Events

February 14, 2022
Professor A. Quarteroni, Politecnico di Milano, Italy
Physics-based and Data-driven Mathematical Models for the Simulation of the Heart Function

February 28, 2022
Professor Emmanuel Breuillard, University of Oxford, UK
Groups, Graphs and Random Walks

March 7, 2022
Professor Noga Alon, Princeton University, USA
Fair Partitions of Random Necklaces

March 21, 2022
Professor C. Bordenave, Institut de Mathématiques de Marseille, France
Strong Asymptotic Freeness for Independent Uniform Variables on Compact Groups

April 4, 2022
Professor Assaf Naor, Princeton University, USA
Extension, Separation and Isomorphicreverse Isoperimetry

May 9, 2022
Professor Afonso Bandeira, ETH Zurich, Switzerland
Matrix Concentration and Free Probability

Sunday, October 3, 2021
Professor Cheng Yu, University of Florida, USA
Global Solutions of the Compressible Navier-Stokes Equations

Sunday, October 17, 2021
Professor R. Speicher, Saarland University, Germany
Free Probability, Random Matrices, and Non-Commutative Rational Functions

Sunday, October 24, 2021
Professor G. Alberti, University of Genoa, Italy
Inverse Problems in PDE with Finite Measurements

Sunday, November 7, 2021 | 4pm
Professor Miklos Ruszinko, Visiting Professor, NYUAD, UAE
Extremal Graph Theory, Ramsey Theory and Szemerédi's Regularity Lemma

Sunday, November 21, 2021 | 4pm
Professor Yuefan Deng, NYUAD & Stony Brook University
Multi-scale and Machine Learning Algorithms for Modeling Platelets and Blood Clots on Supercomputers

Sunday, December 5, 2021
Professor Anna Mazzucato, Penn State University, USA
On Euler Equations with In-flow and Out-flow Boundary Conditions

January 18
Nizar Demni, Institut de Mathématiques de Marseille, France
Stability of the Stokes Immersed Boundary Problem with Bending and Stretching Energy

January 25
Yao Yao, Georgia Institute of Technology, USA
Symmetry and Uniqueness via a Variational Approach

February 1
Jean-Bernard Bru, Basque Center for Applied Mathematics
Lieb–Robinson Bounds for Multi–Commutators

February 22
Titus Lupu, Paris Sorbonne University, France
On a Possible Relation between Random Walk Loop-soups and Gaussian Beta Ensembles

March 3
Jerry Bona, University of Illinois at Chicago, USA
Mathematics and the Ocean

March 8
Sadok Kallel, American University of Sharjah, UAE
Some Applications of Topology to the Neurosciences and Beyond

March 22
Cagri Sert, University of Zürich, Switzerland
Large Deviations and Concentrations for Random Walks on Hyperbolic Spaces

March 29
Mostafa Sabri, Cairo University, Egypt
Spectral Analysis of Large Quantum Graphs

April 5
Zied Ammari, University of Rennes, France
Existence and Uniqueness of Solutions for the Gross-Pitaevskii and Hartree Hierarchy Equations

April 12
Guillaume Cébron, Institut de Mathématiques de Toulouse, France
Asymptotic Freeness of Random Matrices

April 19
Dong Li, Hong Kong University of Sciences and Technology, Hong Kong
On the Stability of Semi-implicit Methods for Phase Field Problems

May 3
Rami El Haddad, St Joseph University, Lebanon
Monte Carlo Techniques with Applications to Markov Chains Simulation

May 10
Moritz Weber, Saarland University, Germany
Quantum Permutations

October 12
Hui Li, Zhejiang University, China
Stability of the Stokes Immersed Boundary Problem with Bending and Stretching Energy

November 2
Zhifei Zhang, Peking University, China
Linear Stability of Pipe Poiseuille Flow at High Reynolds Number Regime

November 9
Boualem Djehiche, Royal Institute of Technology, Sweden
Some Aspects of Mean-field Modeling of Crowd Dynamics

November 16
Emilio Porcu, Khalifa University, UAE
Spatial Statistics within the Data Science Revolution: Past, Present, and Future

November 18
Ruizhao Zi, Central China Normal University, Wuhan, China
Dispersive Effect and Global Well-posedness of the Isentropic Compressible Navier-Stokes Equations and Related Models

