@article{19823, abstract = {The delafossite metals PdCoO2, PtCoO2, and PdCrO2 are among the highest conductivity materials known, with low-temperature mean free paths of tens of microns in the best as-grown single crystals. A key question is whether these very low resistive scattering rates result from strongly suppressed backscattering due to special features of the electronic structure or are a consequence of highly unusual levels of crystalline perfection. We report the results of experiments in which high-energy electron irradiation was used to introduce point disorder to the Pd and Pt layers in which the conduction occurs. We obtain the cross section for formation of Frenkel pairs in absolute units, and cross-check our analysis with first-principles calculations of the relevant atomic displacement energies. We observe an increase of resistivity that is linear in defect density with a slope consistent with scattering in the unitary limit. Our results enable us to deduce that the as-grown crystals contain extremely low levels of in-plane defects of approximately 0.001%. This confirms that crystalline perfection is the most important factor in realizing the long mean free paths and highlights how unusual these delafossite metals are in comparison with the vast majority of other multicomponent oxides and alloys. We discuss the implications of our findings for future materials research.}, author = {Sunko, Veronika and McGuinness, P. H. and Chang, C. S. and Zhakina, E. and Khim, S. and Dreyer, C. E. and Konczykowski, M. and Borrmann, H. and Moll, P. J. W. and König, M. and Muller, D. A. and Mackenzie, A. P.}, issn = {2160-3308}, journal = {Physical Review X}, number = {2}, publisher = {American Physical Society}, title = {{Controlled introduction of defects to delafossite metals by electron irradiation}}, doi = {10.1103/physrevx.10.021018}, volume = {10}, year = {2020}, } @inbook{19986, abstract = {For non-probabilistic programs, a key question in static analysis is termination, which asks whether a given program terminates under a given initial condition. In the presence of probabilistic behaviour, there are two fundamental extensions of the termination question: (a) the almost-sure termination question, which asks whether the termination probability is 1; and (b) the bounded-time termination question, which asks whether the expected termination time is bounded. There are many active research directions to address these two questions; one important such direction is the use of martingale theory for termination analysis. In this chapter, we survey the main techniques of the martingale-based approach to the termination analysis of probabilistic programs.}, author = {Chatterjee, Krishnendu and Fu, Hongfei and Novotný, Petr}, booktitle = {Foundations of Probabilistic Programming}, isbn = {9781108488518}, pages = {221--258}, publisher = {Cambridge University Press}, title = {{Termination Analysis of Probabilistic Programs with Martingales}}, doi = {10.1017/9781108770750.008}, year = {2020}, } @article{20766, abstract = {Reversible catalytic reactions operate under thermodynamic control, and thus, establishing a selective catalytic system poses a considerable challenge. Herein, we report a reversible transfer hydrocyanation protocol that exhibits high selectivity for the thermodynamically less favorable branched isomer. Selectivity is achieved by exploiting the lower barrier for C–CN oxidative addition and reductive elimination at benzylic positions in the absence of a cocatalytic Lewis acid. Through the design of a novel type of HCN donor, a practical, branched-selective, HCN-free transfer hydrocyanation was realized. The synthetically useful resolution of a mixture of branched and linear nitrile isomers was also demonstrated to underline the value of reversible and selective transfer reactions. In a broader context, this work demonstrates that high kinetic selectivity can be achieved in reversible transfer reactions, thus opening new horizons for their synthetic applications.