi s talk we will focus on the problem of design of refracting lenses and des cribe some of the approaches used to solve these problems.\n LOCATION:https://stable.researchseminars.org/talk/PotomacPDE/12/ END:VEVENT BEGIN:VEVENT SUMMARY:Anuj Kumar (Indian Institute of Technology Jodhpur) DTSTART:20260224T160000Z DTEND:20260224T170000Z DTSTAMP:20260404T094505Z UID:PotomacPDE/13 DESCRIPTION:Title: On well-posedness of generalized surface quasi-geostrophic equa tions in borderline Sobolev spaces\nby Anuj Kumar (Indian Institute of Technology Jodhpur) as part of Potomac region PDE seminar\n\n\nAbstract\n Generalized surface quasi-geostrophic equations (gSQG) are a family of act ive scalar equations that interpolate between the 2D incompressible Euler equations and the surface quasi-geostrophic equations (SQG) and extrapolat e beyond SQG to more singular equations. In this talk\, we present a colle ction of results on fractionally dissipative gSQG equations in the most si ngular regime where the order of dissipation is small relative to the orde r of the velocity. For this family\, we establish well-posedness and smoot hing of the solutions in borderline Sobolev spaces. We also discuss corres ponding results in the case of a mildly dissipative counterpart where the fractional Laplacian is replaced by a logarithmic Laplacian in the dissipa tive term. This is based on joint work with M.S Jolly and V. Martinez.\n LOCATION:https://stable.researchseminars.org/talk/PotomacPDE/13/ END:VEVENT BEGIN:VEVENT SUMMARY:Evelyn Sander (George Mason University) DTSTART:20260317T150000Z DTEND:20260317T160000Z DTSTAMP:20260404T094505Z UID:PotomacPDE/15 DESCRIPTION:Title: Bifurcations with cyclic symmetries in partial differential equ ations models in biology and materials science\nby Evelyn Sander (Geor ge Mason University) as part of Potomac region PDE seminar\n\n\nAbstract\n In the study of pattern forming systems of partial differential equations\ , the bifurcation structure of the equilibrium solutions serves as an orga nizing structure of the dynamics. Werner and Spence (1984) developed the t heory of symmetry-breaking pitchfork bifurcation structures for dynamical systems with even and odd symmetries. In recent work with P. Rizzi and T. Wanner\, we were able to extend these results to cases with dihedral symm etries\, giving a computer-assisted proof of such bifurcations in the case of the Ohta-Kawasaki model for diblock copolymers. In current work with M . Breden and T. Wanner\, we extend these results beyond pitchfork bifurcat ions to symmetry-breaking transcritical bifurcations. Additionally\, we ex tend our set of examples to higher dimensions and also to the Shigesada-Ka wasaki-Teramoto model\, a partial differential reaction-diffusion system f or spatial segregation in the coexistence of two competing species.\n LOCATION:https://stable.researchseminars.org/talk/PotomacPDE/15/ END:VEVENT BEGIN:VEVENT SUMMARY:Dennis Kriventsov (Rutgers University) DTSTART:20260217T160000Z DTEND:20260217T170000Z DTSTAMP:20260404T094505Z UID:PotomacPDE/16 DESCRIPTION:Title: Non-minimizing and min-max solutions to Bernoulli problems\ nby Dennis Kriventsov (Rutgers University) as part of Potomac region PDE s eminar\n\n\nAbstract\nBernoulli type free boundary problems have a well-de veloped existence and regularity theory. Much of this\, however\, is restr icted to the case of minimizers of the natural energy (the Alt-Caffarelli functional). I will describe a compactness and regularity theorem that app lies to any critical point instead\, based on a nonlinear frequency formul a and Naber-Valtorta estimates. Then I will explain\, via an example invol ving gravity water waves\, how to use this theorem to find min-max type (m ountain pass) solutions. This is based on joint work with Georg Weiss.