Sacks Prize Recipients

The 2007 Sacks Prize
Adrien Deloro, Rutgers University and Wojciech Moczydlowski, Cornell University

Deloro received his Ph.D. in 2007 from the Université Paris 7, under the supervision of Eric Jaligot. The Prizes and Awards Committee citation notes that his thesis, Groupes simples connexes minimaux de type impair, "deals with the Cherlin-Zilber conjecture, according to which every simple group of finite Morley rank is isomorphic to an algebraic group over an algebraically closed field. In particular, the thesis removes the assumption that there are no bad fields from the classification of minimal counterexamples. Deloro operates with an impressive mastery of a wide range of techniques, which must be interwoven in a very delicate way, and contributes to them in important ways. The result is significant progress on a basic open problem.''

Moczydlowski received his Ph.D. in 2007 from Cornell University under the supervision of Robert Constable. The Committee cited that his thesis, Investigations on sets and types, "contains ground breaking results on constructive set theory and its relation to type theory. Among other things, Moczydlowski proves weak normalization for the theory IZF_R, Intuitionistic Zermelo-Fraenkel Set Theory with Replacement rather than Collection. He also introduces IZF_D, a novel combination of type theory and set theory which has the proof-theoretic power of ZFC, and proves normalization for this theory.''

 

2006 Sacks Prize
Matteo Viale, University of Torino and the University of Paris 7

Viale received his Ph.D. in 2006 from the University of Torino and the University of Paris 7, under the supervision of Alessandro Andretta and Boban Velickovic. The Committee's citation reads: "Viale's thesis makes fundamental contributions to our understanding of the consequences of forcing axioms in the combinatorics of singular cardinals. In particular, it solves a well-known problem, by showing that the Proper Forcing Axiom implies the Singular Cardinals Hypothesis.''

2005 Sacks Prize
Antonio Montalbán, University of Chicago

Montalbán received his Ph.D. in 2005 from Cornell University, under the supervision of Richard Shore. The Committee on Prizes and Awards' citation reads: "The thesis, entitled Beyond the Arithmetic, contains deep and major contributions to an impressively broad array of areas in logic, including computability theory, reverse mathematics, and effective mathematics. It uses a wide arsenal of techniques from set theory, computability theory, proof theory and combinatorics including the development of a new class of invariants for countable linear orderings."

 

2004 Sacks Prize
Joseph Mileti, University of Chicago, and Nathan Segerlind, University of Washington

Mileti received his Ph.D. in 2004 from the University of Illinois at Urbana-Champaign, under the supervision of Carl Jockusch. His thesis, Partition theorems and computability theory, was cited by the Prizes and Awards Committee as containing a "penetrating computability theoretical analyses of Ramsey-type theorems, an important feature of which is an ingeneous completely new proof of the Canonical Ramsey Theorem whose ideas allowed a deep effective analysis of this theorem.''

Segerlind received his Ph.D. in 2004 from the University of California, San Diego, under the supervision of Sam Buss and Russell Impagliazzo. The Committee noted that his thesis, New Separations in Propositional Proof Complexity, "extends switching lemmas, one of the most primary tools in the area, in a very unexpected way, that, among other things allowed him to take, in a single step, one important proof system from an almost complete mystery to being almost completely understood.''

 

2003 Sacks Prize
Itay Ben Yaacov, Massachusetts Institute of Technology

Ben Yaacov received his Ph.D. in 2002 from the University of Paris VII, under the supervision of Daniel Lascar. His thesis, Théories simples : constructions de groupes et interprétabilité généralisée, was cited by the Committee as, "a major contribution to pure model theory on two intimately related fronts: an extension of simplicity theory beyond the first order context, and the interpretability of groups in simple theories.''

2002 Sacks Prize
No prize was awarded.

2001 Sacks Prize
Matthias Aschenbrenner, University of California, Berkeley

Aschenbrenner received his Ph.D. in 2001 from the University of Illinois at Urbana-Champaign, under the direction of Lou van den Dries. His thesis solves a long-standing problem concerning the complexity of the ideal membership problem in the polynomial ring over the integers. Aschenbrenner shows that the complexity of this problem is doubly exponential in the number of variables, which is optimal since single exponential complexity was known to be impossible.

2000 Sacks Prize
Eric Jaligot, Universite Claude Bernard (Lyon-1)

Jaligot received his Ph.D. in 1999 from the Institut Girard Desargues, Universite Claude Bernard (Lyon-1), under the direction of Tuna Altinel and Bruno Poizat. His thesis concerned the Cherlin-Zil'ber Conjecture, which asserts that infinite simple groups of finite Morley rank are algebraic groups over algebraically closed fields.

1999 Sacks Prize
Denis Hirschfeldt, Cornell University and Rene Schipperus, University of Colorado

This was the first year the Prize was awarded under the auspices of the ASL. Denis Hirschfeldt received his Ph.D. in 1999 from Cornell University, under the guidance of Richard Shore. In his thesis, he introduced a new technique for building constructive models which solves an open question which had evaded solution despite attempts by some of the top people in the field. These techniques have since been applied to solve other questions. He also introduced a new class of problems which have since become a focal point for investigations by others. The committee felt that this thesis was marked by ingenuity, insight, originality, and considerable technical prowess. Rene Schipperus received his Ph.D. in 1999 from the University of Colorado, under the guidance of Richard Laver. In his thesis, he introduced new techniques to solve a problem of Erdös on ordinal partition relations which had been open for about 30 years. The thesis has stimulated work which led to some generalizations of Schipperus's result. The committee felt that this result required a quite intricate proof and the thesis introduced a game-theoretic technique that is quite different from what had been tried before in that area.

1998 Sacks Prize - there was no Prize awarded this year.

1997 Sacks Prize
Ilijas Farah, University of Toronto and Tom Scanlon, Mathematical Sciences Research Institute in Berkeley

Farah received his Ph.D. in June, 1997, at the University of Toronto under the direction of Stevo Todorcevic. His thesis contained remarkable results concerning the structure of analytic ideals and their quotients. Scanlon received his Ph.D. form Harvard University in June, 1997, under the direction of Ehud Hrushovski. His thesis provided a model completion for the theory of differential fields connected by a specialization, together with striking applications of the model theory of valued differential fields to diophantine geometry.

1996 Sacks Prize
Dr. Byunghan Kim, Fields Institute and Dr. Itay Neeman, Harvard University

Dr. Kim received his Ph.D. under the direction of Professor Anand Pillay at the University of Notre Dame in August, 1996. His thesis included ground-breaking work in the area of Stability Theory, concerning the study of simple theories. Dr. Neeman wrote his thesis with John Steel at UCLA, earning his degree in June, 1996. In it, he established some striking results in the area of Determinacy in set theory.

1995 Sacks Prize
Dr. Slawomir Solecki, Caltech

Dr. Solecki received his Ph.D. under the direction of Professor Alexander Kechris of Caltech in June, 1995. His doctoral dissertation was entitled "Applications of descriptive set theory to topology and analysis" and was notable for its surprising results connecting modern descriptive set theory with other areas of mathematics such as ergodic theory and harmonic analysis.

1994 Sacks Prize
Gregory Hjorth, California Institute of Technology

The first Sacks Prize was awarded to Professor Gregory Hjorth of the California Institute of Technology, as author of the best dissertation in the field of logic during 1993 and 1994. Hjorth completed his Ph.D. in 1993 under the direction of Professor W. Hugh Woodin at the University of California at Berkeley. His thesis research in descriptive set theory was singled out by the selection committee for its surprising consequences concerning the relationship between projective sets and large cardinals.