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:20260422T212926Z UID:PotomacPDE/1 DESCRIPTION:Title: Avoiding vacuum in superfluidity\nby Pranava Chaitanya Jayanti (Uni versity of Virginia) as part of Potomac region PDE seminar\n\nAbstract: TB A\n LOCATION:https://researchseminars.org/talk/PotomacPDE/1/ END:VEVENT BEGIN:VEVENT SUMMARY:Sanchit Chaturvedi (New York University) DTSTART:20250923T150000Z DTEND:20250923T160000Z DTSTAMP:20260422T212926Z UID:PotomacPDE/2 DESCRIPTION:Title: Zero viscosity limit of 1D viscous conservation laws at the point of fi rst shock formation\nby Sanchit Chaturvedi (New York University) as pa rt of Potomac region PDE seminar\n\n\nAbstract\nDespite the small scales i nvolved\, the compressible Euler equations seem to be a good model even in the presence of shocks. Introducing viscosity is one way to resolve some of these small-scale effects. In this talk\, we examine the vanishing visc osity limit near the formation of a generic shock in one spatial dimension for a class of viscous conservation laws which includes compressible Navi er Stokes. We provide an asymptotic expansion in viscosity of the viscous solution via the help of matching approximate solutions constructed in reg ions where the viscosity is perturbative and where it is dominant. Further more\, we recover the inviscid (singular) solution in the limit\, and we u ncover universal structure in the viscous correctors. This is joint work w ith John Anderson and Cole Graham.\n LOCATION:https://researchseminars.org/talk/PotomacPDE/2/ END:VEVENT BEGIN:VEVENT SUMMARY:Vincent Martinez (Hunter College) DTSTART:20250930T150000Z DTEND:20250930T160000Z DTSTAMP:20260422T212926Z UID:PotomacPDE/3 DESCRIPTION:Title: Unique ergodicity for the damped-driven stochastic KdV equation\nby Vincent Martinez (Hunter College) as part of Potomac region PDE seminar\n \n\nAbstract\nWe discuss the existence\, uniqueness\, and regularity of in variant measures for the damped-driven stochastic Korteweg-de Vries equati on\, where the noise is additive and sufficiently non-degenerate. It is sh own that a simple\, but versatile control strategy\, typically employed to establish exponential mixing for strongly dissipative systems such as the 2D Navier-Stokes equations\, can nevertheless be applied in this weakly d issipative setting to establish elementary proofs of both unique ergodicit y\, albeit without mixing rates\, as well as regularity of the support of the invariant measure. Under the assumption of large damping\, however\, w e are able to deduce the existence of a spectral gap with respect to a Was serstein distance-like function. This is joint work with Nathan Glatt-Holt z (Indiana University) and Geordie Richards (Guelph University).\n LOCATION:https://researchseminars.org/talk/PotomacPDE/3/ END:VEVENT BEGIN:VEVENT SUMMARY:Gavin Stewart (Arizona State University) DTSTART:20251007T150000Z DTEND:20251007T160000Z DTSTAMP:20260422T212926Z 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 sem inar\n\n\nAbstract\nWe consider solutions to the Benjamin-Ono equation tha t are localized in a reference frame moving to the right with constant spe ed. We show that any such solution that decays at least like $\\langle x \ \rangle^{-1-\\epsilon}$ for some $\\epsilon > 0$ in a comoving coordinate frame must in fact decay like $\\langle x \\rangle^{-2}$. In view of the e xplicit soliton solutions\, this decay rate is sharp.