## Homepage of M. Malliaris

Associate Professor
Department of Mathematics
University of Chicago

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

Teaching: most recently, Math 277.

• "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. 367 (2015), 8139--8173. link, 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) "Cofinality spectrum theorems in model theory, set theory, and general topology." J. Amer. Math. Soc. 29 (2016), 237--297. arxiv, journal
• (with S. Shelah) "General topology meets model theory, on p and t." This announces the results of the paper above.
• (with S. Shelah) "Existence of optimal ultrafilters and the fundamental complexity of simple theories." Advances in Math. 290 (2016) 614-681. journal, arxiv
• (with S. Shelah) "Keisler's order has infinitely many classes." Accepted, Israel J. Math. pdf
• (with A. Pillay) "The stable regularity lemma revisited." Proc. Amer. Math. Soc. 144 (2016) 1761--1765. arxiv
• (with C. Terry) "On unavoidable induced subgraphs in large prime graphs." to appear. arxiv
• (with D. Casey) "Notes on cofinality spectrum problems." arxiv
• (with S. Shelah) "A new look at interpretability and saturation." arxiv
• (with A. Peretz) "What simplicity is not." Simplicity: ideals of practice in mathematics and the arts. 51–58, Math. Cult. Arts, Springer, Cham, 2017. link
• 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: 406

Research partially supported by: NSF grants DMS-1300634 and DMS-1001666, a Gödel research prize fellowship, a Sloan research fellowship, and NSF CAREER award 1553653.

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