15150270
Perverse coherent sheaves on blow-up. I. a quiver description
This is the first of two papers studying moduli spaces of a certain class of coherent sheaves, which we call {\it stable perverse coherent sheaves}, on the blowup of a projective surface. They are used to relate usual moduli spaces of stable sheaves on a surface and its blowup. In this first part, we give a quiver (or ADHM) description of moduli spaces for framed perverse coherent sheaves on the blowup of the projective plane.
14508627
PERVERSE COHERENT SHEAVES ON BLOW-UP. II. WALL-CROSSING AND BETTI NUMBERS FORMULA
This is the second of series of papers studyig moduli spaces of a certain class of coherent sheaves, which we call stable perverse coherent sheaves, on the blow-up p: b X → X of a projective surface X at a point 0. The followings are main results of this paper: a) We describe the wall-crossing between moduli spaces caused by twisting of the line bundle O(C) associated with the exceptional divisor C. b) We give the formula for virtual Hodge numbers of moduli spaces of stable perverse coherent sheaves. Moreover we also give proofs of the followings which we observed in a special case in (24): c) The moduli space of stable perverse coherent sheaves is isomorphic to the usual moduli space of stable coherent sheaves on the original surface if the first Chern class is orthogonal to (C). d) The moduli space becomes isomorphic to the usual moduli space of stable coherent sheaves on the blow-up after twisting by O(−mC) for sufficiently largem. Therefore usual moduli spaces of stable sheaves on the blow-up and the original surfaces are connected via wall-crossings.
8936511
Instantons and affine Lie algebras
Various constructions of the affine Lie algebra action on the moduli space of instantons on 4-manifolds are discussed. The analogy between the local-global principle and the role of mass is also explained. The detailed proofs are given in separated papers [16,17].
10853977
Lectures on instanton counting
These notes have two parts. The first is a study of Nekrasov's deformed partition functions $Z(\ve_1,\ve_2,\vec{a};\q,\vec{\tau})$ of N=2 SUSY Yang-Mills theories, which are generating functions of the integration in the equivariant cohomology over the moduli spaces of instantons on $\mathbb R^4$. The second is review of geometry of the Seiberg-Witten curves and the geometric engineering of the gauge theory, which are physical backgrounds of Nekrasov's partition functions. 
The first part is continuation of math.AG/0306198, where we identified the Seiberg-Witten prepotential with $Z(0,0,\vec{a};\q,0)$. 
We put higher Casimir operators to the partition function and clarify their relation to the Seiberg-Witten $u$-plane. We also determine the coefficients of $\ve_1\ve_2$ and $(\ve_1^2+\ve_2^2)/3$ (the genus 1 part) of the partition function, which coincide with two measure factors $A$, $B$ appeared in the $u$-plane integral. 
The proof is based on the blowup equation which we derived in the previous paper.
119132882
Refined Chern-Simons theory and Hilbert schemes of points on the plane
Dedicated to Professor Igor Frenkel on the occasion of his sixtieth birthday Abstract. Aganagic and Shakirov propose a refinement of the SU(N) Chern- Simons theory for links in three manifolds with S 1 -symmetry, such as torus knots in S 3 , based on deformation of the S and T matrices, originally found by Kirillov and Cherednik. We relate the large N limit of the S matrix to the Hilbert schemes of points on the affine plane. As an application, we find an explicit formula for the Euler characteristics of the universal sheaf, applied arbitrary Schur functor.
119569923
Instanton counting on blowup. II. K-theoretic partition
function
AbstractWe study Nekrasov's deformed partition function $Z(\varepsilon_1,\varepsilon_2,\vec{a};\mathfrak q,\boldsymbol\beta)$ of 5-dimensional supersymmetric
Yang-Mills theory compactified on a circle. Mathematically it is the
generating function of the characters of the coordinate rings of the moduli
spaces of instantons on $\mathbb R^4$. We show that it satisfies a system of
functional equations, called blowup equations, whose solution is unique.
As applications, we prove (a) $F(\varepsilon_1,\varepsilon_2,\vec{a};\mathfrak q,\boldsymbol\beta) = \varepsilon_1\varepsilon_2 \log Z(\varepsilon_1,\varepsilon_2,\vec{a};\mathfrak q,\boldsymbol\beta)$ is regular at $\varepsilon_1 = \varepsilon_2 = 0$ (a part of Nekrasov's conjecture), and (b) the genus $1$ parts, which are first several Taylor coefficients of $F(\varepsilon_1,\varepsilon_2,\vec{a};\mathfrak q,\boldsymbol\beta)$, are written explicitly in terms of $\tau = d^2 F(0,0,\vec{a};\mathfrak q,\boldsymbol\beta)/da^2$ in rank $2$ case.
