spencercs.nyu.edu

Professor of Mathematics and Computer Science,

Department of Computer Science,

Courant Institute of Mathematical Sciences,

New York University,

New York, USA.

Discrete mathematics; theoretical computer science; algebra; combinatorics; probabilistic methods; theory of algorithms

A disciple of the late Paul Erdös, he is particularly interested in Ramsey theory, asymptotic combinatorics, probabilistic algorithms and probabilistic methods.

Member of A.M.S., M.A.A., and S.I.A.M.

Putnam Competition Winner 1962

M.A.A. Olympiad Committee 1975-78

N.A.S. Exchange Fellow, Budapest 1976-77

Sloane Foundation Fellow, 1977-81

Editor: Combinatorica, 1979-present

Putnam Competition Committee, 1980

Weizmann Institute (Israel) visitor, 1980

University of Reading (U.K.) visitor, 1981

IREX Exchange Fellow, Budapest, 1984

Ford Award, 1984

Budapest Semesters in Math Advisory Board, 1984-present

Associate Editor: American Math Monthly, 1986-1991

Ford Prize Committee, 1986-89

NSF-CBMS Lecturer, Durango, 1986

M.I.T. visitor, 1987, 1990, 2001

Microsoft visitor, 2003

Editor: SIAM J. of Discrete Math, 1987-1995

Brain Bogglers (as Maxwell Carver), Discover, 1987-89

Editor: Discrete Mathematics, 1988-1996

ARIDAM lecturer, 1988

Polya Prize Committee, 1990

Vice Chair, SIAM Disc Math Group, 1991-1993

Editor, The Annals of Applied Probability, 1990-1994

St. Flour (France) Probability School, Lecturer 1991

Cofounder: Random Structures and Algorithms, 1990

Institute for Mathematics and Its Applications, visitor 1993

AMS Program Committee for National Meetings 1994-5, chair 1995

Invited Speaker, International Congress of Mathematicians, Z¨urich, 1994

Nachdiplom Lectures, ETH (Zurich), Summer 1995

Institute for Advanced Study, visitor 1997, 1998

Chair, SIAM Disc Math Group, 1997-1999

Erdos Memorial Lectures, Hebrew University 2001

Geometric discrepancy theory, in Advances in Discrete and Computational Geometry (B. Chazelle, J. Goodman, R. Pollack, eds.), Contempory Mathematics vol. 223, American Math Soc., pp 355-368

New bounds on crossing numbers, Discrete and Computational Geometry 14 (2000), 623–644 (with J. Pach and G. Toth).

Uniformly Distributed Distances - A Geometric Application of Janson’s Inequality, Combinatorica 19 (1999), 1-14 (with J. Pach)

On the limit values of probabilities for the first order properties of graphs, in Contemporary

Trends in Discrete Mathematics, DIMACS Series vol. 49, Amer. Math. Soc., R. Graham et. al., eds., Amer. Math. Soc. 1999, pp 317-336 (with Lubos Thoma)

Ups and Downs of First Order Sentences on Random Graphs, Combinatorica 20 (2000), 263-280 (with G. Tardos)

Uniform Boundedness of Critical Crossing Probabilities implies Hyperscaling, Random

Structures and Algorithms 15 (1999), 368-413 (with C. Borgs, J.T. Chayes and H. Kesten)

Counting Dyadic Equipartitions of the Unit Square, Discrete Mathematics 257 (2002), 481-499 (with J. Lagarias and J. Vinson)

Packing Ferrers Shaps, Combinatorics Probability and Computing 9 (2000), 205-211 (with N. Alon and Mikl´os B´ona)

Ultrahigh Moments for a Brownian Excursion, in Mathematics and Computer Science Algorithms, Trees, Combinatorics and Probabilities (Daniele Gardy, Abdelkader Mokkadem, Editors) Birkhauser Verlag, 2000, p 323-328

The tenacity of zero-one laws, Electronic J Combinatorics 8 (2001), R17, 15pp (with K. St. John)

Discrete Probability, in Mathematics Unlimited 2001 and Beyond, Springer-Verlag, 2001, Bjorn Engquist, Wilfried Schmid (Eds.), pp.1095–1104.

The degree sequence of a scale-free random graph process, Random Structures & Algorithms 18 (2001), 279-290 (with B. Bollob´as, O. Riordan and G. Tusnady)

Random Graphs, Sets and Tournaments, in Paul Erd˝os and His Mathematics, vol 2. Bolyai Society Mathematical Studies, vol XI. (Eds. G. Halasz, L. Lovasz, M. Simonovits, V. T. Sos) Springer, Berlin, pp 637-648 (2002)

The Strange Logic of Random Graphs (book) Springer, 2001.

Birth of the Infinite Cluster: Finite-Size Scaling in Percolation, Communications in Mathematical Physics vol. 224 (1) 2001, pp 153-204 (with C. Borgs, J. Chayes, H. Kesten),

Packing Random Rectangles, Probab. Theory Relat. Fields 120 (2001), 585-599 (with E.G. Coman, Jr., George Lueker, and Peter Winkler)

Crossing Numbers for Random Graphs, Random Structures & Algorithms 21 (2002), 347-358 (with G´eza Toth)

Random Dyadic Tilings of the Unit Square, Random Structures & Algorithms, 21 (2002), 225-251 (with Svante Janson and Dana Randall)

A Halfliar’s Game, Theoretical Computer Science, 313 (2004), 353-369 (with Ioana Dumitriu)

New results on the distribution of distances determined by a point set, Bolyai Soc. Math. Studies 11, Paul Erdos and his Mathematics, II, (Eds. G. Halasz, L. Lovasz, M. Simonovits, V. T. Sos) Springer, Berlin, J. Bolyai Math. Soc., Budapest, 2002, 499-511. (with E. Makai and J. Pach)

Branching processes with Negative Ospring Distributions, Annals of Combinatorics 7 (2003), 35-47 (with I. Dumitriu and C. Yan)

The Halflie Problem, Journal of Combinatorial Theory, Ser A, 103 (2003), 69-89 (with

C. Yan)

A Scaling Result for Explosive Processes, Electronic J. Combinatorics R31 (2004) (with

M. Mitzenmacher and R. Oliveira)

The Biplanar Crossing Number of the Random Graph, in Towards a Theory of Geometric Graphs, Janos Pach ed., Contemporary Mathematics 342, 2004, AMS. pp. 269-272

Random Subgraphs of Finite Graphs: I. The Scaling Window under the Triangle Condition, Random Structures & Algorithms (with C. Borgs, J.T. Chayes, R. van der Hofstad and G. Slade)

Random subgraphs of finite graphs: II. The lace expansion and the triangle condition, Annals of Probability (with C. Borgs, J.T. Chayes, R. van der Hofstad and G. Slade)

Simulating a Random Walk with Constant Error, Combinatorics, Probability & Computing (with J. N. Cooper)

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