Biography
Eitan Tadmor is a Distinguished University Professor at the University of Maryland (UMd), College Park with a joint appointment at the Department of Mathematics and the Institute for Physical Sciences & Technology.
Tadmor received his Ph.D. in Mathematics from Tel Aviv University in 1978. He began his scientific career as a Bateman Research Instructor in CalTech, 19801982. He held professorship positions at TelAviv University, 19831995, where he chaired the Department of Applied Mathematics from 19911993, and at UCLA, 19952002, where he was the founding codirector of the NSF Institute for Pure and Applied Mathematics (IPAM) from 19992001.
In 2002 he was recruited by UMd to lead the university Center for Scientific Computation and Mathematical Modeling (CSCAMM), and served as its first Director during the fourteenyear period of 8/20027/2016. In 20162017 he was a Senior Fellow at the Institute for Theoretical Studies at ETHZürich. Tadmor was the Principal Investigator (PI) for NSF Focus Research Group on "Kinetic Description of Multiscale Phenomena'' (20082012), and the NSF Research network Kinetic Description of Emerging Challenges in Natural Sciences (KiNet) (20122020).
Tadmor held visiting positions in the universities of Michigan, Paris VI, and Brown, the Courant Institute and at the Weizmann Institute. He serves on the editorial boards of more than a dozen leading international journals and has given numerous invited lectures, including plenary addresses in the international conferences on hyperbolic problems in 1990 1998 and 2010, invited lectures in the 2002 International Congress of Mathematicians (ICM), 2019 ICIAM, and the 2022 AMS Josiah Willard Gibbs Lecture. In 2015 Tadmor was awarded the SIAMETH Peter Henrici prize for "original, broad, and fundamental contributions to the applied and numerical analysis". In 2022 he was awarded the AMSSIAM Norbert Wiener prize in Applied Mathematics for "original contributions to applied and numerical analysis with applications in fluid dynamics, image processing, and collective dynamics". Tadmor is an AMS and SIAM Fellow, and a memeber of the European Academy of Sceince. He published more than one hundred and ninety research papers, mostly in Numerical Analysis and Applied Partial Differential Equations. He was listed on the ISI most cited researchers in mathematics.

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Research accomplishments
Eitan Tadmor
is well known for ...
Eitan Tadmor is well known for his contributions to the theory and computation of Partial Differential Equations with diverse applications to shock waves, kinetic transport, incompressible flows, image processing, and selforganized collective dynamics.
The signature of Professor Tadmor work is the interplay between analytical theories and computational algorithms for such equations. In particular, he has made a series of fundamental contributions to the development of highresolution methods for nonlinear conservation laws, including those associated with the notions of central schemes, entropy stability, spectral viscosity methods, constraint transport, edge detection, and more.
Tadmor has carried out influential work on the rigorous derivation of transport models and their relation to kinetic theories, and on critical thresholds phenomena in such models.
He introduced novel ideas of multiscale descriptions of images, and in recent years, leads an interdisciplinary research program in modeling and analysis of collective dynamics with applications to flocking and opinion dynamics.

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Professional profile ( selected items) ...
