Research Interests
Model theory and its applications to topology, geometry and number theory.
Pure model theory: o-minimal structures and generalizations, NIP theories, notions of ranks and structure theorems for definable sets
Topological groups: definable groups and their connection to Lie groups, Pillay's Principle, compact domination, topological dynamics
Number theory: point counting theorems in tame expansions of o-minimal structures
Algebraic topology: o-minimal homotopy and homology, semi-linear topology and its relation to Berkovich spaces
Complex geometry: o-minimal methods in complex analysis, Zilber's dichotomy
Publications in Journals
Submitted:
Counting algebraic points in expansions of o-minimal structures by a dense set (2017), 12 pages.
Product cones in dense pairs (2017), 11 pages.
(with A. Günaydin and P. Hieronymi), The Choice Property in tame expansions of o-minimal structures (2017), 10 pages.
Small sets in dense pairs (2017), 17 pages.
(with A. Günaydin and P. Hieronymi),
Structure theorems in tame expansions of o-minimal structures by a dense set (2017), upgraded version, 46 pages.
Published:
Semi-linear stars are contractible (2016), Fundamenta Mathematicae , to appear, 17 pages.
(with A. Hasson and G. Keren),
On definable Skolem functions in weakly o-minimal non-valuational structures (2015), Journal of Symbolic Logic , to appear, 16 pages.
(with Y. Peterzil and J. Ramakrishnan),
Interpretable groups are definable ,
Journal of Mathematical Logic , Published online, Vol. 14, No. 1 (2014), 47 pages.
(with M. Edmundo and L. Prelli),
Coverings by open cells ,
Archive for Mathematical Logic , Volume 53 (2014), 307-325.
(with M. Edmundo and L. Prelli),
The universal covering map in o-minimal expansions of groups ,
Topology and its Applications , Volume 160 (2013), 1530-1556.
(with Y. Peterzil),
Lattices in locally definable subgroups of (R^n, +) ,
Notre Dame Journal of Formal Logic , Volume 54, Number 3-4 (2013), 449-461.
Non-standard lattices and o-minimal groups ,
Bulletin of Symbolic Logic , Volume 19 (2013), 56-76.
(with Y. Peterzil),
Definable groups
as homomorphic images of semilinear and field-definable groups ,
Selecta Mathematica N.S. , Volume 18 (2012), 905-940.
(with Y. Peterzil),
Definable quotients of locally definable groups ,
Selecta Mathematica N.S. , Volume 18 (2012), 885-903.
Local analysis for semi-bounded groups ,
Fundamenta Mathematicae , Volume 216 (2012), 223-258.
(with C. Koutras and C. Nomikos),
Notions of bisimulation for Heyting-valued modal languages ,
Journal of Logic and Computation , Volume 22 (2012), 213-235.
Groups definable in linear o-minimal structures: the non-compact case ,
Journal of Symbolic Logic , Volume 75 (2010), 208-220.
Compact domination for groups definable in linear o-minimal structures ,
Archive for Mathematical Logic , Volume 48, Issue 7 (2009), 607-623.
(with M. Edmundo),
Definable group extensions in semi-bounded o-minimal structures ,
Mathematical Logic Quarterly , Volume 55 (2009), 598-604.
A semi-linear group which is not affine ,
Annals of Pure and Applied Logic
156 (2008), 287-289.
(with M. Edmundo),
The universal covering homomorphism in o-minimal expansions of groups ,
Mathematical Logic Quarterly , Volume 53 (2007), 571-582.
(with S. Starchenko),
Groups definable in ordered vector spaces over ordered division rings ,
Journal of Symbolic Logic , Volume 72 (2007), 1108-1140.
(with C. Koutras),
Frame constructions, truth invariance and validity preservation in many-valued modal logic ,
Journal of Applied Non-Classical Logics , Volume 15 - No. 4 (2005), 367-388.
In preparation
Groups definable in weakly o-minimal non-valuational structures .
Affine embeddings for semi-linear tori.
(with C. Koutras) Goldblatt-Thomason theorem for many-valued modal logic.
Ph.D. Thesis
Notes
Notes from seminar talks