History of the NYC Discrete Math REU
Summer 2022. The mentors this year were Kira Adaricheva, Matthew Junge, Guy Moshkovitz, Anna Pun, Eric Rowland, Adam Sheffer (only organizing), and Pablo Soberón.
Participants:
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Arav Agarwal

Julia Carrigan

Connor Donovan

Kendra Ebke

Isaiah Hollars

Rachel Leslie

Na'ama Nevo

Arturo Ortiz San Miguel

Danielle Paulson

Cynthia Marie RiveraSanchez

Glenn Sun

Daniel Zhu
Papers produced during this summer:â€‹

M. Junge, A. Ortiz San Miguel, L. Reeves, and C. Rivera Sánchez, Nonuniversality in clustered ballistic annihilation, Electronic Communications in Probability, 28 (2023): 112.

G. Moshkovitz and D. Zhu, Quasilinear relation between partition and analytic rank, submitted.

J. Carrigan, I. Hollars, and E. Rowland, Natural bijections for contiguous pattern avoidance in words, submitted.

C. Donovan, D. Paulson, and P. Soberón, Colorful and quantitative variations of Krassnolesky's theorem, submitted.

K. Adaricheva, A. Agarwal, and N. Nevo, Representation of convex geometries of convex dimension 3 by spheres, submitted.

G. Moshkovitz and G. Sun, Tight lower bounds for Nullstellensatz proofs, in preparation.

More to appear?
The program was funded by NSF awards DMS1855516 and DMS2051026.
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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 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:â€‹

P. Soberón and Y. Takahashi, Lifting methods in mass partition problems, International Mathematics Research Notices 2023, 14103–14130.

G. Moshkovitz and J. Yu, Sharp Effective FiniteField Nullstellensatz, The American Mathematical Monthly 130 (2023).

J. P. Carvalho and P. Soberón, Counterexamples to the Colorful Tverberg Conjecture for Hyperplanes, Acta Mathematica Hungarica 167 (2022), 385–392.
 I. AxelrodFreed and P. Soberón, Bisections of mass assignments using flags of affine spaces, Discrete & Computational Geometry, to appear.
 N. Frankl and D. Woodruff, On some nonrigid unit distance patterns, Discrete & Computational Geometry, to appear.

M. Junge, Z. McDonald, J. Pulla, and L. Reeves, A stochastic combustion model with thresholds on trees, Journal of Statistical Physics, 190(5), 100.

D. CruzadoPadro, M. Junge, and L. Reeves, Arrivals are universal in coalescing ballistic annihilation, submitted.

H. Ashbach and K. Pichini, An Upper Bound for the Number of Rectangulations of a Planar Point Set, submitted.
 J. Ruotolo, K. Wang, and F. Wei, A sharp bound on the number of independent transversals, submitted.
 I AxelrodFreed, J. P. Carvalho, Y. Takahashi, Quantitative Transversal Theorems in the Plane, submitted

S. Dasu, A. Sheffer, and J. Shen, Structural SzemerédiTrotter for Lattices and their generalizations, in preparation.
 K. Ahrendt, D. Blyschak, A. Ikram, and C. Jones, Coupled Solutions to a Discrete Nabla Caputo Fractional Boundary Value Problem, 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.
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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:â€‹

Alex Cohen and Guy Moshkovitz, Partition and Analytic Rank are Equivalent over Large Fields, Duke Mathematical Journal, to appear. Quanta article.

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

A. Sheffer and O. Silier, Structural SzemerédiTrotter for Cartesian Products, Discrete & Computational Geometry, to appear.

R. Bahl, P. Barnet, T. Johnson, and M. Junge, Diffusionlimited annihilating systems and the increasing convex order, Electronic Journal of Probability 27 (2022), 119.

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.

L. Benitez, M. Junge, H. Lyu, M. Redman, and L. Z. Wang, Threevelocity coalescing ballistic annihilation, Electronic Journal of Probability 28, 118.

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.

E. Bernstein, C. Hamblen, M. Junge, and L. Reeves, Chaseescape on the configuration model, Electronic Communications in Probability 27 (2022): 114.

A. Li, Progress on local properties problems of difference sets, European Journal of Combinatorics 108 (2023), 103618.

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.
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:
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Alex Cohen

David Fitzpatrick

Arunima Grover

Surya Mathialagan

Sherry Sarkar â€‹

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 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.

S. Mathialagan and A. Sheffer, Distinct distances on nonruled surfaces and between circles, Discrete & Computational Geometry, to appear.A. Cohen and

F. de Zeeuw, A SylvesterGallai theorem for cubic curves, European Journal of Combinatorics 103 (2022): 103509.

S. Sarkar and P. Soberón, Tolerance for colorful Tverberg partitions, European Journal of Combinatorics, 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.

D. Fitzpatrick, Distance problems for planar hypercomplex numebrs, manuscript

Program partially funded by NSF awards DMS1802059 and DMS1851420.
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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 HaseLiu

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), 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.