Moduli of vortices and Grassmann manifolds

We use the framework of Quot schemes to give a novel description of the moduli spaces of stable n-pairs, also interpreted as gauged vortices on a closed Riemann surface with target Mat(r x n, C), where n >= r. We then show that these moduli spaces embed canonically into certain Grassmann manifolds, and thus obtain natural Kaehler metrics of Fubini-Study type; these spaces are smooth at least in the local case r=n. For abelian local vortices we prove that, if a certain "quantization" condition is satisfied, the embedding can be chosen in such a way that the induced Fubini-Study structure realizes the Kaehler class of the usual L^2 metric of gauged vortices.Comment: 22 pages, LaTeX. Final version: last section removed, typos corrected, two references added; to appear in Commun. Math. Phy

The K\"ahler Potential of Abelian Higgs Vortices

We calculate the K\"ahler potential for the Samols metric on the moduli space of Abelian Higgs vortices on \mathbbm{R}^{2}, in two different ways. The first uses a scaling argument. The second is related to the Polyakov conjecture in Liouville field theory. The K\"ahler potential on the moduli space of vortices on \mathbbm{H}^{2} is also derived, and we are led to a geometrical reinterpretation of these vortices. Finally, we attempt to find the K\"ahler potential for vortices on \mathbbm{R}^{2} in a third way by relating the vortices to SU(2) Yang-Mills instantons on \mathbbm{R}^{2}\times S^{2}. This approach does not give the correct result, and we offer a possible explanation for this.Comment: 25 page

Rank two quadratic pairs and surface group representations

Let $X$ be a compact Riemann surface. A quadratic pair on $X$ consists of a holomorphic vector bundle with a quadratic form which takes values in fixed line bundle. We show that the moduli spaces of quadratic pairs of rank 2 are connected under some constraints on their topological invariants. As an application of our results we determine the connected components of the $\mathrm{SO}_0(2,3)$-character variety of $X$.Comment: 37 pages, 1 figur

Brauer group of moduli spaces of pairs

We show that the Brauer group of any moduli space of stable pairs with fixed determinant over a curve is zero.Comment: 12 pages. Final version, accepted in Communications in Algebr

Effectiveness of computer-based auditory training in improving the perception of noise-vocoded speech

Five experiments were designed to evaluate the effectiveness of “high-variability” lexical training in improving the ability of normal-hearing subjects to perceive noise-vocoded speech that had been spectrally shifted to simulate tonotopic misalignment. Two approaches to training were implemented. One training approach required subjects to recognize isolated words, while the other training approach required subjects to recognize words in sentences. Both approaches to training improved the ability to identify words in sentences. Improvements following a single session (lasting 1–2 h) of auditory training ranged between 7 and 12 %pts and were significantly larger than improvements following a visual control task that was matched with the auditory training task in terms of the response demands. An additional three sessions of word- and sentence-based training led to further improvements, with the average overall improvement ranging from 13 to 18 %pts. When a tonotopic misalignment of 3 mm rather than 6 mm was simulated, training with several talkers led to greater generalization to new talkers than training with a single talker. The results confirm that computer-based lexical training can help overcome the effects of spectral distortions in speech, and they suggest that training materials are most effective when several talkers are included

Maximal surface group representations in isometry groups of classical Hermitian symmetric spaces

Higgs bundles and non-abelian Hodge theory provide holomorphic methods with which to study the moduli spaces of surface group representations in a reductive Lie group G. In this paper we survey the case in which G is the isometry group of a classical Hermitian symmetric space of non-compact type. Using Morse theory on the moduli spaces of Higgs bundles, we compute the number of connected components of the moduli space of representations with maximal Toledo invariant.Comment: v2: added due credits to the work of Burger, Iozzi and Wienhard. v3: corrected count of connected components for G=SU(p,q) (p \neq q); added due credits to the work of Xia and Markman-Xia; minor corrections and clarifications. 31 page

Linguistic processing of accented speech across the lifespan.

In most of the world, people have regular exposure to multiple accents. Therefore, learning to quickly process accented speech is a prerequisite to successful communication. In this paper, we examine work on the perception of accented speech across the lifespan, from early infancy to late adulthood. Unfamiliar accents initially impair linguistic processing by infants, children, younger adults, and older adults, but listeners of all ages come to adapt to accented speech. Emergent research also goes beyond these perceptual abilities, by assessing links with production and the relative contributions of linguistic knowledge and general cognitive skills. We conclude by underlining points of convergence across ages, and the gaps left to face in future work

Topological Reduction of 4D SYM to 2D σ\sigma--Models

By considering a (partial) topological twisting of supersymmetric Yang-Mills compactified on a 2d space with `t Hooft magnetic flux turned on we obtain a supersymmetric $\sigma$-model in 2 dimensions. For N=2 SYM this maps Donaldson observables on products of two Riemann surfaces to quantum cohomology ring of moduli space of flat connections on a Riemann surface. For N=4 SYM it maps $S$-duality to $T$-duality for $\sigma$-models on moduli space of solutions to Hitchin equations.Comment: 30 pages, harvma

Bogomolny equations for vortices in the noncommutative torus

We derive Bogomolny-type equations for the Abelian Higgs model defined on the noncommutative torus and discuss its vortex like solutions. To this end, we carefully analyze how periodic boundary conditions have to be handled in noncommutative space and discussed how vortex solutions are constructed. We also consider the extension to an $U(2)\times U(1)$ model, a simplified prototype of the noncommutative standard model.Comment: 23 pages, no figure