Following the idea of [Far16], we develop the foundations for the geometric Langlands program on the Fargues-Fontaine curve. In particular, we define a category of-adic sheaves on the stack BunG of G-bundles on the Fargues-Fontaine curve, prove a geometric Satake equivalence over the Fargues-Fontaine curve, and study the stack of L-parameters. As applications, we prove finiteness results for the cohomology of local Shimura varieties and general moduli spaces of local shtukas, and define L-parameters associated with irreducible smooth representations of G(E), a map from the spectral Bernstein center to the Bernstein center, and the spectral action of the category of perfect complexes on the stack of L-parameters on the category of-adic sheaves on BunG.

Geometrization of the local Langlands correspondence

A Real-Time GARCH-MIDAS model

A new decomposition-integrated air quality index prediction model

Purpose Stock markets are essential for households for wealth creation and for firms for raising financial resources for capacity expansion and growth. Market participants, therefore, need an understanding of stock price movements. Stock market indices and individual stock prices reflect the macroeconomic environment and are subject to external and internal shocks. It is important to disentangle the impact of macroeconomic shocks, market uncertainty and speculative elements and examine them separately for prediction. To aid households, firms and policymakers, the paper proposes a granular decomposition-based prediction framework for different time periods in India, characterized by different market states with varying degrees of uncertainty. Design/methodology/approach Ensemble empirical mode decomposition (EEMD) and fuzzy-C-means (FCM) clustering algorithms are used to decompose stock prices into short, medium and long-run components. Multiverse optimization (MVO) is used to combine extreme gradient boosting regression (XGBR), Facebook Prophet and support vector regression (SVR) for forecasting. Application of explainable artificial intelligence (XAI) helps identify feature contributions. Findings We find that historic volatility, expected market uncertainty, oscillators and macroeconomic variables explain different components of stock prices and their impact varies with the industry and the market state. The proposed framework yields efficient predictions even during the COVID-19 pandemic and the Russia–Ukraine war period. Efficiency measures indicate the robustness of the approach. Findings suggest that large-cap stocks are relatively more predictable. Research limitations/implications The paper is on Indian stock markets. Future work will extend it to other stock markets and other financial products. Practical implications The proposed methodology will be of practical use for traders, fund managers and financial advisors. Policymakers may find it useful for assessing the impact of macroeconomic shocks and reducing market volatility. Originality/value Development of a granular decomposition-based forecasting framework and separating the effects of explanatory variables in different time scales and macroeconomic periods. 

Macroeconomic shocks, market uncertainty and speculative bubbles: a decomposition-based predictive model of Indian stock markets

In this paper, we give a geometric construction of the Jacquet-Langlands transfer for automorphic forms of higher weights by studying the geometry of the mod $p$ fibres of different Hodge type Shimura varieties which satisfy a mild assumption and the cohomological correspondences between them.

A Geometric Jacquet-Langlands Transfer for automorphic forms of higher weights

Let $k$ be an algebraically closed field of characteristic $p$. Denote by $W(k)$ the ring of Witt vectors of $k$. Let $F$ denote a totally ramified finite extension of $W(k)[1/p]$ and $\mathcal{O}$ the its ring of integers. For a connected reductive group scheme $G$ over $\mathcal{O}$, we study the category $P_{L^+G}(Gr_G,\Lambda)$ of $L^+G$-equivariant perverse sheaves in $\Lambda$-coefficient on the affine Grassmannian $Gr_G$ where $\Lambda=\mathbb{Z}_{\ell}$ and $\mathbb{F}_{\ell}$ and prove it is equivalent as a tensor category to the category of finitely generated $\Lambda$-representations of the Langlands dual group of $G$.

The integral geometric Satake equivalence in mixed characteristic.

Which component of air quality index drives stock price volatility in China: a decomposition-based forecasting method

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The integral geometric Satake equivalence in mixed characteristic.

Which component of air quality index drives stock price volatility in China: a decomposition-based forecasting method