\nOur proof has two m ain ingredients. The first is microlocal dispersive estimates for the Benj amin-Ono equation in a moving frame\, which allow us to prove spatial deca y of the solution provided the nonlinearity has sufficient decay. The seco nd is a careful normal form analysis\, which allows us to obtain rapid dec ay of the nonlinearity for a transformed equation while assuming only mode st 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://researchseminars.org/talk/PotomacPDE/4/ END:VEVENT BEGIN:VEVENT SUMMARY:Juraj Foldes (University of Virginia) DTSTART:20251028T150000Z DTEND:20251028T160000Z DTSTAMP:20260422T212926Z UID:PotomacPDE/5 DESCRIPTION:Title: Almost sure local well-posedness of Nonlinear Schrödinger equation \nby Juraj Foldes (University of Virginia) as part of Potomac region PDE s eminar\n\n\nAbstract\nDuring the talk\, we will discuss the local solution s of the super-critical cubic Schrödinger equation (NLS) on the whole spa ce with general differential operator. Although such a problem is known to be ill-posed\, we show that the random initial data yield almost sure loc al well-posedness. Using estimates in directional spaces\, we improve and extend known results for the standard Schrödinger equation in various dir ections: higher dimensions\, more general operators\, weaker regularity as sumptions on the initial conditions. In particular\, we show that in 3D\, the classical cubic NLS is stochastically\, locally well-posed for any ini tial data with regularity in $H^\\varepsilon$ for any $\\varepsilon > 0$\, compared to the known results $\\varepsilon > 1/6$ . The proofs are based on precise estimates in frequency space using various tools from Harmonic analysis. This is a joint project with Jean-Baptise Casteras (Lisbon Univ ersity)\, Itamar Oliviera (University of Birmingham)\, and Gennady Uraltse v (University of Virginia\, University of Arkansas).\n LOCATION:https://researchseminars.org/talk/PotomacPDE/5/ END:VEVENT BEGIN:VEVENT SUMMARY:Jose Madrid Padilla (Virginia Tech) DTSTART:20251202T160000Z DTEND:20251202T170000Z DTSTAMP:20260422T212926Z UID:PotomacPDE/6 DESCRIPTION:by Jose Madrid Padilla (Virginia Tech) as part of Potomac regi on PDE seminar\n\nAbstract: TBA\n LOCATION:https://researchseminars.org/talk/PotomacPDE/6/ END:VEVENT BEGIN:VEVENT SUMMARY:Tai Melcher (University of Virginia) DTSTART:20251118T160000Z DTEND:20251118T170000Z DTSTAMP:20260422T212926Z UID:PotomacPDE/7 DESCRIPTION:by Tai Melcher (University of Virginia) as part of Potomac reg ion PDE seminar\n\nAbstract: TBA\n LOCATION:https://researchseminars.org/talk/PotomacPDE/7/ END:VEVENT BEGIN:VEVENT SUMMARY:Bjoern Bringmann (Princeton University) DTSTART:20260310T150000Z DTEND:20260310T160000Z DTSTAMP:20260422T212926Z 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 Poto mac region PDE seminar\n\n\nAbstract\nThere has been much recent progress on the local solution theory for geometric singular SPDEs. However\, the g lobal theory is still largely open. In this talk\, we discuss the global w ell-posedness of the stochastic Abelian-Higgs model in two dimension\, whi ch is a geometric singular SPDE arising from gauge theory. The proof is ba sed on a new covariant approach\, which consists of two parts: First\, we introduce covariant stochastic objects\, which are controlled using covari ant heat kernel estimates. Second\, we control nonlinear remainders using a covariant monotonicity formula\, which is inspired by earlier work of Ha milton. \n\nThis is joint work with S. Cao.\n LOCATION:https://researchseminars.org/talk/PotomacPDE/8/ END:VEVENT BEGIN:VEVENT SUMMARY:Jeffrey Galkowski (University College London) DTSTART:20251111T160000Z DTEND:20251111T170000Z DTSTAMP:20260422T212926Z UID:PotomacPDE/9 DESCRIPTION:Title: Spectral asymptotics for the Schrödinger equation with bounded\, unstr uctured potentials\nby Jeffrey Galkowski (University College London) a s part of Potomac region PDE seminar\n\n\nAbstract\nHigh energy spectral a symptotics for Schrödinger operators on compact manifolds have been well studied since the early 1900s and it is now well known that they are intim ately related to the structure of periodic geodesics. In this talk\, we di scuss analogous questions for Schrödinger operators\, $-\\Delta +V$ on $\ \mathbb{R}^d$\, where $V$ is bounded together with all of its derivatives. Since the geodesic flow on $\\mathbb{R}^d$ has no periodic trajectories ( or indeed looping trajectories) one might guess that the spectral projecto r has a full asymptotic expansion. Indeed\, for (quasi) periodic $V$ this has been known since the work of Parnovski–Shterenberg in 2016. We show that when $d=1$\, full asymptotic expansions continue to hold for any such $V$. When $d=2$\, we give a large class of potentials whose spectral proj ectors have full asymptotics. Nevertheless\, in \n$d\\geq 2$\, we construc t examples where full asymptotics fail. Based on joint work with L. Parnov ski and R. Shterenberg.