This paper gives a new way of constructing Landau-Ginzburg mirrors using deformation theory of Lagrangian immersions motivated by the works of Seidel, Strominger-Yau-Zaslow and Fukaya-Oh-Ohta-Ono. Moreover we construct a canonical functor from the Fukaya category to the mirror category of matrix factorizations. This functor derives homological mirror symmetry under some explicit assumptions. As an application, the construction is applied to spheres with three orbifold points to produce their quantum-corrected mirrors and derive homological mirror symmetry. Furthermore we discover an enumerative meaning of the (inverse) mirror map for elliptic curve quotients. Contents 1. Introduction 1 Acknowledgement 10 2. Algebraic construction of localized mirror functor 10 3. Immersed Lagrangian Floer theory and generalized SYZ construction 17 4. Geometric construction of localized mirror functor 23 5. Generalized SYZ for a finite-group quotient 27

The Geostationary Environment Monitoring Spectrometer (GEMS) is scheduled for launch in February 2020 to monitor air quality (AQ) at an unprecedented spatial and temporal resolution from a geostationary Earth orbit (GEO) for the first time. With the development of UV–visible spectrometers at sub-nm spectral resolution and sophisticated retrieval algorithms, estimates of the column amounts of atmospheric pollutants (O3, NO2, SO2, HCHO, CHOCHO, and aerosols) can be obtained. To date, all the UV–visible satellite missions monitoring air quality have been in low Earth orbit (LEO), allowing one to two observations per day. With UV–visible instruments on GEO platforms, the diurnal variations of these pollutants can now be determined. Details of the GEMS mission are presented, including instrumentation, scientific algorithms, predicted performance, and applications for air quality forecasts through data assimilation. GEMS will be on board the Geostationary Korea Multi-Purpose Satellite 2 (GEO-KOMPSAT-2) satellite series, which also hosts the Advanced Meteorological Imager (AMI) and Geostationary Ocean Color Imager 2 (GOCI-2). These three instruments will provide synergistic science products to better understand air quality, meteorology, the long-range transport of air pollutants, emission source distributions, and chemical processes. Faster sampling rates at higher spatial resolution will increase the probability of finding cloud-free pixels, leading to more observations of aerosols and trace gases than is possible from LEO. GEMS will be joined by NASA’s Tropospheric Emissions: Monitoring of Pollution (TEMPO) and ESA’s Sentinel-4 to form a GEO AQ satellite constellation in early 2020s, coordinated by the Committee on Earth Observation Satellites (CEOS).

Abstract. The Geostationary Ocean Color Imager (GOCI) onboard the Communication, Ocean, and Meteorological Satellite (COMS) is the first multi-channel ocean color imager in geostationary orbit. Hourly GOCI top-of-atmosphere radiance has been available for the retrieval of aerosol optical properties over East Asia since March 2011. This study presents improvements made to the GOCI Yonsei Aerosol Retrieval (YAER) algorithm together with validation results during the Distributed Regional Aerosol Gridded Observation Networks -Northeast Asia 2012 campaign (DRAGON-NE Asia 2012 campaign). The evaluation during the spring season over East Asia is important because of high aerosol concentrations and diverse types of Asian dust and haze. Optical properties of aerosol are retrieved from the GOCI YAER algorithm including aerosol optical depth (AOD) at 550 nm, fine-mode fraction (FMF) at 550 nm, single-scattering albedo (SSA) at 440 nm, Ångström exponent (AE) between 440 and 860 nm, and aerosol type. The aerosol models are created based on a global analysis of the Aerosol Robotic Networks (AERONET) inversion data, and covers a broad range of size distribution and absorptivity, including nonspherical dust properties. The Cox-Munk ocean bidirectional reflectance distribution function (BRDF) model is used over ocean, and an improved minimum reflectance technique is used over land. Because turbid water is persistent over the Yellow Sea, the land algorithm is used for such cases. The aerosol products are evaluated against AERONET observations and MODIS Collection 6 aerosol products retrieved from Dark Target (DT) and Deep Blue (DB) algorithms during the DRAGON-NE Asia 2012 campaign conducted from March to May 2012. Comparison of AOD from GOCI and AERONET resulted in a Pearson correlation coefficient of 0.881 and a linear regression equation with GOCI AOD = 1.083 × AERONET AOD − 0.042. The correlation between GOCI and MODIS AODs is higher over ocean than land. GOCI AOD shows better agreement with MODIS DB than MODIS DT. The other GOCI YAER products (AE, FMF, and SSA) show lower correlation with AERONET than AOD, but still show some skills for qualitative use.

Fixing a weakly unobstructed Lagrangian torus in a symplectic manifold X, we define a holomorphic function W known as the Floer potential. We construct a canonical A ∞ -functor from the Fukaya category of X to the category of matrix factorizations of W . It provides a unified way to construct matrix factorizations from Lagrangian Floer theory. The technique is applied to toric Fano manifolds to transform Lagrangian branes to matrix factorizations. Using the method, we also obtain an explicit expression of the matrix factorization mirror to the real locus of the complex projective space. arXiv:1406.4597v3 [math.SG] 30 Sep 2016 1≤j≤n z δ(a j ,−1) j and m pq = T k/2 1≤j≤n z δ(a j ,1) j if i = 0, m qp = T k/2 z i and m pq = T k/2 if i = 0. δ(a, b) = 1 when a = b and zero otherwise. (2) m qp = m pq = 0 otherwise.