Hydrodynamics is an old example of effective description complex matter, which describes the system's behavior at large length and timescales lumps microscopic details into transport coefficients. A combination hydrodynamics gauge-gravity duality, was first explored in context string theory, has proven promising for a strongly correlated electron fluids. This Colloquium explains how to apply th...

The moduli stack MX(E8) of principal E8-bundles over a smooth projective curve X carries a natural divisor ∆. We study the pull-back of the divisor ∆ to the moduli stack MX(P ), where P is a semi-simple and simply connected group such that its Lie algebra Lie(P ) is a maximal conformal subalgebra of Lie(E8). We show that the divisor ∆ induces “Strange Duality”-type isomorphisms between the Verl...

The paper engages with Stevenson’s novel The Strange Case of Dr Jekyll and Mr Hyde from the perspective of essential duality embedded in every one’s nature: it explicates the entangling nature of binaries and the aesthetics of non-disjunction of the binary self/Other as embodied in the figures of Dr Jekyll and Mr Hyde respectively. By the novel’s end, the two aspects, the Jekyllean and the Hyde...

The elastic leptoproduction of φ measured by the H1 collaboration at HERA is described by a perturbative QCD model, based on open ss̄ production and parton hadron duality, proposed by Martin et al. We observe that both the total cross section and the ratio of the longitudinal and transverse cross sections are well reproduced with an effective strange-quark mass ms ∼ 320 − 380 MeV for various glu...

This paper is a slightly revised version of an introduction into singularity theory corresponding to a series of lectures given at the ``Advanced School and Conference on homological and geometrical methods in representation theory'' at the International Centre for Theoretical Physics (ICTP), Miramare - Trieste, Italy, 11-29 January 2010. We show how to associate to a triple of posit...

A squarefree module over a polynomial ring S = k[x1, . . . , xn] is a generalization of a Stanley-Reisner ring, and allows us to apply homological methods to the study of monomial ideals more systematically. The category Sq of squarefree modules is equivalent to the category of finitely generated left Λ-modules, where Λ is the incidence algebra of the Boolean lattice 2. The derived category D(S...

The quantum world is allegedly strange. But it? What if there’s a simple mathematical explanation, and solution? success of mechanics (QM) arises from the accuracy its probability predictions, which are obtained by squaring amplitudes (the Born rule). Suppose for moment that nature uses negative QM’s equations. When squared they would yield same probabilities, confirmed experiments technologica...

Finite Quot schemes were used by Bertram, Johnson, and the first author to study Le Potier's strange duality conjecture on del Pezzo surfaces when one of moduli spaces is Hilbert scheme points. In order rigorously enumerate finite scheme, we space limit stable pairs in which target has rank a smooth complex projective surface. We obtain an embedding this into that induces perfect obstruction th...