ALEXANDER S. KECHRIS
Professor of Mathematics
CV
Publications
Research Interests
Foundations of mathematics; mathematical logic and set theory;
their interactions with analysis, dynamical systems and
combinatorics. 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
2018-2019
Fall: Math 117a, Computability Theory
Winter: Math 1b, Practical, Linear Algebra
Spring: Math 6c, Introduction to Discrete Mathematics
Selected Publications
- (with F. Shinko) Realizations of countable Borel
equivalence relations, preprint, 2019. Click here
for the .pdf file
- The theory of countable Borel equivalence relations,
preprint, 2019. Click here for the .pdf file
- (with V. Quorning) Co-induction and invariant random
subgroups, to appear in Groups, Geometry, and
Dynamics, 2019. Click here for the .pdf file and also arXiv
- (with P.J. Burton) Weak containment
of measure preserving group actions, to appear in
Erg. Theory and Dynam. Systems, 2019. Click here for the .pdf
file and ETDS online version
- (with A.S. Marks) Descriptive graph combinatorics,
preprint, 2018. Click here for the .pdf file
- Quasi-invariant measures for continuous group actions,
preprint, 2018. Click here for the .pdf file
- (with R. Chen) Structurable equivalence relations,
Fund. Math., 242 (2018), 109--185. Click here for the .pdf file.
arXiv expanded version https://arxiv.org/abs/1606.01995v3
- (with A. Nies and K. Tent) The complexity of
topological group isomorphism, J. Symb. Logic, 83(3)
(2018), 1190--1203. Click here for the .pdf file
- The spaces of measure preserving equivalence relations
and graphs, preprint, 2018. Click here for the
.pdf
file
- (with P.J. Burton) Invariant random subgroups and
action versus representation maximality,
Proc. Amer. Math. Soc., 145(9) (2017), 3961--3971. 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, in: Foundations of
Mathematics, Essays in Honor of W. Hugh Woodin's 60th
Birthday, Ed. by A.E. Caicedo et al., Contemp. Math., 690,
69-85, Amer. Math. Soc., 2017. Click here 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.
- (with H.L. Macdonald) Borel equivalence relations and
cardinal algebras, Fund. Math., 235
(2016), 183--198. 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: click here for the .pdf file
- (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: Click here for the .pdf file
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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