ALEXANDER S. KECHRIS
Professor of Mathematics
Diploma, Mechanical & Electrical Engineering, National
Technical University of Athens, 1969
Ph.D., Mathematics, UCLA, 1972
CV
Publications
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.
Teaching
Fall, Winter, Spring 2015-16: Math 116, Mathematical
Logic and Axiomatic Set Theory
Selected Recent Publications
- (with P.J. Burton) Invariant random subgroups and action
versus representation maximality, preprint, 2016.
Click here for the .pdf
file
- (with R. Chen) Structurable equivalence
relations, preprint, 2016. Click here for the .pdf file
- (with A.S. Marks) Descriptive graph combinatorics, preprint,
2016. Click her for the .pdf file
- (Co-edited with B. Loewe and J.R. Steel), Ordinal
Definability and Recursion Theory: The Cabal Seminar, Volume
III, Lecture Notes in Logic 43, Cambridge
University Press, 2016.
- (with D.A. Martin) On the theory of $\Pi^1_3$ sets of
reals, II, in:
Ordinal Definability and Recursion Theory: The Cabal
Seminar, Volume III, Lecture Notes in Logic 43,
Cambridge University Press, 2016, 200-219.
- The spaces of measure preserving equivalence relations and
graphs, preprint, 2016. Click here for the .pdf
file
- (with H.L. Macdonald) Borel equivalence relations and
cardinal algebras, Fund. Math., to appear. Click here for
the .pdf file
- (with M. Sokic and S. Todorcevic) Ramsey properties of
finite measure algebras and topological dynamics of the group
of measure preserving automorphisms: some results and an open
problem, preprint 2015. Click here for the .pdf file
- Commentary on Problem 50 (of Banach) in the Scottish Book,
in: R. D. Mauldin, The Scottish Book, Second Edition,
Birkhäuser, 2015, 127-129. Click here for the .pdf file
- (with
O. Angel and R. Lyons) Random orderings and unique
ergodicity of automorphism groups, J. European Math.
Society, 16 (2014), 2059-2095. Click here for
the .pdf
file
- Dynamics of non-archimedean Polish groups, European
Congress of Mathematics, Krakow, 2-7 July, 2012, 375-397, R.
Latala et al., Eds., European Math. Society, 2014.
- (with C. T. Conley and R.D. Tucker-Drob) Ultraproducts of
measure preserving actions and graph combinatorics, Erg.
Theory and Dynam. Systems, 33 (2013), 334-373.
- (with C.T. Conley) Measurable chromatic and independence
numbers for ergodic graphs and group actions,
Groups, Geometry, and Dynamics, 7 (2013), 127-180.
- (with R.D. 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, 406, 265-299, Cambridge University Press,
2013.
- (with C.T. Conley and B.D. Miller) Stationary probability
measures and topological realizations, Israel. J. Math., 198
(1)
(2013), 333-345.
- Trigonometric series and set theory, Wiadomosci
Matematyczne, 48(2) (2012), 109–118. Click here for the .pdf
file
- (Co-edited with B. Loewe and J.R., 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,
Fund. Math. 218 (2012), 69-94.
- In memoriam: Gregory Hjorth (1963-2011),
Bulletin of Symbolic Logic 17(3) (2011), 471-477.
- Global
aspects
of ergodic group actions, Mathematical Surveys and
Monographs, 160, American Mathematical Society,
2010.
- Corrections and Updates: [pdf].
- Weak containment in the space of actions of a free group,
Israel J. Math., 189 (2012), 461--507.
- (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.R. Steel) Games,
Scales,
and Suslin Cardinals: The Cabal Seminar, Volume I, Lecture Notes
in Logic 31, Cambridge University Press, 2008.
- (with W.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 W.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]
RTG Logic Meetings at Caltech
Logic in Southern California 2015-16:
February 20, 2016
Logic in Southern
California 2014-15: March 7, 2015
Logic in Southern
California 2013-2014: March 8, 2014
Logic in
Southern California 2012-13: November 17, 2012
Logic
in
Southern California 2011-12: February 18, 2012
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for mailing address, fax and telephone numbers, and e-mail
address.
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