November 23
Our Visiting Scholars Series: Taoufik Hmidi, NYU Abu Dhabi
Vortex Dynamics and Relative Equilibria

November 30
Our Visiting Scholars Series: Houssam Abdul-Rahman, NYU Abu Dhabi
Many-body Localization in Disordered Oscillator Systems

December 7
Xinliang An, National University of Singapore
Anisotropic Dynamical Horizons Arising in Gravitational Collapse

December 14
Our Visiting Scholars Series: Richard Aoun, NYU Abu Dhabi
Random Walks on Linear Groups: Limit Theorems and Stationary Measures

January 28
Djalil Chafai, Université Paris Dauphine, France
About the Spectrum of Non Hermitian Random Matrices

February 2
Gennady Mishuris, Aberystwyth University, UK
Dynamic Fracture Propagation in Discrete Structures

February 4
Chiara Marcolla, TII - Technology Innovation Institute, UAE
Locator Polynomial, Hermitian Codes and Geometrical Characterization of Minimum-Weight Codewords

February 9
Fioralba Cakoni, Rutgers University, USA
Transmission Eigenvalues in Inverse Scattering Theory

February 19
Michele Coti Zelati, Imperial College London, UK
Time-scales in Fluid Mechanics

February 26
Mike Keane, University of Leiden and TU Delft, The Netherlands
Classification of Substitution Dynamical Systems

March 1
Khaled Saleh, University of Lyon, France
A Convergent FV - FE Scheme for the Stationary Compressible Navier-Stokes Equations

October 1
Salah Medhi, University of Lorraine, France
Representation Theoretic Analysis on Locally Symmetric Spaces

October 8
Jun Zhang, NYU Shanghai, China
Symmetry Breaking Bifurcations in Fluid-Structure Interaction

October 15
Wei-Xi Li, Wuhan University, China
Spectral Analysis for Fokker-Planck operator and Witten Laplacian

October 22
Moses Boudourides, NYUAD, UAE
Network Science or Applied Graph Theory? Examining the Network of Indirect Collaborations in a Department of Mathematics

October 29
Sandro Salsa, Politecnico of Milan, Italy
On Two-phase Free Boundary Problems with Distributed Sources

November 3
Konrad Waldorf, University of Greifswald, Germany
Functorial Field Theories and Spin Geometry

November 17
Mohamed Malloug, Tunisia
Stabilisation for the Wave and Klein Gordonequations in Exterior Domain and in Waveguide

November 26
Konstantin Tikhomirov, Georgia Institute of Technology, USA
Singularity of Discrete Random Matrices

January 20
Diego Pallara, University of Salento, Italy
Perimeters and Short-time Behavior of the Heat Semigroup in Different Contexts

January 22
Charles Collot, New York University New York, USA
On Separation for the Unsteady Prandtl’s Equations and Related Problems

January 27
Pietro Caputo, University of Roma 3, Italy
Random Walks in Directed Random Networks: Stationary Distribution and Mixing Time

January 29
Jacob Bedrossian, Maryland University, USA
Lagrangian Chaos and Passive Scalar Turbulence

February 3
Sergei Rogosin, Belarusian State University, Belarus
Modelling with Fractional Calculus: from Mathematical Curiosity to Real Life Processes and Materials

February 10
Roland Duduchava, Razmadze Mathematical Institute
Boundary Value Problems on Hypersurfaces and Γ-convergence

February 17
Jean-Renaud Pycke, University of Evry Val d Essone
A Challenge: Running a Marathon in Less than Two Hours. How Does Mathematics Help to Determine the Best Running-strategy?

February 19
Anna Mazzucato, Penn State University, USA
Boundary Layers and the Vanishing Viscosity Limit in Incompressible Flows

February 24
Elias Wegert, Technische Universität Bergakademie Freibergugal
Nonlinear Riemann-Hilbert Problems

February 24
Nathanael Berestycki, University of Vienna, Austria
Dimers and Imaginary Geometry

February 26
Massimiliano Berti, SISSA, Italy
Dynamics of Water Waves

March 3
Hatem Zaag, University of Paris 13, France
Blowup Higher Order Semilinear Parbolic Equations

March 5
Jose Antonio Carrillo, Imperial College London, UK
Nonlinear Aggregation-Diffusion Equations in the Diffusion dominated and Fair Competitions Regimes