Pofessional profile (selected items)
Selected professional Appointments
• Senior Fellow, Institute for Theoretical Studies (ITS), ETHZurich, 20162017
• Director, Center for Scientific Computation and Math. Modeling (CSCAMM), Univ. of Maryland, 20022016
• Founding CoDirector, NSF Institute for Pure and Applied Math. (IPAM), UCLA, 1999
• Director, The Sackler Institute of Scientific Computation, TelAviv University, 19931996
• Chair, Department of Applied Mathematics, TelAviv University, 19911993
Selected synergistic activities
• Director, NSF Research Network, Kinetic description in .... natural sciences (KINet), 20122020
• Program Committee, International Congress of Mathematicians (ICM2018), Riode Janeiro Aug.2018
• PI, NSF Focus Research Group: Kinetic Description of Multiscale Phenomena, 20082012
• Scientific Committee, Abel Symposium on “Nonlinear PDEs”, Oslo, Sep. 2010
• CoChair, The International conference on Hyperbolic Problems,
U. of Maryland, Hyp2008, and CalTech, Hyp2002
Selected invited talks
• AMS Josiah Willard Gibbs Lecture, 2022
• Invited speaker, Int'l Congress Industrial and Applied Mathematics (ICIAM), Valencia, 2019
• Nachdiplom Lectures, ETHZ\"{u}rich, 2017
• ``Leçons JacquesLouis Lions 2016'' (3 lectures),
UPMC, Sorbonne Universités, Paris June, 2016
• SIAM invited address, Joint Math. Meeting, Baltimore, Maryland, January 2014
• Plenary lectures 
 The 13th int’l conference on Hyperbolic Problems (Hyp2010) Beijing, June, 2010
 Foundations of Computational Mathematics (FoCM2008) HongKong, June, 2008
 SIAM Conference of Analysis of PDEs, Boston, MA, July 2006
• Invited speaker, International Congress of Mathematicians (ICM), Beijing Aug. 2002
Selected editorial boards
Acta Numerica, 2009—present
SIAM Journal on Math. Analysis (SIMA), 2004present
Journal of Foundations of Computational Mathematics (JFoCM), 2004present
SIAM Journal on Numerical Analysis (SINUM), 1990—2013
Selected recognitions
Member, Academia Europaea, 2022
Member, European Academy of Sciences, 2022
AMSSIAM Norbert Wiener prize for original contributions to applied and numerical analysis with applications in ... 2022
SIAM Fellow 2021
SIAMETHZ Henrici Prize for original contributions to applied analysis and numerical analysis, 2015
Member, Cosmos Club, Washington DC, 2013
AMS Fellow, 2012 inaugural class of Fellows of the American Mathematical Society
Listed, Most cited researchers in mathematics (ISIHighlyCited.com), 2003
Rothschild Fellowship, Mathematics, 1980

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Key words (with selected references) ...
Career narrative
including ten principal publications
Career narrative
including ten principal publications
1 Convergence of spectral methods for nonlinear conservation laws
SIAM J. Numerical Analysis 26 (1989) 30—44
This paper introduced the Spectral Viscosity method — the first systematic method to treat shock discontinuities with spectral calculations. A followup a large body of related works.
2 Nonoscillatory central differencing for hyperbolic conservation laws
(with H. Nessyahu), J. of Computational Physics 87 (1990) 408—463
This paper introduced the NessyahuTadmor scheme  the forerunner for the class of highresolution "central schemes", and led to a large number of publications on related blackbox solvers for a wide variety of problems governed by multidimensional systems of nonlinear conservation laws and related PDEs.
3 A kinetic formulation of multidimensional scalar conservation laws and related equations
(with P.L. Lions & B. Perthame) J. Amer. Math. Soc. 7 (1994) 169—191
Velocity averaging, kinetic formulations and regularizing effects in quasilinear PDEs
(with Terence Tao) Communications Pure & Applied Math. 60 (2007), 1488—1521
These papers provide the systematic treatment of kinetic formulation of entropic solutions for nonlinear conservation laws and related convectiondiffusion equations and derivation of novel regularizing results.
4 Entropy stability theory for difference approximations of nonlinear conservation laws and related time dependent problems
Acta Numerica 12 (2003), 451—512
Here we introduced a novel family of entropy conservative schemes and provides a general framework for studying entropy stability of difference approximations for nonlinear systems of conservation laws by comparison.
5 A multiscale image representation using hierarchical (BV,L^{2}) decompositions
(with S. Nezzar and L. Vese) Multiscale Modeling & Simulation 2 (2004) 554—579
We introduce a novel hierarchical decomposition of images and solutions of equations in critical regularity spaces into multiscale components.
6 A new model for selforganized dynamics and its flocking behavior
(with S. Motsch) J. Stat. Physics 144(5) (2011) 923—947
Introduced a new model for far from equilibrium selforganized dynamics based on relative distances.
