Analysis and Applied Math Seminar

This page contains the calendar of events for the Analysis and Applied Math Seminar at the University of Toronto. The seminar meets regulary on Fridays, 1:10 - 2 pm, Room 6183 in the Bahen Centre. For more information, please contact one of the organizers: Robert Jerrard or Amir Moradifam.

Further information about this seminar is posted here:



Stability of Federer curvature measures

by Quentin Merigot | University of Toronto and Fields Institute
Time: 14:10  (Friday, Sep. 24, 2010)
Location: BA6183, Bahen Center, 40 St George St
The curvature measures defined by Federer provide a notion of extrinsic curvature for a large class of compact subsets of the Euclidean space that includes compact convex sets and compact smooth submanifolds. These curvature measures are defined through a tube formula that generalizes those of Steiner and Weyl. In this presentation, we will study the somewhat simpler notion of boundary measure, which can be used to recover the curvature measures through polynomial fitting. The boundary measure of a compact set K with respect to a bounded open set E is the pushforward of the restriction of the Lebesgue measure to E by the projection function onto K. Our main result is the following: the boundary measure of a compact set K depends continuously on K (for the Hausdorff distance); moreover, if one endows the set of measures with a given mass with the Wasserstein distance (from optimal transportation), the dependence is 1/2-Hölder. This stability result will be obtained either by a fine study of the covering numbers of the medial axis of a compact set (also called "ambiguous locus" in Riemanian geometry) or as the consequence of a L^1 stability result for gradient of convex functions. If time permits, we will briefly discuss the algorithmic aspects of computing boundary measures.

