History of the NYC Discrete Math REU

Summer 2020. The mentors this year are Matthew Junge, Guy Moshkovitz, Adam Sheffer, and Pablo Soberon. The participants (in alphabetical order):

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• Riti Bahl

• Luis Benitez Norat

• Travis Dillon

• Clare Hamblen

• Anqi Li

• Jack Messina

• Hanna Mularczyk

• Kukai Nakahata

• Max Redman

• Olivine Silier

• Yaqian Tang

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Papers produced during this summer:​

• A. Cohen and G. Moshkovitz, Structure vs. Randomness for Bilinear Maps, to appear in the 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, submitted to a journal.

• T. Dillon, Discrete quantitative Helly-type theorems with boxes, submitted to a journal.

• R. Bahl, N. Eikmeier, A. Fraser, M. Junge, F. Keesing, K. Nakahata, and L. Z. Wang, Modeling COVID-19 Spread in Small Colleges, submitted to a journal.

• J. A. Messina and P. Soberón, Isometric and Affine Copies of a Set in Volumetric Helly Results, submitted to a journal.

• L. Benitez, M. Junge, H. Lyu, M. Redman, and L. Z. Wang, Three-velocity coalescing ballistic annihilation, submitted to a journal.

• P. Soberón and Y. Tang, Tverberg’s theorem, disks, and Hamiltonian cycles, to be submitted soon.

• A. Sheffer and O. Silier, Structural Szemerédi-Trotter for Cartesian Products, in preparation. 

• A. Li, Local Property Thresholds for Difference Sets, in preparation.

• R. Bahl, P. Barnet, T. Johnson, and M. Junge, Parking respects the increasing-convex order, in preparation.

• G. Moshkovitz and H. Mularczyk, How Many Monotone Functions Are There?  in preparation.

• Alex Cohen and Guy Moshkovitz, An Optimal Inverse Theorem, in preparation. 

• More to appear?

The program is partially funded by NSF awards DMS-1802059,

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

Summer of 2019. The mentors this year are Adam Sheffer, Pablo Soberon, and Frank de Zeeuw. The participants (in alphabetical order):

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• Alex Cohen  

• David Fitzpatrick 

• Arunima Grover

• Surya Mathialagan  

• Sherry Sarkar ​

• Alexander Xue

• Yingyi Zhu

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Papers produced during this summer:

• 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. Sarkar, A. Xue, and P. Soberón, Quantitative combinatorial geometry for concave functions, submitted to a journal.

• S. Mathialagan, On bipartite distinct distances in the plane, submitted to a journal. 

• 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.

• A. Cohen and F. de Zeeuw, A Sylvester-Gallai theorem for cubic curves, submitted to a journal.

• S. Mathialagan and A. Sheffer, Distinct distances on non-ruled surfaces and between circles, submitted to a journal.

Program partially funded by NSF awards DMS-1802059 and DMS-1851420.        

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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 (in alphabetical order):

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• Sara Fish (Caltech)

• Matthew Hase-Liu (Harvard)

• Robert Krueger (Miami University)

• Ruifan Yang (Boston College)

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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.

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