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 

• 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 

• 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, in preparation.

• 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 J. Yu, Sharp Effective Finite-Field Nullstellensatz, in preparation.

• 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.

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 Summer 2020. The mentors this year were Matthew Junge, Guy Moshkovitz, Adam Sheffer, and Pablo Soberon. The participants:

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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, 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.

• 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.

• 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.

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

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

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

• E. Bernstein, C. Hamblen, M. Junge, and L. Reeves, Chase-escape on the configuration model, in preparation.

The program is 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  

• David Fitzpatrick 

• Arunima Grover

• Surya Mathialagan  

• Sherry Sarkar ​

• Alexander Xue

• Yingyi Zhu

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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, accepted under revision. 

• 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.        

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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:

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• Sara Fish 

• Matthew Hase-Liu 

• Robert Krueger

• Ruifan Yang 

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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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