7 ENO reconstruction and ENO interpolation are stable
(with U. Fjordholm and S. Mishra) Foundations Computational Math. 13(2) (2012), 139—159
First stability proof for the ENO reconstruction, indicating a remarkable rigidity for ENO procedure of arbitrary order of accuracy and on nonuniform meshes.
8 Hierarchical construction of bounded solutions in critical regularity spaces
Communications in Pure & Applied Math. 69(6) (2016) 1087—1109}}
A novel multiscale constriction of uniformly bounded solutions of LU=f for general f's in the critical regularity spaces (U,f)∈ (X,L^{p}) (motivated by results of Bourgain & Brezis). The intriguing critical aspect here is that although the problems are linear, the nonlinear \emph{hierarchical} construction of their solution, U=\sum_{j} u_{j}, is not.
The solutions are realized in terms of nonlinear representations which we introduced earlier in the context of image processing.
The u_{j}'s are constructed recursively as proper minimizers, yielding the hierarchical decomposition of “images” U.
9 Construction of approximate entropy measurevalued solutions for hyperbolic systems of conservation laws
(with U. Fjordholm, R. Kappeli and S. Mishra) Foundations Comput. Math. 17 (2017) 763—827
and the related work
On the computation of measurevalued solutions (with U. Fjordholm and S. Mishra) Acta Numerica 25 (2016) 567—679
A first detailed numerical procedure which constructs stable approximations to entropy measure valued solutions together with sufficient conditions that guarantee their convergence for multiD \emph{systems} of conservation laws.
A broader view of our paradigm for the computation of measurevalued solutions of both  compressible and incompressible Euler equations, is surveyed in the 2016 Acta Numerica article.
10 Topologicallybased fractional diffusion and emergent dynamics with shortrange interactions
(with R. Shvydkoy) SIAM J. Math. Anal. 52(6) (2020) 5792—5839
Introduce a new class of models for emergent dynamics based on a new communication protocol which incorporates shortrange kernels adapted to the local density which form \emph{topological neighborhoods}. We prove flocking behavior and (global) regularity via an application of a De Giorgitype method.
 CV 2022

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and significant contributions listed below
(other lists by
[subject]
and [chronological]
order)
Highresolution approximations of nonlinear conservation laws
1 Nonoscillatory central differencing for hyperbolic conservation laws
H. Nessyahu and E. Tadmor, J. of Computational Physics 87 (1990) 408–463.
This paper introduced the NessyahuTadmor scheme  the forerunner for the class of highresolution "central schemes", which offer blackbox solvers for a wide variety of problems governed by multidimensional systems of nonlinear conservation laws and related PDEs, consult CentPack.
Related followup work can be found in the 1990 JCP work with A. Kurganov on New high resolution central schemes for nonlinear conservation laws and convectiondiffusion equations.
2 Local error estimates for discontinuous solutions of nonlinear hyperbolic equations
E. Tadmor, SIAM J. Numerical Analysis 28 (1991) 891906.
This paper introduced a novel L^{1}convergence rate theory for nonlinear conservation laws and related HamiltonJacobi equations. The theory, based on onesided stability estimates, provides an alternative to the standard KrushkovKuznetzov theory and led to optimal L^{1}convergence rates. A large body of related works, including the 2001 work (with C.T Lin) on L^{1}stability and error estimates for approximate HamiltonJacobi solutions can be found here.
3 ENO reconstruction and ENO interpolation are stable (+errata)
U. Fjordholm, S. Mishra and E. Tadmor, Foundations of Computational Math. 13(2) (2012), 139159.
The ENO reconstruction procedure was introduced in 1987 by Harten et. al. in the context of accurate simulations for piecewise smooth solutions of nonlinear conservation laws. Despite the extensive literature on the construction and implementation of ENO method and its variants, the question of its stability remained open during the last 25 years.
