Mark Poor

H.C. Wang Assistant Professor

Publications

  • A Shelah group in ZFC (with A. Rinot), \url{https://arxiv.org/abs/2305.11155},  submitted.

  • Singularity of maps of several variables and a problem of Mycielski concerning prevalent homeomorphisms (with R. Balka, M. Elekes, V. Kiss),  Adv. Math. 385, 2021.

  • Characterizing the spectra of cardinalities of branches of Kurepa trees (with S. Shelah), Pac. J. Math.  311. no. 2, pp. 423–453. 2021.

  • A Haar meager set that is not strongly Haar meager (with M. Elekes, D. Nagy,  Z. Vidnyánszky), Israel J. Math. 235, pp 91-109., 2020.

  • Answer to a question of Ros\l{}anowski and Shelah,  J. Math. Log. 21. no. 3, 2021.

  • Cardinal invariants of Haar null and Haar meager sets (with M. Elekes), P. Roy. Soc. Edinb. A. 151, no. 5,  pp. 1568 - 1594. 2021.

     

Mark Schachner

Ph.D. Student

Hanul Jeon

Ph.D. Student

Anthony Graves-McCleary

Ph.D. Candidate

Dexuan Hu

Ph.D. Candidate

Luke Serafin

Ph.D. Candidate

Sumun Iyer

Ph.D. Candidate

Sebastian Junge

Ph.D. Candidate

Romin Abdolahzadi

Ph.D Candidate

Slawomir Solecki

Professor

Publications

  • Generic measure preserving transformations and the closed groups they generate, Invent. Math., to appear

  • Monoid actions and ultrafilter methods in Ramsey theory, Forum of Mathematics, Sigma. 7 (2019), e2
  • Unitary representations of the groups of measurable and continuous functions with values in the circle, J. Funct. Anal. 267 (2014), 3105--3124
  • Abstract approach to finite Ramsey theory and a self-dual Ramsey theorem, Adv. Math. 248 (2013), 1156--1198
  • \(G_\delta\) ideals of compact sets, J. Eur. Math. Soc., 13 (2011), 853--882
  • The coset equivalence relation and topologies on subgroups, Amer. J. Math., 11 (2009), 571--605
  • Projective Fraisse limits and the pseudo-arc, Trans. Amer. Math. Soc., 358 (2006), 3077--3096, joint with T. Irwin
  • The structure of the space of composants of an indecomposable continuum, Adv. Math., 166 (2002), 149--192
  • Analytic ideals and their applications, Ann. Pure Appl. Logic, 99 (1999), 51--72
  • Decomposing Borel sets and functions and the structure of Baire class 1 functions, J. Amer. Math. Soc., 11 (1998), 521--550
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