Homepage of M. Malliaris

Assistant Professor
Department of Mathematics
University of Chicago

Research: My research interests are in model theory, in particular classification of unstable theories.

Teaching: REU

Available papers: Abstracts and more information

  • "Realization of \phi-types and Keisler's order," Ann. Pure Appl. Logic 157 (2009) 220-224. link
  • ''The characteristic sequence of a first-order formula,'' J Symb Logic 75, 4 (2010) 1415-1440. PDF, link.
  • "Edge distribution and density in the characteristic sequence," Ann Pure Appl Logic 162, 1 (2010) 1-19. PDF, link
  • "Hypergraph sequences as a tool for saturation of ultrapowers,'' J Symb Logic 77, 1 (2012) 195-223. PDF, link
  • "Independence, order, and the interaction of ultrafilters and theories," Ann Pure Appl Logic, 163, 11 (2012) 1580-1595. PDF, link
  • (with S. Shelah) "Regularity lemmas for stable graphs.'' Trans. Amer. Math Soc, 366 (2014), 1551-1585. link, PDF
  • (with S. Shelah) "Constructing regular ultrafilters from a model-theoretic point of view." Trans. Amer. Math. Soc., accepted. PDF, arxiv
  • (with S. Shelah) "Model-theoretic properties of ultrafilters built by independent families of functions." JSL 79, 1 (2014) 103-134. PDF, arxiv
  • (with S. Shelah) "A dividing line within simple unstable theories." Advances in Math 249 (2013) 250--288. PDF, link
  • (with S. Shelah) "Saturating the random graph with an independent family of small range." 14 pages. arxiv
  • (with S. Shelah) "Cofinality spectrum theorems in model theory, set theory, and general topology." 48 pages. PDF, arxiv
  • (with S. Shelah) "General topology meets model theory, on p and t." This announces the results of the paper above.
    Proc Natl Acad Sci USA 110, 33 (2013) 13300-13305. PDF, link
  • (with S. Shelah) "Existence of optimal ultrafilters and the fundamental complexity of simple theories." 61 pages. arxiv
  • Thesis: Persistence and Regularity in Unstable Model Theory. PDF; here is a brief overview

    Contact information:
    Department of Mathematics
    University of Chicago
    5734 S. University Avenue
    Chicago, IL 60637

    Email: (my three initials) at math; see URL.

    Office: E 318

    Open problems in model theory

    Logic Day, April 24, 2013

    Other links

    Research partially supported by: NSF grants DMS-1300634 and DMS-1001666, a Gödel research prize fellowship (2011), and a Sloan research fellowship (2014).

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