Virasoro constraints and the Chern classes of the Hodge bundle

We analyse the consequences of the Virasoro conjecture of Eguchi, Hori and Xiong for Gromov-Witten invariants, in the case of zero degree maps to the manifolds CP^1 and CP^2 (or more generally, smooth projective curves and smooth simply-connected projective surfaces). We obtain predictions involving intersections of psi and lambda classes on the compactification of M_{g,n}. In particular, we show that the Virasoro conjecture for CP^2 implies the numerical part of Faber's conjecture on the tautological Chow ring of M_g.Comment: 12 pages, latex2

Study of tooling concepts for manufacturing operations in space Final report

Mechanical linkage device for manufacturing operations with orbital workshop

Computing top intersections in the tautological ring of MgM_g

We derive effective recursion formulae of top intersections in the tautological ring $R^*(M_g)$ of the moduli space of curves of genus $g\geq 2$. As an application, we prove a convolution-type tautological relation in $R^{g-2}(M_g)$.Comment: 18 page

Is the energy density of the ground state of the sine-Gordon model unbounded from below for beta^2 > 8 pi ?

We discuss Coleman's theorem concerning the energy density of the ground state of the sine-Gordon model proved in Phys. Rev. D 11, 2088 (1975). According to this theorem the energy density of the ground state of the sine-Gordon model should be unbounded from below for coupling constants beta^2 > 8 pi. The consequence of this theorem would be the non-existence of the quantum ground state of the sine-Gordon model for beta^2 > 8 pi. We show that the energy density of the ground state in the sine-Gordon model is bounded from below even for beta^2 > 8 pi. This result is discussed in relation to Coleman's theorem (Comm. Math. Phys. 31, 259 (1973)), particle mass spectra and soliton-soliton scattering in the sine-Gordon model.Comment: 22 pages, Latex, no figures, revised according to the version accepted for publication in Journal of Physics

Perturbative Chern-Simons Theory From The Penner Model

We show explicitly that the perturbative SU(N) Chern-Simons theory arises naturally from two Penner models, with opposite coupling constants. As a result computations in the perturbative Chern-Simons theory are carried out using the Penner model, and it turns out to be simpler and transparent. It is also shown that the connected correlators of the puncture operator in the Penner model, are related to the connected correlators of the operator that gives the Wilson loop operator in the conjugacy class.Comment: 7 Pages, Published Versio

Noncommutative resolutions of discriminants

We give an introduction to the McKay correspondence and its connection to quotients of $\mathbb{C}^n$ by finite reflection groups. This yields a natural construction of noncommutative resolutions of the discriminants of these reflection groups. This paper is an extended version of E.F.'s talk with the same title delivered at the ICRA.Comment: 15 pages, 4 figures. Final version to appear in Contemporary Mathematics 705, "Representations of Algebras

A McKay correspondence for reflection groups

We construct a noncommutative desingularization of the discriminant of a finite reflection group G as a quotient of the skew group ring A=S∗G. If G is generated by order 2 reflections, then this quotient identifies with the endomorphism ring of the reflection arrangement A(G) viewed as a module over the coordinate ring SG/(Δ) of the discriminant of G. This yields, in particular, a correspondence between the nontrivial irreducible representations of G to certain maximal Cohen–Macaulay modules over the coordinate ring SG/(Δ). These maximal Cohen–Macaulay modules are precisely the nonisomorphic direct summands of the coordinate ring of the reflection arrangement A(G) viewed as a module over SG/(Δ). We identify some of the corresponding matrix factorizations, namely, the so-called logarithmic (co-)residues of the discriminant

Directionally asymmetric self-assembly of cadmium sulfide nanotubes using porous alumina nanoreactors: Need for chemohydrodynamic instability at the nanoscale

We explore nanoscale hydrodynamical effects on synthesis and self-assembly of cadmium sulfide nanotubes oriented along one direction. These nanotubes are synthesized by horizontal capillary flow of two different chemical reagents from opposite directions through nanochannels of porous anodic alumina which are used primarily as nanoreactors. We show that uneven flow of different chemical precursors is responsible for directionally asymmetric growth of these nanotubes. On the basis of structural observations using scanning electron microscopy, we argue that chemohydrodynamic convective interfacial instability of multicomponent liquid-liquid reactive interface is necessary for sustained nucleation of these CdS nanotubes at the edges of these porous nanochannels over several hours. However, our estimates clearly suggest that classical hydrodynamics cannot account for the occurrence of such instabilities at these small length scales. Therefore, we present a case which necessitates further investigation and understanding of chemohydrodynamic fluid flow through nanoconfined channels in order to explain the occurrence of such interfacial instabilities at nanometer length scales.Comment: 26 pages, 6 figures; http://www.iiserpune.ac.in/researchhighlight

Vibrational modes of circular free plates under tension

The vibrational frequencies of a plate under tension are given by the eigenvalues $\omega$ of the equation $\Delta^2u-\tau\Delta u=\omega u$. This paper determines the eigenfunctions and eigenvalues of this bi-Laplace problem on the ball under natural (free) boundary conditions. In particular, the fundamental modes --- the eigenfunctions of the lowest nonzero eigenvalue --- are identified and found to have simple angular dependence.Comment: 17 pages. To be submitted for publication shortly

Topological String Partition Functions as Polynomials

We investigate the structure of the higher genus topological string amplitudes on the quintic hypersurface. It is shown that the partition functions of the higher genus than one can be expressed as polynomials of five generators. We also compute the explicit polynomial forms of the partition functions for genus 2, 3, and 4. Moreover, some coefficients are written down for all genus.Comment: 22 pages, 6 figures. v2:typos correcte