Skein Modules from Skew Howe Duality and Affine Extensions

We show that we can release the rigidity of the skew Howe duality process for ${\mathfrak sl}_n$ knot invariants by rescaling the quantum Weyl group action, and recover skein modules for web-tangles. This skew Howe duality phenomenon can be extended to the affine ${\mathfrak sl}_m$ case, corresponding to looking at tangles embedded in a solid torus. We investigate the relations between the invariants constructed by evaluation representations (and affinization of them) and usual skein modules, and give tools for interpretations of annular skein modules as sub-algebras of intertwiners for particular $U_q({\mathfrak sl}_n)$ representations. The categorification proposed in a joint work with A. Lauda and D. Rose also admits a direct extension in the affine case

The Supply Side of CO2 with Country Heterogeneity

Several recent articles have analyzed climate policy giving explicit attention to the non-renewable character of carbon resources. In most of this literature the economy is treated as a single unit, which in the context of climate policy seems reasonable to interpret as the whole world. However, carbon taxes and other climate policies differ substantially across countries. With such heterogeneity, the effects on emission paths of changes in taxes, costs and subsidies may be very different from what one finds for a hypothetical world of identical countries.climate change, exhaustible resources, renewable energy, green paradox

Concerns for Equity and the Optimal Co-Payments for Publicly Provided Health Care

In countries where health care is publicly provided and where equity considerations play an important role in policy decisions, it is often argued that an increase in co-payments is unacceptable as it will be particularly harmful to the less well-off in society. The present paper derives socially optimal co-payments in a simple model of health care where people differ in income and in severity of illness. The social optimum depends on the welfare weights given to persons with different levels of expected utility. Increased concern for equity may increase optimal co-payments for illnesses with homogeneous severity across the population. For illnesses where the severity varies strongly across the population, optimal co-payments go down as a response to increased concern for equity, provided income differences in the society are sufficiently small.public health, co-payments, equity concerns

Climate Change and Carbon Tax Expectations

If governments cannot commit to future carbon tax rates, investments in greenhouse gas mitigation will be based on uncertain and/or wrong predictions about these tax rates. Predictions about future carbon tax rates are also important for decisions made by owners of non-renewable carbon resources. The effects of the size of expected future carbon taxes on near-term emissions and investments in substitutes for carbon energy depend significantly on how rapidly extraction costs increase with increasing total extraction. In addition, the time profile of the returns to investments in non-carbon substitutes is important for the effects on emissions and investments.climate change, carbon tax, green paradox, commitment, exhaustible resources

Central limit theorems for multilevel Monte Carlo methods

In this work, we show that uniform integrability is not a necessary condition for central limit theorems (CLT) to hold for normalized multilevel Monte Carlo (MLMC) estimators and we provide near optimal weaker conditions under which the CLT is achieved. In particular, if the variance decay rate dominates the computational cost rate (i.e., $\beta > \gamma$), we prove that the CLT applies to the standard (variance minimizing) MLMC estimator. For other settings where the CLT may not apply to the standard MLMC estimator, we propose an alternative estimator, called the mass-shifted MLMC estimator, to which the CLT always applies. This comes at a small efficiency loss: the computational cost of achieving mean square approximation error $\mathcal{O}(\epsilon^2)$ is at worst a factor $\mathcal{O}(\log(1/\epsilon))$ higher with the mass-shifted estimator than with the standard one

Chebyshev polynomials and the Frohman-Gelca formula

Using Chebyshev polynomials, C. Frohman and R. Gelca introduce a basis of the Kauffman bracket skein module of the torus. This basis is especially useful because the Jones-Kauffman product can be described via a very simple Product-to-Sum formula. Presented in this work is a diagrammatic proof of this formula, which emphasizes and demystifies the role played by Chebyshev polynomials.Comment: 13 page

Cutting Costs of Catching Carbon - Intertemporal Effects under Imperfect Climate Policy

We use a two-period model to investigate intertemporal effects of cost reductions in climate change mitigation technologies for the power sector. With imperfect climate policies, cost reductions related to carbon capture and storage (CCS) may be more desirable than com-parable cost reductions related to renewable energy. The finding rests on the incentives fossil resource owners face. With regulations of emissions only in the future, cheaper renewables speed up extraction (the ‘green paradox’), whereas CCS cost reductions make fossil resources more attractive for future use and lead to postponement of extraction.climate change, exhaustible resources, carbon capture and storage, renewable energy, green paradox