April 28
Fabio Paronetto, University of Padova, Italy
Existence Results for Evolution of Mixed Type and for a Generalized Tricomi Equation

May 12
Konrad Waldorf, University of Greifswald, Germany
Functorial Field Theories and Spin Geometry

September 11
Weiren Zhao, NYU Abu Dhabi, UAE
Long Time Behavior of Alfven Waves

September 18
Qingtao Chen, NYU Abu Dhabi, UAE
Recent Progress of Various Volume Conjectures for Links as Well as 3-Manifolds

September 23
Henry Segerman, Oklahoma State University, USA
3D Shadows: Casting Light on the Fourth Dimension

September 25
Manuel Gnann, Technical University of Munich, Germany
Analysis of Moving Contact Line Motion

October 9      
Daniel Grady, NYU Abu Dhabi, UAE
Geometric Invariants of Vector Bundles and the Index of Differential Operators

October 16    
Amjad Tufaha, American University of Sharjah, UAE
On The Third Boundary Condition

October 24    
David Gerard Varet, Paris University 7, France
The Mathematics of Boundary Layer Theory

October 28    
Athanasios Tzavaras, King Abdullah University of Science and Technology, KSA
Instability Leading to Localization in High Strain-rate Deformations of Metals

November 1  
Taoufik Hmidi, University of Rennes, France
Non Uniform Relative Equilibria for Euler Equations

November 6  
Fabio Martinelli, Roma Tre University, Italy
Universality Results for Kinetically Constrained Spin Models

November 18
Tarek Elgindi, San Diego University, USA
Diffusion and Mixing

November 20
Pierre Nolin, City University Hong Kong, Hong Kong
No Exceptional Words for Site Percolation on Z^3"

December 4  
Ivan Kaygorodov, University of ABC, Brazil
Generalized Derivations of Non-associative Algebras

December 9  
Eduardo Garcia Portuguese, Charles III University of Madrid, Spain
Goodness-of-fit Tests for Regression: The Functional Data Case

December 11
Yu Deng, University of Southern California, USA
Long-time Strichartz Estimates on Non-rectangular Tori

January 28    
Christiane Tretter, University of Bern, Switzerland
Challenges in Non-selfadjoint Spectral Problems

January 30    
Heinz Langer, Vienna University of Technology, Austria
Transition Functions of Sturm-Liouville Operators, Canonical Systems and Strings

February 4    
Peter Semrl, University of Ljubljana, Slovenia
Isometries of Grassmann Spaces

February 11 
Thanos Tzavaras KAUST, Saudi Arabia
Relative Entropy and Applications to the Convergence of Thermomechanical Theories

February 12 
Giovanni Peccati
Wiener Chaos: Structure and Scaling Limits - Part One             

February 14 
Giovanni Peccati
Wiener Chaos: Structure and Scaling Limits - Part Two

February 18 
Salah Mehdi, University of Lorraine, France
From the Dynamics of an Electron to Representations of Lie Groups

February 20 
Yves Le Jan, University Sud, Mathematics d'Orsay Paris, France
Markovian Networks

February 25 
Hans Knupfer, University of Heidelberg, Germany
Domain Theory for Thin Ferromagnetic Films with Perpendicular Anisotropy

February 27 
Yves Le Jan, University Sud, Mathematics d'Orsay Paris, France
Markovian Networks

March 25      
John Huerta, University of Lisbon, Portugal
G2 and the Rolling Ball

April 1           
Mounir Hajli, School of Mathematical Sciences, Shanghai Jiao Tong University, China
The Canonical Metrics on Toric Varieties

April 2           
Dr. Hyder Shah, Sukkur IBA University, Pakistan
Tracing the Ventilation Pathways of the Deep North Pacific Ocean using Lagrangian Particles

April 8           
Ning Jiang, Wuhan University, China
Incompressible Navier-Stokes-Maxwell system with Ohm's law limit from two-species Vlasov-Maxwell-Boltzmann System

April 10         
Luigi Berselli, University of Pisa, Italy
When Mathematicians Are... Close to a Volcano

April 15         
Bernardo D'Auria, Universidad Carlos III de Madrid, Spain
Portfolio Optimization with Insider Information on the Interest Rates

April 22         
Paolo Antonelli, Gran Sasso Science Institute, Italy
Analysis of Finite Energy Weak Solutions for Some Models Describing Quantum Fluids