\n LOCATION:https://researchseminars.org/talk/PotomacPDE/9/ END:VEVENT BEGIN:VEVENT SUMMARY:Anping Pan (Penn State University) DTSTART:20260120T160000Z DTEND:20260120T170000Z DTSTAMP:20260422T212926Z UID:PotomacPDE/10 DESCRIPTION:Title: Variational principle and Lagrangian formulations of hydrodynamic equa tions\nby Anping Pan (Penn State University) as part of Potomac region PDE seminar\n\n\nAbstract\nThe seminal work by Arnold and Ebin-Marsden ba ck in 60-70s uncovered the geodesic interpretation of incompressible Euler equation. This geometric framework has since been extensively developed\, and the variational nature of inviscid incompressible hydrodynamic models are now well understood. However\, existing frame work fails to extend to viscous hydrodynamics. Based on Hamilton-Pontryagin action principle in g eometric mechanics\, we developed a framework to realize many viscous hydr odynamic models as critical points of stochastic action functionals. This variational principle also echoes Constantin-Iyer's stochastic Lagrangian formulation of Navier-Stokes equation. We'll also discuss analysis of loca l well-posedness and Lagrangian analyticity of fluid PDEs in this Lagrangi an framework. This talk is based on joint work with A.Mazzucato.\n LOCATION:https://researchseminars.org/talk/PotomacPDE/10/ END:VEVENT BEGIN:VEVENT SUMMARY:Sathyanarayanan Chandramouli (University of Massachusetts Amherst) DTSTART:20260127T160000Z DTEND:20260127T170000Z DTSTAMP:20260422T212926Z UID:PotomacPDE/11 DESCRIPTION:Title: Dispersive shock waves in the discrete nonlinear Schrödinger equation \nby Sathyanarayanan Chandramouli (University of Massachusetts Amherst ) as part of Potomac region PDE seminar\n\n\nAbstract\nIn conservative med ia\, the dispersive regularization of gradient catastrophe gives rise to d ispersive shock waves (DSWs). Unlike classical viscous shocks\, a DSW is a highly oscillatory nonlinear wavetrain whose leading edge propagates fast er than the long-wave speed\, while the entire structure expands over time . A powerful framework for describing DSWs is Whitham modulation theory (W MT)\, a nonlinear WKB-type approach that captures the slow evolution of wa ve parameters such as amplitude\, wavelength\, and frequency.\n\nIn this t alk\, we study DSWs in the one-dimensional discrete\, defocusing nonlinear Schrödinger equation (DNLS)\, with a particular focus on strongly discre te regimes approaching the anti-continuum limit (ACL)\, as well as interme diate regimes bridging the ACL and the continuum limit. Using WMT in combi nation with asymptotic reductions\, we analyze the long-time evolution of step initial data and elucidate how lattice-induced dispersion alters shoc k structure. Our analysis reveals a sharp discretization threshold beyond which continuum DSW dynamics are recovered\, as well as a rich variety of intermediate shock morphologies unique to the discrete setting. Finally\, we apply these results to shock wave formation in ultracold atomic gases c onfined in optical lattices\, within the framework of the tight-binding ap proximation.\n LOCATION:https://researchseminars.org/talk/PotomacPDE/11/ END:VEVENT BEGIN:VEVENT SUMMARY:Henok Mawi (Howard University) DTSTART:20260324T150000Z DTEND:20260324T160000Z DTSTAMP:20260422T212926Z UID:PotomacPDE/12 DESCRIPTION:Title: Optimal transport and Monge-Ampère type equations in the design of fr eeform optical surfaces\nby Henok Mawi (Howard University) as part of Potomac region PDE seminar\n\n\nAbstract\nA freeform optical surface\, sim ply stated\, refers to an optical surface (lens or mirror) whose shape lac ks rotational symmetry. The use of such surfaces allows generation of comp lex\, compact and highly efficient imaging systems. Mathematically\, the d esign of freeform optical surfaces is an inverse problem that can be studi ed by using variational technique of optimal transportation theory and non linear partial differential equations of Monge-Ampère type. In this talk we will focus on the problem of design of refracting lenses and describe s ome of the approaches used to solve these problems.