We relate the notion of dimension expanders to quiver representations and their general subrepresentations, and use this relation to establish sharp existence results.

Markus Reineke

We verify the Mukai conjecture for Fano quiver moduli spaces associated to dimension vectors in the interior of the fundamental domain.

Markus Reineke

The energetic landscape at the interface between electron donating and accepting molecular materials favors efficient conversion of intermolecular charge-transfer states (CTS) into free charge carriers in high-performance organic solar cells. Here, we elucidate how interfacial energetics, charge generation and radiative recombination are affected by structural ordering. We experimentally determine the CTS binding energy of a series of model, small molecule donor-acceptor blends, where the used acceptors (B2PYMPM, B3PYMPM and B4PYMPM) differ only in the nitrogen position of their lateral pyridine rings. We find that the formation of an ordered, face-on molecular packing in B4PYMPM is beneficial to efficient, field-independent charge separation, leading to fill factors over 70% in photovoltaic devices. This is rationalized by a comprehensive computational protocol showing that, compared to the more amorphous and isotropically oriented B2PYMPM, the higher order of the B4PYMPM molecules provides more delocalized CTS. Furthermore, we find no correlation between the quantum efficiency of radiative free charge carrier recombination and the bound or unbound nature of the CTS. This work highlights the importance of structural ordering at donor-acceptor interfaces for efficient free carrier generation and shows that more ordering and less bound CT states do not preclude efficient radiative recombination.

Xiangkun Jia Lorenzo Soprani Giacomo Londi Seyed Mehrdad Hosseini Felix Talnack Stefan Mannsfeld Safa Shoaee Dieter Neher Sebastian Reineke Luca Muccioli Gabriele D'Avino Koen Vandewal David Beljonne Donato Spoltore X. Jia S. Reineke L. Soprani L. Muccioli G. Londi D. Beljonne S. M. Hosseini S. Shoaee D. Neher F. Talnack S. Mannsfeld G. D'Avino K. Vandewal D. Spoltore

The theory of cluster algebras of S. Fomin and A. Zelevinsky has assigned a fan to each Dynkin diagram. Then A. Buan, R. Marsh, M. Reineke, I. Reiten and G. Todorov have generalized this construction using arbitrary quivers on Dynkin diagrams. In the special case of the unioriented quiver of type A, we describe the cohomology ring of the toric variety associated to this fan. A natural base is obtained and an explicit rule is given for the product of any two generators.

Frederic Chapoton

We present a particular connection between classical partition combinatorics and the theory of quiver representations. Specifically, we give a bijective proof of an analogue of A. L. Cauchy's Durfee square identity to multipartitions. We then use this result to give a new proof of M. Reineke's identity in the case of quivers $Q$ of Dynkin type $A$ of arbitrary orientation. Our identity is stated in terms of the lacing diagrams of S. Abeasis - A. Del Fra, which parameterize orbits of the representation space of $Q$ for a fixed dimension vector.

Richard Rimanyi Anna Weigandt Alexander Yong

Most materials recently developed for room temperature phosphorescence (RTP) lack of practical relevance due to their inconvenient crystalline morphology. Using amorphous material systems instead, programmable luminescent tags (PLTs) based on organic biluminescent emitter molecules with easy processing and smooth sample shapes were presented recently. Here, the effective quenching of the emitters RTP by molecular oxygen (O2) and the consumption of the excited singlet O2 through a chemical reaction represent the central features. With customized activation schemes, high resolution content can be written and later erased multiple times into such films, providing a versatile yet simple photonic platform for information storage. However, two important limitations remain: (i) The immutable fluorescence of the emitters outshines the phosphorescent patterns by roughly one order of magnitude, allowing read-out of the PLTs only after the excitation source is turned off. (ii) The programming of these systems is a rather slow process, where lowest reported activation times are still > 8 s. Here, a material-focused approach to PLTs with fast activation times of 120 +/- 20 ms and high-contrast under continuous-wave (cw) illumination is demonstrated, leading to accelerated programming on industry relevant time scales and a simplified readout process both by eye and low cost cameras.

Max Gmelch Tim Achenbach Ausra Tomkeviciene Sebastian Reineke

It is shown that rational points over finite fields of moduli spaces of stable quiver representations are counted by polynomials with integer coefficients. These polynomials are constructed recursively using an identity in the Hall algebra of a quiver.

Markus Reineke

We show that the generic Hall algebra of nilpotent representations of an oriented cycle specialised at $q=0$ is isomorphic to the generic extension monoid in the sense of Reineke. This continues the work of Reineke.

Stefan Wolf

We derive a combinatorial formula for quantized Donaldson-Thomas invariants of the m-loop quiver. Our main tools are the combinatorics of noncommutative Hilbert schemes and a degenerate version of the Cohomological Hall algebra of this quiver.

Markus Reineke

We construct small desingularizations of moduli spaces of semistable quiver representations for indivisible dimension vectors using deformations of stabilites and a dimension estimate for nullcones. We apply this construction to several classes of GIT quotients.

Markus Reineke