April 29
Khalid Koufany, Université de Lorraine, France
Compression Semigroups of Open Orbits

January 22     
Jacob Bedrossian, University of Maryland, USA
Landau Damping and Nonlinear Echoes

January 29     
Dario Bini, University of Pisa, Italy
Matrix Equations, Matrix Functions, and Infinite Toeplitz Matrices

February 5     
Urs Schreiber, Czech Academy of Sciences, Czech Republic
Super Lie n-algebra of Super p-branes

February 12  
Daniel Sternheimer, Rikkyo University, Japan & University of Bourgogne, France
An Algebraic Framework for Deformations, Quantizations, Symmetries and Physical Applications

February 19  
Jacob Van Den Berg, VU University, The Netherlands
Near­critical and Frozen Percolation

February 26  
Alessandro Portaluri, Torino University, Italy
Stability Dreams (with a Symplectic Friend) in Celestial Mechanics

March 26       
Daniele Mundici, University of Firenze, Italy
Consistent (and Inconsistent) Probability

April 2            
Abdenacer Makhlouf, University of Haute Alsace, Mulhouse, France
Rota-Baxter Structures on Nonassociative Algebras and Related Structures

April 9            
Mike Cranston, University of California, USA
The Parabolic Anderson Model

April 16          
Andrey Krutov, Institute of Mathematics, Polish Academy of Sciences, Poland
Lie Algebroids Over Infinite Jet Spaces

April 20          
Alfio Quarteroni, Ecole Polytechnique Fédérale de Lausanne, Switzerland & Politecnico di Milano, Italy
Mathematical Models for the Heart Function

April 23          
Salim Messaoudi, King Fahd University of Petroleum and Minerals, KSA
Blow Up in a Nonlinear Damped Wave Equation with Variable Exponents of Nonlinearity

April 30          
Ning Jiang, Wuhan University, China
On Well-posedness of Ericksen-Leslie’s Parabolic-hyperbolic Liquid Crystal Model

May 7             
Alexander Guterman, Lomonosov Moscow State University, Russia 
Semiring Matrix Invariants: From Tropical Rank to Arctic Rank

October 1      
Francesco Calogero, University of Rome "La Sapienza", Italy
Zeros of Polynomials and Solvable Nonlinear Evolution Equations

October 29    
Jean-Marc Delort, L'Université Paris 13, France
Dispersive equations and water waves

November 5  
Erik Broman Chalmers University of Technology, Sweden
Covering a Subset of R^d by Poissonian Random Sets

November 19
Yu Deng, NYU New York, USA
Spacetime Resonance and Asymptotic Behavior for Wave Equations

November 26
Timothy Budd, Institut de Physique Théorique, CEA, Saclay, France
Conformal Loop Ensembles, Random Surfaces, and Lattice Walks

December 12
Edriss Titi, Texas A&M University, USA
Determining the Global Dynamics of the two-dimensional Navier-Stokes Equations by a Scalar ODE

December 13
Edriss Titi, Texas A&M University, USA
What is Mathematics? A Journey through Examples

August 28                
Slim Ibrahim, NYUAD and University of Victoria, Canada
Finite-time Blow-up for the Inviscid Primitive Equation

September 4             
Tarek El Gindi, Princeton University, USA
Propagation of Singularities in the Incompressible 2d Euler Equations

September 18          
Ghurumuruhan Ganesan, NYUAD, UAE
Infection Spread and Stability in Random Graph

September 25          
Oleg Kudryavtsev, Russian Customs Academy, Rostov-on-Don, Russia
Efficient Pricing Options in Models Admitting Jumps: A Numerical Wiener-Hopf Factorization Method

October 9                 
Domenico Fiorenza, Rome University, Italy
Dr. Sullivan or: How I Learned to Stop Worrying and Love Rational Homotopy Theory

October 16             
Ali Maalaoui, American University of Ras Al Khaimah, UAE
Sign-Changing Solutions and Symmetries in Problems with Critical Non-linearity

October 30                  
Yves LeJan, NYUAD, UAE
Morkov Loops Homology

November 6                
Salem Ben Said, Universite de Lorraine, France
One of the Things You Can Do With SL (2, R)

