Some recent papers
-
Definability of restricted Theta functions and families of abelian varietiess,
(with Y. Petrzil),
Duke Math. J. 162 (2013), no. 4, 731--765,
available at ArXiv
-
Vapnik-Chervonenkis density in some theories without the
independence property, I,
(with M. Aschenbrenner, A. Dolich, D. Haskell and D. Macpherson),
Trans. Amer. Math. Soc. 368 (2016), no. 8, 5889–5949,
available at ArXiv
-
Vapnik-Chervonenkis density in some theories without the
independence property, II,
(with M. Aschenbrenner, A. Dolich, D. Haskell and D. Macpherson),
Notre Dame J. Form. Log. 54 (2013), no. 3-4, 311--363,
available at ArXiv
-
On forking and definability of types in some dp-minimal theories,
(with P. Simon),
The Journal of Symbolic Logic, 79(2014), pp 1020-1024,
available at ArXiv
-
Topological groups, μ-types and their stabilizers,
(with Y. Petrzil),
J. Eur. Math. Soc. (JEMS) 19 (2017), no. 10, 2965–2995,
available at ArXiv
-
Regularity lemma for distal structures,
(with A. Chernikov),
J. Eur. Math. Soc. (JEMS) 20 (2018), no. 10, 2437–2466,
available at ArXiv
-
Solvable Lie groups definable in o-minimal theories,
(with A. Conversano and A. Onshuus),
J. Inst. Math. Jussieu 17 (2018), no. 2, 441–452,
available at ArXiv
-
A note on the Erdos-Hajnal property for stable graphs,
(with A. Chernikov),
Proc. Amer. Math. Soc. 146 (2018), no. 2, 785–790,
available at ArXiv
-
Remarks on Tao's algebraic regularity lemma,
(with A. Pillay),
preprint,
available at ArXiv
-
A note on o-minimal flows and the Ax-Lindemann-Weierstrass
theorem for abelian varieties over C,
(with A. Y.Peterzil),
Enseign. Math. 63 (2017), no. 3-4, 251–261,
available at ArXiv
-
NIP, Keisler measures and combinatorics, Seminaire
Bourbaki. Vol. 2015/2016. Exposes 1104–1119.
Asterisque No. 390 (2017), Exp. No. 1114, 303–334, available at
Bourbaki website
-
Ramsey growth in some NIP structures,
(with A. A.Chernikov and M.Thomas),
J. Inst. Math. Jussieu (2019), 1–29,
available at ArXiv
-
Definable regularity lemmas for NIP hypergraphs,
(with A. A.Chernikov),
preprint,
available at ArXiv
-
Cutting lemma and Zarankiewicz's problem in distal structure,
(with A. A.Chernikov and D.Galvin),
preprint,
available at ArXiv
-
A model-theoretic generalization of the Elekes-Szabó theorem,
(with A. A.Chernikov),
preprint,
available at ArXiv
-
Algebraic and o-minimal flows on complex and real tori,
(with A. Y.Peterzil),
Adv. Math. 333 (2018), 539–569,
available at ArXiv
-
O-minimal flows on nilmanifolds,
(with A. Y.Peterzil),
preprint,
available at ArXiv
Research notes
-
On Grothendieck's approach to
stability
In this note we state and give an elementary proof of
a simplified version of
Grothendieck's theorem that implies, and in fact is equivalent to,
the strong version the Fundamental Theorem of Stability Theory.
This version of Grothendieck's theorem came out of discussions at
Notre Dame Model Theory seminar in March 2017 during reading
Itai Ben Yaacov's paper