Szilárd Szabó

Algebraic Nahm transform for parabolic Higgs bundles on P 1

We formulate the Nahm transform in the context of parabolic Higgs bundles on P^1 and extend its scope in completely algebraic terms. This transform requires parabolic Higgs bundles to satisfy an admissibility condition and allows Higgs fields to have poles of arbitrary order and arbitrary behavior. Our methods are constructive in nature and examples are provided. The extended Nahm transform is established as an algebraic duality between moduli spaces of parabolic Higgs bundles. The guiding principle behind the construction is to investigate the behavior of spectral data near the poles of Higgs fields.

Harmonic Functions and Instanton Moduli Spaces on the Multi-Taub–NUT Space

Explicit construction of the basic SU(2) anti-instantons over the multi-Taub–NUT geometry via the classical conformal rescaling method is exhibited. These anti-instantons satisfy the so-called weak holonomy condition at infinity with respect to the trivial flat connection and decay rapidly. The resulting unit energy anti-instantons have trivial holonomy at infinity.We also fully describe their unframed moduli space and find that it is a five dimensional space admitting a singular disk-fibration over

The Plancherel Theorem for Fourier–Laplace–Nahm Transform for Connections on the Projective Line

{\mathbb{R}^3}

Two-dimensional moduli spaces of rank 2 Higgs bundles over CP1 with one irregular singular point

.On the way, we work out in detail the twistor space of the multi-Taub–NUT geometry together with its real structure and transform our anti-instantons into holomorphic vector bundles over the twistor space. In this picture we are able to demonstrate that our construction is complete in the sense that we have constructed a full connected component of the moduli space of solutions of the above type.We also prove that anti-instantons with arbitrary high integer energy exist on the multi-Taub–NUT space.

Two-dimensional moduli spaces of irregular Higgs bundles

Working memory (WM) is thought to have a fixed and limited capacity. However, the origins of these capacity limitations are debated, and generally attributed to active, attentional processes. Here, we show that the existence of interference among items in memory mathematically guarantees fixed and limited capacity limits under very general conditions, irrespective of any processing assumptions. Assuming that interference (a) increases with the number of interfering items and (b) brings memory performance to chance levels for large numbers of interfering items, capacity limits are a simple function of the relative influence of memorization and interference. In contrast, we show that time-based memory limitations do not lead to fixed memory capacity limitations that are independent of the timing properties of an experiment. We show that interference can mimic both slot-like and continuous resource-like memory limitations, suggesting that these types of memory performance might not be as different as commonly believed. We speculate that slot-like WM limitations might arise from crowding-like phenomena in memory when participants have to retrieve items. Further, based on earlier research on parallel attention and enumeration, we suggest that crowding-like phenomena might be a common reason for the 3 major cognitive capacity limitations. As suggested by Miller (1956) and Cowan (2001), these capacity limitations might arise because of a common reason, even though they likely rely on distinct processes.

Hitchin fibrations on moduli of irregular Higgs bundles and motivic wall-crossing

We prove that the Fourier–Laplace–Nahm transform for connections with finitely many logarithmic singularities and a double pole at infinity on the projective line, all with semi-simple singular parts, is a hyper-Kähler isometry.

Nahm transform and parabolic minimal Laplace transform

Abstract We extend our earlier construction of Nahm transformation for parabolic Higgs bundles on the projective line to solutions with not necessarily semisimple residues and show that it determines a holomorphic mapping on corresponding moduli spaces. The construction relies on suitable elementary modifications of the logarithmic Dolbeault complex.