November 13              
Giuseppe Coclite, Università di Bari, Italy
A Model For The Morphogens Evolution In A Growing Tissue

November 20              
Sergei Avdonin, Kuwait University, Kuwait
Control and Inverse Problems for the Wave Equation on Graphs

November 27              
Edriss Titi, Texas A&M University, USA
Is Dispersion a Stabilizing or Destabilizing Mechanism? Landua-damping in Fast Oscillating Turbulent Flows

December 4                
Mohsen Masmoudi University of Lorraine, France
From Lie to Leibniz

December 11              
Said Benayadi, University of Lorraine, France
Quadratic Lie Superalgebras

January 31
Victor Gayral, University of Reims, France                 
Locally Compact Quantum Groups from Equivariant Quantization

February 7
Oleksiy Karlovich, New York University Abu Dhabi
On Convolution Type Operator with Piecewise Continuous Symbols on Variable Lebesgue Spaces

February 14
Dan Grady, New University of Lisbon, Portugal
Applications of Higher Topos Theory in Physics

February 21
Hatem Zaag, CNRS and University of Paris 13, France
New Blow-up Behavior for a Heat Equation with a Critical Nonlinear Gradient Term

February 24
Vakhtang Kokilashvili, Javakhishvili Tbilisi State University, Georgia
Extrapolation Theorems in Some Non-standard Banach Function Spaces and Applications

February 28
Charlie Johnson, The College of William and Mary
Eigenvalues, Multiplicities, and Graphs

March 8
Thierry Levy, Universite Pierre et Marie Curie
Large N Two-dimensional Yang-Mills

March 15
Jean Michel, Universite de Paris Ouest, France and Khalifa University, UAE
The Programming Language GAP

April 3
Oktay Pashaev , Izmir Institute of Technology, Turkey
Quantum Calculus in Classical Hydrodynamics and Quantum Theory

April 10
Laurent Mertz, NYU Shanghai, China
Stochastic Variational Inequalities and Applications to Engineering Mechanics

April 24
Janusz Grabowski, Polish Academy of Sciences
Graded Bundles as Generalizations of Vector Bundles

May 8
Anish Sarkar, Indian Statistical Institute in New Delhi, India
Directed Random Trees, Convergence to Brownian Web and Some Applications

September 6                  
Kanat Abdulmalikov (UAEU, UAE)
Mutually Unbiased Bases, Lie Algebras and Finite Geometry

September 12                
Wayne Lawton, USA
Multivariate Prediction and Spectral Factorization

September 13                
Ryad Ghanam Virginia Commonwealth University in Qatar, Qatar
Representations of Low Dimensional Lie Algebras and Applications

September 20                
Giovanni Bellettini, Tor Vergata Toma, Italy
A Notion of Area for the Graph of a Discontinuous Map from the Plane to the Plane

September 27                
Friedrich Wagemann, Universite de Nantes, France
An Example of a Rigid Leibniz Algebra with non-trivial HL^2

October 5                     
Sadok Kallel, American University of Sharjah, UAE
How to "Split" a Space in Algebraic Topology

October 13                     
Martin V. de Hoop, Rice University, USA
The Seismic Inverse Problem: Stability and Reconstruction

October 18                     
Mahir Hadzic, King’s College, London, UK
On Stable Melting and Freezing in the Stefan Problem

November 1                   
Qassem Al Mdallal, UAEU, UAE
Numerical Simulation of Viscous Flow Past a Circular Cylinder Subject to a Circular Motion

November 15                 
Alina Sirbu, Universita di Bologna, Italy
Data-driven Management of Large Computing Systems

November 17                 
Pierluigi Contucci, Universita di Bologna, Italy
Some Exact Solutions in Statistical Mechanics and their Applications in Physics and Beyond

November 22                 
Nordine Mir, Texas A&M in Qatar, Qatar
Artin Approximation and CR Geometry

December 13                 
Roberto Fernandez, Utrech University, Netherland
Ancestors, Simulations and Theorems in Statistical Mechanics

December 15                 
David Ginsbourger, University of Bern, Switzerland
Positive Definite Kernels for Deterministic and Stochastic Approximations of Invariant Functions

February 1                 
Abdelghani Zeghib, ENS Lyon, France
Configuration Space: Geometry, Topology, Dynamics, Physics and Technology