}, author = {Bhawal, Benjamin N. and Reisenbauer, Julia and Ehinger, Christian and Morandi, Bill}, issn = {1520-5126}, journal = {Journal of the American Chemical Society}, number = {25}, pages = {10914--10920}, publisher = {American Chemical Society}, title = {{Overcoming selectivity issues in reversible catalysis: A transfer hydrocyanation exhibiting high kinetic control}}, doi = {10.1021/jacs.0c03184}, volume = {142}, year = {2020}, } @article{20806, abstract = {Regulation of phosphatidylinositol phosphates plays a crucial role in signal transduction, membrane trafficking or autophagy. Members of the myotubularin family of lipid phosphatases contribute to phosphoinositide metabolism by counteracting the activity of phosphoinositide kinases. The mechanisms determining their subcellular localization and targeting to specific membrane compartments are still poorly understood. We show here that the inactive phosphatase MTMR9 localizes to the intermediate compartment and to the Golgi apparatus and is able to recruit its active phosphatase partners MTMR6 and MTMR8 to these locations. Furthermore, MTMR8 and MTMR9 co-localize with the small GTPase RAB1A and regulate its localization. Loss of MTMR9 expression compromises the integrity of the Golgi apparatus and results in altered distribution of RAB1A and actin nucleation-promoting factor WHAMM. Loss or overexpression of MTMR9 leads to decreased rate of protein secretion. We demonstrate that secretion of physiologically relevant cargo exemplified by the WNT3A protein is affected after perturbation of MTMR9 levels.}, author = {Doubravská, Lenka and Dostál, Vojtěch and Knop, Filip and Libusová, Lenka and Macůrková, Marie}, issn = {0014-4827}, journal = {Experimental Cell Research}, number = {1}, publisher = {Elsevier}, title = {{Human myotubularin-related protein 9 regulates ER-to-Golgi trafficking and modulates WNT3A secretion}}, doi = {10.1016/j.yexcr.2019.111709}, volume = {386}, year = {2020}, } @article{19306, author = {Kazatskaya, Anna and Yuan, Lisa and Amin-Wetzel, Niko Paresh and Philbrook, Alison and de Bono, Mario and Sengupta, Piali}, issn = {2578-9430}, journal = {microPublication Biology}, number = {9}, publisher = {Caltech Library}, title = {{The URX oxygen-sensing neurons in C. elegans are ciliated}}, doi = {10.17912/MICROPUB.BIOLOGY.000303}, volume = {2020}, year = {2020}, } @article{14891, abstract = {We give the first mathematically rigorous justification of the local density approximation in density functional theory. We provide a quantitative estimate on the difference between the grand-canonical Levy–Lieb energy of a given density (the lowest possible energy of all quantum states having this density) and the integral over the uniform electron gas energy of this density. The error involves gradient terms and justifies the use of the local density approximation in the situation where the density is very flat on sufficiently large regions in space.}, author = {Lewin, Mathieu and Lieb, Elliott H. and Seiringer, Robert}, issn = {2578-5885}, journal = {Pure and Applied Analysis}, number = {1}, pages = {35--73}, publisher = {Mathematical Sciences Publishers}, title = {{ The local density approximation in density functional theory}}, doi = {10.2140/paa.2020.2.35}, volume = {2}, year = {2020}, } @article{15036, abstract = {The assembly of a septin filament requires that homologous monomers must distinguish between one another in establishing appropriate interfaces with their neighbors. To understand this phenomenon at the molecular level, we present the first four crystal structures of heterodimeric septin complexes. We describe in detail the two distinct types of G-interface present within the octameric particles, which must polymerize to form filaments. These are formed between SEPT2 and SEPT6 and between SEPT7 and SEPT3, and their description permits an understanding of the structural basis for the selectivity necessary for correct filament assembly. By replacing SEPT6 by SEPT8 or SEPT11, it is possible to rationalize Kinoshita's postulate, which predicts the exchangeability of septins from within a subgroup. Switches I and II, which in classical small GTPases provide a mechanism for nucleotide-dependent conformational change, have been repurposed in septins to play a fundamental role in molecular recognition. Specifically, it is switch I which holds the key to discriminating between the two different G-interfaces. Moreover, residues which are characteristic for a given subgroup play subtle, but pivotal, roles in guaranteeing that the correct interfaces are formed.