@inproceedings{20054, author = {Horta, Sharona}, booktitle = {Proceedings of the MATSUS Spring 2025 Conference}, location = {Sevilla, Spain}, publisher = {Fundació de la comunitat valenciana SCITO}, title = {{Solid state diffusion in metal-semiconductors core-shell nanoparticle}}, doi = {10.29363/nanoge.matsusspring.2025.220}, year = {2025}, } @article{20043, abstract = {We establish an isomorphism of complex K-theory of the moduli space M of “SL n​ ”-Higgs bundles of degree d and rank n (in the sense of Hausel–Thaddeus) and twisted complex K-theory of the orbifold M of PGL n​ -Higgs bundles of degree e, where (n,d)=(n,e)=1. Along the way, we prove the vanishing of torsion for H ∗ ( M ) and certain twisted complex K-theory groups of M . We also extend Arinkin’s autoduality of compactified Jacobian to a derived equivalence between SL n​ - and PGL n​ -Hitchin systems over the elliptic locus. In the appendix, we develop a formalism of G-sheaves of spectra, generalising equivariant homotopy theory to a relative setting.}, author = {Groechenig, Michael and Shen, Shiyu}, issn = {1435-9863}, journal = {Journal of the European Mathematical Society}, publisher = {EMS Press}, title = {{Complex K-theory of moduli spaces of Higgs bundles}}, doi = {10.4171/jems/1601}, year = {2025}, } @inproceedings{20051, abstract = {We revisit the majority problem in the population protocol communication model, as first studied by Angluin et al. (Distributed Computing 2008). We consider a more general version of this problem known as plurality consensus, which has already been studied intensively in the literature. In this problem, each node in a system of n nodes, has initially one of k different opinions, and they need to agree on the (relative) majority opinion. In particular, we consider the important and intensively studied model of Undecided State Dynamics. Our main contribution is an almost tight lower bound on the stabilization time: we prove that there exists an initial configuration, even with bias \Delta = \omega(\sqrt{n\log n}), where stabilization requires \Omega(kn\log \frac {\sqrt n} {k \log n}) interactions, or equivalently, \Omega(k\log \frac {\sqrt n} {k \log n}) parallel time for any k = o\left(\frac {\sqrt n}{\log n}\right). This bound is tight for any k \le n^{\frac 1 2 - \epsilon}, where \epsilon >0 can be any small constant, as Amir et al.~(PODC'23) gave a O(k\log n) parallel time upper bound for k = O\left(\frac {\sqrt n} {\log ^2 n}\right).}, author = {El-Hayek, Antoine and Elsässer, Robert and Schmid, Stefan}, booktitle = {Proceedings of the ACM Symposium on Principles of Distributed Computing}, isbn = { 9798400718854}, location = {Huatulco, Mexico}, publisher = {Association for Computing Machinery}, title = {{An almost tight lower bound for plurality consensus with undecided state dynamics in the population protocol model}}, doi = {10.1145/3732772.3733505}, year = {2025}, } @inproceedings{19982, abstract = {Dynamically maintaining the minimum cut in a graph G under edge insertions and deletion is a fundamental problem in dynamic graph algorithms for which no conditional lower bound on the time per operation exists. In an n-node graph the best known (1 + o (1))-approximate algorithm takes update time [14]. If the minimum cut is guaranteed to be (log n )o (1), a deterministic exact algorithm with n o (1) update time exists [8]. We present the first fully dynamic algorithm for (1 + o (1))-approximate minimum cut with n o(1) update time. Our main technical contribution is to show that it suffices to consider small-volume cuts in suitably contracted graphs.}, author = {El-Hayek, Antoine and Henzinger, Monika H and Li, Jason}, booktitle = {Proceedings of the 2025 Annual ACM-SIAM Symposium on Discrete Algorithms}, location = {New Orleans, LA, United States}, pages = {750--784}, publisher = {Society for Industrial and Applied Mathematics}, title = {{Fully dynamic approximate minimum cut in subpolynomial time per operation}}, doi = {10.1137/1.9781611978322.22}, year = {2025}, } @article{20669, abstract = {Ice cliffs and supraglacial ponds are key drivers of mass loss on debris-covered glaciers. However, the relationship between melt ponds and adjacent ice cliffs has not been fully explored. We investigated the seasonal drainage patterns of a melt pond on the debris-covered Zhuxi Glacier in southeast Tibet and estimated the mass loss of its adjacent ice cliff during 2023-2024. Using hourly time-lapse photogrammetry we built a series of high-resolution point clouds to quantify the evolution of the ice cliff-pond system. Our findings indicate that subaerial melting and undercutting were the primary mechanisms of ice cliff mass loss during summer. In winter when the pond water level dropped, ice cliff calving became the dominant mode of ice loss. As the water level rose in spring, calving and subaerial melting occurred simultaneously and