ALEXANDER S. KECHRIS
Professor of Mathematics
Diploma, Mechanical & Electrical Engineering, National Technical University of
Athens, 1969
Ph.D., Mathematics, UCLA, 1972
Research Interests
Foundations of mathematics; mathematical logic and set theory; their interactions
with analysis and dynamical systems. Recent projects include the study of foundational
and set theoretic questions, and the application of the methodology and results of
descriptive set theory, in classical real analysis, harmonic analysis, dynamical systems
(especially ergodic theory and topological dynamics), model theory, and combinatorics.
Courses Taught
Spring 2009/10: Math 116c Mathematical Logic and Axiomatic Set Theory, Math 290 Reading, Math 390 Research
Winter 2009/10: Math 98 Independent Reading, Ma/CS 116b Mathematical Logic amd Axiomatic set Theory, Math 290 Reading, Math 390 Research
Fall 2009/10: Math 290 Reading, Math 390 Research
Spring 2008/09: Math 117c Computability Theory, Math 290 Reading, Math 390 Research
Winter 2008/09: Math 117b Computability Theory, Math 290 Reading, Math 390 Research
Fall 2008/09: Math 117a Computability Theory, Math 290 Reading, Math 390 Research
Spring 2007/08: Ma/CS 6c Introduction to Discrete Mathematics, Math 290 Reading, Math 390 Research
Winter 2007/08: Math 118b Topics in Mathematical Logic, Math 290 Reading, Math 390 Research
Fall 2007/08: Math 116a Mathematical Logic and Axiomatic Set Theory, Math 290 Reading, Math 390 Research
Selected Recent Publications
-
(Co-edited with B. Loewe and J. Steel)
Wadge Degrees and Projective Ordinals: The Cabal Seminar, Volume II,
Lecture Notes in Logic 37, Cambridge University Press, 2012.
-
(with M. Sokic) Dynamical properties of the automorphism groups of the
random poset and random distributive lattice, preprint, 2011.
Click here for the .pdf file.
-
In memoriam: Gregory Hjorth (1963-2011), Bulletin of Symbolic Logic
17(3) (2011), 471-477.
-
(with C. Conley and R. Tucker-Drob) Ultraproducts of measure preserving
actions and graph combinatorics, Erg. Theory and Dynam. Systems, to
appear.
Click here for the .pdf file.
-
(with R. Tucker-Drob) The complexity of
classification problems in ergodic theory, Appalachian Set Theory, Ed.
by J. Cummings and E. Schimmerling, London Math. Society Lecture Note
Series, to appear.
Click here for the
.pdf file.
-
(with C.T. Conley) Measurable chromatic and independence numbers for
ergodic graphs and group actions, Groups, Geometry, and Dynamics,
to appear.
Click here for the
.pdf file.
- Global aspects of ergodic group actions,
Mathematical
Surveys and Monographs, 160, American Mathematical Society, 2010.
-
Weak containment in the space of actions of a free
group, Israel J. Math., to appear.
Click here for the
.pdf file.
- (with A. Ioana and T.
Tsankov) Subequivalence relations and positive-definite functions,
Groups, Geometry, and Dynamics 3(4) (2009), 579-625.
- Set theory and dynamical systems, Logic, Methodology
and Philosophy of Science, Proc. of the Thirteenth International
Congress, Ed. C. Glymour et al., College Publ., London, 2009, 97-107.
- (Co-edited with B. Loewe and J. Steel)
Games, Scales, and Suslin Cardinals: The Cabal Seminar, Volume I,
Lecture Notes in Logic 31, Cambridge University Press, 2008.
- (with H. Woodin) The equivalence of partition
properties and determinacy,
in: Games, Scales, and Suslin Cardinals: The Cabal Seminar, Volume I,
Lecture Notes in Logic 31, Cambridge University Press, 2008, 355-378.
- (with H. Woodin) Generic codes for uncountable
ordinals, partition properties, and elementary embeddings,
in: Games, Scales, and Suslin Cardinals: The Cabal Seminar, Volume I,
Lecture Notes in Logic 31, Cambridge University Press, 2008, 379-397.
- (with B.D. Miller) Means on
equivalence relations, Israel. J. Math. 163 (2008), 241-262.
- (with T. Tsankov) Amenable actions and almost invariant sets,
Proc. Amer. Math. Soc. 136(2) (2008), 687-697.
- (with C. Rosendal) Turbulence, amalgamation and generic automorphisms of
homogeneous structures, Proceedings of the London Math. Society,
94(3) (2007), 302–350.
- Unitary representations and modular actions, Journal of Math. Sciences,
140(3)
(2007), 398-425.
- (with G. Hjorth) Rigidity theorems for actions of product groups and
countable Borel equivalence relations, Memoirs of the Amer. Math. Soc.,
177, No. 833, 2005.
