Research
Model theory, as well as applications
(algebra, geometry, number theory,..).
Current graduate students
Gregory Cousins (Notre Dame), Leo Jimenez (Notre Dame). Nicolas Chavarria Gomez.
Postdocs
Current: Gabe Conant, Michael Wibmer. Future: Remi Jaoui, Chieu Minh Tran.
Teaching
Spring 2019, Math 20630, Introduction to Mathematical Reasoning, Pasquerilla 112, MWF 11.3012.20
Seminars at Notre Dame.
Model Theory seminar, 11 am, Tuesday. 125 HH
Logic seminar: 2 pm Tuesdays. 125 HH
EDITORIAL.
I am an Associate Editor of Journal AMS, and an editor of Algebra and Number Theory ( http://msp.org/publications/journals/#ant)
and EditorinChief (joint with Mic Detlefsen) of the Notre Dame Journal of Formal Logic ( http://www3.nd.edu/~ndjfl/ )
Lecture
Notes from a sequence of courses at Illinois 20022003:
Model
Theory
Stability
Theory
Applied
Stability Theory
Lecture notes from recent advanced courses at Notre Dame.
Pseudofinite model theory: lectures notes from Fall 2014 course
Categorical Logic. Notes from Spring 2017 course
Stability Theory. Notes from Autumn 2018 course
Slides of some talks
Compact spaces, definability.
Slides from Tarski lectures, Berkeley, April 2009.
Measures in model
theory. Slides from talk in Logic and Set theory meeting, Chennai, Aug.
2010
Model
theory, stability, and the free group, Notes from a series of 5 talks
at a workshop on geometric group theory and logic, UIC, Aug. 2011
First
order theories, Goedel lecture, ASL European Meeting, Barcelona 2011.
Recent preprints, and other unpublshed things. (Please contact me directly if
you want electronic files of other papers from my complete list of
publications.)
Lecture notes on strongly minimal
sets with a generic automorphism (graduate course in UIUC, 1999)
Model Theory
Remarks on Tao's algebraic regularity lemma (with S. Starchenko).
Universal covers of commutative finite Morley rank groups (with M. Bays, B. Hart).
Remarks and questions on infinitesimal stabilizers.
Strongly minimal pseudofinite structures.
Generalized PicardVessiot extensions and differential Galois cohomology (with Z. Chatzidakis).
Definable topological dynamics for SL(2,Q_p) (with D. Penazzi and N. Yao)
Domination and regularity
Pseudofinite groups and VCdimension (with G.Conant)
Structure and regularity for subsets of groups with finite VCdimension (with G. Conant and C. Terry)
Amenability and definability (with E.Hrushovski and K. Krupinski)