Dates in this series

· Friday, Jan. 08, 2010: Temporal evolution of attractive Bose-Einstein condensate in a quasi 1D cigar-shape trap modeled through the semiclassical limit of the focusing Nonlinear Schrödinger Equation (Alex Tovbis)
· Friday, Jan. 15, 2010: Diffusion of waves in a random environment: problems and results (Jeffrey Schenker)
· Friday, Jan. 22, 2010: The Calderón Problem - From the Past to the Present (Leo Tzou)
· Friday, Jan. 22, 2010: 2D Schrödinger with a strong magnetic field: dynamics and spectral asymptotics near boundary  (Victor Ivrii)
· Friday, Feb. 19, 2010: Global existence for a free boundary problem with non-standard sources (Maria Gualdani)
· Monday, Feb. 22, 2010: Finding the Three Dimensional Structure of Molecules That We Don’t Know How To Crystallize (Shamgar Gurevich)
· Friday, Feb. 26, 2010: On Long Time Behavior of Coating Flow (Marina Chugunova)
· Friday, Mar. 05, 2010: Solutions with vortices of a semi-stiff boundary value problem for the Ginzburg-Landau equation (Leonid Berlyand)
· Friday, Mar. 26, 2010: Eventual regularization of the slightly supercritical fractional Burgers equation (Chi Hin Chan)
· Friday, Apr. 09, 2010: On the solvability conditions for some non Fredholm operators (Vitali Vougalter)
· Tuesday, Apr. 13, 2010: Some problems in unique continuation (Alex Ionescu)
· Friday, Apr. 16, 2010: Smoother critical subsolutions to Hamilton-Jacobi Equation (Albert Fathi)
· Friday, Apr. 16, 2010: Entropy method for line energies (Radu Ignat)
· Friday, May. 14, 2010: Semiclassical evolution for the nonlinear Schrödinger equation (Alessandro Selvitella)
· Thursday, Jul. 08, 2010: Improving sharp Hardy-Sobolev inequalities by optimal remainder norms (Adele Ferone)
· Friday, Sep. 03, 2010: Ergodic methods in combinatorics (Nikos Frantzikinakis)
· Friday, Sep. 24, 2010: Stability of Federer curvature measures (Quentin Merigot)
· Friday, Oct. 01, 2010: Regularity of the extremal solution in fourth order nonlinear eigenvalue problems,  (Amir Moradifam)
· Friday, Oct. 08, 2010: Non-uniqueness of the Navier-Stokes equation in the hyperbolic setting (Magda Czubak)
· Friday, Oct. 15, 2010: 2D- and 3D-Magnetic Schrödinger Operator: Short Loops and Pointwise Spectral Asymptotics (Victor Ivrii)
· Friday, Oct. 22, 2010: Rigidity of Sobolev isometric embeddings (Robert Jerrard)
· Friday, Oct. 29, 2010: Ultimately Schwarzschildean Spacetimes and the Black Hole Stability Problem (Gustav Holzegel)
· Friday, Nov. 05, 2010: Bursting shear flow as cycle-to-cycle homoclinic chaos (Lennaert van Veen)
· Friday, Nov. 05, 2010: Localization for the random displacement model (Michael Loss)
· Friday, Nov. 12, 2010: Double Bubbles from Euclidean to Gauss Space (Frank Morgan)
· Friday, Nov. 19, 2010: Coarsening in energy-driven systems (Dejan Slepcev)
· Friday, Nov. 26, 2010: Hartree-Fock theory for atoms with closed shells (Marcel Griesemer)
· Monday, Nov. 29, 2010: Normally hyperbolic trapped sets and quasinormal modes for black holes (Maciej Zworski)
· Friday, Dec. 03, 2010: Interaction between internal and surface waves in a two layers fluid (Catherine Sulem)
· Friday, Dec. 17, 2010: The influence of large drift on front propagation (Mohammad El Smaily)
· Friday, Jan. 07, 2011: Mean field limits for interacting Bose gases and the Cauchy problem for Gross-Pitaevskii hierarchies (Thomas Chen)
· Friday, Feb. 04, 2011: Some problems concerning a Quasilinear Schrödinger Equation (Alessandro Selvitella)
· Friday, Feb. 11, 2011: Energy-based fracture evolution (Christopher Larsen)
· Friday, Feb. 18, 2011: On global well-posedness of defocusing energy-critical nonlinear Schrödinger equations on certain Riemannian manifolds (Alex Ionescu)
· Friday, Mar. 04, 2011: Infinitesimal inverse spectral geometry and applications in mathematical physics,  (Achim Kempf)
· Friday, Mar. 11, 2011: Numerical study of one-dimensional Bose-Einstein condensates in a random potential (Ziad Musslimani)
· Friday, Mar. 18, 2011: New conserved integrals for fluid flow in multi-dimensions (Stephen Anco)
· Friday, Apr. 08, 2011: Renormalization group approach to perturbation theory for PDEs (Walid K. Abou Salem)
· Friday, Jun. 10, 2011: Extensions of the disc algebra (Vassili Nestoridis)
· Friday, Jun. 17, 2011: Stability of planar fronts for a non--local phase kinetics equation with a conservation law in $D \le 3$ (Enza Orlandi)
· Friday, Jul. 15, 2011: Damped-driven Hamiltonian PDE (Sergei Kuksin)
· Friday, Jul. 15, 2011: Self-similar asymptotics of solutions to the Navier-Stokes system in two dimensional exterior domain (Christophe Lacave)
