History of the NYC Discrete Math REU
Summer 2024. The mentors this year were Johanna Franklin, Guy Moshkovitz, Jinyoung Park, Anna Pun, Adam Sheffer, and Pablo Soberón.
Participants:
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Sanjana Das
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Djeneba Diop
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Sierra Edelstein
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Noah Giddings
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Marcus Gozon
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Senem Isik
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Carter Kelly
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Deron Lessure
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Neely Lovvorn
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Oscar Murillo-Espinoza
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tahda queer
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Tomasz Slusarczyk
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Iris Ye
Papers produced during this summer:
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S. Das, C. Pohoata, and A. Sheffer, Expanding Polynomials for Sets with Additive Structure, submitted.
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S. Işık and J. Park, Random Lipschitz functions on graphs with weak expansion, submitted.
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D. Lessure and P. Soberon, Partitions of mass assignments with spheres and wedges, in preparation.
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N. Lovvorn, O. Murillo-Espinoza, and A. Sheffer, Expected degrees in random plane graphs, submitted.
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M. Gozon and G. Moshkovitz, The approximability of commutative rank over finite fields, in preparation.
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G. Moshkovitz and T. Slusarczyk, A new approach to triangle removal, in preparation.
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S. Das and A. Sheffer, Distinct Distances Between a Line and a Polynomial Strip, in preparation.
- More to appear.
The program was funded by NSF awards DMS-1855516 and DMS-2051026 and by Jane Street.
Summer 2023. The mentors this year were Matthew Junge, Sandra Kingan, Guy Moshkovitz, Anna Pun, Eric Rowland, Adam Sheffer (only organizing), and Pablo Soberón.
Participants:
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Santiago Adams
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Kimberly Affeld
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Christian Dean
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Timothy Edwards
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Anna Hugo
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Nancy Jiang
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Nzingha Joseph
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Sean Li
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Megan Paasche
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Connor Panish
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Jesus Sistos Barron
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Christina Yu
Papers produced during this summer:
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P. Soberón and C. Yu, High-dimensional envy-free partitions, submitted.
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T. Edwards and P. Soberón, Extensions of discrete Helly theorems for boxes, submitted.
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K. Affeld, C. Dean, M. Junge, H. Lyu, C. Panish, and L. Reeves, Four-parameter coalescing ballistic annihilation, submitted.
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S. Adams and S. R. Kingan, Pancyclicity in Almost-Planar Graphs, in preparation
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S. Li and G. Moshkovitz, Diophantine equations in low rank, in preparation.
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More to appear?
The program was funded by NSF awards DMS-1855516 and DMS-2051026 and by Jane Street.
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
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Julia Carrigan
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Connor Donovan
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Kendra Ebke
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Isaiah Hollars
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Rachel Leslie
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Na'ama Nevo
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Arturo Ortiz San Miguel
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Danielle Paulson
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Cynthia Marie Rivera-Sanchez
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Glenn Sun
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Daniel Zhu
Papers produced during this summer:
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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.
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G. Moshkovitz and D. Zhu, Quasi-linear relation between partition and analytic rank, submitted.
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J. Carrigan, I. Hollars, and E. Rowland, A natural bijection for contiguous pattern avoidance in words, Discrete Math 347 (2024), 113793.
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K. Adaricheva, A. Agarwal, and N. Nevo, Representation of convex geometries of convex dimension 3 by spheres, Acta Mathematica Hungarica, to appear.
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C. Donovan, D. Paulson, and P. Soberón, Colorful and quantitative variations of Krassnolesky's theorem, submitted.
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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:
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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 2023, 14103–14130.
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G. Moshkovitz and J. Yu, Sharp Effective Finite-Field Nullstellensatz, The American Mathematical Monthly 130 (2023), 720–727.
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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.
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M. Junge, Z. McDonald, J. Pulla, and L. Reeves, A stochastic combustion model with thresholds on trees, Journal of Statistical Physics, 190(5), 100.
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H. Ashbach and K. Pichini, An Upper Bound for the Number of Rectangulations of a Planar Point Set, Electronic Journal of Combinatorics, accepted.
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D. Cruzado-Padro, M. Junge, and L. Reeves, Arrivals are universal in coalescing ballistic annihilation, submitted.
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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
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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.
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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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Alex Cohen and Guy Moshkovitz, Partition and Analytic Rank are Equivalent over Large Fields, Duke Mathematical Journal 172 (2023), 2433–2470. Quanta article.
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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. Also, Discrete Analysis 12(2022).
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A. Sheffer and O. Silier, Structural Szemerédi-Trotter for Cartesian Products, Discrete & Computational Geometry, to appear.
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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.
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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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L. Benitez, M. Junge, H. Lyu, M. Redman, and L. Z. Wang, Three-velocity coalescing ballistic annihilation, Electronic Journal of Probability 28, 1-18.
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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.
- P. Soberón and Y. Tang, Tverberg’s Theorem, Disks, and Hamiltonian Cycles, Annals of Combinatorics 25 (2021), 995--1005.
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E. Bernstein, C. Hamblen, M. Junge, and L. Reeves, Chase-escape on the configuration model, Electronic Communications in Probability 27 (2022): 1-14.
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A. Li, Progress on local properties problems of difference sets, European Journal of Combinatorics 108 (2023), 103618.
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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.
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, manuscript
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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 89 (2020), 103162.
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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.