ice loss from calving accounted for approximately 19.5 % of total ice loss from February to July 2024. Our results reveal the transitional state of this ice cliff-pond system, exhibiting characteristics of both melt hotspots and lake-terminating calving fronts, and highlight the interplay between seasonal drainage-refill pond and differing modes of ice loss on adjacent ice cliff. Future research should focus on additional high-resolution monitoring of similar systems and incorporation of ice cliff-pond dynamics in glacier-scale numerical models. }, author = {He, Zhen and Westoby, Matthew and Ren, Shaoting and Zhao, Chuanxi and He, Yifei and Zhang, Tianzhao and Yang, Wei}, issn = {1727-5652}, journal = {Journal of Glaciology}, publisher = {Cambridge University Press}, title = {{Quantifying the seasonal dynamics of a transitional ice cliff-pond system on a debris-covered glacier}}, doi = {10.1017/jog.2025.10104}, volume = {71}, year = {2025}, } @phdthesis{19759, abstract = {Despite generating remarkable results in various computer vision tasks, deep learning comes with some surprising shortcomings. For example, tiny perturbations, often imperceptible to the human eye, can completely change the predictions of image classifiers. Despite a decade of research, the field has made limited progress in developing image classifiers that are both accurate and robust. This thesis aims to address this gap. As our first contribution, we aim to simplify the process of training certifiably robust image classifiers. We do this by designing a convolutional layer that does not require executing an iterative procedure in every forward pass, but relies on an explicit bound instead. We also propose a loss function that allows optimizing for a particular margin more precisely. Next, we provide an overview and comparison of various methods that create robust image classifiers by constraining the Lipschitz constant. This is important since generally longer training times and more parameters improve the performance of robust classifiers, making it challenging to determine the most practical and effective methods from existing literature. In 1-Lipschitz classification, the performance of current methods is still much worse than what we expect on the simple tasks we consider. Therefore, we next investigate potential causes of this shortcoming. We first consider the role of the activation function. We prove a theoretical shortcoming of the commonly used activation function, and provide an alternative without it. However this theoretical improvement does barely translate to the empirical performance of robust classifiers, suggesting a different bottleneck. Therefore, in the final chapter, we study how the performance depends on the amount of training data. We prove that in the worst case, we might require far more data to train a robust classifier compared to a normal one. We furthermore find that the amount of training data is a key determinant of the performance current methods achieve on popular datasets. Additionally, we show that linear subspaces exist with tiny data variance, and yet we can still train very accurate classifiers after projecting into those subspaces. This shows that on the datasets considered, enforcing robustness in classification makes the task strictly more challenging. }, author = {Prach, Bernd}, issn = {2663-337X}, pages = {84}, publisher = {Institute of Science and Technology Austria}, title = {{Robust image classification with 1-Lipschitz networks}}, doi = {10.15479/10.15479/at-ista-19759}, year = {2025}, } @inproceedings{19741, abstract = {Quantitative automata model beyond-boolean aspects of systems: every execution is mapped to a real number by incorporating weighted transitions and value functions that generalize acceptance conditions of boolean w-automata. Despite the theoretical advances in systems analysis through quantitative automata, the first comprehensive software tool for quantitative automata (Quantitative Automata Kit, or QuAK) was developed only recently. QuAK implements algorithms for solving standard decision problems, e.g., emptiness and universality, as well as constructions for safety and liveness of quantitative automata. We present the architecture of QuAK, which reflects that all of these problems reduce to either checking inclusion between two quantitative automata or computing the highest value achievable by an automaton—its so-called top value. We improve QuAK by extending these two algorithms with an option to return, alongside their results, an ultimately periodic word witnessing the algorithm’s output, as well as implementing a new safety-liveness decomposition algorithm that can handle nondeterministic automata, making QuAK more informative and capable.