John Smillie

Professor Emeritus

Publications

  • Ergodicity of billiard flows and quadratic differentials (with S. Kerckhoff and H. Masur), Annals of Mathematics 124 (1986), 293–311.
  • Polynomial diffeomorphisms of C2 VI: connectivity of J (with E. Bedford), Annals of Mathematics, 148 (1998), 695–735.
  • Polynomial diffeomorphisms of C2 VII: hyperbolicity and external rays (with E. Bedford), Ann. Scient. Ec. Norm. Sup. 4 (32) (1999), 455–497.
  • The dynamics of billiard flows in rational polygons; in Encyclopedia of Mathematical Sciences, vol. 100 (edited by Yu. Sinai), Springer-Verlag, 1999.
  • Billiards on rational-angled triangles (with R. Kenyon), Comment. Math. Helv. 75 (2000), 65–108.
  • Dynamics in Two Complex Dimensions; in Proceedings of the International Congress of Mathematicians, Beijing 2002, Vol. III: Invited Lectures, Higher Education Press, Beijing 2002, pp. 373–382.
  • Real polynomial diffeomorphisms with maximal entropy: tangencies (with E. Bedford), Annals of Mathematics 160 (2004), 1–26.
Klarman Hall

smillie@math.cornell.edu

Education

  • Ph.D. (1977) University of Chicago

Departments and programs

Alfred H. Schatz

Professor Emeritus

Publications

  • Superconvergence in finite element methods and meshes which are locally symmetric with respect to a point (with I. Sloan and L. Wahlbin), SIAM Journal of Numerical Analysis, to appear.
  • Interior maximum norm estimates for Ritz Galerkin methods, part II (with L. Wahlbin), Mathematics of Computation, to appear.
  • Some new error estimates for Ritz Galerkin methods with minimal regularity assumptions (with J. Wang), Mathematics of Computation, submitted.
Klarman Hall

607/255-2383

Education

  • Ph.D. (1964) New York University

Departments and programs

Leonard Gross

Professor Emeritus

Klarman Hall

gross@math.cornell.edu
607/255-4110

Education

  • Ph.D. (1958) University of Chicago

 

Departments and programs

Daniel Halpern-Leistner

Associate Professor

Publications

  • The equivariant Verlinde formula on the moduli of Higgs bundles (appendix by Constantin Teleman), arXiv preprint arXiv:1608.01754(2016).
  • The derived category of a GIT quotient, Journal of the American Mathematical Society 28, no. 3 (2015): 871-912.
  • On the structure of instability in moduli theory, arXiv preprint arXiv:1411.0627 (2014).
Klarman Hall

511 Malott Hall
daniel.hl@cornell.edu
607/2556334

Education

  • Ph.D. (2013) University of California, Berkeley

Departments and programs

Alexander Vladimirsky

Professor

Publications

  • Optimal control with budget constraints and resets (with R. Takei, W. Chen, Z. Clawson, and S. Kirov), SIAM J. on Control and Optimization 53 no.2 (2015), 712–744.
  • Fast two-scale methods for Eikonal equations (with A. Chacon), SIAM J.on Scientific Computing 34 no.2 (2012), A547-A578.
  • An efficient method for multiobjective optimal control and optimal control subject to integral constraints (with A. Kumar), Journal of Computational Mathematics 28 no. 4 (2010), 517–551.
  • Homogenization of metric Hamilton-Jacobi equations (with A. M. Oberman and R. Takei), Multiscale Modeling and Simulation 8 no. 1 (2009), 269–295.
  • Label-setting methods for multimode stochastic shortest path problems on graphs, Mathematics of Operations Research 33 no. 4 (2008), 821–838.
  • A fast method for approximating invariant manifolds (with J. Guckenheimer), SIAM J. on Applied Dynamical Systems 3 no. 3 (2004), 232–260.
  • Ordered upwind methods for static Hamilton-Jacobi equations: theory & algorithms (with J. A. Sethian), SIAM Journal on Numerical Analysis 41 no. 1 (2003), 325–363.
  • Fast methods for the Eikonal and related Hamilton-Jacobi equations on unstructured meshes (with J. A. Sethian), Proc. Natl. Acad. Sci. USA 97 no. 11 (2000), 5699–5703.
Klarman Hall

561 Malott Hall
vladimirsky@cornell.edu
607/255-9871

Education

  • Ph.D., Applied Mathematics, University of California, Berkeley (2001).
  • B.A., Applied Mathematics (with high honors), University of California, Berkeley (1995).

