Homepage of M. Malliaris
Assistant Professor
Department of Mathematics
University of Chicago
Research:
My research interests are in model theory, in particular classification of theories.
Teaching: Ultrafilters (spring), and recently, Math 277 and Math 310.
Available papers: Abstracts, more papers, and other information
"Realization of \phitypes and Keisler's order,"
Ann. Pure Appl. Logic 157 (2009) 220224.
link
''The characteristic sequence of a firstorder formula,'' J Symb Logic 75, 4 (2010) 14151440.
PDF,
link.
"Edge distribution and density in the characteristic sequence,"
Ann Pure Appl Logic 162, 1 (2010) 119.
PDF,
link
"Hypergraph sequences as a tool for saturation of ultrapowers,'' J Symb Logic 77, 1 (2012) 195223.
PDF,
link
"Independence, order, and the interaction of ultrafilters and theories," Ann Pure Appl Logic,
163, 11 (2012) 15801595. PDF,
link
(with S. Shelah) "Regularity lemmas for stable graphs.'' Trans. Amer. Math Soc,
366 (2014), 15511585.
link, PDF
(with S. Shelah) "Constructing regular ultrafilters from a
modeltheoretic point of view."
Trans. Amer. Math. Soc. 367 (2015), 81398173.
link, arxiv
(with S. Shelah) "Modeltheoretic properties of ultrafilters built by independent families of functions." JSL 79, 1 (2014) 103134. PDF,
arxiv
(with S. Shelah) "A dividing line within simple unstable theories." Advances in Math
249 (2013) 250288.
PDF, link
(with S. Shelah) "Saturating the random graph with an independent
family of small range." Logic Without Borders.
arxiv,
link
(with S. Shelah)
"Cofinality spectrum theorems in model theory, set theory, and general
topology." J. Amer. Math. Soc. 29 (2016), 237297. PDF,
arxiv,
journal
(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) 1330013305.
PDF,
link
(with S. Shelah)
"Existence of optimal ultrafilters and the fundamental complexity of simple theories."
Advances in Math. 290 (2016) 614681. journal,
arxiv, PDF
(with S. Shelah)
"Keisler's order has infinitely many classes." arxiv
(with A. Pillay)
"The stable regularity lemma revisited."
Proc. Amer. Math. Soc. 144 (2016) 17611765. arxiv
(with C. Terry) "On unavoidable induced subgraphs in
large prime graphs." 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:
Open problems in model theory
Other links
Research partially supported by:
NSF grants DMS1300634 and DMS1001666,
a Gödel research prize fellowship,
a Sloan research fellowship,
and NSF CAREER award 1553653.
visits since April 2012
(courtesy of digits.net)
 space 
