Adam Sheffer

A mathematician and computer scientist who spends much of his time supporting promising students.

Associate Professor of Mathematics at the City University of New York (Baruch College and the Graduate Center).

Member of Baruch's Discrete Math Group.

adamsh -at- gmail.com

Home

Activities I'm currently excited about:

Activities

I founded and am the director of the NYC Discrete Math REU.
I'm an organizer of the Polymath Jr Program.
My book Polynomial Methods and Incidence Theory was published by Cambridge University Press.
I'm an organizer of the NYC Geometry Seminar (an article about the long history of this seminar).
I designed the Baruch College Computer Science Program and am the Director of Computer Science.
My blog Some Plane Truths has not been very active recently, but I am still hopeful about fixing that...
My favorite activity.

A few more links:

I am an editor of the Journal of Computational Geometry.
My page with up-to-date results on numbers of plane graphs.
Lecture notes on Additive Combinatorics and more.

Research Papers:

Papers

S. Dasu, A. Sheffer, and J. Shen, Structural Szemerédi-Trotter for Lattices and their generalizations, submitted.
T. Aldape, J. Liu, G. Pylypovych, A. Sheffer, M.-Q. Vo,
Distinct Distances in R^3 Between Quadratic and Orthogonal Curves,submitted.
M. Balko, A. Sheffer, and R. Tang, The constant of point-line incidence constructions, Comput. Geom. Theory Appl., to appear.
A. Sheffer and O. Silier, A structural Szemerédi-Trotter Theorem for Cartesian Products, Discrete Comput. Geom., accepted.
S. Mathialagan and A. Sheffer, Distinct distances on non-ruled surfaces and between circles, Discrete Comput. Geom. 69 (2023), 422--452.
A. Sheffer and J. Zahl, Distinct distances in the complex plane, Trans. Amer. Math. Soc. 374 (2021), 6691--6725.
T. Do and A. Sheffer, A General Incidence Bound in R^d and Related Problems, Eur. J. Combin. 95 (2021), 103330.
E. A. Palsson, S. Senger, and A. Sheffer, On the Number of Discrete Chain, Proc. Amer. Math. Soc. 149 (2021), 5347--5358.
M. Hase-Liu and A. Sheffer, Sum-Product Phenomena for Planar Hypercomplex Numbers, Eur. J. Combin. 89 (2020), 103162.
S. Fish, C. Pohoata, and A. Sheffer, Local Properties via Color Energy Graphs and Forbidden Configurations, SIAM J. Discrete Math. 34 (2020), 177--187.
C. Pohoata and A. Sheffer, Local Properties in Colored Graphs, Distinct Distances, and Difference Sets, Combinatorica 39 (2019), 705--714.
S. Bardwell-Evans and A. Sheffer, A Reduction for the Distinct Distances Problem in R^d, J. Combinat. Theory A 166 (2019), 171--225.
S. Fish, B. Lund, and A. Sheffer, A Construction for Difference Sets with Local Properties, Eur. J. Combin. 79 (2019), 237--243.
A. Sheffer, E. Szabó, and J. Zahl, Point-curve incidences in the complex plane, Combinatorica 38 (2018), 487--499.
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.
C. Pohoata and A. Sheffer, Higher Distance Energies and Expanders with Structure, under a major revision.
A. Sheffer, Lower bounds for incidences with hypersurfaces, Discrete Analysis 2016:16.
B. Lund, A. Sheffer, and F. de Zeeuw, Bisector energy and few distinct distances, Discrete Comput. Geom. 56 (2016), 337--356.
A. Sheffer, J. Zahl, and F. de Zeeuw, Few distinct distances implies no heavy lines or circles, Combinatorica 36 (2016), 349--364.
I. Pak, A. Sheffer, and M. Tassy, Fast domino tileability, Discrete Comput. Geom. 56 (2016), 377--394.
M. Sharir, A. Sheffer, and N. Solomon, Incidences with curves in R^d, Electr. J. Comb. 23 (2016), P4.16.
M. Sharir, A. Sheffer, and J. Zahl, Improved bounds for incidences between points and circles, Combinat. Probab. Comput. 24 (2015), 490--520.
J. Cilleruelo, M. Sharir, and A. Sheffer, A note on distinct distances in rectangular lattices, Discrete Math. 336 (2014), 37--40.
A. Basit and A. Sheffer, Incidences with k-non-degenerate sets and their applications, Journal of Computational Geometry 5 (2014), 284--302.
V. Dujmović, P. Morin and A. Sheffer, Crossings in grid drawings, Electr. J. Comb. 21(1) (2014).
M. Sharir, A. Sheffer, and J. Solymosi, Distinct distances on two lines, J. Combinat. Theory A 120 (2013), 1732--1736.
M. Sharir and A. Sheffer, Counting plane graphs: Cross-graph charging schemes, Combinat. Probab. Comput. 22 (2013), 935--954.
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.
M. Ben-Ner, A. Schulz, and A. Sheffer, On numbers of pseudo-triangulations, Comput. Geom. Theory Appl. 46 (2013), 688--699.
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.
M. Sharir, A. Sheffer, and E. Welzl, On degrees in random triangulations, J. Combinat. Theory A 118 (2011), 1979--1999.
M. Sharir and A. Sheffer, Counting triangulations of planar point sets, Electr. J. Comb. 18 (2011)

Non-Research works (Surveys, mentoring, and more):

Others

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.
A. Sheffer, Distinct Distances: Open Problems and Current Bounds, Manuscript.
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.

A. Li, Progress on local properties problems of difference sets, European Journal of Combinatorics 108 (2023), 103618.
H. Ashbach and K. Pichini, An Upper Bound for the Number of Rectangulations of a Planar Point Set, Electronic Journal of Combinatorics, accepted.
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 ℓp Spaces, Computational Geometry: Theory and Applications 100 (2022): 101785. Won $1,000 Young Researchers Award.
R. A. Krueger, Generalized Ramsey Numbers: Edge-Coloring Forbidding Paths with Few Colors, Electronic Journal of Combinatorics (2020), P1--44.
A. Bruner and M. Sharir, Distinct distances between a collinear set and an arbitrary set of points, Discrete Mathematics, 341 (2018), 261-265.
S. Mathialagan, On bipartite distinct distances in the plane, Electronic Journal of Combinatorics 28 (2021), P4.33.
A. Balsera, Incidences with Pfaffian Curves and Functions, submitted.
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.)

Email 1: adamsh -at- gmail.com (preferred)
Email 2: adam.sheffer -at- baruch.cuny.edu.

Contact