}, author = {Rosa, Higor Vinícius Dias and Leonardo, Diego Antonio and Brognara, Gabriel and Brandão-Neto, José and D'Muniz Pereira, Humberto and Araújo, Ana Paula Ulian and Garratt, Richard Charles}, issn = {0022-2836}, journal = {Journal of Molecular Biology}, keywords = {Molecular Biology, Structural Biology}, number = {21}, pages = {5784--5801}, publisher = {Elsevier}, title = {{Molecular recognition at septin interfaces: The switches hold the key}}, doi = {10.1016/j.jmb.2020.09.001}, volume = {432}, year = {2020}, } @article{15037, abstract = {Protein abundance and localization at the plasma membrane (PM) shapes plant development and mediates adaptation to changing environmental conditions. It is regulated by ubiquitination, a post-translational modification crucial for the proper sorting of endocytosed PM proteins to the vacuole for subsequent degradation. To understand the significance and the variety of roles played by this reversible modification, the function of ubiquitin receptors, which translate the ubiquitin signature into a cellular response, needs to be elucidated. In this study, we show that TOL (TOM1-like) proteins function in plants as multivalent ubiquitin receptors, governing ubiquitinated cargo delivery to the vacuole via the conserved Endosomal Sorting Complex Required for Transport (ESCRT) pathway. TOL2 and TOL6 interact with components of the ESCRT machinery and bind to K63-linked ubiquitin via two tandemly arranged conserved ubiquitin-binding domains. Mutation of these domains results not only in a loss of ubiquitin binding but also altered localization, abolishing TOL6 ubiquitin receptor activity. Function and localization of TOL6 is itself regulated by ubiquitination, whereby TOL6 ubiquitination potentially modulates degradation of PM-localized cargoes, assisting in the fine-tuning of the delicate interplay between protein recycling and downregulation. Taken together, our findings demonstrate the function and regulation of a ubiquitin receptor that mediates vacuolar degradation of PM proteins in higher plants.}, author = {Moulinier-Anzola, Jeanette and Schwihla, Maximilian and De-Araújo, Lucinda and Artner, Christina and Jörg, Lisa and Konstantinova, Nataliia and Luschnig, Christian and Korbei, Barbara}, issn = {1674-2052}, journal = {Molecular Plant}, keywords = {Plant Science, Molecular Biology}, number = {5}, pages = {717--731}, publisher = {Elsevier}, title = {{TOLs function as ubiquitin receptors in the early steps of the ESCRT pathway in higher plants}}, doi = {10.1016/j.molp.2020.02.012}, volume = {13}, year = {2020}, } @article{15055, abstract = {Markov decision processes (MDPs) are the defacto framework for sequential decision making in the presence of stochastic uncertainty. A classical optimization criterion for MDPs is to maximize the expected discounted-sum payoff, which ignores low probability catastrophic events with highly negative impact on the system. On the other hand, risk-averse policies require the probability of undesirable events to be below a given threshold, but they do not account for optimization of the expected payoff. We consider MDPs with discounted-sum payoff with failure states which represent catastrophic outcomes. The objective of risk-constrained planning is to maximize the expected discounted-sum payoff among risk-averse policies that ensure the probability to encounter a failure state is below a desired threshold. Our main contribution is an efficient risk-constrained planning algorithm that combines UCT-like search with a predictor learned through interaction with the MDP (in the style of AlphaZero) and with a risk-constrained action selection via linear programming. We demonstrate the effectiveness of our approach with experiments on classical MDPs from the literature, including benchmarks with an order of 106 states.