Adam Sheffer
A mathematician and computer scientist who spends much of his time supporting promising students.
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Associate Professor of Mathematics at the City University of New York (Baruch College and the Graduate Center).
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Member of Baruch's Discrete Math Group.
adamsh -at- gmail.com
Activities I'm currently excited about:​
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I founded and am the director of the NYC Discrete Math REU.
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I'm an organizer of the Polymath Jr Program.
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My book Polynomial Methods and Incidence Theory was published by Cambridge University Press.
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I'm an organizer of the NYC Geometry Seminar (an article about the long history of this seminar).
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I designed the Baruch College Computer Science Program and am the Director of Computer Science.
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My blog Some Plane Truths has not been very active recently, but I am still hopeful about fixing that...
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A few more links:
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I am an editor of the Journal of Computational Geometry.
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My page with up-to-date results on numbers of plane graphs.
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Lecture notes on Additive Combinatorics and more.
Research Papers:
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S. Das, C. Pohoata, and A. Sheffer, Expanding polynomials for sets with additive structure, submitted.
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N. Lovvorn, O. Murillo-Espinoza, and A. Sheffer, Expected degrees in random plane graphs, submitted
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S. Dasu, A. Sheffer, and J. Shen, Structural Szemerédi-Trotter for Lattices and their generalizations, submitted.
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T. Aldape, J. Liu, G. Pylypovych, A. Sheffer, M.-Q. Vo,
Distinct Distances in R^3 Between Quadratic and Orthogonal Curves, Eur. J. Combin. 120 (2024), 103993. -
M. Balko, A. Sheffer, and R. Tang, The constant of point-line incidence constructions, Comput. Geom. Theory Appl., to appear.
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A. Sheffer and O. Silier, A structural Szemerédi-Trotter Theorem for Cartesian Products, Discrete Comput. Geom., accepted.
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S. Mathialagan and A. Sheffer, Distinct distances on non-ruled surfaces and between circles, Discrete Comput. Geom. 69 (2023), 422--452.
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A. Sheffer and J. Zahl, Distinct distances in the complex plane, Trans. Amer. Math. Soc. 374 (2021), 6691--6725.
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T. Do and A. Sheffer, A General Incidence Bound in R^d and Related Problems, Eur. J. Combin. 95 (2021), 103330.
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E. A. Palsson, S. Senger, and A. Sheffer, On the Number of Discrete Chain, Proc. Amer. Math. Soc. 149 (2021), 5347--5358.
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M. Hase-Liu and A. Sheffer, Sum-Product Phenomena for Planar Hypercomplex Numbers, Eur. J. Combin. 89 (2020), 103162.
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S. Fish, C. Pohoata, and A. Sheffer, Local Properties via Color Energy Graphs and Forbidden Configurations, SIAM J. Discrete Math. 34 (2020), 177--187.
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C. Pohoata and A. Sheffer, Local Properties in Colored Graphs, Distinct Distances, and Difference Sets, Combinatorica 39 (2019), 705--714.
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S. Bardwell-Evans and A. Sheffer, A Reduction for the Distinct Distances Problem in R^d, J. Combinat. Theory A 166 (2019), 171--225.
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S. Fish, B. Lund, and A. Sheffer, A Construction for Difference Sets with Local Properties, Eur. J. Combin. 79 (2019), 237--243.
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A. Sheffer, E. Szabó, and J. Zahl, Point-curve incidences in the complex plane, Combinatorica 38 (2018), 487--499.
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J. Fox, J. Pach, A. Sheffer, A. Suk, and J. Zahl, A semi-algebraic version of Zarankiewicz's problem, Journal of the European Mathematical Society 19 (2017), 1785--1810.
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C. Pohoata and A. Sheffer, Higher Distance Energies and Expanders with Structure, under a major revision.
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A. Sheffer, Lower bounds for incidences with hypersurfaces, Discrete Analysis 2016:16.
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B. Lund, A. Sheffer, and F. de Zeeuw, Bisector energy and few distinct distances, Discrete Comput. Geom. 56 (2016), 337--356.
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A. Sheffer, J. Zahl, and F. de Zeeuw, Few distinct distances implies no heavy lines or circles, Combinatorica 36 (2016), 349--364.
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I. Pak, A. Sheffer, and M. Tassy, Fast domino tileability, Discrete Comput. Geom. 56 (2016), 377--394.