}, author = {Chalupa, Marek and Henzinger, Thomas A and Mazzocchi, Nicolas Adrien and Sarac, Naci E}, booktitle = {31st International Conference on Tools and Algorithms for the Construction and Analysis of Systems}, isbn = {9783031906428}, issn = {1611-3349}, pages = {303--312}, publisher = {Springer Nature}, title = {{Automating the analysis of quantitative automata with QuAK}}, doi = {10.1007/978-3-031-90643-5_16}, volume = {15696}, year = {2025}, } @unpublished{21858, abstract = {The recent surge in high-quality open-source Generative AI text models (colloquially: LLMs), as well as efficient finetuning techniques, have opened the possibility of creating high-quality personalized models that generate text attuned to a specific individual’s needs and are capable of credibly imitating their writing style by refining an open-source model with that person’s own data. The technology to create such models is accessible to private individuals, and training and running such models can be done cheaply on consumer-grade hardware. While these advancements are a huge gain for usability and privacy, this position paper argues that the practical feasibility of impersonating specific individuals also introduces novel safety risks. For instance, this technology enables the creation of phishing emails or fraudulent social media accounts, based on small amounts of publicly available text, or by the individuals themselves to escape AI text detection. We further argue that these risks are complementary to—and distinct from—the much-discussed risks of other impersonation attacks such as image, voice, or video deepfakes, and are not adequately addressed by the larger research community, or the current generation of open- and closed-source models.}, author = {Iofinova, Eugenia B and Jovanovic, Andrej and Alistarh, Dan-Adrian}, booktitle = {arXiv}, title = {{Position: It's time to act on the risk of efficient personalized text generation}}, doi = {10.48550/arXiv.2502.06560}, year = {2025}, } @phdthesis{20138, abstract = {The evolution shapes the world around us. Not only in biology, where the fittest individuals spread their genes but also in physics and social dynamics, the evolutionary forces determine the development of a state of matter or public opinions. Many models describe these dynamics. This thesis examines the role of the structure in the models of selection. The population structure is represented as a graph or a network, and each vertex is occupied by one individual. Every individual has a type and fitness that represents the reproductive potential and depends on the type, occupied vertex, and the arrangement of the neighbors. The evolution is modeled in discrete steps; in one step, one individual is replaced by a neighbor selected randomly with the influence of fitness. The role of the networks is widely examined in the literature. The structures that promote the spread of the desired type compared to the structureless case are called amplifiers. The existence of amplifiers in various settings is an intensively studied topic, and in some settings, the amplifiers have been identified. Moreover, there are other important questions about the number of steps until one type spreads over the whole network (fixation time), the computational complexity, and the questions about the robustness of these processes. This thesis explores the role of structure in evolution from many perspectives. First, it introduces different models and various choices that can be made in the models of evolution. It highlights the role of the structure in the real world and how this is reflected in these models. Then, it describes the previous results and open problems. Second, the thesis describes an amplifier for two variants of the Moran process: one with a constant birth rate and the other with a constant death rate. This is an important contribution to the robustness of the amplification. Third, the thesis determines the complexity of spatial games. These are processes where the fitness comes from a game, and the strength of selection is high. It shows that determining the fate of cooperation in these games is a PSPACE-complete problem. Fourth, the thesis describes the amplifier of cooperation for spatial games. This is the first amplifier in this setting. Fifth, the thesis examines the coexistence in the Moran process with environmental heterogeneity. In this setting, the fitness depends not only on the type of the individual but also on the occupied vertex. The chapter determines the relationship between the interactions of vertices of different types and the coexistence time. Sixth, the thesis examines the social balance on networks and proposes a stochastic dynamic partially aware of the state of the graph, which reaches a balanced position quickly. Finally, the thesis presents conclusions and outlines the directions for future work. }, author = {Svoboda, Jakub}, issn = {2663-337X}, pages = {167}, publisher = {Institute of Science and Technology Austria}, title = {{Structural properties of games