}, author = {Brázdil, Tomáš and Chatterjee, Krishnendu and Novotný, Petr and Vahala, Jiří}, issn = {2374-3468}, journal = {Proceedings of the 34th AAAI Conference on Artificial Intelligence}, keywords = {General Medicine}, location = {New York, NY, United States}, number = {06}, pages = {9794--9801}, publisher = {Association for the Advancement of Artificial Intelligence}, title = {{Reinforcement learning of risk-constrained policies in Markov decision processes}}, doi = {10.1609/aaai.v34i06.6531}, volume = {34}, year = {2020}, } @article{15057, abstract = {Vaccinia virus–related kinase (VRK) is an evolutionarily conserved nuclear protein kinase. VRK-1, the single Caenorhabditis elegans VRK ortholog, functions in cell division and germline proliferation. However, the role of VRK-1 in postmitotic cells and adult life span remains unknown. Here, we show that VRK-1 increases organismal longevity by activating the cellular energy sensor, AMP-activated protein kinase (AMPK), via direct phosphorylation. We found that overexpression of vrk-1 in the soma of adult C. elegans increased life span and, conversely, inhibition of vrk-1 decreased life span. In addition, vrk-1 was required for longevity conferred by mutations that inhibit C. elegans mitochondrial respiration, which requires AMPK. VRK-1 directly phosphorylated and up-regulated AMPK in both C. elegans and cultured human cells. Thus, our data show that the somatic nuclear kinase, VRK-1, promotes longevity through AMPK activation, and this function appears to be conserved between C. elegans and humans.}, author = {Park, Sangsoon and Artan, Murat and Han, Seung Hyun and Park, Hae-Eun H. and Jung, Yoonji and Hwang, Ara B. and Shin, Won Sik and Kim, Kyong-Tai and Lee, Seung-Jae V.}, issn = {2375-2548}, journal = {Science Advances}, number = {27}, publisher = {American Association for the Advancement of Science}, title = {{VRK-1 extends life span by activation of AMPK via phosphorylation}}, doi = {10.1126/sciadv.aaw7824}, volume = {6}, year = {2020}, } @inproceedings{15059, abstract = {In this paper we present a room temperature radiometer that can eliminate the need of using cryostats in satellite payload reducing its weight and improving reliability. The proposed radiometer is based on an electro-optic upconverter that boosts up microwave photons energy by upconverting them into an optical domain what makes them immune to thermal noise even if operating at room temperature. The converter uses a high-quality factor whispering gallery mode (WGM) resonator providing naturally narrow bandwidth and therefore might be useful for applications like microwave hyperspectral sensing. The upconversion process is explained by providing essential information about photon conversion efficiency and sensitivity. To prove the concept, we describe an experiment which shows state-of-the-art photon conversion efficiency n=10-5 per mW of pump power at the frequency of 80 GHz.}, author = {Wasiak, Michal and Botello, Gabriel Santamaria and Abdalmalak, Kerlos Atia and Sedlmeir, Florian and Rueda Sanchez, Alfredo R and Segovia-Vargas, Daniel and Schwefel, Harald G. L. and Munoz, Luis Enrique Garcia}, booktitle = {14th European Conference on Antennas and Propagation}, location = {Copenhagen, Denmark}, publisher = {IEEE}, title = {{Compact millimeter and submillimeter-wave photonic radiometer for cubesats}}, doi = {10.23919/eucap48036.2020.9135962}, year = {2020}, } @article{15061, abstract = {The actin cytoskeleton, a dynamic network of actin filaments and associated F-actin–binding proteins, is fundamentally important in eukaryotes. α-Actinins are major F-actin bundlers that are inhibited by Ca2+ in nonmuscle cells. Here we report the mechanism of Ca2+-mediated regulation of Entamoeba histolytica α-actinin-2 (EhActn2) with features expected for the common ancestor of Entamoeba and higher eukaryotic α-actinins. Crystal structures of Ca2+-free and Ca2+-bound EhActn2 reveal a calmodulin-like domain (CaMD) uniquely inserted within the rod domain. Integrative studies reveal an exceptionally high affinity of the EhActn2 CaMD for Ca2+, binding of which can only be regulated in the presence of physiological concentrations of Mg2+. Ca2+ binding triggers an increase in protein multidomain rigidity, reducing conformational flexibility of F-actin–binding domains via interdomain cross-talk and consequently inhibiting F-actin bundling. In vivo studies uncover that EhActn2 plays an important role in phagocytic cup formation and might constitute a new drug target for amoebic dysentery.