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 Rivera-Sanchez

• Glenn Sun

• Daniel Zhu  

Papers produced during this summer:​

• G. Moshkovitz and D. Zhu, Quasi-linear relation between partition and analytic rank, submitted. 

• M. Junge, A. Ortiz San Miguel, L. Reeves, and C. Rivera Sánchez, Non-universality in clustered ballistic annihilation, submitted.

• J. Carrigan, I. Hollars, and E. Rowland, Bijective proofs of word avoidance identities, in preparation.

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

• 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.

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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 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, to appear.

• G. Moshkovitz and J. Yu, Sharp Effective Finite-Field Nullstellensatz, The American Mathematical Monthly, to appear.

• J. P. Carvalho and P. Soberón, Counterexamples to the Colorful Tverberg Conjecture for Hyperplanes, Acta Mathematica Hungarica, 2022.

• 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.

• D. Cruzado-Padro, M. Junge, and L. Reeves, Arrivals are universal in coalescing ballistic annihilation, submitted.

• M. Junge, Z. McDonald, J. Pulla, and L. Reeves, A stochastic combustion model with thresholds on trees, 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.

• S. Dasu, A. Sheffer, and J. Shen, Structural Szemerédi-Trotter for Lattices and their generalizations, 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.

• 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:​ 

• 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.

• 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.

• 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.

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

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

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  

• 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.

• 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, submitted to a journal.

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

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