Topological properties of punctual Hilbert schemes of almost-complex fourfolds (I)

In this article, we study topological properties of Voisin's punctual Hilbert schemes of an almost-complex fourfold $X$. In this setting, we compute their Betti numbers and construct Nakajima operators. We also define tautological bundles associated with any complex bundle on $X$, which are shown to be canonical in $K$-theory

Google Earth Engine Open-Source Code for Land Surface Temperature Estimation from the Landsat Series

Land Surface Temperature (LST) is increasingly important for various studies assessing land surface conditions, e.g., studies of urban climate, evapotranspiration, and vegetation stress. The Landsat series of satellites have the potential to provide LST estimates at a high spatial resolution, which is particularly appropriate for local or small-scale studies. Numerous studies have proposed LST retrieval algorithms for the Landsat series, and some datasets are available online. However, those datasets generally require the users to be able to handle large volumes of data. Google Earth Engine (GEE) is an online platform created to allow remote sensing users to easily perform big data analyses without increasing the demand for local computing resources. However, high spatial resolution LST datasets are currently not available in GEE. Here we provide a code repository that allows computing LSTs from Landsat 4, 5, 7, and 8 within GEE. The code may be used freely by users for computing Landsat LST as part of any analysis within GEE

Topological quantum field theory and four-manifolds

I review some recent results on four-manifold invariants which have been obtained in the context of topological quantum field theory. I focus on three different aspects: (a) the computation of correlation functions, which give explicit results for the Donaldson invariants of non-simply connected manifolds, and for generalizations of these invariants to the gauge group SU(N); (b) compactifications to lower dimensions, and relations with three-manifold topology and with intersection theory on the moduli space of flat connections on Riemann surfaces; (c) four-dimensional theories with critical behavior, which give some remarkable constraints on Seiberg-Witten invariants and new results on the geography of four-manifolds.Comment: 10 pages, LaTeX. Talk given at the 3rd ECM, Barcelona, July 2000; references adde

Vertex Operators, Grassmannians, and Hilbert Schemes

We describe a well-known collection of vertex operators on the infinite wedge representation as a limit of geometric correspondences on the equivariant cohomology groups of a finite-dimensional approximation of the Sato grassmannian, by cutoffs in high and low degrees. We prove that locality, the boson-fermion correspondence, and intertwining relations with the Virasoro algebra are limits of the localization expression for the composition of these operators. We then show that these operators are, almost by definition, the Hilbert scheme vertex operators defined by Okounkov and the author in \cite{CO} when the surface is $\mathbb{C}^2$ with the torus action $z\cdot (x,y) = (zx,z^{-1}y)$.Comment: 20 pages, 0 figure

An Approach to N=4{\cal N}=4 ADE Gauge Theory on K3

We propose a recipe for determination of the partition function of ${\cal N}=4$ $ADE$ gauge theory on $K3$ by generalizing our previous results of the SU(N) case. The resulting partition function satisfies Montonen-Olive duality for $ADE$ gauge group.Comment: 28 pages, Latex, enlarged published versio