on graphs}}, doi = {10.15479/AT-ISTA-20138}, year = {2025}, } @article{21144, abstract = {This paper deals with the algorithmic aspects of solving feasibility problems of semidefinite programming (SDP), aka linear matrix inequalities (LMIs). Since in some SDP instances all feasible solutions have irrational entries, numerical solvers that work with rational numbers can only find an approximate solution. We study the following question: Is it possible to certify feasibility of a given SDP using an approximate solution that is sufficiently close to some exact solution? Existing approaches make the assumption that there exist rational feasible solutions (and use techniques such as rounding and lattice reduction algorithms). We propose an alternative approach that does not need this assumption. More specifically, we show how to construct a system of polynomial equations whose set of real solutions is guaranteed to have an isolated correct solution (assuming that the target exact solution is maximum-rank). This allows, in particular, for us to use algorithms from real algebraic geometry for solving systems of polynomial equations, yielding a hybrid (or symbolic-numerical) method for SDPs. We experimentally compare it with a pure symbolic method in [D. Henrion, S. Naldi, and M. Safey El Din, SIAM J. Optim., 26 (2016), pp. 2512–2539]; the hybrid method was able to certify feasibility of many SDP instances on which the aforementioned paper failed. Our approach may have further applications, such as refining an approximate solution using methods of numerical algebraic geometry for systems of polynomial equations.}, author = {Kolmogorov, Vladimir and Naldi, Simone and Zapata, Jeferson}, issn = {1095-7189}, journal = {SIAM Journal on Optimization}, number = {3}, pages = {1630--1654}, publisher = {Society for Industrial and Applied Mathematics}, title = {{Certifying solutions of degenerate semidefinite programs}}, doi = {10.1137/24m1664691}, volume = {35}, year = {2025}, } @inproceedings{21074, abstract = {Neural models learn representations of high-dimensional data on low-dimensional manifolds. Multiple factors, including stochasticities in the training process, model architectures, and additional inductive biases, may induce different representations, even when learning the same task on the same data. However, it has recently been shown that when a latent structure is shared between distinct latent spaces, relative distances between representations can be preserved, up to distortions. Building on this idea, we demonstrate that exploiting the differential-geometric structure of latent spaces of neural models, it is possible to capture precisely the transformations between representational spaces trained on similar data distributions. Specifically, we assume that distinct neural models parametrize approximately the same underlying manifold, and introduce a representation based on the pullback metric that captures the intrinsic structure of the latent space, while scaling efficiently to large models. We validate experimentally our method on model stitching and retrieval tasks, covering autoencoders and vision foundation discriminative models, across diverse architectures, datasets, pretraining schemes and modalities. Code is available at the following link.}, author = {Yu, Hanlin and Inal, Befrin and Arvanitidis, Georgios and Hauberg, Soren and Locatello, Francesco and Fumero, Marco}, booktitle = {39th Annual Conference on Neural Information Processing Systems}, issn = {1049-5258}, location = {San Diego, CA, United States}, publisher = {Neural Information Processing Systems Foundation}, title = {{Connecting neural models latent geometries with relative geodesic representations}}, volume = {38}, year = {2025}, } @inproceedings{21076, abstract = {In many scientific experiments, the data annotating cost constraints the pace for testing novel hypotheses. Yet, modern machine learning pipelines offer a promising solution—provided their predictions yield correct conclusions. We focus on Prediction-Powered Causal Inferences (PPCI), i.e., estimating the treatment effect in an unlabeled target experiment, relying on training data with the same outcome annotated but potentially different treatment or effect modifiers. We first show that conditional calibration guarantees valid PPCI at population level. Then, we introduce a sufficient representation constraint transferring validity across experiments, which we propose to enforce in practice in Deconfounded Empirical Risk Minimization, our new model-agnostic training objective. We validate our method on synthetic and real-world scientific data, solving impossible problem instances for Empirical Risk Minimization even with standard invariance constraints. In particular, for the first time, we achieve valid causal inference on a scientific experiment with complex recording and no human annotations, fine-tuning a foundational model on our similar annotated experiment.