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 Axelrod-Freed
Edo Biluar
Danyil Blyschak
John Francis Burkhart
Joao Carvalho
William Chang
Dario Cruzado-Padro
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. Axelrod-Freed and P. Soberón, Bisections of mass assignments using flags of affine spaces, submitted to a journal.
G. Moshkovitz and J. Yu, Sharp Effective Finite-Field 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_t-minor free graphs, in preparation.
D. Cruzado-Padro, 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 Szemerédi-Trotter for Lattices and Semi-Lattices, in prepartion.
G. Moshkovitz and A. Murthy, Near-tight bounds for near-sunflower 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 DMS-1802059, DMS-1855516, and DMS-2051026.

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 Helly-type theorems, SIAM Journal of Discrete Math 35 (2021), 1615-1627.
T. Dillon, Discrete quantitative Helly-type 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 COVID-19 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), 995--1005.
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, Three-velocity 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, Diffusion-limited annihilating systems and the increasing convex order, submitted to a journal.
A. Sheffer and O. Silier, Structural Szemerédi-Trotter for Cartesian Products, submitted to a journal.
E. Bernstein, C. Hamblen, M. Junge, and L. Reeves, Chase-escape 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 DMS-1802059,

DMS-1851420, DMS-1953141, and DMS-2028892.

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 Sylvester-Gallai 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): 1-8.
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 non-ruled surfaces and between circles, accepted under revision.
A. Cohen and F. de Zeeuw, A Sylvester-Gallai 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 DMS-1802059 and DMS-1851420.

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 Hase-Liu
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), 237--243.
S. Fish, C. Pohoata, and A. Sheffer, Local Properties via Color Energy Graphs and Forbidden Configurations, SIAM Journal of Discrete Math. 34 (2020), 177--187.
M. Hase-Liu and A. Sheffer, Sum-Product Phenomena for Planar Hypercomplex Numbers, European Journal of Combinatorics, accepted.
R. A. Krueger, Generalized Ramsey Numbers: Edge-Coloring Forbidding Paths with Few Colors, Electronic Journal of Combinatorics, accepted.

This program was partially funded by NSF award DMS-1802059.

Earlier than 2018. Adam Sheffer has been mentoring undergrad research projects for many years before the CUNY Combinatorics REU. In the years 2014-2017 Adam was running such projects in Caltech, and before that in Israel.

A few earlier papers from undergraduate projects mentored by Adam:

S. Bardwell-Evans and A. Sheffer, A Reduction for the Distinct Distances Problem in R^d, Journal of Combinatorial Theory A 166 (2019), 171--225.
A. Bruner and M. Sharir, Distinct distances between a collinear set and an arbitrary set of points, Discrete Mathematics 341, 261-265.
M. Ben-Ner, A. Schulz, and A. Sheffer, On numbers of pseudo-triangulations,
Comput. Geom. Theory Appl. 46, 688--699.

History of the NYC Discrete Math REU

T. Dillon, Discrete quantitative Helly-type 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 COVID-19 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), 995--1005.

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, Three-velocity 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, Diffusion-limited annihilating systems and the increasing convex order, submitted to a journal.

A. Sheffer and O. Silier, Structural Szemerédi-Trotter for Cartesian Products, submitted to a journal.

E. Bernstein, C. Hamblen, M. Junge, and L. Reeves, Chase-escape 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 DMS-1802059,