Nicolas Templier

Professor

Publications

  • On the Ramanujan conjecture for automorphic forms over function fields I. Geometry. (with W. Sawin), Journal of the AMS, 34 no.3 (2021), 653—746.

  • Families of L-functions and their symmetry (with P. Sarnak and S.W. Shin), proceedings of Simons symposium on the trace formula,  Springer-Verlag (2016).
  • Sato-Tate theorem for families and low-lying zeros of automorphic L-functions (with S.W. Shin), Invent. Math., 203 no.1 (2016), 1-177.
  • Hybrid sup-norm bounds for Hecke-Maass cusp forms, J. Eur. Math. Soc. 17 no.8 (2015), 2069--2082.
  • Large values of modular forms, Cambridge Journal of Mathematics, 2 no.1 (2014), 91–116.
  • A non-split sum of coefficients of modular forms, Duke Math. J., 157 no.1 (2011), 109–165.

Éva Tardos

Jacob Gould Schurman Professor

Publications

Network Games and extensions

Mechanism Design

Social Networks

Classification

Clustering and facility location

Network Design

Routing Disjoint Paths and Packets in Networks

Scheduling

Generalized Flow

  • A. Goldberg, S. Plotkin, E. Tardos: Combinatorial algorithms for the generalized circulation problem, Mathematics of Operations Research, 16/2, 1991, 351-381. Preliminary version has appeared in the Proceedings of the 29th Annual IEEE Symposium on the Foundations of Computer Science (1988), 432-443.
  • E. Tardos and K. Wayne. Simple Generalized Maximum Flow Algorithms. Proceedings of the 6th International Integer Programming and Combinatorial Optimization Conference   (IPCO'98), Houston, 1998, pp. 310-324.

Packing and Covering Algorithms

  • P. Klein, S. Plotkin, C. Stein and E. Tardos, Faster approximation algorithms for the unit capacity concurrent flow problem with applications to routing and finding sparse cuts.  SIAM Journal on Computing, 23/3, 1994,. 466-487. Preliminary version has appeared in the proceedings of the 22nd Annual ACM Symposium on the Theory of Computing (1990), 310-321.
  • T. Leighton, F. Makedon, S. Plotkin, C. Stein, E. Tardos, S. Tragoudas: Fast Approximation Algorithms for Multicommodity Flow Problems, Journal of Computer and System Sciences, 50 (STOC'91 special issue), 1995, pp. 228--243. Preliminary version has appeared in the Proceedings of the 23rd Annual ACM Symposium on the Theory of Computing (1991), 101-110.
  • S.A. Plotkin, D. Shmoys, and E. Tardos, Fast approximation algorithms for fractional packing and covering problems, to appear in Mathematics of Operations Research. ORIE TR-999.  Preliminary version has appeared in the Proceedings of the 32nd Annual IEEE Symposium on the Foundations of Computer Science (1991), 495-505.

Networks with transit times

  • B. Hoppe and E. Tardos: Polynomial Time Algorithms for Some Evacuation Problems. In the proceeding of the 5th Annual ACM-SIAM Symposium on Discrete Algorithms, January 1994, pp. 433-441. .
  • B. Hoppe and E. Tardos: The Quickest Transshipment Problem, journal version of the paper in the proceeding of the 6th Annual ACM-SIAM Symposium on Discrete Algorithms, 1995 pp. 512-521.
  • L. Fleischer and E. Tardos. Efficient Continuous-Time Dynamic Network Flow Algorithms. Operations Research Letters 23 (1998) pp. 71-80.

Effective bandwidth

Finding cuts in graphs

Separating cutting planes

  • L. Fleischer and E. Tardos: Separating Maximally Violated Comb Inequalities in Planar Graphs, tech report version of the paper in the Proceedings of the 5th International Integer Programming and Combinatorial Optimization Conference (IPCO), June 1996, pp. 475-489.

Other Miscellaneous papers

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).

Michael E. Stillman

Professor, Stephen H. Weiss Presidential Fellow

Publications

  • Algebraic geometry of Bayesian networks (with L. Garcia and B. Sturmfels), preprint (2003).
  • Toric Hilbert schemes (with I. Peeva), Duke Math. J. 111 (2002), 419–449.
  • Computations in Algebraic Geometry with Macaulay 2 (D. Eisenbud, D. Grayson, M. Stillman, B. Sturmfels, eds.), Springer, 2001.
  • Computing sheaf cohomology on toric varieties (with D. Eisenbud and M. Mustata), J. Symbolic Computation 29 (2000), 583–600.
  • A criterion for detecting m-regularity (with D. Bayer), Invent. Math. 87 (1987), 1–11.

