Related papers: Dualities and Twins: Reflections on Hapgood
I introduce new Langlands duality conjectures concerning skein modules of 3-manifolds, which we have made recently with David Ben-Zvi, Sam Gunningham, and Pavel Safronov. I recount some historical motivation and some recent special cases…
This is an introduction to orientifolds with emphasis on applications to duality. Based on lectures given at the 1997 Trieste Summer School on Particle Physics and Cosmology, Italy.
We will report on recent advances in the understanding of non-perturbative interconnections between different string dualities. Weak-strong coupling duality (S-duality) and T-duality (symmetry under compactification on dual tori) allows one…
In the revised version of the paper, we correct misprints and add some new statements.
This is a sequel to the author's book "Derived Langlands" which introduced an embedding of the category of admissible representations of a locally p-adic group in to the derived category of the monomial category of the group. This article…
A modestly revised version of lecture notes that were distributed to accompany my four lectures at the 2017 Spring School of Analysis at Paseky, sponsored by Charles University, Prague. They are an introductory survey of Rubio de Francia…
In this paper we take some classical ideas from commutative algebra, mostly ideas involving duality, and apply them in algebraic topology. To accomplish this we interpret properties of ordinary commutative rings in such a way that they can…
We introduce the notion of a bicollapsible 2-complex. This allows us to generalize the hyperbolicity of one-relator groups with torsion to a broader class of groups with presentations whose relators are proper powers. We also prove that…
This article is an extended version of a talk given in Oxford in June 2021 as part of an online meeting `Ninety minutes of CCC' to mark the 90th birthday of Sir Roger Penrose. I assemble some questions that I have been asked or have asked…
These notes are our contribution to the Proceedings of the ICM 2026. We discuss some results we have obtained (in part jointly with coauthors) regarding the representation theory of reductive algebraic groups over algebraically closed…
These are extended notes of a course given at Tulane University for the 2015 Clifford Lectures. Their aim is to present structure results for group schemes of finite type over a field, with applications to Picard varieties and automorphism…
The paper gives a review of progress towards extending the Thurston programme to the Poincare duality case. For a full abstract, see the published version at the above link.
We suggest a multilevel model, to represent aggregate train-passing events from the Staffordshire bridge monitoring system. We formulate a combined model from simple units, representing strain envelopes (of each train passing) for two types…
These are slides for a talk given by the authors at the conference "Current developments and directions in the Langlands program" held in honor of Robert Langlands at the Northwestern University in May of 2008. The slides can be used as a…
In the concluding session of the Joint International Conference titled Econophys-2017 and Asia Pacific Econophysics Conference (APEC)-2017, held in Jawaharlal Nehru University and Delhi University during November 15-18, 2017, a brief…
We present a technique for deriving certain new natural dualities for any variety of algebras generated by a finite Heyting chain. The dualities we construct are tailored to admit a transparent translation to the more pictorial…
A talk presented at International Conference ICMP-2000, London, England
The objective of this paper is to introduce and study completions and local homology of comodules over Hopf algebroids, extending previous work of Greenlees and May in the discrete case. In particular, we relate module-theoretic to…
Thermodynamic stable interaction pair potentials which are not of the form ``positive function + real continuous function of positive type'' are presented in dimension one. Construction of such a potential in dimension two is sketched.…
We present the first corpus annotated with preposition supersenses, unlexicalized categories for semantic functions that can be marked by English prepositions (Schneider et al., 2015). That scheme improves upon its predecessors to better…