February 3                 
Vladimir Sergeichuk, Institute of Mathematics of the Ukrainian Academy of Sciences
Miniversal Deformations

February 8                 
Mourad Sini, RICAM, Austria and University of Kuwait
Multiscale Analysis of the Acoustic Diffraction by a Large Number of Small Inhomogeneities and Applications

February 24                 
Hatem Zaag, Universite de Paris 13, France
Energy Methods and Blow-up Rate for Semilinear Wave Equations

March 1
Salah-Eddine Kabbaj, KFPUM, KSA
A Simple Conjecture in Dimension Theory

March 1                     
Michel Pavon, Florence, Italy
Optimal Transport and Schroedinger Bridges from a Control and Computational Perspective

March 4   
Nader Masmoudi, NYU, USA
Mixing, Enhanced Dissipation and Inviscid Damping in the Inviscid Limit of the Navier-Stokes Equations Near the 2D Couette Flow

March 8
Elisha Falbel University of Paris 6, France
Geometric Contact Structures on Three Manifolds

March 15
Masayoshi Kaneda, Nazabayev University, Kazakhstan
Quasi-Multipliers and Algebrizations of an Operator Space, and Extreme Points of Its Unit Ball

March 29                     
Brian Lins, College William and Mary, USA
Continuous Selections of the Inverse Numerical Range Map

March 31                     
Michael Pevzner, University of Reims, France
Symmetry Breaking Operators for Reductive Pairs

April 5
Mine Caglar, Koc University, Turkey
Conditional Speed of Branching Brownian Motion and an Application to Random Obstacles

April 12                    
Partha Guha, S.N. Bose National Centre for Basic Sciences, Kolkata, India
Jacobi Last Multiplier: Weaving Different Facets of Dynamical Systems                                       

April 26                        
Vincenzo Vespri, Universita’ di Firenze, Italy
Harnack Estimates at Large for Quasilinear Parabolic Equations

May 10                         
Zaher Hani, Georgiatech University, USA
Energy Dynamics Across Scales and Wave Turbulence in Hamiltonian PDE

February 16, 2022
Dr Luigi Alfonsi, University of Hertfordshire, UK
Higher Quantum Geometry and Global String Duality

February 23, 2022
Professor Dmitri Pavlov, Texas Tech University, USA
The Geometric Cobordism Hypothesis

March 8, 2022
Professor David White, Denison University, USA
The Kervaire Invariant, Multiplicative Norms, and N-infinity Operads

March 16, 2022
Professor Guo Chuan Thiang, Beijing International Center for Mathematical Research, China
How Open Space Index Theory Appears in Physics

March 30, 2022
Dr Martin Palmer-Anghel, Romanian Academy, Romania
Mapping Class group Representations via Heisenberg, Schrodinger and Stone-von Neumann

April 6, 2022
Professor Kiyonori Gomi, Tokyo Institute of Technology, Japan
Differential KO-theory via Gradations and Mass Terms

April 13, 2022
Professor Mario Velásquez, Universidad Nacional de Colombia
The Baum-Connes Conjecture for Groups and Groupoids

April 27, 2022
Professor Amnon Neeman, Australian National University, Australia
Bounded T-structures and Stability Conditions

May 11, 2022
Professor Alex Fok, NYU Shanghai, Shanghai
Equvariant Twisted KK-theory of Noncompact Lie Groups

October 20, 2021
Dr Carlo Collari, NYU Abu Dhabi, UAE
Multipath Cohomology of Directed Graphs

November 3, 2021
Dr Dimitry Leites, NYU Abu Dhabi, UAE
Classification of Simple Lie Superalgebras in Characteristic 2 and Possible Applications to the Calogero Model

November 10, 2021
Dr Dan Grady, Texas Tech University, USA
The Geometric Cobordism Hypothesis

November 17, 2021
Dr Grigorios Giotopoulos, Heriot-Watt and NYU Abu Dhabi, UAE
Braided Homotopy Lie Algebras and Noncommutative Field Theories

December 8, 2021
Professor Michael Semenov-Tian-Shansky, Institut Math. de Bourgogne, Dijon, France
and Steklov Math. Institute, Russia
Poisson–Lie Groups and differential Galois Theory

December 15, 2021
Dr Dimitry Leites, NYU Abu Dhabi, UAE 
Supersymmetry between the Schroedinger and Korteveg - deVries Operators