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M. Sharir, A. Sheffer, and N. Solomon, Incidences with curves in R^d, Electr. J. Comb. 23 (2016), P4.16.
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M. Sharir, A. Sheffer, and J. Zahl, Improved bounds for incidences between points and circles, Combinat. Probab. Comput. 24 (2015), 490--520.
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J. Cilleruelo, M. Sharir, and A. Sheffer, A note on distinct distances in rectangular lattices, Discrete Math. 336 (2014), 37--40.
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A. Basit and A. Sheffer, Incidences with k-non-degenerate sets and their applications, Journal of Computational Geometry 5 (2014), 284--302.
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V. Dujmović, P. Morin and A. Sheffer, Crossings in grid drawings, Electr. J. Comb. 21(1) (2014).
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M. Sharir, A. Sheffer, and J. Solymosi, Distinct distances on two lines, J. Combinat. Theory A 120 (2013), 1732--1736.
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M. Sharir and A. Sheffer, Counting plane graphs: Cross-graph charging schemes, Combinat. Probab. Comput. 22 (2013), 935--954.
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M. Sharir, A. Sheffer, and E. Welzl, Counting plane graphs: Perfect matchings, spanning cycles, and Kasteleyn's technique, J. Combinat. Theory A 120 (2013) 777--794.
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M. Ben-Ner, A. Schulz, and A. Sheffer, On numbers of pseudo-triangulations, Comput. Geom. Theory Appl. 46 (2013), 688--699.
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M. Hoffmann, A. Schulz, M. Sharir, A. Sheffer, C. D. Tóth, and E. Welzl,
Counting plane graphs: Flippability and its applications, Thirty Essays on Geometric Graph Theory (J. Pach, ed.), Springer, 2013, pp. 303--326. -
A. Dumitrescu, A. Schulz, A. Sheffer, and Cs. D. Tóth, Bounds on the maximum multiplicity of some common geometric graphs, SIAM J. Discrete Math. 27 (2013), 802--826.
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M. Sharir, A. Sheffer, and E. Welzl, On degrees in random triangulations, J. Combinat. Theory A 118 (2011), 1979--1999.
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M. Sharir and A. Sheffer, Counting triangulations of planar point sets, Electr. J. Comb. 18 (2011)
Non-Research works (Surveys, mentoring, and more):
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K. Adaricheva, B. Brubaker, P. Devlin, S. J. Miller, V. Reiner, A. Seceleanu, A. Sheffer, Y. Zeytuncu, When Life Gives You Lemons, Make Mathematicians, Notices of the AMS, March 2021, 375--378.
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A. Sheffer, Distinct Distances: Open Problems and Current Bounds, Manuscript.
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A. Sheffer, Your First Math Talk, Manuscript.
Selected Mentored Projects:
These are a few examples of research papers that were produced by projects that I mentored, but to which I did not add my name. There are more.
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A. Li, Progress on local properties problems of difference sets, European Journal of Combinatorics 108 (2023), 103618.
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H. Ashbach and K. Pichini, An Upper Bound for the Number of Rectangulations of a Planar Point Set, Electronic Journal of Combinatorics, accepted.
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M. AlQady, R. Chabot, W. Dudarov, L. Ge, M. Juvekar, S. Kundeti, N. Kundu, K. Lu, Y. Moreno, S. Peng, S. Speas, J. Starzycka, H. Steinthal, A. Vitko, Distinct Distances with â„“p Spaces, Computational Geometry: Theory and Applications 100 (2022): 101785. Won $1,000 Young Researchers Award.
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R. A. Krueger, Generalized Ramsey Numbers: Edge-Coloring Forbidding Paths with Few Colors, Electronic Journal of Combinatorics (2020), P1--44.
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A. Bruner and M. Sharir, Distinct distances between a collinear set and an arbitrary set of points, Discrete Mathematics, 341 (2018), 261-265.
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S. Mathialagan, On bipartite distinct distances in the plane, Electronic Journal of Combinatorics 28 (2021), P4.33.
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A. Balsera, Incidences with Pfaffian Curves and Functions, submitted.
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R(K6−e,K4)=30, D. James, E. Kahan, and E. Rauer, submitted
City University of New York (CUNY),
Baruch College and the Graduate Center,
Department of Mathematics,
VC 6-220.
Phone: 646-312-4021.
(Please send an email rather leave a voicemail.)
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Email 1: adamsh -at- gmail.com (preferred)
Email 2: adam.sheffer -at- baruch.cuny.edu.