We use Coulomb branch indices of Argyres-Douglas theories on S1×L(k,1) to quantize moduli spaces H of wild/irregular Hitchin systems. In particular, we obtain formulae for the "wild Hitchin characters" -- the graded dimensions of the... more
We use Coulomb branch indices of Argyres-Douglas theories on S1×L(k,1) to quantize moduli spaces H of wild/irregular Hitchin systems. In particular, we obtain formulae for the "wild Hitchin characters" -- the graded dimensions of the Hilbert spaces from quantization -- for four infinite families of H, giving access to many interesting geometric and topological data of these moduli spaces. We observe that the wild Hitchin characters can always be written as a sum over fixed points in H under the U(1) Hitchin action, and a limit of them can be identified with matrix elements of the modular transform STkS in certain two-dimensional chiral algebras. Although naturally fitting into the geometric Langlands program, the appearance of chiral algebras, which was known previously to be associated with Schur operators but not Coulomb branch operators, is somewhat surprising.
The aim of this paper is to study the birational geometry of certain moduli spaces of abelian surfaces with some additional structures. In particular, we investigate moduli of abelian surfaces with a symmetric theta structure and an odd... more
The aim of this paper is to study the birational geometry of certain moduli spaces of abelian surfaces with some additional structures. In particular, we investigate moduli of abelian surfaces with a symmetric theta structure and an odd theta characteristic. More precisely, on one hand, for a (d1,d2)-polarized abelian surfaces, we study how the parity of d1 and d2 influence the relation between the datum of a canonical level structure and that of a symmetric theta structure. On the other, for certain values of d1 and d2, the datum of a theta characteristic, seen as a quadratic form on the points of 2-torsion induced by a symmetric line bundle, is necessary in order to well-define Theta-null maps. Finally we use these Theta-null maps and preceding work of other authors on the representations of the Heisenberg group to study the birational geometry and the Kodaira dimension these moduli spaces.
As one of the processor's ALU performance issues, the carry propagation during the addition operation limits the speed of arithmetic operation. This work aims to build an Efficient Hardware Design for an Adder based on Residual Numbering... more
As one of the processor's ALU performance issues, the carry propagation during the addition operation limits the speed of arithmetic operation. This work aims to build an Efficient Hardware Design for an Adder based on Residual Numbering System (RNS), with a pre-specified special set of moduli to simplify the implementation for proving the feasibility of its usage. Our design can be divided into three basic components: two conversion modules, and an addition module. The conversion modules here are based on a special set of moduli numbers to simplify the hardware implementation. In this work, we focus on forward conversion (conventional to RNS) leaving reverse converter {RNS to conventional} for future works. Depending on this notion, we implemented each component individually in VHDL and then to assemble these components with each other to build a whole RNS-Adder. Simulation results are very attractive in terms of critical path delay.
The framed little 2-discs operad is homotopy equivalent to the Kimura-Stasheff-Voronov cyclic operad of moduli spaces of genus zero stable curves with tangent rays at the marked points and nodes. We show that this cyclic operad is formal,... more
The framed little 2-discs operad is homotopy equivalent to the Kimura-Stasheff-Voronov cyclic operad of moduli spaces of genus zero stable curves with tangent rays at the marked points and nodes. We show that this cyclic operad is formal, meaning that its chains and its homology (the Batalin-Vilkovisky operad) are quasi-isomorphic cyclic operads. To prove this we introduce a new complex of graphs in which the differential is a combination of edge deletion and contraction, and we show that this complex resolves BV as a cyclic operad.
In this second part, we discretize the operadic and PROPic structures of the first part. We also introduce the notion of operadic correlation functions and use them in conjunction with operadic maps from the cell level to the discretized... more
In this second part, we discretize the operadic and PROPic structures of the first part. We also introduce the notion of operadic correlation functions and use them in conjunction with operadic maps from the cell level to the discretized objects to define the relevant actions.
We construct stable sheaves over K3 fibrations using a relative Fourier-Mukai transform which describes the sheaves in terms of spectral data similar to the construction for elliptic fibrations. On K3 fibered Calabi-Yau threefolds we show... more
We construct stable sheaves over K3 fibrations using a relative Fourier-Mukai transform which describes the sheaves in terms of spectral data similar to the construction for elliptic fibrations. On K3 fibered Calabi-Yau threefolds we show that the Fourier-Mukai transform induces an embedding ion of the relative Jacobian of spectral line bundles on spectral covers into the moduli space of sheaves of given invariants. This makes the moduli space of spectral sheaves to a generic torus fibration over the moduli space of curves of given arithmetic genus on the Calabi-Yau manifold.
