Research
Model theory, in and for itself, as well as applications
(algebra, geometry, number theory,..).
Current graduate students
Gregory Cousins (Notre Dame), Mike Haskell (Notre Dame), Leo Jimenez (Notre Dame). Somayeh Vojdani graduated in summer 2016.
Recent graduate students from Leeds include Rizos Sklinos, now at Lyon, Charlotte Kestner and Davide Penazzi, both now at University of Central Lancashire, Gareth Boxall, now at Stellenbosch, South Africa, and Joel (Ronnie) Nagloo, a postdoc at CUNY, New York, and moving to Bronx Community College. Ningyuan Yao got his PH.D. from SunYatSen University in 2015, working under my supervision, and now has a position at Fudan University, China.
Postdocs
Recent postdocs at Leeds include Jakub Gismatullin (Wroclaw) and Davide Penazzi (UCLAN). Current postdoc at Notre Dame: Gabriel Conant.
Teaching
Autumn 2016, Math 10560. Calculus II, MWF 2  2.50, 131 de Bartolo.
Spring 2017, Math 80520, Categorical Logic, MWF 1.3011.20, 116, Pasquerilla
Seminars at Notre Dame.
Model Theory seminar, 11 am, Tuesday. 125 HH
Logic seminar: 2 pm Tuesdays. 125 HH
Model Theory program at Notre Dame, June 6  24, 2016.
See https://www3.nd.edu/~cmnd/programs/cmnd2016/
for information and registration
EDITORIAL.
I am an editor of Algebra and Number Theory.
http://msp.org/publications/journals/#ant
I am also a Managing Editor (with Mic Detlefsen) of the Notre Dame Journal of Formal Logic.
http://www3.nd.edu/~ndjfl/
Also from February 2017 an Associate Editor of Journal of the American Mathematical Society
CV, January 2016
Publications, January 2016
Lecture
Notes from a sequence of courses at Illinois 20022003:
Model
Theory
Stability
Theory
Applied
Stability Theory
Some
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
publications.)
Lecture notes on strongly minimal
sets with a generic automorphism (graduate course in UIUC, 1999)
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
Connected
components of groups and ominimality I (with A. Conversano)
Connected
components of groups and ominimality II (with A. Conversano)
A
note on generically stable measures and fsg groups (with E. Hrushovski
and P. Simon)
Affine
Nash groups (with E. Hrushovski)
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.
Weight and
measure in NIP theories
On Levi subgroups and the Levi
decomposition for groups definable in ominimal structures (with A.
Conversano)
On
algebraic relations between solutions of a generic Painlevé
equation (with Ronnie Nagloo)
Topological dynamics and
definable groups
On Borel equivalence relations
and Lascar strong types (with K. Krupinski and S. Solecki)
On the
canonical base property (with E. Hrushovski and D. Palacin).
Some model theory of SL(2,R)
(with J. Gismatullin and D. Penazzi).
On the
algebraic independence of generic Painleve transcendents (with J.
Nagloo)
On groups and fields
interpretable in torsionfree hyperbolic groups (with C. Perin, R.
Sklinos, K, Tent)
Generic stability and stability
(with H. Adler and E. Casanovas)
On
compactifications and the topological dynamics of definable groups
(with J. Gismatullin and D. Penazzi).
Relative ManinMumford 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).
Universal covers of commutative finite Morley rank groups (with M. Bays, B. Hart).
On function field MordellLang and ManinMumford (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 modeltheoretic connected components (with K. Krupinski).
Remarks and questions on infinitesimal stabilizers.
Saturated free algebras revisited (with Rizos Sklinos).
Strongly minimal pseudofinite structures.
Galois theory, functional LindemannWeierstrass, and Manin maps (with D. Bertrand)
On minimal flows, definable amenability, and ominimality (with Ningyuan Yao)
The stable regularity lemma revisited (with M. Malliaris)
Pseudofinite model theory: lectures notes from Fall 2014 course
Remarks on compactifications of pseudofinite groups
Topological dynamics and the complexity of strong types (with K. Krupinski and T. Rzepecki)
On definable Galois groups and the canonical base property (with D. Palacin)
Stable groups and expansions of (Z,+,0) (with G. Conant)
The free group has the dimensional order property (with R. Sklinos)
On maximal stable quotients of groups definable in NIP theories (with M. Haskel)
Some definable Galois theory and examples (with O. Leon Sanchez)
Interpretations and differential Galois extensions (with M. Kamensky)
The PicardVessiot theory, constrained cohomology, and linear differential algebraic groups.
Amenability, definable groups, and automorphism groups (with K. Krupinski).
Generalized PicardVessiot extensions and differential Galois cohomology (with Z. Chatzidakis).