}, author = {Pinotsis, Nikos and Zielinska, Karolina and Babuta, Mrigya and Arolas, Joan L. and Kostan, Julius and Khan, Muhammad Bashir and Schreiner, Claudia and Testa Salmazo, Anita P and Ciccarelli, Luciano and Puchinger, Martin and Gkougkoulia, Eirini A. and Ribeiro, Euripedes de Almeida and Marlovits, Thomas C. and Bhattacharya, Alok and Djinovic-Carugo, Kristina}, issn = {1091-6490}, journal = {Proceedings of the National Academy of Sciences of the United States of America}, number = {36}, pages = {22101--22112}, publisher = {National Academy of Sciences}, title = {{Calcium modulates the domain flexibility and function of an α-actinin similar to the ancestral α-actinin}}, doi = {10.1073/pnas.1917269117}, volume = {117}, year = {2020}, } @article{15063, abstract = {We consider the least singular value of a large random matrix with real or complex i.i.d. Gaussian entries shifted by a constant z∈C. We prove an optimal lower tail estimate on this singular value in the critical regime where z is around the spectral edge, thus improving the classical bound of Sankar, Spielman and Teng (SIAM J. Matrix Anal. Appl. 28:2 (2006), 446–476) for the particular shift-perturbation in the edge regime. Lacking Brézin–Hikami formulas in the real case, we rely on the superbosonization formula (Comm. Math. Phys. 283:2 (2008), 343–395).}, author = {Cipolloni, Giorgio and Erdös, László and Schröder, Dominik J}, issn = {2690-0998}, journal = {Probability and Mathematical Physics}, keywords = {General Medicine}, number = {1}, pages = {101--146}, publisher = {Mathematical Sciences Publishers}, title = {{Optimal lower bound on the least singular value of the shifted Ginibre ensemble}}, doi = {10.2140/pmp.2020.1.101}, volume = {1}, year = {2020}, } @article{15064, abstract = {We call a continuous self-map that reveals itself through a discrete set of point-value pairs a sampled dynamical system. Capturing the available information with chain maps on Delaunay complexes, we use persistent homology to quantify the evidence of recurrent behavior. We establish a sampling theorem to recover the eigenspaces of the endomorphism on homology induced by the self-map. Using a combinatorial gradient flow arising from the discrete Morse theory for Čech and Delaunay complexes, we construct a chain map to transform the problem from the natural but expensive Čech complexes to the computationally efficient Delaunay triangulations. The fast chain map algorithm has applications beyond dynamical systems.}, author = {Bauer, U. and Edelsbrunner, Herbert and Jablonski, Grzegorz and Mrozek, M.}, issn = {2367-1734}, journal = {Journal of Applied and Computational Topology}, number = {4}, pages = {455--480}, publisher = {Springer Nature}, title = {{Čech-Delaunay gradient flow and homology inference for self-maps}}, doi = {10.1007/s41468-020-00058-8}, volume = {4}, year = {2020}, } @article{15070, abstract = {This workshop focused on interactions between the various perspectives on the moduli space of Higgs bundles over a Riemann surface. This subject draws on algebraic geometry, geometric topology, geometric analysis and mathematical physics, and the goal was to promote interactions between these various branches of the subject. The main current directions of research were well represented by the participants, and the talks included many from both senior and junior participants.}, author = {Anderson, Lara and Hausel, Tamás and Mazzeo, Rafe and Schaposnik, Laura}, issn = {1660-8933}, journal = {Oberwolfach Reports}, keywords = {Organic Chemistry, Biochemistry}, number = {2}, pages = {1357--1417}, publisher = {European Mathematical Society}, title = {{Geometry and physics of Higgs bundles}}, doi = {10.4171/owr/2019/23}, volume = {16}, year = {2020}, } @inproceedings{15071, abstract = {A mesophilic methanogenic culture, designated JL01, was isolated from Holocene permafrost in the Russian Arctic [1]. After long-term extensive cultivation at 15°C it turned out to be a tied binary culture of archaeal (JL01) and bacterial (Sphaerochaeta associata GLS2) strains. Strain JL01 was a strict anaerobe and grew on methanol, acetate and methylamines as energy and carbon sources. Cells were irregular coccoid, non-motile, non-spore-forming, and Gram-stainpositive. Optimum conditions for growth were 24-28 oC, pH 6.8–7.3 and 0.075-0.1 M