\n LOCATION:https://researchseminars.org/talk/PotomacPDE/12/ END:VEVENT BEGIN:VEVENT SUMMARY:Anuj Kumar (Indian Institute of Technology Jodhpur) DTSTART:20260224T160000Z DTEND:20260224T170000Z DTSTAMP:20260422T212926Z UID:PotomacPDE/13 DESCRIPTION:Title: On well-posedness of generalized surface quasi-geostrophic equations i n borderline Sobolev spaces\nby Anuj Kumar (Indian Institute of Techno logy Jodhpur) as part of Potomac region PDE seminar\n\n\nAbstract\nGeneral ized surface quasi-geostrophic equations (gSQG) are a family of active sca lar equations that interpolate between the 2D incompressible Euler equatio ns and the surface quasi-geostrophic equations (SQG) and extrapolate beyon d SQG to more singular equations. In this talk\, we present a collection o f results on fractionally dissipative gSQG equations in the most singular regime where the order of dissipation is small relative to the order of th e velocity. For this family\, we establish well-posedness and smoothing of the solutions in borderline Sobolev spaces. We also discuss corresponding results in the case of a mildly dissipative counterpart where the fractio nal Laplacian is replaced by a logarithmic Laplacian in the dissipative te rm. This is based on joint work with M.S Jolly and V. Martinez.\n LOCATION:https://researchseminars.org/talk/PotomacPDE/13/ END:VEVENT BEGIN:VEVENT SUMMARY:Evelyn Sander (George Mason University) DTSTART:20260317T150000Z DTEND:20260317T160000Z DTSTAMP:20260422T212926Z UID:PotomacPDE/15 DESCRIPTION:Title: Bifurcations with cyclic symmetries in partial differential equations models in biology and materials science\nby Evelyn Sander (George Maso n University) as part of Potomac region PDE seminar\n\n\nAbstract\nIn the study of pattern forming systems of partial differential equations\, the b ifurcation structure of the equilibrium solutions serves as an organizing structure of the dynamics. Werner and Spence (1984) developed the theory o f symmetry-breaking pitchfork bifurcation structures for dynamical system s 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 symmetries\ , giving a computer-assisted proof of such bifurcations in the case of the Ohta-Kawasaki model for diblock copolymers. In current work with M. Brede n and T. Wanner\, we extend these results beyond pitchfork bifurcations to symmetry-breaking transcritical bifurcations. Additionally\, we extend ou r set of examples to higher dimensions and also to the Shigesada-Kawasaki- Teramoto model\, a partial differential reaction-diffusion system for spat ial segregation in the coexistence of two competing species.\n LOCATION:https://researchseminars.org/talk/PotomacPDE/15/ END:VEVENT BEGIN:VEVENT SUMMARY:Dennis Kriventsov (Rutgers University) DTSTART:20260217T160000Z DTEND:20260217T170000Z DTSTAMP:20260422T212926Z UID:PotomacPDE/16 DESCRIPTION:Title: Non-minimizing and min-max solutions to Bernoulli problems\nby Den nis Kriventsov (Rutgers University) as part of Potomac region PDE seminar\ n\n\nAbstract\nBernoulli type free boundary problems have a well-developed existence and regularity theory. Much of this\, however\, is restricted t o the case of minimizers of the natural energy (the Alt-Caffarelli functio nal). I will describe a compactness and regularity theorem that applies to any critical point instead\, based on a nonlinear frequency formula and N aber-Valtorta estimates. Then I will explain\, via an example involving gr avity water waves\, how to use this theorem to find min-max type (mountain pass) solutions. This is based on joint work with Georg Weiss.