Here we prove that the ENO reconstruction and ENO interpolation procedures are stable in the sense that the size of the of the jumps after ENO reconstruction relative to the jump of the underlying cell averages is bounded. These estimates, which are shown to hold for ENO reconstruction and interpolation of arbitrary order of accuracy and on nonuniform meshes, indicate a remarkable rigidity of the piecewisepolynomial ENO procedure.
Kinetic formulation and regularizing effects in
nonlinear conservation laws and related problems
4 A kinetic formulation of multidimensional scalar conservation laws and related equations
P.L. Lions, B. Perthame and E. Tadmor, J. American Math. Society 7 (1994) 169–191.
This paper provides a systematic treatment of kinetic formulation of entropic solutions for nonlinear conservation laws and related convectiondiffusion equations and the first derivation of regularizing effects using the averaging lemma.
It was followed by a large body of works which utilized the kinetic formulation and their new regularizing effects for conservation laws, related degenerate equations and their numerical approximations.
In particular, a followup 1994 CMP work with P.L. Lions and B. Perthame on Kinetic formulation of the isentropic gas dynamics and psystems.
5 Velocity averaging, kinetic formulations and regularizing effects in quasilinear PDEs
E. Tadmor and Terence Tao, Communications Pure & Applied Mathematics 60 (2007), 1488–1521.
The present paper provides the first quantitative velocity averaging result for second order equations, thus paving the way for a full family of new results for regularizing effects in secondorder degenerate nonlinear parabolic equations, in particular in the anisotropic cases where relatively little was known prior to this contribution. The method of proof is based on a delicate multipliers techniques, dyadic decomposition and refined estimates on LittlewoodPaley blocks to verify the socalled "truncation property".
The spectral viscosity method —
computation of the
Gibbs phenomenon
6 Recovering pointwise values of discontinuous data within spectral accuracy
D. Gottlieb and E. Tadmor, in “Progress and Supercomputing in Computational Fluid Dynamics”,
Proc. 1984 U.S.Israel Workshop on Progress in Scientific Computing, Vol. 6 (E. M. Murman and S. S.
Abarbanel, eds.), Birkhauser, Boston (1985) 357375 [SIAM Rev 28(4) 1986].
Here we show how the pointvalues of a piecewise smooth function can be recovered from its spectral content, so that the accuracy depend solely on the local smoothness. This paper was the forerunner for large body of work which followed on the 90s and 00s, on computation of the Gibbs phenomenon (Gottlieb, Shu, Gelb, Tanner and others). In particular, these GottliebTadmor mollifiers were subsequently improved to (root) exponential accuracy (with J. Tanner) and motivated the development of effective spectral edge detectors (with A. Gelb).
7 Convergence of spectral methods for nonlinear conservation laws
E. Tadmor, SIAM J. Numerical Analysis 26 (1989) 30–44.
The Spectral Viscosity (SV) method was developed in 1989 as a systematic approach for treating shock discontinuities in spectral calculations, by adding a spectrally small amount of highfrequencies diffusion. The resulting SVapproximation is stable without sacrificing spectral accuracy, recovering a spectrally accurate approximation of (the projection of the) entropy solution. Subsequently, the SV method was implemented by many practitioners in highly accurate spectral computations of nonlinear equations; consult here.
8 Filters, mollifiers and the computation of the Gibbs phenomenon
E. Tadmor, Acta Numerica 16 (2007) 305378.
This 2007 Acta Numerica review contains a summary of the developments during 19852007 on detection of edges in pieciewise smooth spectral data and the high resolution reconstriction of the data between those edges.
Critical thresholds in Eulerian dynamics
9 Spectral dynamics of the velocity gradient field in restricted flows
H. Liu and E. Tadmor, Communications in Mathematical Physics 228 (2002), 435–466.
In this paper we initiate a systematic study of global regularity vs. finite time blowup gradients of the fundamental Eulerian equation,
u_{t}+ u·∇_{x}u= F, which shows up in different contexts dictated by the different modeling of F's. The analysis is based on the spectral dynamics tracing the eigenvalues of the velocity gradient which determine the boundaries of the critical threshold surfaces in configuration space.