\n LOCATION:https://stable.researchseminars.org/talk/PotomacPDE/16/ END:VEVENT BEGIN:VEVENT SUMMARY:Jason Murphy (University of Oregon) DTSTART:20260407T150000Z DTEND:20260407T160000Z DTSTAMP:20260404T094505Z UID:PotomacPDE/17 DESCRIPTION:Title: Recovering the nonlinearity from the scattering map\nby Jas on Murphy (University of Oregon) as part of Potomac region PDE seminar\n\n \nAbstract\nWe will discuss the problem of recovering an unknown gauge-inv ariant nonlinearity from the (small-data) scattering map in the setting of nonlinear Schrödinger equations. After reviewing several results concer ning local nonlinearities\, we will discuss a recent preliminary result fo r nonlocal (Hartree-type) nonlinearities. The talk will cover joint works with L. Campos\, G. Chen\, R. Killip\, and M. Visan.\n LOCATION:https://stable.researchseminars.org/talk/PotomacPDE/17/ END:VEVENT BEGIN:VEVENT SUMMARY:Daniel Restrepo (Johns Hopkins University) DTSTART:20260414T150000Z DTEND:20260414T160000Z DTSTAMP:20260404T094505Z UID:PotomacPDE/18 DESCRIPTION:Title: Convergence of semilinear parabolic flows with general initial data\nby Daniel Restrepo (Johns Hopkins University) as part of Potomac region PDE seminar\n\n\nAbstract\nWe study the long-time behavior of solu tions to semilinear parabolic equations in Euclidean space that arise as g radient flows of an energy functional J. Under fairly general assumptions\ , this problem reduces to analyzing the behavior of Palais–Smale sequenc es (i.e.\, almost critical points) of J. In this unbounded setting\, Palai s–Smale sequences are generally non-compact\, as they may asymptotically decompose into superpositions of two or more critical points drifting apa rt to infinity. This phenomenon is commonly referred to as bubbling in the parabolic literature.\n\nIn this talk\, we present a method to rule out b ubbling for gradient flows associated with a certain class of semilinear p arabolic equations. Our approach is based on a sharp stability estimate fo r almost critical points of J\, which yields a flexible framework for prov ing convergence of gradient flows arising from constrained minimization pr oblems.\n\nAs applications\, we establish convergence for a diffuse model of volume-preserving mean curvature flow\, as well as convergence to a uni que ground state for a class of semilinear equations within the framework of Berestycki–Lions.\n LOCATION:https://stable.researchseminars.org/talk/PotomacPDE/18/ END:VEVENT BEGIN:VEVENT SUMMARY:Ivan Medri (University of Virginia) DTSTART:20260331T150000Z DTEND:20260331T160000Z DTSTAMP:20260404T094505Z UID:PotomacPDE/19 DESCRIPTION:Title: Optimal transport as a transform for scalar conservation laws\nby Ivan Medri (University of Virginia) as part of Potomac region PDE s eminar\n\n\nAbstract\nWe present a framework in which optimal transport pr ovides a nonlinear coordinate system for scalar conservation laws. In one dimension\, this is realized through the Cumulative Distribution Transform (CDT)\, which recasts transport-dominated dynamics into a representation where evolution becomes simpler.\n\nFrom this perspective\, nonlinear solu tion features\, such as translations and dilations\, are captured by a low -dimensional structure in transform space. We show that\, for one-dimensio nal conservation laws\, the dynamics can be accurately approximated using a small number of transport-based modes\, offering an alternative to class ical linear representations such as Fourier or Proper Orthogonal Decomposi tion (POD) expansions.\n\nThese results suggest new directions for the ana lysis of nonlinear PDEs and for the design of efficient reduced-order mode ls tailored to transport-dominated regimes. This is ongoing joint work wit h the groups of Prof. Gustavo Rohde (University of Virginia) and Prof. Har bir Antil (George Mason University).\n LOCATION:https://stable.researchseminars.org/talk/PotomacPDE/19/ END:VEVENT BEGIN:VEVENT SUMMARY:Seyed Banihashemi (University of Maryland) DTSTART:20260421T150000Z DTEND:20260421T160000Z DTSTAMP:20260404T094505Z UID:PotomacPDE/20 DESCRIPTION:by Seyed Banihashemi (University of Maryland) as part of Potom ac region PDE seminar\n\nAbstract: TBA\n LOCATION:https://stable.researchseminars.org/talk/PotomacPDE/20/ END:VEVENT END:VCALENDAR