Model theory, as well as applications
(algebra, geometry, number theory,..).
Complete list of publications
Current graduate students
Gregory Cousin (graduated summer 2019, and will be at McMaster 2019-20), Leo Jimenez, Nicolas Chavarria Gomez.
Current: Remi Jaoui, Chieu Minh Tran, Daniel Hoffmann (on a Polish grant 2019-20).
Recent: Gabriel Conant, now at Cambridge, England, and Michael Wibmer, now at Graz, Austria.
Fall 2019, Math 60510, Basic Logic I, Graduate Course, MWF, 10.30-11.20.
Seminars at Notre Dame.
Model Theory seminar, 11 am, Tuesday. 125 HH
Logic seminar: 2 pm Tuesdays. 125 HH
I am an Associate Editor of Journal AMS, and an editor of Algebra and Number Theory ( http://msp.org/publications/journals/#ant)
and Editor-in-Chief (joint with Mic Detlefsen) of the Notre Dame Journal of Formal Logic ( http://www3.nd.edu/~ndjfl/ )
Notes from a sequence of courses at Illinois 2002-2003:
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
Pseudofinite model theory and combinatorics, Mini-course in Fudan, May 2019
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.
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
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
Lecture notes on strongly minimal
sets with a generic automorphism (graduate course in UIUC, 1999)
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 Picard-Vessiot 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 VC-dimension (with G.Conant)
Structure and regularity for subsets of groups with finite VC-dimension (with G. Conant and C. Terry)
Amenability and definability (with E.Hrushovski and K. Krupinski)
A note on the effective listing of types in DCF_0.