Model theory, in and for itself, as well as applications
(algebra, geometry, number theory,..).
Current postgraduate students
Ningyuan Yao (visiting scholar atLeeds and Notre Dame, from Sun Yat Sen University, China), Gregory Cousins (Notre Dame), Mike Haskell (Notre Dame), Somayeh Vojdani (Notre Dame).
Recent graduate students from Leeds include Rizos Sklinos, now at Munster, Charlotte Kestner and Davide Penazzi, both now at University of Central Lancashire, Gareth Boxall, now at Stellenbosch, South Africa, and Joel (Ronnie) Nagloo, who will take up a postdoc at CUNY, New York.
Recent postdocs at Leeds include Jakub Gismatullin (Wroclaw) and Davide Penazzi.
Autumn 2014, Topics in Mathematical Logic ( Around the model theory of pseudofinite structures). MWF, 9.25 am. Lecture Notes
Spring 2015, Topics in Math. Logic (undergraduates): MWF 11.30.
Seminars at Notre Dame.
Model Theory seminar:
Notes from a sequence of courses at Illinois 2002-2003:
recent preprints, notes, slides of talks, and other 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)
Logarithmic derivatives on
nonconstant commutative algebraic groups. Slides from talk on Modnet
meeting, Barcelona, November 2008.
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.
On the isotriviality of
projective iterative D-varieties (with P. Kowalski)
components of groups and o-minimality I (with A. Conversano)
components of groups and o-minimality II (with A. Conversano)
note on generically stable measures and fsg groups (with E. Hrushovski
and P. Simon)
Nash groups (with E. Hrushovski)
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.
measure in NIP theories
On Levi subgroups and the Levi
decomposition for groups definable in o-minimal structures (with A.
algebraic relations between solutions of a generic Painlevé
equation (with Ronnie Nagloo)
Topological dynamics and
On Borel equivalence relations
and Lascar strong types (with K. Krupinski and S. Solecki)
canonical base property (with E. Hrushovski and D. Palacin).
Some model theory of SL(2,R)
(with J. Gismatullin and D. Penazzi).
algebraic independence of generic Painleve transcendents (with J.
On groups and fields
interpretable in torsion-free hyperbolic groups (with C. Perin, R.
Sklinos, K, Tent)
Generic stability and stability
(with H. Adler and E. Casanovas)
compactifications and the topological dynamics of definable groups
(with J. Gismatullin and D. Penazzi).
Talk at LMS prospects in Maths
meeting, Manchester, Dec. 2012.
Oxford, February 2013.
Relative Manin-Mumford for semiabelian surfaces (with D. Bertrand, D. Masser, U. Zannier).
External definability and groups in NIP theories (with A. Chernikov and P. Simon).
Remarks on Tao's algebraic regularity lemma (with S. Starchenko).
Some model theory of fibrations and algebraic reductions (with R. Moosa).
Nash groups, Colloquium, Waterloo, November 2013.
Universal covers of commutative finite Morley rank groups (with M. Bays, B. Hart).
On function field Mordell-Lang and Manin-Mumford (with F. Benoist and E. Bouscaren).
Semiabelian varieties over separably closed fields, maximal divisible subgroups, and exact sequences (revised, with F. Benoist and E. Bouscaren).
Generalized Bohr compactifications and model-theoretic connected components (with K. Krupinski).
Interpretations and differential Galois extensions (with M. Kamensky).
Remarks and questions on infinitesimal stabilizers.
Saturated free algebras revisited (with Rizos Sklinos).
Strongly minimal pseudofinite structures.
Galois theory, functional Lindemann-Weierstrass, and Manin maps (with D. Bertrand)
On minimal flows, definable amenability, and o-minimality (with Ningyuan Yao)
The stable regularity lemma revisited (with M. Malliaris)
Pseudofinite model theory: lectures notes from Fall 2014 course