Previous Years

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:

Arav Agarwal
Julia Carrigan
Connor Donovan
Kendra Ebke
Isaiah Hollars
Rachel Leslie
Na'ama Nevo
Arturo Ortiz San Miguel
Danielle Paulson
Cynthia Marie Rivera-Sanchez
Glenn Sun
Daniel Zhu

Papers produced during this summer:

M. Junge, A. Ortiz San Miguel, L. Reeves, and C. Rivera Sánchez, Non-universality in clustered ballistic annihilation, Electronic Communications in Probability, 28 (2023): 1-12.
G. Moshkovitz and D. Zhu, Quasi-linear relation between partition and analytic rank, submitted.
J. Carrigan, I. Hollars, and E. Rowland, A natural bijection for contiguous pattern avoidance in words, Discrete Math, to appear.
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 DMS-1855516 and DMS-2051026.

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:

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 Finite-Field Nullstellensatz, The American Mathematical Monthly 130 (2023), 720–727.
J. P. Carvalho and P. Soberón, Counterexamples to the Colorful Tverberg Conjecture for Hyperplanes, Acta Mathematica Hungarica 167 (2022), 385–392.
I. Axelrod-Freed and P. Soberón, Bisections of mass assignments using flags of affine spaces, Discrete & Computational Geometry, to appear.
N. Frankl and D. Woodruff, On some non-rigid 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.
H. Ashbach and K. Pichini, An Upper Bound for the Number of Rectangulations of a Planar Point Set, Electronic Journal of Combinatorics, accepted.
D. Cruzado-Padro, M. Junge, and L. Reeves, Arrivals are universal in coalescing ballistic annihilation, submitted.
J. Ruotolo, K. Wang, and F. Wei, An Asymptotically Sharp Bound on the Maximum Number of Independent Transversals, Electronic Journal of Combinatorics (2024), P1.68.
I Axelrod-Freed, J. P. Carvalho, Y. Takahashi, Quantitative Transversal Theorems in the Plane, submitted
S. Dasu, A. Sheffer, and J. Shen, Structural Szemerédi-Trotter for Lattices and their generalizations, submitted.
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 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:

Alex Cohen and Guy Moshkovitz, Partition and Analytic Rank are Equivalent over Large Fields, Duke Mathematical Journal 172 (2023), 2433–2470. 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 12(2022).
A. Sheffer and O. Silier, Structural Szemerédi-Trotter for Cartesian Products, Discrete & Computational Geometry, to appear.
R. Bahl, P. Barnet, T. Johnson, and M. Junge, Diffusion-limited annihilating systems and the increasing convex order, Electronic Journal of Probability 27 (2022), 1-19.
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.
L. Benitez, M. Junge, H. Lyu, M. Redman, and L. Z. Wang, Three-velocity coalescing ballistic annihilation, Electronic Journal of Probability 28, 1-18.
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.
E. Bernstein, C. Hamblen, M. Junge, and L. Reeves, Chase-escape on the configuration model, Electronic Communications in Probability 27 (2022): 1-14.
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 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.
S. Mathialagan and A. Sheffer, Distinct distances on non-ruled surfaces and between circles, Discrete & Computational Geometry, to appear.A. Cohen and
F. de Zeeuw, A Sylvester-Gallai 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): 1-8.
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 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 89 (2020), 103162.
R. A. Krueger, Generalized Ramsey Numbers: Edge-Coloring Forbidding Paths with Few Colors, Electronic Journal of Combinatorics (2020), P1--44.

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

History of the NYC Discrete Math REU

T. Dillon, Discrete quantitative Helly-type theorems with boxes, to appear in Advances in Applied Mathematics.

L. Benitez, M. Junge, H. Lyu, M. Redman, and L. Z. Wang, Three-velocity coalescing ballistic annihilation, Electronic Journal of Probability 28, 1-18.

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.

E. Bernstein, C. Hamblen, M. Junge, and L. Reeves, Chase-escape on the configuration model, Electronic Communications in Probability 27 (2022): 1-14.

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.