Adrian Lewis

Samuel B. Eckert Professor of Engineering

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.

Anil Nerode

Distinguished Professor of Arts and Sciences in Mathematics

Publications

  • Logic, Categories, Lambda Calculus (with R. Platek, G. Odifreddi), in preparation, 500 pp.
  • Finsler Control Theory and its applications (with W. Kohn, V. Brayman), in preparation, 300 pp.
  • Tableaux for constructive concurrent dynamic logic (with D. Wijesekera), Annals of Pure and Applied Logic 135 (2005), 1–72.
  • Effective completeness theorems for modal logic (with S. Ganguli), Annals of Pure and Applied Logic 128 no. 1-3 (2004), 141–195.
  • Control synthesis in hybrid systems with Finsler dynamics (with Wolf Kohn and Vladimir Brayman), Houston Journal of Mathematics 28 no. 2 (2003), 353–375.
  • Control in hybrid systems (with W. Kohn, V. Brayman, and P. Cholewinski), Int. J. Hybrid Systems 3 (2003).
  • Automata Theory and Its Applications (with Bakhadyr Khoussainov), Birkhauser, 2001, 430 pp.

I am also an editor of journals in these fields.

Lionel Levine

Professor

Publications

  • Formation of large-scale random structure by competitive erosion (with S. Ganguly and S. Sarkar), Annals of Probability, to appear.
  • Sandpiles on the square lattice (with B. Hough and D. C. Jerison), Communications in Mathematical Physics (2019) 367:33--87
  • The Apollonian structure of integer superharmonic matrices (with W. Pegden and C. Smart), Annals of Mathematics (2017) 186:1--67
  • Apollonian structure in the abelian sandpile (with Wesley Pegden and Charles K. Smart), Geometric and Functional Analysis 26 (2016), no. 1, 306-336.
  • Threshold state and a conjecture of Poghosyan, Poghosyan, Priezzhev and Ruelle, Communications in Mathematical Physics 335 no. 2 (2015), 1003–1017.
  • Internal DLA and the Gaussian free field (with D. Jerison and S. Sheffield), Duke Mathematical Journal 163 no. 2 (2014), 267–308.
  • Equations solvable by radicals in a uniquely divisible group (with C.J. Hillar and D. Rhea), Bulletin of the London Mathematical Society 45 (2013), 61–79.
  • Logarithmic fluctuations for internal DLA (with D. Jerison and S. Sheffield), Journal of the American Mathematical Society 25 (2012), 271–301.
  • Parallel chip-firing on the complete graph: devil's staircase and Poincaré rotation number, Ergodic Theory and Dynamical Systems 31 (2011), 891–910.
  • Driving sandpiles to criticality and beyond (with A. Fey and D. B. Wilson), Physical Review Letters 104 (2010), 145703.

Dexter Kozen

Joseph Newton Pew, Jr. Professor Emeritus

Publications

  • Language constructs for non-well-founded computation (with Jean-Baptiste Jeannin and Alexandra Silva), in Matthias Felleisen and Philippa Gardner, editors, 22nd European Symposium on Programming (ESOP 2013), volume 7792 of Lecture Notes in Computer Science, pages 61-80, Rome, Italy, March 2013. Springer.
  • On Moessner’s theorem (with Alexandra Silva), The American Mathematical Monthly, 120(2):131-139, February 2013.
  • Left-handed completeness (with Alexandra Silva), in Wolfram Kahl and Timothy G. Griffin, editors, Proc. Conf. Relational and Algebraic Methods in Computer Science (RAMiCS 2012), volume 7560 of Lecture Notes in Computer Science, pages 162-178, Cambridge, UK, September 2012. Springer.
  • New; in Proc. 28th Conf. Math. Found. Programming Semantics (MFPS XXVIII), Bath, England, June 2012, Elsevier Electronic Notes in Theoretical Computer Science (Ulrich Berger and Michael Mislove, eds.), 13–38.
  • Realization of coinductive types; in Proc. 27th Conf. Math. Found. Programming Semantics (MFPS XXVII), Pittsburgh, PA, May 2011, Elsevier Electronic Notes in Theoretical Computer Science (Michael Mislove and Joel Ouaknine, eds.), 148–155.

Robert Kleinberg

Associate Professor

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