Departments and programs

Links

Steven Strogatz

Susan and Barton Winokur Distinguished Professor for the Public Understanding of Science and Mathematics, Stephen H. Weiss Presidential Fellow

Publications

  • Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry, and Engineering, 3rd edition, CRC Press, 2024.
  • Infinite Powers: How Calculus Reveals the Secrets of the Universe, Houghton Mifflin Harcourt, 2019.
  • Collective dynamics of 'small-world' networks (with D. J. Watts), Nature 393 (1998), 440–442.
  • Sync: The Emerging Science of Spontaneous Order, Hyperion, 2003.
  • Synchronization of pulse-coupled biological oscillators (with R. E. Mirollo), SIAM Journal on Applied Mathematics 50, 1645-1662 (1990).
Klarman Hall

533 Malott Hall
shs7@cornell.edu

Education

  • Ph.D. (1986) Harvard University

Departments and programs

Links

Keywords

Dynamical systems applied to physics, biology and social science

Laurent Saloff-Coste

Abram R. Bullis Professor of Mathematics

Publications

  • Gambler's ruin estimates on finite inner uniform domains (with P. Diaconis and K. Houston-Edwards) Ann. Appl. Probab. 31 (2021).
  • Left-invariant geometries on SU(2) are uniformly doubling (with N. Eldredge and M. Gordina) Geom. Funct. Anal. 28 (2018).
  • Random walks and isoperimetric profiles under moment conditions (with T. Zheng) Ann. Probab. 44 (2016).
  • Random walks on free solvable groups (with T. Zheng), Mathematische Zeitschrift 279 (2015), 811–848.
  • Neumann and Dirichlet heat kernels in inner uniform domains (with P. Gyrya), Astérisque No. 336 (2011)
  • Stability results for Harnack inequalities (with A. Grigor'yan), Annales de l’Institut Fourier 55 (2005), 825–890.
Klarman Hall

567 Malott Hall
lsc@math.cornell.edu

Education

  • Ph.D. (1983) and Doctorat d'Etat (1989) Université Paris VI

Departments and programs

Links

Richard Rand

Professor, Stephen H. Weiss Presidential Fellow

Publications

  • Analysis of a remarkable singularity in a nonlinear DDE (with M. Davidow and B. Shayak), Nonlinear Dynamics 90 (2017), 317-323.

  • Low-power photothermal self-oscillation of bimetallic nanowires (with R. De Alba, T.S. Abhilash, H.G. Craighead and J.M. Parpia), Nano Letters 17(7) (2017), 3995.

  • An Asymptotic Analysis of Queues with Delayed Information and Time Varying Arrival Rates (with J. Pender and E. Wesson), Nonlinear Dynamics 91 (2018), 2411-2427.

  • Mathieu’s Equation and Its Generalizations: Overview of Stability Charts and Their Features (with I. Kovacic and S.M. Sah), Applied Mechanics Reviews vol.70 (2018), 020802.   

  • Phase Locking of Electrostatically Coupled Thermo-optically Driven MEMS Limit Cycle Oscillators (with A.T. Zehnder and S. Krylov), Int. J. of Non-Linear Mechanics vol.102 (2018), 92-100.

  • The Dynamics of One Way Coupling in a System of Nonlinear Mathieu Equations (with A. Bernstein and R. Meller) The Open Mechanical Engineering Journal 12 (2018) 108-123.

Klarman Hall

rrand@cornell.edu
607/255-8198

Education

  • Sc.D. (1967) Columbia University

Departments and programs

Links

Camil Muscalu

Professor

Publications

  • Calderón commutators and the Cauchy integral on Lipschitz curves revisited III. Polydisc extensions, Rev. Mat. Iberoamericana 30 (2014), 1413–1437.
  • Calderón commutators and the Cauchy integral on Lipschitz curves revisited II. The Cauchy integral and its generalizations, Rev. Mat. Iberoamericana 30 (2014), 1089–1122.
  • Calderón commutators and the Cauchy integral on Lipschitz curves revisited I. First commutator and generalizations, Rev. Mat. Iberoamericana 30 (2014), 727–750.
  • Multi-linear multipliers associated to simplexes of arbitrary length (with T. Tao and C. Thiele); in Advances in Analysis: The Legacy of Elias M. Stein, Princeton University Press, (2014) 346-402.
  • Classical and Multilinear Harmonic Analysis, Vol. II (with W. Schlag), Cambridge Studies in Advanced Mathematics 138, Cambridge University Press, xvi + 324 pp., 2013.
  • Classical and Multilinear Harmonic Analysis, Vol. I (with W. Schlag), Cambridge Studies in Advanced Mathematics 137, Cambridge University Press, xviii + 370 pp., 2013.
  • Paraproducts with flag singularities I. A case study, Rev. Mat. Iberoamericana 23 (2007), 705–742.
  • Bi-parameter paraproducts (with J. Pipher, T. Tao, and C. Thiele), Acta Math. 193 (2004), 269–296.
  • LpLp estimates for the biest I & II (with T. Tao and C. Thiele), Math. Ann. 329 (2004), 401–426 and 427–461.
  • The bi-Carleson operator (with T. Tao and C. Thiele), GAFA 16 (2006), 230­–277.
  • Multi-linear operators given by singular multipliers (with T. Tao and C. Thiele), J. Amer. Math. Soc. 15 (2002), 469–496.
Klarman Hall

519 Malott Hall
camil@math.cornell.edu

Education

  • Ph.D. (2000) Brown University

Departments and programs

Links

John H. Hubbard

Professor

Publications

Klarman Hall

431 Malott Hall
jhh8@cornell.edu
607/255-6495

Education

  • Doctorat d'Etat (1973) Université de Paris Sud

Departments and programs

Links

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