TY - JOUR AB - We give a cohomological interpretation of both the Kac polynomial and the refined Donaldson-Thomas-invariants of quivers. This interpretation yields a proof of a conjecture of Kac from 1982 and gives a new perspective on recent work of Kontsevich-Soibelman. Thisis achieved by computing, via an arithmetic Fourier transform, the dimensions of the isotypical components of the cohomology of associated Nakajima quiver varieties under the action of a Weyl group. The generating function of the corresponding Poincare polynomials is an extension of Hua's formula for Kac polynomials of quivers involving Hall-Littlewood symmetric functions. The resulting formulae contain a wide range of information on the geometry of the quiver varieties. AU - Tamas Hausel AU - Letellier, Emmanuel AU - Rodríguez Villegas, Fernando ID - 1442 IS - 3 JF - Annals of Mathematics TI - Positivity for Kac polynomials and DT-invariants of quivers VL - 177 ER - TY - CHAP AB - Here we survey several results and conjectures on the cohomology of the total space of the Hitchin system: the moduli space of semi-stable rank n and degree d Higgs bundles on a complex algebraic curve C. The picture emerging is a dynamic mixture of ideas originating in theoretical physics such as gauge theory and mirror symmetry, Weil conjectures in arithmetic algebraic geometry, representation theory of finite groups of Lie type and Langlands duality in number theory. AU - Tamas Hausel ID - 1443 T2 - Handbook of Moduli: Volume II TI - Global topology of the Hitchin system VL - 25 ER - TY - JOUR AB - We study connections between the topology of generic character varieties of fundamental groups of punctured Riemann surfaces, Macdonald polynomials, quiver representations, Hilbert schemes on Cx × Cx, modular forms and multiplicities in tensor products of irreducible characters of finite general linear groups. AU - Tamas Hausel AU - Letellier, Emmanuel AU - Rodríguez Villegas, Fernando ID - 1469 JF - Advances in Mathematics TI - Arithmetic harmonic analysis on character and quiver varieties II VL - 234 ER - TY - JOUR AB - We show that a natural isomorphism between the rational cohomology groups of the two zero-dimensional Hilbert schemes of n-points of two surfaces, the affine plane minus the axes and the cotangent bundle of an elliptic curve, exchanges the weight filtration on the first set of cohomology groups with the perverse Leray filtration associated with a natural fibration on the second set of cohomology groups. We discuss some associated hard Lefschetz phenomena. AU - De Cataldo, Mark A AU - Tamas Hausel AU - Migliorini, Luca ID - 1470 JF - Journal of Singularities TI - Exchange between perverse and weight filtration for the Hilbert schemes of points of two surfaces VL - 7 ER - TY - JOUR AU - Aceto, Luca AU - Henzinger, Monika H AU - Sgall, Jiří ID - 11758 IS - 1 JF - Information and Computation SN - 0890-5401 TI - 38th International Colloquium on Automata, Languages and Programming VL - 222 ER - TY - JOUR AB - The development of a functional tissue requires coordination of the amplification of progenitors and their differentiation into specific cell types. The molecular basis for this coordination during myotome ontogeny is not well understood. Dermomytome progenitors that colonize the myotome first acquire myocyte identity and subsequently proliferate as Pax7-expressing progenitors before undergoing terminal differentiation. We show that the dynamics of sonic hedgehog (Shh) signaling is crucial for this transition in both avian and mouse embryos. Initially, Shh ligand emanating from notochord/floor plate reaches the dermomyotome, where it both maintains the proliferation of dermomyotome cells and promotes myogenic differentiation of progenitors that colonized the myotome. Interfering with Shh signaling at this stage produces small myotomes and accumulation of Pax7-expressing progenitors. An in vivo reporter of Shh activity combined with mouse genetics revealed the existence of both activator and repressor Shh activities operating on distinct subsets of cells during the epaxial myotomal maturation. In contrast to observations in mice, in avians Shh promotes the differentiation of both epaxial and hypaxial myotome domains. Subsequently, myogenic progenitors become refractory to Shh; this is likely to occur at the level of, or upstream of, smoothened signaling. The end of responsiveness to Shh coincides with, and is thus likely to enable, the transition into the growth phase of the myotome. AU - Kahane, Nitza AU - Ribes, Vanessa AU - Anna Kicheva AU - Briscoe, James AU - Kalcheim, Chaya ID - 1726 IS - 8 JF - Development TI - The transition from differentiation to growth during dermomyotome-derived myogenesis depends on temporally restricted hedgehog signaling VL - 140 ER - TY - JOUR AB - Cells at different positions in a developing tissue receive different concentrations of signaling molecules, called morphogens, and this influences their cell fate. Morphogen concentration gradients have been proposed to control patterning as well as growth in