History of the NYC Discrete Math REU
Summer 2021. The mentors this year were Nóra Frankl, Areeba Ikram, Matthew Junge, Guy Moshkovitz, Adam Sheffer, Pablo Soberón, and Fan Wei. Participants:

Hannah Ashbach

Ilani AxelrodFreed

Edo Biluar

Danyil Blyschak

John Francis Burkhart

Joao Carvalho

William Chang

Dario CruzadoPadro

Christina Jones

Zoe Ann McDonald

Anushka Murthy

Jean Pulla

Jake Ruotolo

Junxuan (Helen) Shen

Yuki Takahashi

Kevin Wang

Dora Woodruff

Jeffery Yu
Papers produced during this summer:

J. P. Carvalho and P. Soberón, Counterexamples to the Colorful Tverberg Conjecture for Hyperplanes, submitted to a journal.

P. Soberón and Y. Takahashi, Lifting methods in mass partition problems, submitted to a journal.

I. AxelrodFreed and P. Soberón, Bisections of mass assignments using flags of affine spaces, submitted to a journal.

G. Moshkovitz and J. Yu, Sharp Effective FiniteField Nullstellensatz, submitted to a journal.

J. Ruotolo, K. Wang, and F. Wei, A sharp bound on the number of independent transversals, in preparation.

W. Chang and F. Wei, Bounding the number of maximal cliques in K_tminor free graphs, in preparation.

D. CruzadoPadro, M. Junge, and L. Reeves, Universality in coalescing ballistic annihilation, in preparation.

T. Johnson, M. Junge, Z. McDonald, J. Pulla, and L. Reeves, The threshold frog model, in preparation.

H. Ashbach and K. Pichini, An Upper Bound for the Number of Rectangulations of a Planar Point Set, in preparation.

J. Shen, Structural SzemerédiTrotter for Lattices and SemiLattices, in prepartion.

G. Moshkovitz and A. Murthy, Neartight bounds for nearsunflower variants, in preparation.

K. Ahrendt, D. Blyschak, A. Ikram, and C. Jones, Coupled Solutions to a Discrete Nabla Caputo Fractional Boundary Value Problem, in preparation.

N. Frankl and Dora Woodruff, Unit distance paths and cycles on the sphere, in preparation.

E. Biluar and N. Frankl, On the number of unit distance simplices with few vertices, in preparation.
The program was funded by NSF awards DMS1802059, DMS1855516, and DMS2051026.
Summer 2020. The mentors this year were Matthew Junge, Guy Moshkovitz, Adam Sheffer, and Pablo Soberon. The participants:

Riti Bahl

Luis Benitez Norat

Travis Dillon

Clare Hamblen

Anqi Li

Jack Messina

Hanna Mularczyk

Kukai Nakahata

Max Redman

Olivine Silier

Yaqian Tang
Papers produced during this summer:

A. Cohen and G. Moshkovitz, Structure vs. Randomness for Bilinear Maps, Proceedings of the 53rd Annual ACM Symposium on Theory of Computing (STOC), 2021.

T. Dillon and P. Soberón, A mélange of diameter Hellytype theorems, SIAM Journal of Discrete Math 35 (2021), 16151627.

T. Dillon, Discrete quantitative Hellytype theorems with boxes, to appear in Advances in Applied Mathematics.

R. Bahl, N. Eikmeier, A. Fraser, M. Junge, F. Keesing, K. Nakahata, and L. Z. Wang, Modeling COVID19 Spread in Small Colleges, Plos one 16, e0255654.

P. Soberón and Y. Tang, Tverberg’s Theorem, Disks, and Hamiltonian Cycles, Annals of Combinatorics 25 (2021), 9951005.

J. A. Messina and P. Soberón, Isometric and Affine Copies of a Set in Volumetric Helly Results, Computational Geometry: Theory and Applications 103 (2022), 101855.

L. Benitez, M. Junge, H. Lyu, M. Redman, and L. Z. Wang, Threevelocity coalescing ballistic annihilation, submitted to a journal.