- (with V.G. Pestov and S. Todorcevic) Fraïssé
limits, Ramsey theory and topological dynamics of automorphism groups,
Geometric and Functional Analysis 15 (1) (2005), 106-189.
- (with B. D. Miller)
Topics in Orbit Equivalence, Lecture Notes in Mathematics, Springer,
Vol. 1852, 2004
- (with S. Gao) On the classification of Polish metric spaces up to isometry, Memoirs of Amer. Math. Soc.,
766, Amer. Math. Soc., 2003.
- (with C. W. Henson, J. Iovino and E. Odell)
Analysis and
Logic, London Math. Soc. Lecture Notes Series, 262, Cambridge University Press,
2002.
- (with S. Jackson and A. Louveau) Countable Borel equivalence relations, J. Math. Logic
2(1) (2002), 1-80.
- (with S.R. Buss, A. Pillay, and R.A. Shore) The prospects for mathematical logic in
the 21st century, Bull. Symb. Logic 7(2) (2001), 169-196.
- (with J.D. Clemens and S. Gao) Polish metric spaces: Their classification and
isometry groups, Bull. Symb. Logic 7(3) (2001), 361-375.
- (with G. Hjorth) Recent developments in the theory of Borel reducibility, Fund.
Math. 170(1) (2001), 21-52 (volume dedicated to the memory of J. Los).
- (with N. Sofronidis) A strong generic ergodicity property of unitary and
self-adjoint operators, Ergodic Theory and Dynam. Systems
21
(2001), no. 5, 1459-1479.
- (co-edited with M. Foreman, A. Louveau, and B. Weiss) Descriptive
Set Theory and Dynamical Systems, London
Math. Soc. Lecture Note Series 277, 231-259, Cambridge University
Press, 2000.
- Descriptive Dynamics, in: Descriptive Set Theory and Dynamical Systems, Ed. by M.
Foreman et al., London Math. Soc. Lecture Note Series 277, 231-259,
Cambridge University Press, 2000.
- On the classification problem for rank 2 torsion-free abelian groups, J. London
Math. Soc. 62(2) (2000), 437-450.
- (with S. Adams) Linear algebraic groups and countable Borel equivalence relations,
J. Amer. Math. Soc. 13(4) (2000), 909-943.
- (with R. Camerlo) Countable structures with a fixed group of automorphisms,
Israel J. Math. 117 (2000), 105-124.
- (with R. Dougherty) How many Turing degrees are there? in: Computability Theory
and Its Applications, Current Trends and Open Problems, Ed. by P.A. Cholak et al.,
Contemp. Math. 257, 83-95, Amer. Math. Soc., 2000.
- (with G. Hjorth) The complexity of the classification of Riemann surfaces and
complex manifolds, Ill. J. Math. 44(1) (2000), 104-137.
- New directions in descriptive set theory, Bull. Symb. Logic
5(2)
(1999), 161-174.
- (with A. Gordon) Measurable enumeration of eigenelements, Applicable Analysis
71
(1999), 41-62.
- (with S. Solecki and S. Todorcevic) Borel chromatic numbers, Adv. in Math.
141
(1999), 1-44.
- The descriptive classification of some classes of C*-algebras, Proc. 6th Asian
Logic Conference (C.T. Chong, et al., eds.) World Scientific, Singapore (1998), 121-149.
- Rigidity properties of Borel ideals on the integers, Topology and Its Appl.
85
(1998), 195-205.
- (with G. Hjorth and A. Louveau) Borel equivalence relations induced by actions of the
symmetric group, Ann. Pure and Appl. Logic 92 (1998), 63-112.
- On the concept of coanalytic-completeness, Proc. Amer. Math. Soc.
125(6)
(1997), 1811-1814.
- (with G. Hjorth) New dichotomies for Borel equivalence relations, Bull. Symb.
Logic 3(3) (1997), 329-346.
- (with A. Louveau) The classification of hypersmooth Borel equivalence relations,
J. Amer. Math. Soc. 10(1) (1997), 215-242.
- Set theory and uniqueness for trigonometric series, preprint, 1997.
Click here for the
.pdf file.
- (with H. Becker)
The Descriptive Set Theory of Polish Group Actions, London Math.
Soc. Lecture Note Series, 232, Cambridge University Press, 1996.
- Corrections and Updates: [pdf]
- (with G. Hjorth) Borel equivalence relations and classifications of countable models,
Ann. Pure and Appl. Logic 82 (1996), 221-272.
- (with G. Hjorth) Analytic equivalence relations and Ulm-type classifications, J.
Symb. Logic 60 (1995), 1273-1300.
-
Classical Descriptive Set Theory, Graduate Texts in Mathematics, 156, Springer, 1995.
- Corrections and Updates: [pdf]
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