56166210
Fermionic T-duality and Morita equivalence
In this paper we investigate the relationship between the so-called fermionic T-duality and the Morita equivalence of noncommutative supertori. We first get an action satisfying the BRST invariance under nonvanishing constant R-R and NS-NS backgrounds in the hybrid formalism. We investigate the effect of bosonic T-duality transformation together with fermionic T-duality transformation in this background and look for the resultant symmetry of transformations. We find that the duality transformations correspond to Morita equivalence of noncommutative supertori. In particular, we obtain the symmetry group $ {\text{SO}}\left( {2,2,\mathcal{V}_\mathbb{Z}^0} \right) $ in two dimensions, where $ \mathcal{V}_\mathbb{Z}^0 $ denotes Grassmann even number whose body part belongs to $ \mathbb{Z} $.
15189596
Numerical tests of the Kugo-Ojima color confinement criterion
The Kugo-Ojima color confinement criterion, which is based on the BRST symmetry of QCD is numerically tested by the lattice Landau gauge simulation. We first discuss the BRST symmetry on the lattice and the Gribov copy problem. The horizon function defined by Zwanziger based on the U-linear definition of the gauge field and that based on log U are compared. The parameter u which is expected to be $-1\delta^a_b$ in the continuum theory was found to be $-0.7\delta^a_b$ in the strong coupling region. There are about 20% difference between the two horizon functions, but in the weak coupling region, the expectation value of the horizon function is suggested to be zero or negative.
19609772
Monte Carlo Simulator and Ancillary Response Generator of Suzaku XRT/XIS System for Spatially Extended Source Analysis
We have developed a framework for the Monte-Carlo simulation of the X-Ray Telescopes (XRT) and the X-ray Imaging Spectrometers (XIS) onboard Suzaku, mainly for the scientific analysis of spatially and spectroscopically complex celestial sources. A photon-by-photon instrumental simulator is built on the ANL platform, which has been successfully used in ASCA data analysis. The simulator has a modular structure, in which the XRT simulation is based on a ray-tracing library, while the XIS simulation utilizes a spectral "Redistribution Matrix File" (RMF), generated separately by other tools. Instrumental characteristics and calibration results, e.g., XRT geometry, reflectivity, mutual alignments, thermal shield transmission, build-up of the contamination on the XIS optical blocking filters (OBF), are incorporated as completely as possible. Most of this information is available in the form of the FITS (Flexible Image Transport System) files in the standard calibration database (CALDB). This simulator can also be utilized to generate an "Ancillary Response File" (ARF), which describes the XRT response and the amount of OBF contamination. The ARF is dependent on the spatial distribution of the celestial target and the photon accumulation region on the detector, as well as observing conditions such as the observation date and satellite attitude. We describe principles of the simulator and the ARF generator, and demonstrate their performance in comparison with in-flight data.
37574050
Development of a built-in analog-to-digital converter for a X-ray astronomy detector with the SOI CMOS technology
We have been developing a novel X-ray astronomy detector combined with a CMOS readout circuit on a monolithic chip using the SOI CMOS technology. As a part of the development, we have fabricated a prototype of an analog-to-digital converter (ADC) component aiming for building it into the detector itself. We used the OKI 0.2 µm CMOS fully depleted Silicon-On-Insulator process. The prototype ADC consists of a pre-amplifier and two delta-sigma (ΔΣ) modulators. The two modulators process a series of analog input signal alternately to improve the readout speed (∼100 kHz), and output the digital bit-stream signal. An external Field Programmable Gate Array works as a decimation filter and converts the bit-stream signal into a 12-bit digital signal. We evaluated the prototype ADC and obtained the first results as follows: the power consumption of 40 mW, the equivalent input noise of ∼80 µV rms, and the integral non-linearity of less than 0.8%.
18937326
The Landau gauge lattice QCD simulation and the gluon propagator
Abstract The gluon propagator in the Landau gauge lattice QCD simulation is measured. The data suggests the confinement mechanism of the Gribov-Zwanziger theory.