· Friday, Jul. 22, 2011: The theorem of characterization of the maximum principle (Julián López-Gómez)
· Friday, Sep. 09, 2011: A semiclassical proof of Quillen's theorem (Maciej Zworski)
· Friday, Sep. 16, 2011: Rayleigh-Benard convection: Bounds on the Nusselt number (Christian Seis)
· Friday, Sep. 16, 2011: Bounds on the cost of root finding  (Scott Sutherland)
· Friday, Sep. 23, 2011: Thin films for the Ginzburg-Landau model (Bernardo Galvao-Sousa)
· Friday, Sep. 30, 2011: The signature operator on stratified pseudomanifolds (Pierre Albin)
· Friday, Oct. 07, 2011: Breakdown Criteria for Nonvacuum Einstein Equations (Arick Shao)
· Friday, Oct. 14, 2011: Local well-posedness of the KdV equation with almost periodic initial data (Kotaro Tsugawa)
· Friday, Oct. 21, 2011: Anderson localization triggered by spin disorder (Daniel Egli)
· Friday, Oct. 28, 2011: From the Analysis of Einstein-Maxwell Spacetimes in General Relativity to Gravitational Radiation (Lydia Bierri)
· Friday, Nov. 11, 2011: Regularity of Eigenstates in Regular Mourre Theory (Matthias Westrich)
· Friday, Nov. 18, 2011: Sharp Stability Estimates in Geometric Variational Problems (Francesco Maggi)
· Friday, Nov. 25, 2011: Inverting the Attenuated X-Ray Transform (Nicholas Hoell)
· Friday, Dec. 02, 2011: Developments in High-Order Discontinuous Galerkin Methods for Hyperbolic Conservation Laws (Lilia Krivodonova)
· Monday, Jan. 23, 2012: Wet drop impact (Robert Deegan)
· Friday, Jan. 27, 2012: Flux norm approach to finite-dimensional homogenization approximation with non-separated scales and high contrast (Leonid Berlyand)
· Friday, Feb. 03, 2012: Critical Sobolev Inequalities and Navier-Stokes Equations (Yun Wang)
· Friday, Feb. 10, 2012: On Singularity Formation Under Mean Curvature Flow (Gang Zhou)
· Friday, Feb. 17, 2012: Integro-differential equations and multiscale representations (Prashant Athavale)
· Friday, Mar. 02, 2012: Pursuit Laws for Mobile Robots (Bruce Francis)
· Friday, Mar. 16, 2012: Nonzero positive solutions of systems of elliptic boundary value problems (Kunquan Lan)
· Friday, Mar. 23, 2012: Wet drop impact (Robert Deegan)
· Friday, Apr. 13, 2012: Global Minimization and the Energy Landscape for a Variational Problem with Long-Range Interactions (Rustum Choksi)
· Friday, Jun. 01, 2012: Information Transmission over Optical Fibers Using the Nonlinear Fourier (Mansoor Yousefi)
· Tuesday, Jul. 31, 2012: The Kato square root problem on vector bundles with generalised bounded geometry (Lashi Bandara)
· Friday, Sep. 28, 2012: On a variational problem exhibiting concentration near a curve (Andres Contreras)
· Friday, Oct. 05, 2012: Global results for linear waves on expanding Schwarzschild de Sitter cosmologies (Volker Schlue)
· Friday, Oct. 12, 2012: Hamiltonian dynamics of a particle interacting with a wave field (Daniel Egli)
· Friday, Oct. 19, 2012: Null Cones to Infinity, Curvature Flux, and Bondi Mass (Arick Shao)
· Friday, Oct. 26, 2012: Coupled Nonlinear Oscillators: Linking Dynamical Systems Theory with Engineering Applications, (Antonio Palacios)
· Friday, Nov. 02, 2012: Short-time behaviour of hypoelliptic heat kernels on Lie groups (Joint Seminar with Inverse Problems and Image Analysis Seminar) (Abdol-Reza Mansouri)
· Friday, Nov. 09, 2012: Harmonic maps of conic surfaces (Jesse Gell-Redman)
· Friday, Nov. 16, 2012: Monge-Kantorovich for Problems in Signal Processing and Control (Joint with the Inverse Problems and Image Analysis Seminar) (Allen Tannenbaum)
· Friday, Nov. 23, 2012: TBA (Yaiza Canzani)
· Friday, Dec. 07, 2012: TBA (Walter Craig)
· Friday, Dec. 07, 2012: Vortex Filament Interactions (Walter Craig)
· Friday, Dec. 14, 2012: JOINT SEMINAR: ANALYSIS AND APPLIED MATH / INVERSE PROBLEMS AND IMAGE ANALYSIS SEMINAR -- The circular area signature for graphs of periodic functions (Jeffrey Calder)
· Friday, Jan. 11, 2013: Higher-order time asymptotics of fast diffusion in Euclidean space (using dynamical systems methods) (Robert McCann)
· Friday, Jan. 18, 2013: A Differential Equation For The Principal Directions And Radii Of A Surface (Daniel Mayost)
· Friday, Jan. 25, 2013: Axisymmetric critical points on the sphere of a nonlocal isoperimetric problem (Ihsan Topaloglu)
· Friday, Feb. 01, 2013: Blow-up for linear and non-linear wave equations on black hole spacetimes (Stefanos Aretakis)
· Friday, Feb. 08, 2013: Null singularities in general relativity (Jonathan Luk)
· Friday, Mar. 01, 2013: Continuous dissipative solutions of the Euler equations (Camillo De Lellis)
· Friday, Mar. 22, 2013: TBA (Keisuke Takasao)