\n LOCATION:https://researchseminars.org/talk/PotomacPDE/16/ END:VEVENT BEGIN:VEVENT SUMMARY:Jason Murphy (University of Oregon) DTSTART:20260407T150000Z DTEND:20260407T160000Z DTSTAMP:20260422T212926Z UID:PotomacPDE/17 DESCRIPTION:Title: Recovering the nonlinearity from the scattering map\nby Jason Murp hy (University of Oregon) as part of Potomac region PDE seminar\n\n\nAbstr act\nWe will discuss the problem of recovering an unknown gauge-invariant nonlinearity from the (small-data) scattering map in the setting of nonlin ear Schrödinger equations. After reviewing several results concerning lo cal nonlinearities\, we will discuss a recent preliminary result for nonlo cal (Hartree-type) nonlinearities. The talk will cover joint works with L . Campos\, G. Chen\, R. Killip\, and M. Visan.\n LOCATION:https://researchseminars.org/talk/PotomacPDE/17/ END:VEVENT BEGIN:VEVENT SUMMARY:Daniel Restrepo (Johns Hopkins University) DTSTART:20260414T150000Z DTEND:20260414T160000Z DTSTAMP:20260422T212926Z 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 solutions t o semilinear parabolic equations in Euclidean space that arise as gradient flows of an energy functional J. Under fairly general assumptions\, this problem reduces to analyzing the behavior of Palais–Smale sequences (i.e .\, almost critical points) of J. In this unbounded setting\, Palais–Sma le sequences are generally non-compact\, as they may asymptotically decomp ose into superpositions of two or more critical points drifting apart to i nfinity. This phenomenon is commonly referred to as bubbling in the parabo lic literature.\n\nIn this talk\, we present a method to rule out bubbling for gradient flows associated with a certain class of semilinear paraboli c equations. Our approach is based on a sharp stability estimate for almos t critical points of J\, which yields a flexible framework for proving con vergence of gradient flows arising from constrained minimization problems. \n\nAs applications\, we establish convergence for a diffuse model of volu me-preserving mean curvature flow\, as well as convergence to a unique gro und state for a class of semilinear equations within the framework of Bere stycki–Lions.\n LOCATION:https://researchseminars.org/talk/PotomacPDE/18/ END:VEVENT BEGIN:VEVENT SUMMARY:Ivan Medri (University of Virginia) DTSTART:20260331T150000Z DTEND:20260331T160000Z DTSTAMP:20260422T212926Z 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 seminar\ n\n\nAbstract\nWe present a framework in which optimal transport provides a nonlinear coordinate system for scalar conservation laws. In one dimensi on\, this is realized through the Cumulative Distribution Transform (CDT)\ , which recasts transport-dominated dynamics into a representation where e volution becomes simpler.\n\nFrom this perspective\, nonlinear solution fe atures\, such as translations and dilations\, are captured by a low-dimens ional structure in transform space. We show that\, for one-dimensional con servation laws\, the dynamics can be accurately approximated using a small number of transport-based modes\, offering an alternative to classical li near representations such as Fourier or Proper Orthogonal Decomposition (P OD) expansions.\n\nThese results suggest new directions for the analysis o f nonlinear PDEs and for the design of efficient reduced-order models tail ored to transport-dominated regimes. This is ongoing joint work with the g roups of Prof. Gustavo Rohde (University of Virginia) and Prof. Harbir Ant il (George Mason University).\n LOCATION:https://researchseminars.org/talk/PotomacPDE/19/ END:VEVENT BEGIN:VEVENT SUMMARY:Seyed Banihashemi (University of Maryland) DTSTART:20260421T150000Z DTEND:20260421T160000Z DTSTAMP:20260422T212926Z UID:PotomacPDE/20 DESCRIPTION:by Seyed Banihashemi (University of Maryland) as part of Potom ac region PDE seminar\n\nAbstract: TBA\n LOCATION:https://researchseminars.org/talk/PotomacPDE/20/ END:VEVENT END:VCALENDAR