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

• (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, 2012.
  Click here for the .pdf file
• (with C. Conley and B. Miller) Stationary probability measures and topological realizations, Israel. J. Math., to appear.
  Click here for the .pdf file.
• (with O. Angel and R. Lyons) Random orderings and unique ergodicity of automorphism groups, preprint, 2012.
  Click here for the .pdf file.
• Dynamics of non-archimedean Polish groups, to appear in the Proceedings of the European Congress of Mathematics, Krakow, Poland, 2012.
  Click here for the .pdf file.
• 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. 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., to appear.
  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. 
• Corrections and Updates: pdf file.
• 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. 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
• A typical reader's reaction to the book
• Corrections and Updates:  [pdf]
• (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]

   

Logic in Southern California 2012: February 18

Logic in Southern California 2012: November 17

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