It led to a large body of work which demonstrated \emph{a generic scenario of critical threshold phenomena}, where global regularity depends on the initial configurations of density, velocity divergence and the spectral gap of the 2×2 velocity gradient. This includes showing that rotational forcing prolongs the lifespan of subcritical 2D shallowwater solutions, global regularity results for subcritical 2D restricted EulerPoisson and for 3D radial EulerPoisson equations, and a surprising global existence result for a large set of subcritical initial data in the 4D restricted Euler eqs. Additional refrences can be found here
Entropy stability —
difference approximations of nonlinear conservation laws
10 Entropy stability theory for difference approximations of nonlinear conservation laws
and related time dependent problems
E. Tadmor, Acta Numerica 12 (2003), 451512.
Entropy stability plays an important role in the dynamics of nonlinear systems of conservation laws and related convectiondiffusion equations.
The paper provides a stateoftheart summary for the a body of works during 19872007 on the topic of entropy stability (beginning with the 1987 Math. Comp. work The numerical viscosity of entropy stable schemes for systems of conservation laws. I.
Here, we developed a general theory of entropy stability for difference approximations for nonlinear equations, which
provides precise characterization of entropy stability using comparison principles. In particular, we construct a new family of entropy stable schemes which retain the precise entropy decay of the NavierStokes equations. They contain no artificial numerical viscosity. The theory can be found in the followup developments here.
11 Construction of approximate entropy measurevalued solutions for hyperbolic systems of conservation laws
U. Fjordholm, R. Kappeli S. Mishra and E. Tadmor, Foundations of Computational Mathematics 17 (2017) 763827.
We present the first detailed numerical procedure which constructs stable approximations to entropy measure valued solutions and provide sufficient conditions that guarantee these approximations converge to an entropy measure valued solution as the mesh is refined, thus providing a viable numerical framework for systems of conservation laws in several space dimensions. A large number of numerical experiments that illustrate the proposed schemes are presented and are utilized to examine several interesting properties of the computed entropy measure valued solutions.
A broader view of our paradigm for the computation of measurevalued solutions of both  compressible and incompressible Euler equations, is surveyed in this 2016
Acta Numerica article.
Numerical methods for PDEs —
translatory boundary conditions, SSP timediscretizations, ...
12 Schemeindependent stability criteria for difference approximations of hyperbolic
initialboundary value problems. II
M. Goldberg and E. Tadmor, Mathematics of Computation 36 (1981) 603–626.
The development of easily checkable stability criteria for finitedifference approximations of initial boundary value systems with translatory boundary conditions. This led a series of works in the eighties, and it became a standard tool in the stability theory for approximations of initialboundary value problem of hyperbolic type.
13 High order time discretization methods with the strong stability property
S. Gottlieb, C.W. Shu and E. Tadmor, SIAM Review 43 (2001) 89–112.
We construct, analyze and implement the class of strong stabilitypreserving (SSP) highorder time discretizations for semidiscrete method of lines approximations of PDEs. These highorder methods preserve the strong stability properties of firstorder Euler time stepping and have proved very useful, especially in solving hyperbolic PDEs. Since its publication in 2001, this work has become a standard reference on SSP solvers.
Hierarchical decompositions —
applications to image processing and PDEs
14a A multiscale image representation using hierarchical (BV, L2) decompositions
E. Tadmor, S. Nezzar and L. Vese, Multiscale Modeling & Simulation 2 (2004) 554–579.
The paper introduces a novel hierarchical decomposition of images, the forerunner of recently developed iteration methods in image processing. Questions of convergence, energy decomposition, localization and adaptivity are discussed. Subsequently, our approach was used in applications to synthetic and real images. The approach developed here was pursued in a series of works, including the 2011 SIAM J. Imaging Sciences paper with P. Athavale on Integrodifferential equations based on (BV, L^{1}) image decomposition. Additional refrences can be found here.
14b Hierarchical construction of bounded solutions in critical regularity spaces
Communications in Pure & Applied Mathematics 69(6) (2016) 10871109.