Alex Cohen and Guy Moshkovitz, An Optimal Inverse Theorem, submitted to a journal.

R. Bahl, P. Barnet, T. Johnson, and M. Junge, Diffusionlimited annihilating systems and the increasing convex order, submitted to a journal.

A. Sheffer and O. Silier, Structural SzemerédiTrotter for Cartesian Products, submitted to a journal.

E. Bernstein, C. Hamblen, M. Junge, and L. Reeves, Chaseescape on the configuration model, submitted to a journal.

A. Li, Local Property Thresholds for Difference Sets, submitted to a journal.
The program was partially funded by NSF awards DMS1802059,
DMS1851420, DMS1953141, and DMS2028892.
Summer of 2019. The mentors this year were Adam Sheffer, Pablo Soberon, and Frank de Zeeuw. The participants:

Alex Cohen

David Fitzpatrick

Arunima Grover

Surya Mathialagan

Sherry Sarkar

Alexander Xue

Yingyi Zhu
Papers produced during this summer:

S. Sarkar, A. Xue, and P. Soberón, Quantitative combinatorial geometry for concave functions, Journal of Combinatorial Theory A 182 (2021), to appear

A. Cohen, A SylvesterGallai result for concurrent lines in the complex plane, Discrete & Computational Geometry, to appear.

A. Xue and P. Soberón, Balanced convex partitions of lines in the plane, Discrete & Computational Geometry, to appear.

A. Cohen and M. Nathanson, Sinkhorn limits in finitely many steps, Linear Algebra and its Applications 589 (2020): 18.

S. Mathialagan, On bipartite distinct distances in the plane, Electronic Journal of Combinatorics 28 (2021), P4.33.

S. Mathialagan and A. Sheffer, Distinct distances on nonruled surfaces and between circles, accepted under revision.

A. Cohen and F. de Zeeuw, A SylvesterGallai theorem for cubic curves, accepted under revision.

D. Fitzpatrick, Distance problems for planar hypercomplex numebrs, submitted to a journal.

S. Sarkar and P. Soberón, Tolerance for colorful Tverberg partitions, submitted to a journal.

Program partially funded by NSF awards DMS1802059 and DMS1851420.
Part of our 2018 team
Summer of 2018. This was the first year of the REU. The mentors were Adam Sheffer and Rados Radoicic. The participants:

Sara Fish

Matthew HaseLiu

Robert Krueger

Ruifan Yang
Papers produced during this summer:

S. Fish, B. Lund, and A. Sheffer, A Construction for Difference Sets with Local Properties, European Journal of Combinatorics 79 (2019), 237243.

S. Fish, C. Pohoata, and A. Sheffer, Local Properties via Color Energy Graphs and Forbidden Configurations, SIAM Journal of Discrete Math. 34 (2020), 177187.

M. HaseLiu and A. Sheffer, SumProduct Phenomena for Planar Hypercomplex Numbers, European Journal of Combinatorics, accepted.

R. A. Krueger, Generalized Ramsey Numbers: EdgeColoring Forbidding Paths with Few Colors, Electronic Journal of Combinatorics, accepted.
This program was partially funded by NSF award DMS1802059.
Earlier than 2018. Adam Sheffer has been mentoring undergrad research projects for many years before the CUNY Combinatorics REU. In the years 20142017 Adam was running such projects in Caltech, and before that in Israel.
A few earlier papers from undergraduate projects mentored by Adam:

S. BardwellEvans and A. Sheffer, A Reduction for the Distinct Distances Problem in R^d, Journal of Combinatorial Theory A 166 (2019), 171225.

A. Bruner and M. Sharir, Distinct distances between a collinear set and an arbitrary set of points, Discrete Mathematics 341, 261265.

M. BenNer, A. Schulz, and A. Sheffer, On numbers of pseudotriangulations,
Comput. Geom. Theory Appl. 46, 688699.