Contact

Institute of Mathematics of the AS CR
Žitná 25, CZ - 115 67 Praha 1, Czech Republic

Phone: +420 222 090 715 (office)
E-mail: zapletal at math.cas.cz

Current research

I work on the interface between forcing, analysis, Ramsey theory, and descriptive set theory. I outlined the theory of definable proper forcing in my book "Forcing Idealized", Cambridge Tracts in Mathematics 174, Cambridge University Press 2008. My current work elaborates on the problems left open in that book and the relationship with the proper forcing technologies of Saharon Shelah .

I wrote two papers on the applications of the ergodic iteration theorem, showing that the n-localization property and the weak Sacks property are preserved under the countable support iteration of definable forcing. The papers share the same technology and I am currently busy joining them into one.

I showed that a number of classical infinitary Ramsey theorems can be parametrized in a canonical way by a Borel probability measure.

With Saharon Shelah, I showed that products of finite sets with submeasures associated with each generate a canonical bounding forcing adding no independent reals. This result is still not typed.

Current teaching

In the summer term of 2009 I teach a course Descriptive Set Theory: Borel Equivalence Relations at Department of Mathematical Analysis of Faculty of Mathematics and Physics, Charles University. We meet every Thursday at 3:40pm in K12. I wrote a preliminary version of notes for this course and its continuation. The map of Borel equivalence relations is here . The exam is available here ; it is due on the last day of class, May 21.

Resume

Education and degrees

• DSc. in Mathematics, Czech Academy of Sciences 2007
• Ph. D. in Mathematics, The Pennsylvania State University 1995, supervisor T. Jech
• M. A. in Mathematics, Charles University, Prague 1994
• B. A. in Mathematics, Charles University, Prague 1990

Employment

• 2009 Purkyně Fellow, Czech Academy of Sciences
• 2005-present associate professor, University of Florida
• 2000-2005 assistant professor, University of Florida
• 1998-2000 John Wesley Young instructor, Dartmouth College
• 1996-1998 Bateman research instructor, California Institute of Technology
• 1995-1996 postdoctoral fellow, Mathematical Sciences Research Institute Berkeley
• 1990-1995 teaching assistant, The Pennsylvania State University

Grants and fellowships

• 2009/2010 AKTION project 2009/9, cooperation between CAS and Kurt Goedel Center in Vienna
• 2009-present Purkyně fellowship, Czech Academy of Sciences
• 2009-present grant IAA100190902 of Grant Agency of the Academy of Sciences of the Czech Republic
• 2008-present NSF grant DMS 0801114, $110000
• 2006-2007 NSF grant DMS 0532644 (PI) to organize special year in logic at UF, $138000
• 2003-2006 grant GA ČR 201-03-0933 of the Grant Agency of Czech Republic
• 2003-2006 NSF grant DMS 0335481 to organize an annual logic conference at UF, $15000
• 2003-2006 NSF grant DMS 0300201 $103827
• 2000-2003 NSF grant DMS 0071437, $61431
• 2000-2003 grant GA ČR 201-00-1466 of the Grant Agency of Czech Republic
• 1997-2000 grant GA ČR 201-97-0216 of the Grant Agency of Czech Republic

Publications

• Preserving P-points in definable forcing , submitted to Fundamenta Mathematicae
• Canonization of equivalence relations and proper forcing, with Vladimir Kanovei, submitted to Fundamenta Mathematicae
• Increasing delta one two by a Namba-style forcing , with Richard Ketchersid and Paul Larson, J. Symbolic Logic 72 (2007), 1372--1378
• On the structure of stationary sets, with Qi Feng and Thomas Jech, Sci. China Ser. A 50 (2007) 615-627
• Forcing with quotients, with Michael Hrušák, Archive Math. Logic 47 (2008), 719-739
• Forcing idealized , Cambridge Tracts in Mathematics, Cambridge University Press 2008, ISBN 9780521874267
• Proper forcing and rectangular Ramsey theorems, Israel J. Math. 152 (2006), 29--47
• Between Maharam's and von Neumann's problem, with Ilijas Farah, Math. Research Letters 11 (2004), 673--684
• Four and more, Ann. Pure Appl. Logic, with Ilijas Farah, Ann. Pure Appl. Logic 140 (2006), 3--39
• Descriptive set theory and definable forcing, Memoirs Amer. Math. Soc. 793 (2004)
• Games with creatures, with S. Shelah, Comm. Math. Univ. Carolinae 44 (2003), 9--23
• Duality and the PCF theory, with S. Shelah, Math. Research Letters 9 (2002), 585--595
• Forcing with ideals of closed sets, Comm. Math. Univ. Carolinae 43,1 (2002), 181--188
• Isolating cardinal invariants, J. Math. Logic, 2003, 143-162
• Terminal notions in set theory, Ann. Pure Appl. Logic 109 (2001), 89--116
• Transfinite open games, Topology and Its Applications 111 (2001), 289--297
• Killing ideals and adding reals, J. Symbolic Logic 65 (2000), 747--755
• The nonstationary ideal and the other sigma ideals on omega one, Trans. Amer. Math. Soc. 352 (2000), 3981--3993
• Terminal notions, Bull. Symbolic Logic 5 (1999), 470--484
• On the Alaoglu-Birkhoff equivalence of posets, with S. Todorcevic, Illinois J. Math. 43 (1999), 281--292
• Canonical models for aleph one combinatorics, with S. Shelah, Ann. Pure Appl. Logic 98 (1999), 217--259
• Proper forcing and absoluteness in L(R), with I. Neeman, Comm. Math. Univ. Carolinae 39 (1998), 281--301
• A dichotomy for forcing notions, Math. Res. Lett. 5 (1998) 213--226
• Preserving sigma-ideals, J. Symbolic Logic 63 (1998), 1437--1441
• Keeping additivity of the null ideal small, Proc. Amer. Math. Soc. 125 (1997), 2443--2451
• Embeddings of Cohen algebras, with S. Shelah, Adv. Math. 126 (1997), 93--119
• Semi-Cohen boolean algebras, with B. Balcar and T. Jech, Ann. Pure Appl. Logic 87 (1997), 187--208
• Strongly almost disjoint functions, Israel J. Math. 97 (1997), 101--111
• Small forcings and Cohen reals, J. Symbolic Logic 62 (1997), 280--284
• Splitting number at uncountable cardinals, J. Symbolic Logic 62 (1997), 35--42
• A classification of definable partial orders on omega one, Fund. Math. 153 (1997), 141-144
• Characterization of the club forcing, in Papers on General Topology and Applications, S. Andima, R. Flagg, G. Itzkowitz, Y. Kong, R. Kopperman amd P. Misra, eds., Annals of the New York Academy of Sciences 806 (1996), 476--484
• A new proof of Kunen inconsistency, Proc. Amer. Math. Soc. 124 (1996), 2203-2205
• More on the cut and choose game, Ann. Pure Appl. Logic 76 (1995), 291--301

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