}, author = {Cadei, Riccardo and Demirel, Ilker and De Bartolomeis, Piersilvio and Lindorfer, Lukas and Cremer, Sylvia and Schmid, Cordelia and Locatello, Francesco}, booktitle = {39th Annual Conference on Neural Information Processing Systems}, issn = {1049-5258}, location = {San Diego, CA, United States}, publisher = {Neural Information Processing Systems Foundation}, title = {{Prediction-powered causal inferences}}, volume = {38}, year = {2025}, } @inproceedings{21072, abstract = {Language and vision-language models have shown impressive performance across a wide range of tasks, but their internal mechanisms remain only partly understood. In this work, we study how individual attention heads in text-generative models specialize in specific semantic or visual attributes. Building on an established interpretability method, we reinterpret the practice of probing intermediate activations with the final decoding layer through the lens of signal processing. This lets us analyze multiple samples in a principled way and rank attention heads based on their relevance to target concepts. Our results show consistent patterns of specialization at the head level across both unimodal and multimodal transformers. Remarkably, we find that editing as few as 1% of the heads, selected using our method, can reliably suppress or enhance targeted concepts in the model output. We validate our approach on language tasks such as question answering and toxicity mitigation, as well as vision-language tasks including image classification and captioning. Our findings highlight an interpretable and controllable structure within attention layers, offering simple tools for understanding and editing large-scale generative models.}, author = {Basile, Lorenzo and Maiorca, Valentino and Doimo, Diego and Locatello, Francesco and Cazzaniga, Alberto}, booktitle = {39th Annual Conference on Neural Information Processing Systems}, issn = {1049-5258}, location = {San Diego, CA, United States}, publisher = {Neural Information Processing Systems Foundation}, title = {{Head pursuit: Probing attention specialization in multimodal transformers}}, volume = {38}, year = {2025}, } @inproceedings{21068, abstract = {Causal reasoning and discovery, two fundamental tasks of causal analysis, often face challenges in applications due to the complexity, noisiness, and highdimensionality of real-world data. Despite recent progress in identifying latent causal structures using causal representation learning (CRL), what makes learned representations useful for causal downstream tasks and how to evaluate them are still not well understood. In this paper, we reinterpret CRL using a measurement model framework, where the learned representations are viewed as proxy measurements of the latent causal variables. Our approach clarifies the conditions under which learned representations support downstream causal reasoning and provides a principled basis for quantitatively assessing the quality of representations using a new Test-based Measurement EXclusivity (T-MEX) score. We validate T-MEX across diverse causal inference scenarios, including numerical simulations and real-world ecological video analysis, demonstrating that the proposed framework and corresponding score effectively assess the identification of learned representations and their usefulness for causal downstream tasks. Reproducible code can be found at https://github.com/shimenghuang/a-measurement-perspective-of-crl.}, author = {Yao, Dingling and Huang, Shimeng and Cadei, Riccardo and Zhang, Kun and Locatello, Francesco}, booktitle = {39th Annual Conference on Neural Information Processing Systems}, issn = {1049-5258}, location = {San Diego, CA, United States}, publisher = {Neural Information Processing Systems Foundation}, title = {{The third pillar of causal analysis? A measurement perspective on causal representations}}, volume = {38}, year = {2025}, } @inproceedings{21070, abstract = {Deep learning systems deployed in real-world applications often encounter data that is different from their in-distribution (ID). A reliable model should ideally abstain from making decisions in this out-of-distribution (OOD) setting. Existing state-of-the-art methods primarily focus on feature distances, such as k-th nearest neighbors and distances to decision boundaries, either overlooking or ineffectively using in-distribution statistics. In this work, we propose a novel angle-based metric for OOD detection that is computed relative to the in-distribution structure. We demonstrate that the angles between feature representations and decision boundaries, viewed from the mean of in-distribution features, serve as an effective discriminative factor between ID and OOD data. We evaluate our method on nine ImageNet-pretrained models. Our approach achieves the lowest FPR in 5 out