Zach Hunter

On acknowledgments | My CV and research statement | Contact me

Hello! I am currently a third year PhD student at ETH Zurich, under the supervision of Benny Sudakov. My main research interests are in extremal and probabilistic combinatorics, often involving graph theory, additive combinatorics, Ramsey theory, or pattern containment. I also am interested in discrete geometry, although I have yet to publish anything in this area.

Email: zach.hunter@math.ethz.ch -- I welcome any questions/comments about my work.

Collaborators: Daniel Carter (x4), Debsoumya Chakraborti, Micha Christoph, Xiying Du, Christian Elsholtz, António Girão (x4), Matthew Kwan (x2), Teng Liu, Rose McCarty, Aleksa Milojević (x6), Richard Montgomery, Kevin O'Bryant, Cosmin Pohoata (x3), Teo Petrov, Laura Proske, Lisa Sauermann (x3), Mehtaab Sawhney, Alex Scott, Benny Sudakov (x7), István Tomon (x4), Jacques Verstraete, Yuval Wigderson, Shengtong Zhang, Daniel Zhu.

Completed Papers:

  1. Large point-line matchings and small Nikodym sets (with Cosmin Pohoata, Jacques Verstraete, and Shengtong Zhang), Arxiv.
  2. A Hal\'asz-type theorem for permutation anticoncentration (with Cosmin Pohoata and Daniel Zhu), Arxiv.
  3. Gaussian random graphs and Ramsey numbers (with Aleksa Milojević and Benny Sudakov), Arxiv.
  4. On random matrices with large corank (with Matthew Kwan, Lisa Sauermann, and Mehtaab Sawhney), Arxiv.
  5. Exponential anticoncentration of the permanent (with Matthew Kwan and Lisa Sauermann), Arxiv.
  6. Cyclic subsets of tournaments (with Teng Liu, Aleksa Milojević and Benny Sudakov), Arxiv.
  7. An improved construction for the triangle removal lemma, Arxiv.
  8. $C_4$-free subgraphs of high degree with geometric applications (with Aleksa Milojević, Benny Sudakov, and István Tomon), Arxiv.
  9. Almost-full transversals in equi-$n$-squares (with Debsoumya Chakraborti, Micha Christoph, Richard Montgomery, and Teo Petrov), Arxiv.
  10. Monochromatic odd cycles in edge-coloured complete graphs (with António Girão), Arxiv.
  11. Long induced paths in $K_{s,s}$-free graphs (with Aleksa Milojević, Benny Sudakov, and István Tomon), Arxiv.
  12. Disjoint pairs in set systems and combinatorics of low rank matrices (with Aleksa Milojević, Benny Sudakov, and István Tomon), Arxiv.
  13. Blowups of triangle-free graphs (with António Girão and Yuval Wigderson),Arxiv.
  14. Improving Behrend's construction: Sets without arithmetic progressions in integers and over finite fields (with Christian Elsholtz, Laura Proske, and Lisa Sauermann), Arxiv.
  15. Induced Ramsey problems for trees and graphs with bounded treewidth (with Benny Sudakov), Arxiv.
  16. New lower bounds for $r_3(N)$, Arxiv; later merged into paper 21.
  17. Kővári-Sós-Turán for hereditary families (with Aleksa Milojević, Benny Sudakov, and István Tomon), Arxiv, in JCTB.
  18. On the diameter of finite Sidon sets (with Daniel Carter and Kevin O'Bryant), Arxiv, accepted to Acta Hungarica.
  19. Induced subdivisions in $K_{s,s}$-free graphs with polynomial average degree (with António Girão, Arxiv, in IMRN.
  20. Some remarks on off-diagonal Ramsey numbers of vector spaces over $\F_2$ (with Cosmin Pohoata), Arxiv, accepted to Mathematical Proceedings of the Cambridge Philosophical Society.
  21. On a method of Alweiss, Arxiv.
  22. Induced $C_4$-free graphs with large average degree (with Xiying Du, António Girão, Rose McCarty, and Alex Scott), Arxiv, in JCTB.
  23. A notion of twins, Arxiv.
  24. Lower bounds for multicolor van der Waerden numbers, Arxiv, in Israel Journal of Mathematics.
  25. A new upper bound to (a variant of) the pancake problem, Arxiv.
  26. Corner-free subsets via the torus, Arxiv.
  27. A short proof that $w(3,k) \ge (1-o(1))k^2$, Arxiv.
  28. A note on large induced subgraphs with prescribed residues in bipartite graphs, Arxiv, Electronic Journal of Combinatorics.
  29. Optimally reconstructing caterpillar graphs, Arxiv.
  30. Improved lower bounds for van der Waerden numbers, Arxiv, Quanta article, Combinatorica.
  31. An asymptotically tight lower bound for superpatterns with small alphabets, Arxiv, Combinatorial Theory.
  32. Metropolized Multiscale Forest Recombination for Redistricting (with Eric Autry, Daniel Carter, Gregory Herschlag, and Jonathan Mattingly), Arxiv, in Multiscale Modeling & Simulation.
  33. A Merge-Split Proposal for Reversible Monte Carlo Markov Chain Sampling of Redistricting Plans (with Eric Autry, Daniel Carter, Gregory Herschlag, and Jonathan Mattingly), Arxiv.
  34. Optimal Legislative County Clustering in North Carolina (with Daniel Carter, Dan Teague, Gregory Herschlag, and Jonathon Mattingly), Arxiv, in Statistics and Public Policy.