
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:
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Hannah Ashbach
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Ilani Axelrod-Freed
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Edo Biluar
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Danyil Blyschak
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John Francis Burkhart
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Joao Carvalho
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William Chang
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Dario Cruzado-Padro
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Christina Jones
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Zoe Ann McDonald
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Anushka Murthy
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Jean Pulla
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Jake Ruotolo
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Junxuan (Helen) Shen
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Yuki Takahashi
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Kevin Wang
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Dora Woodruff
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Jeffery Yu
Papers produced during this summer:
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P. Soberón and Y. Takahashi, Lifting methods in mass partition problems, International Mathematics Research Notices, to appear.
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G. Moshkovitz and J. Yu, Sharp Effective Finite-Field Nullstellensatz, The American Mathematical Monthly, to appear.
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J. P. Carvalho and P. Soberón, Counterexamples to the Colorful Tverberg Conjecture for Hyperplanes, Acta Mathematica Hungarica, 2022.
- I. Axelrod-Freed and P. Soberón, Bisections of mass assignments using flags of affine spaces, submitted to a journal.
- N. Frankl and Dora Woodruff, On some non-rigid unit distance patterns, submitted to a journal.
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H. Ashbach and K. Pichini, An Upper Bound for the Number of Rectangulations of a Planar Point Set, submitted to a journal.
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J. Ruotolo, K. Wang, and F. Wei, A sharp bound on the number of independent transversals, in preparation.
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W. Chang and F. Wei, Bounding the number of maximal cliques in K_t-minor free graphs, in preparation.
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D. Cruzado-Padro, M. Junge, and L. Reeves, Universality in coalescing ballistic annihilation, in preparation.
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T. Johnson, M. Junge, Z. McDonald, J. Pulla, and L. Reeves, The threshold frog model, in preparation.
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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.
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K. Ahrendt, D. Blyschak, A. Ikram, and C. Jones, Coupled Solutions to a Discrete Nabla Caputo Fractional Boundary Value Problem, in preparation.
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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:
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Riti Bahl
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Luis Benitez Norat
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Travis Dillon
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Clare Hamblen
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Anqi Li
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Jack Messina
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Hanna Mularczyk
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Kukai Nakahata
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Max Redman
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Olivine Silier
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Yaqian Tang
Papers produced during this summer:
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A. Cohen and G. Moshkovitz, Structure vs. Randomness for Bilinear Maps, Proceedings of the 53rd Annual ACM Symposium on Theory of Computing (STOC), 2021.
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T. Dillon and P. Soberón, A mélange of diameter Helly-type theorems, SIAM Journal of Discrete Math 35 (2021), 1615-1627.
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T. Dillon, Discrete quantitative Helly-type theorems with boxes, to appear in Advances in Applied Mathematics.
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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.
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P. Soberón and Y. Tang, Tverberg’s Theorem, Disks, and Hamiltonian Cycles, Annals of Combinatorics 25 (2021), 995--1005.
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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.
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L. Benitez, M. Junge, H. Lyu, M. Redman, and L. Z. Wang, Three-velocity coalescing ballistic annihilation, submitted to a journal.
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Alex Cohen and Guy Moshkovitz, An Optimal Inverse Theorem, submitted to a journal. Quanta article.
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R. Bahl, P. Barnet, T. Johnson, and M. Junge, Diffusion-limited annihilating systems and the increasing convex order, submitted to a journal.
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A. Sheffer and O. Silier, Structural Szemerédi-Trotter for Cartesian Products, submitted to a journal.
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E. Bernstein, C. Hamblen, M. Junge, and L. Reeves, Chase-escape on the configuration model, submitted to a journal.
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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:
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Alex Cohen
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David Fitzpatrick
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Arunima Grover
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Surya Mathialagan
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Sherry Sarkar
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Alexander Xue
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Yingyi Zhu
Papers produced during this summer:
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S. Sarkar, A. Xue, and P. Soberón, Quantitative combinatorial geometry for concave functions, Journal of Combinatorial Theory A 182 (2021), to appear
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A. Cohen, A Sylvester-Gallai result for concurrent lines in the complex plane, Discrete & Computational Geometry, to appear.
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A. Xue and P. Soberón, Balanced convex partitions of lines in the plane, Discrete & Computational Geometry, to appear.
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S. Mathialagan and A. Sheffer, Distinct distances on non-ruled surfaces and between circles, Discrete & Computational Geometry, to appear.A. Cohen and
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F. de Zeeuw, A Sylvester-Gallai theorem for cubic curves, European Journal of Combinatorics 103 (2022): 103509.
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S. Sarkar and P. Soberón, Tolerance for colorful Tverberg partitions, European Journal of Combinatorics, to appear.
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A. Cohen and M. Nathanson, Sinkhorn limits in finitely many steps, Linear Algebra and its Applications 589 (2020): 1-8.
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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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D. Fitzpatrick, Distance problems for planar hypercomplex numebrs, submitted to a journal.
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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:
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Sara Fish
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Matthew Hase-Liu
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Robert Krueger
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Ruifan Yang
Papers produced during this summer:
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S. Fish, B. Lund, and A. Sheffer, A Construction for Difference Sets with Local Properties, European Journal of Combinatorics 79 (2019), 237--243.
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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.
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M. Hase-Liu and A. Sheffer, Sum-Product Phenomena for Planar Hypercomplex Numbers, European Journal of Combinatorics, accepted.
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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:
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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.
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A. Bruner and M. Sharir, Distinct distances between a collinear set and an arbitrary set of points, Discrete Mathematics 341, 261-265.
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M. Ben-Ner, A. Schulz, and A. Sheffer, On numbers of pseudo-triangulations,
Comput. Geom. Theory Appl. 46, 688--699.