of 9 ImageNet models, obtains the best average FPR overall, and consistently ranking among the top 3 across all evaluated models. Furthermore, we highlight the benefits of contrastive representations by showing strong performance with ResNet SCL and CLIP architectures. Finally, we demonstrate that the scale-invariant nature of our score enables an ensemble strategy via simple score summation. }, author = {Demirel, Berker and Fumero, Marco and Locatello, Francesco}, booktitle = {39th Annual Conference on Neural Information Processing Systems}, issn = {1049-5258}, location = {San Diego, CA, United States}, publisher = {Neural Information Processing Systems Foundation}, title = {{Out-of-Distribution detection with relative angles}}, volume = {38}, year = {2025}, } @article{20326, abstract = {Ag2Se is a promising n-type thermoelectric material, but its performance is limited by excessive carrier concentration, compositional inhomogeneity, and phase instability, challenges rooted in a narrow homogeneity range and uncontrolled Ag+ diffusion in the superionic phase. Here, we address these issues by exploiting liquid–solid interface reactions using CdSe complexes that remove surface excess Ag to yield stoichiometric Ag2Se and generate CdSe nanodomains that inhibit Ag+ diffusion and constrain grain growth. The resulting Ag2Se-CdSe nanocomposites exhibit a reproducible, stable figure of merit (zT) of 1.04 between 300 and 390 K. Beyond demonstrating high performance, we elucidate the interfacial chemical reactions that give rise to the observed microstructure and transport properties, providing a foundation for rationally engineering interfacial chemistry to tailor transport properties across diverse thermoelectric material systems.}, author = {Liu, Yu and Kleinhanns, Tobias and Horta, Sharona and Dutkiewicz, Ewelina and Lu, Shaoqing and Spadaro, Maria Chiara and Genç, Aziz and Chen, Lei and Lim, Khak Ho and Hong, Min and Arbiol, Jordi and Ibáñez, Maria}, issn = {1520-5126}, journal = {Journal of the American Chemical Society}, number = {35}, pages = {32199--32208}, publisher = {American Chemical Society}, title = {{Liquid-solid interface reactions drive enhanced thermoelectric performance in Ag2Se}}, doi = {10.1021/jacs.5c11435}, volume = {147}, year = {2025}, } @article{20331, abstract = {Here, we present a foundational investigation of charge transport through three BODIPY-based molecules using the scanning tunneling microscope–break junction (STM-BJ) technique. We demonstrate that molecular conductance through the BODIPY core can be measured by introducing aurophilic linkers at the 2,6-positions. By varying these linkers, we systematically modulate the frontier molecular orbital energies and fine-tune transport behavior. Our experimental results are supported by DFT-based calculations, which feature a new computationally efficient correction to standard PBE-level transmission predictions. Together, these findings establish the viability of BODIPY-based systems for molecular junction applications and lay the groundwork for future studies of their single-molecule optoelectronic properties.}, author = {York, Emma and Stone, Ilana and Shi, Wanzhuo and Roy, Xavier and Venkataraman, Latha}, issn = {1530-6992}, journal = {Nano Letters}, number = {36}, pages = {13697--13702}, publisher = {American Chemical Society}, title = {{Tuning conductance in BODIPY-based single-molecule junctions}}, doi = {10.1021/acs.nanolett.5c03764}, volume = {25}, year = {2025}, } @article{19370, abstract = {Sex-linked and autosomal loci experience different selective pressures and evolutionary dynamics. X (or Z) chromosomes are often hemizygous in males (or females), as Y (or W) chromosomes often degenerate. Such hemizygous regions can be under greater efficacy of selection, as recessive mutations are immediately exposed to selection in the heterogametic sex leading to faster adaptation and faster divergence on the X chromosome (the so-called Faster-X or Faster-Z effect). However, in young nonrecombining regions, Y/W chromosomes often have many functional genes, and many X/Z-linked loci are therefore diploid. The sheltering of recessive mutations on the X/Z by the Y/W homolog is expected to drive slower adaptation for diploid X/Z loci, i.e. a reduction in the efficacy of selection. While the Faster-X effect has been studied extensively, much less is known empirically about the evolutionary dynamics of diploid X or Z chromosomes. Here, we took advantage of published population genomic data in the female-heterogametic human parasite Schistosoma japonicum to characterize the gene content and diversity levels of the diploid and hemizygous regions of the Z chromosome. We used different metrics of selective pressures acting on genes to test for differences in the efficacy of selection in hemizygous and diploid Z regions, relative to autosomes. We found consistent patterns suggesting reduced Ne, and reduced efficacy of purifying selection, on both hemizygous and diploid Z regions. Moreover, relaxed selection was particularly pronounced for female-biased genes on the diploid Z, as predicted by recent theoretical work.