Noam Zeilberger

Member, School of Mathematics, Institute for Advanced Study (located in Princeton, NJ)
email: [my full name] at gmail.com

Background

This year I am participating in the Special Year on Univalent Foundations at the IAS. Before that, I spent a year at the IMDEA Software institute in Madrid, and before that two years in Paris at Laboratoire PPS and Equipe πr², on a fellowship of the Fondation Sciences Mathématiques de Paris. I got my PhD in 2009 from CMU SCS, after six great years living in Pittsburgh.

I am currently looking for an exciting job: please hire me!

Research Interests

I am interested broadly in the connections between logic and language and computation, and am excited by the potential of [type/category] theory as a means of facilitating communication and reaching unity across different disciplines. I have spent time thinking about the Curry-Howard correspondence in general, and more specifically about:

Recently, I have also become interested in the notion of zero-knowledge from cryptography/complexity theory, and how it relates to notions of knowledge from proof theory.

Dissertation

PhD in computer science, 2009, Carnegie Mellon University
The Logical Basis of Evaluation Order and Pattern-Matching.
Committee: Peter Lee (co-advisor), Frank Pfenning (co-advisor), Robert W. Harper, Paul-André Melliès (external member)

Techniques from linear logic and infinitary proof theory (connected to the old idea of a "proof-theoretic semantics" of logic) yield new insights into seemingly extra-logical features of modern programming languages. By applying the Curry-Howard correspondence to focusing proofs, we develop a polarized type theory in which evaluation order is explicitly reflected at the level of types, and which has built-in support for pattern-matching. This framework provides an elegant, uniform account of both untyped and intrinsically well-typed computation, and moreover can be extended with an extrinsic (Curry-style) type system to express and enforce more refined semantic properties of programs. We apply these ideas to explore the theory of typing and subtyping for intersection and union types in the presence of effects, giving a simplified explanation of some of the unusual artifacts of existing systems.

Publications

Polarity and the logic of delimited continuations.
In Proceedings of the Twenty-Fifth Annual IEEE Symposium on Logic in Computer Science (LICS 2010). [twelf code] [slides]
Defunctionalizing focusing proofs.
Presented at the 2009 International Workshop on Proof-Search in Type Theories. [twelf code] [more twelf]
Refinement types and computational duality.
In Proceedings of the 2009 Workshop on Programming Languages meets Program Verification (PLPV 09). [agda code]
Focusing on binding and computation.
With Dan Licata and Bob Harper. In Proceedings of the Twenty-Third Annual IEEE Symposium on Logic in Computer Science (LICS 08). [tech report]
Focusing and higher-order abstract syntax.
In Proceedings of the 35th Annual ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages (POPL 08). [coq code] [notes]
On the unity of duality.
Annals of Pure and Applied Logic 153:1 (2008), special issue on "Classical logic and computation". [doi]

Selected talks

Substructural Type Theory.
March 22, 2013, IAS.
HOPE for a type-theoretic understanding of zero-knowledge.
September 9, 2012, at the 1st ACM SIGPLAN workshop on Higher-Order Programming with Effects. (Note: the slides seem to render funny with Firefox -- best viewed in Chrome or Safari.)
BONUS: slides for the "15 minute" version I gave October 4th at the IAS postdoc seminar series.
Towards a Non-Commutative Logic of Effects.
December 2-3, 2010, at MSR Cambridge and at the Oxford OASIS Seminar.
Symmetry and Asymmetry in Logic (Rereading Dummett through Girard [and vice versa!]).
March 22, 2010, at Proofs and Meaning.
Towards a Proof-Theoretic Semantics of Programming.
October 21, 2009, at the Groupe de travail Théorie des types et réalisabilité.
Polarity and duality in type theory.
February 20, 2008 at DTP 08.

Other papers

Soundness of labelled deduction.
August, 2005. An attempt at a constructive proof of the soundness of labelled deduction for intuitionistic logic. This is essentially a variation on the usual "prime context" approach establishing completeness of intuitionistic logic with respect to Kripke semantics, but avoiding proof-by-contradiction, and using the subformula property to stay finitary. For a more novel approach, see Jason Reed and Frank Pfenning's "Intuitionistic letcc via labelled deduction".
Modal BI and Separation Logic.
June, 2005. Describes how to extend the logic of bunched implications with an S4-like box modality, and its relationship to "purity" in separation logic.
Nathack: a natural language interface for nethack.
January, 2003. With Cassia Martin, David Molnar, and Dev Purkayastha. As the title suggests, this was a natural language interface for nethack! Done with a mix of prolog, embedded lua, and scary hacking within nethack's internal C source. Our code is lying around somewhere, and I could dig it up upon request.

Historical documents

Letter from Per Martin-Löf to Michael Dummett, dated 5 March 1976
On Dummett's invitation, Martin-Löf gave a series of eight lectures at Oxford's All Souls College, with Dummett and Dag Prawitz in the audience. This letter (dated shortly before Dummett's 1976 William James Lectures) was accompanied by Peter Hancock's notes on the first half of this series. Thanks to Peter Hancock for the scanned copy.

Et cetera

The Paralyzing Paradoxes of Professor Polaro
My research blog, primarily about proofs and programs (and nowadays primarily silent!)
Wikipedia editing / the nLab
Knowledge is a collaborative effort.
And Quiet Flows the Mon
A photography project from the dark days after the 2004 U.S. Presidential Elections.
In Tune With Fun
A true-life story about learning the accordion.

We may just be cockroaches at the base of a very large garbage mountain.
Dana Scott (on mathematics)