We use a multiscale approach to construct uniformly bounded solutions of $div(U)=f$ for general $f$'s in the critical regularity space $Ld(Td)$. The study of this equation and related problems was motivated by results of Bourgain & Brezis. The intriguing critical aspect here is that although the problems are linear, construction of their solution is not. These constructions are special cases of a rather general framework for solving linear equations $LU=f$ in critical regularity spaces $(U,f)\in \; (X,Lp(Td))$. The solutions are realized in terms of nonlinear hierarchical representations $U=\sum $_{j} u_{j} which we introduced earlier in the context of image processing. The $u$_{j}$$'s are constructed recursively as proper minimizers, yielding the hierarchical decomposition of “images” $U$.
Selforganized dynamics — flocking and opinion dynamics
15 Heterophilious dynamics enhances consensus
S. Motsch and E. Tadmor, SIAM Review 56(4) (2014) 577–621 (with Introduction by D. J. Higham).
Nature and human societies offer many examples of selforganized behavior.
Ants form colonies, birds fly in flocks, mobile networks coordinate a rendezvous, and human opinions evolve into parties.
These are simple examples of collective dynamics that tend to selforganize into largescale clusters of colonies, flocks, parties, etc.
We review a general class of models for selforganized dynamics based on alignment.
Prototypical examples are the local HegselmannKrause model for opinion dynamics,
and the Vicsek model for flocking, the global CuckerSmale model for flocking, and its local version version
advocated in A new model for selforganized dynamics and its flocking behavior (with S. Motsch).
A natural question which arises in this context is to ask when
and how clusters emerge through the selfalignment of agents, and what types of “rules
of engagement” influence the formation of such clusters. Of particular interest to us are
cases in which the selforganized behavior tends to concentrate into one cluster, reflecting
a consensus of opinions.
Standard models for selforganized dynamics assume that the intensity of alignment increases as agents get closer, reflecting
a common tendency to align with those who think or act alike. “Similarity
breeds connection” reflects our intuition that increasing the intensity of alignment as the
difference of positions decreases is more likely to lead to a consensus. We argue here that
the converse is true: when the dynamics is driven by local interactions, it is more likely
to approach a consensus when the interactions among agents increase as a function of
their difference in position. Heterophily  the tendency to bond more with those who are
different rather than with those who are similar, plays a decisive role in the process of
clustering. We point out that the number of clusters in heterophilious dynamics decreases
as the heterophily dependence among agents increases. In particular, sufficiently strong
heterophilious interactions enhance consensus.
What is the qualitative behavior of selforganized dynamics for very large groups (N → ∞)?
Agentbased models lend themselves to standard kinetic and hydrodynamics descriptions originated in the 2008 KRM paper From particle to kinetic and hydrodynamic descriptions of flocking (with S.Y. Ha). The latter govern``social hydrodynamics" and their critical threshold phenomena are studied the 2016 M3AS paper Critical thresholds in 1D Euler equations with nonlocal forces (with J. A. Carrillo, Y.P. Choi and C. Tan) and the recent series works on Eulerian dynamics with a commutator forcing (with Shvydkoy and He).
16 Topologicallybased fractional diffusion and emergent dynamics with shortrange interactions
R. Shvydkoy & E. Tadmor, SIAM J. Math. Anal. 52(6) (2020) 57925839.
We introduce a new class of models for emergent dynamics. It is based on a new communication protocol which incorporates two main features: shortrange kernels which restrict the communication to local geometric balls, and anisotropic communication kernels, adapted to the local density in these balls, which form \emph{topological neighborhoods}. We prove flocking behavior  the emergence of global alignment for regular, nonvacuous solutions of such models. The (global) regularity and hence unconditional flocking of the onedimensional model is proved via an application of a De Giorgitype method. To handle the singular kernels used for geometric and topological communication, we develop a new analysis for \emph{local} fractional elliptic operators, interesting for its own sake, encountered in the construction of our class of models.
[Acknowledgement]

