Witten Genus and Elliptic genera for proper actions

In this paper, we construct for the first time, the Witten genus and elliptic genera on noncompact manifolds with a proper cocompact action by an almost connected Lie group and prove vanishing and rigidity results that generalise known results for compact group actions on compact manifolds. We also compute our genera for some interesting examples.Comment: 26 pages. A conjecture remove

ASEAN-5 Macroeconomic Forecasting Using a GVAR Model

This paper examines and evaluates macroeconomic forecasts for the original ASEAN-5 members in the context of a global vector autoregressive (GVAR) model covering 20 countries, grouped into nine countries/regions. After estimating the GVAR model, we generate 12 one-quarter-ahead forecasts for the next quarter including real GDP, inflation, short-term interest rates, real exchange rates, and real equity prices over the period 2009Q1–2011Q4, with four out-of-sample forecasts over the period 2009Q1–2009Q4. Forecast evaluation results based on the panel Diebold-Mariano (DM) tests show the GVAR forecasts tend to outperform forecasts based on the benchmark country-specific models, especially for short-term interest rates and real equity prices, emphasizing the interdependencies in the global financial market.Macroeconomic Forecasting; Global vector autoregressive model (GVAR); Southeast Asia

Generalized Witten Genus and Vanishing Theorems

We construct a generalized Witten genus for spin$^c$ manifolds, which takes values in level 1 modular forms with integral Fourier expansion on a class of spin$^c$ manifolds called string$^c$ manifolds. We also construct a mod 2 analogue of the Witten genus for $8k+2$ dimensional spin manifolds. The Landweber-Stong type vanishing theorems are proven for the generalized Witten genus and the mod 2 Witten genus on string$^c$ and string (generalized) complete intersections in (product of) complex projective spaces respectively.Comment: 28 page