many developing tissues. Some outstanding questions about tissue patterning by morphogen gradients are the following: What are the mechanisms that regulate gradient formation and shape? Is the positional information encoded in the gradient sufficiently precise to determine the positions of target gene domain boundaries? What are the temporal dynamics of gradients and how do they relate to patterning and growth? These questions are inherently quantitative in nature and addressing them requires measuring morphogen concentrations in cells, levels of downstream signaling activity, and kinetics of morphogen transport. Here we first present methods for quantifying morphogen gradient shape in which the measurements can be calibrated to reflect actual morphogen concentrations. We then discuss using fluorescence recovery after photobleaching to study the kinetics of morphogen transport at the tissue level. Finally, we present particle tracking as a method to study morphogen intracellular trafficking. AU - Anna Kicheva AU - Holtzer, Laurent AU - Wartlick, Ortrud AU - Schmidt, Thomas S AU - González-Gaitán, Marcos A ID - 1727 IS - 5 JF - Cold Spring Harbor Protocols TI - Quantitative imaging of morphogen gradients in drosophila imaginal discs VL - 8 ER - TY - JOUR AB - We report on hole g-factor measurements in three terminal SiGe self-assembled quantum dot devices with a top gate electrode positioned very close to the nanostructure. Measurements of both the perpendicular as well as the parallel g-factor reveal significant changes for a small modulation of the top gate voltage. From the observed modulations, we estimate that, for realistic experimental conditions, hole spins can be electrically manipulated with Rabi frequencies in the order of 100 MHz. This work emphasises the potential of hole-based nano-devices for efficient spin manipulation by means of the g-tensor modulation technique. AU - Ares, Natalia AU - Georgios Katsaros AU - Golovach, Vitaly N AU - Zhang, Jianjun AU - Prager, Aaron A AU - Glazman, Leonid I AU - Schmidt, Oliver G AU - De Franceschi, Silvano ID - 1760 IS - 26 JF - Applied Physics Letters TI - SiGe quantum dots for fast hole spin Rabi oscillations VL - 103 ER - TY - JOUR AB - We report an electric-field-induced giant modulation of the hole g factor in SiGe nanocrystals. The observed effect is ascribed to a so-far overlooked contribution to the g factor that stems from the mixing between heavy- and light-hole wave functions. We show that the relative displacement between the confined heavy- and light-hole states, occurring upon application of the electric field, alters their mixing strength leading to a strong nonmonotonic modulation of the g factor. AU - Ares, Natalia AU - Golovach, Vitaly N AU - Georgios Katsaros AU - Stoffel, Mathieu AU - Fournel, Frank AU - Glazman, Leonid I AU - Schmidt, Oliver G AU - De Franceschi, Silvano ID - 1759 IS - 4 JF - Physical Review Letters TI - Nature of tunable hole g factors in quantum dots VL - 110 ER - TY - JOUR AB - The geometric aspects of quantum mechanics are emphasized most prominently by the concept of geometric phases, which are acquired whenever a quantum system evolves along a path in Hilbert space, that is, the space of quantum states of the system. The geometric phase is determined only by the shape of this path and is, in its simplest form, a real number. However, if the system has degenerate energy levels, then matrix-valued geometric state transformations, known as non-Abelian holonomies-the effect of which depends on the order of two consecutive paths-can be obtained. They are important, for example, for the creation of synthetic gauge fields in cold atomic gases or the description of non-Abelian anyon statistics. Moreover, there are proposals to exploit non-Abelian holonomic gates for the purposes of noise-resilient quantum computation. In contrast to Abelian geometric operations, non-Abelian ones have been observed only in nuclear quadrupole resonance experiments with a large number of spins, and without full characterization of the geometric process and its non-commutative nature. Here we realize non-Abelian non-adiabatic holonomic quantum operations on a single, superconducting, artificial three-level atom by applying a well-controlled, two-tone microwave drive. Using quantum process tomography, we determine fidelities of the resulting non-commuting gates that exceed 95 per cent. We show that two different quantum gates, originating from two distinct paths in Hilbert space, yield non-equivalent transformations when applied in different orders. This provides evidence for the non-Abelian character of the implemented holonomic quantum operations. In combination with a non-trivial two-quantum-bit gate, our method suggests a way to universal holonomic quantum computing. AU - Abdumalikov, Abdufarrukh A AU - Johannes Fink AU - Juliusson, K AU - Pechal, M AU - Berger, Stefan T AU - Wallraff, Andreas AU - Filipp, Stefan ID - 1785 IS - 7446 JF - Nature TI - Experimental realization of non-Abelian non-adiabatic geometric gates VL - 496 ER -