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 - RodrÃguez 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 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
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 - 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 -