}, author = {Mrnjavac, Andrea and Vicoso, Beatriz}, issn = {1759-6653}, journal = {Genome Biology and Evolution}, number = {2}, publisher = {Oxford University Press}, title = {{Reduced efficacy of selection on a young Z chromosome region of schistosoma japonicum}}, doi = {10.1093/gbe/evaf021}, volume = {17}, year = {2025}, } @phdthesis{19393, abstract = {Rotations constitute one of the fundamental symmetries in physics, characterized by their intricate group structure and infinite dimensional representations. In contrast to classical rotations, quantum mechanics unveils the SO(3) symmetry group structure, manifesting in phenomena without classical counterparts, from angular momentum quantization to non-trivial addition of angular momenta. While most studies of topological physics have focused on two-band systems, the SO(3) symmetry group of quantum rotors offers an inherently more complex platform with unprecedented possibilities for exploring topological phenomena. Despite their ubiquity in nature– from molecules to nanorotors– their potential for hosting topological phases has remained largely unexamined. In this thesis, we mainly focus on periodically driven linear molecules as a prototype for studying topological phenomena in quantum rotors. Recent technological advances in coherent control of molecules, particularly through precisely shaped laser pulses, have made it possible to investigate linear rotors in the context of topology. While planar rotors have received some attention in recent years, threedimensional rotors–particularly linear molecules–harbor substantially richer topological phenomena due to their non-abelian nature and their additional angular degrees of freedom. We demonstrate that these systems can host novel edge states and topological features fundamentally impossible in planar systems. We begin by establishing a theoretical bridge between periodically kicked rotors and "crystalline" lattices in angular momentum space. Using non-interacting linear molecules as our primary example, we show how quantum interference and revival patterns lead to the possibility to simulate band models with arbitrary number of bands N. While our framework applies to various quantum rotors, including nanorotors and kicked Bose-Einstein condensates, linear molecules provide an ideal experimental platform due to their abovementioned precise controllability. The core of this work examines adiabatic dynamics of 3D quantum rotors, establishing a geometric framework based on the Euler class to characterize its non-abelian topology. The non-Hermitian nature of the system enables novel braiding behaviors and topological transitions impossible in static systems, leading to an anomalous Dirac string phase with edge states in each gap, even though the Berry phases are all zero. These features can be directly observed through molecular alignment and rotational level populations. These findings establish quantum rotors as an alternative platform for studying multi-band topological physics, while suggesting practical implementations for quantum computation where topological protection could offer natural resilience against decoherence. The rich structure of three-dimensional rotation groups, combined with the tunability of topological features through driving parameters, makes this platform particularly valuable for exploring fundamental physics and developing quantum technologies.}, author = {Karle, Volker}, issn = {2663-337X}, pages = {192}, publisher = {Institute of Science and Technology Austria}, title = {{Non-equilibrium topological phases with periodically driven molecules and quantum rotors}}, doi = {10.15479/AT-ISTA-19393}, year = {2025}, } @article{20603, abstract = {We study the growth of sumsets A+B⊂S⊂G, where S does not contain an arithmetic progression of length 2k+1, and where G is a commutative group, in which every nonzero element has an order of at least 2k+1. More specifically, we show the following: if A,B⊂G are sets such that A+B does not contain an arithmetic progression of length 2k+1, then |A+B|≥|A|2k−13k−2|B|k3k−2. As an application we derive upper bounds on the cardinality of the summands in sumsets A+B+C contained in the set of t-th powers, where t≥2 is an integer. In particular, we show that min(|A|,|B|,|C|)≪(logN)4/5 for t=2, and min(|A|,|B|,|C|)≪t(logN)1/2 for t≥3.}, author = {Elsholtz, Christian and Ruzsa, Imre Z. and Wurzinger, Lena}, issn = {1730-6264}, journal = {Acta Arithmetica}, pages = {289--303}, publisher = {Institute of Mathematics}, title = {{Sumset growth in progression-free sets}}, doi = {10.4064/aa250115-14-7}, volume = {220}, year = {2025}, }