NaCl. Phylogenetic tree reconstructions based on 16S rRNA and concatenated alignment of broadly conserved protein-coding genes revealed its close relation to Methanosarcina mazei S-6 T (similarity 99.5%). The comparison of whole genomic sequences (ANI) of the isolate and the type strain of M.mazei was 98.5%, which is higher than the values recommended for new species. Thus strain JL01 (=VKM B-2370=JCM 31898) represents the first M. mazei isolated from permanently subzero Arcticsediments. The long-term co-cultivation of JL01 with S. associata GLS2T showed the methane production without any additional carbon and energy sources. Genome analysis of S. associata GLS2T revealed putative genes involved in methanochondroithin catabolism.}, author = {Oshurkova, Viktoriia and Troshina, Olga and Trubitsyn, Vladimir and Ryzhmanova, Yana and Bochkareva, Olga and Shcherbakova, Viktoria}, booktitle = {Proceedings of 1st International Electronic Conference on Microbiology}, location = {Virtual}, publisher = {MDPI}, title = {{Characterization of methanosarcina mazei JL01 isolated from holocene arctic permafrost and study of the archaeon cooperation with bacterium Sphaerochaeta associata GLS2T}}, doi = {10.3390/ecm2020-07116}, year = {2020}, } @article{15072, abstract = {The interaction among fundamental particles in nature leads to many interesting effects in quantum statistical mechanics; examples include superconductivity for charged systems and superfluidity in cold gases. It is a huge challenge for mathematical physics to understand the collective behavior of systems containing a large number of particles, emerging from known microscopic interactions. In this workshop we brought together researchers working on different aspects of many-body quantum mechanics to discuss recent developments, exchange ideas and propose new challenges and research directions.}, author = {Hainzl, Christian and Schlein, Benjamin and Seiringer, Robert and Warzel, Simone}, issn = {1660-8933}, journal = {Oberwolfach Reports}, number = {3}, pages = {2541--2603}, publisher = {European Mathematical Society}, title = {{Many-body quantum systems}}, doi = {10.4171/owr/2019/41}, volume = {16}, year = {2020}, } @inproceedings{15074, abstract = {We introduce a new graph problem, the token dropping game, and we show how to solve it efficiently in a distributed setting. We use the token dropping game as a tool to design an efficient distributed algorithm for the stable orientation problem, which is a special case of the more general locally optimal semi-matching problem. The prior work by Czygrinow et al. (DISC 2012) finds a locally optimal semi-matching in O(Δ⁵) rounds in graphs of maximum degree Δ, which directly implies an algorithm with the same runtime for stable orientations. We improve the runtime to O(Δ⁴) for stable orientations and prove a lower bound of Ω(Δ) rounds.}, author = {Brandt, Sebastian and Keller, Barbara and Rybicki, Joel and Suomela, Jukka and Uitto, Jara}, booktitle = {34th International Symposium on Distributed Computing}, location = {Virtual}, publisher = {Schloss Dagstuhl - Leibniz-Zentrum für Informatik}, title = {{Brief announcement: Efficient load-balancing through distributed token dropping}}, doi = {10.4230/LIPIcs.DISC.2020.40}, volume = {179}, year = {2020}, } @inproceedings{15077, abstract = {We consider the following dynamic load-balancing process: given an underlying graph G with n nodes, in each step t≥ 0, one unit of load is created, and placed at a randomly chosen graph node. In the same step, the chosen node picks a random neighbor, and the two nodes balance their loads by averaging them. We are interested in the expected gap between the minimum and maximum loads at nodes as the process progresses, and its dependence on n and on the graph structure. Variants of the above graphical balanced allocation process have been studied previously by Peres, Talwar, and Wieder [Peres et al., 2015], and by Sauerwald and Sun [Sauerwald and Sun, 2015]. These authors left as open the question of characterizing the gap in the case of cycle graphs in the dynamic case, where weights are created during the algorithm’s execution. For this case, the only known upper bound is of 𝒪(n log n), following from a majorization argument due to [Peres et al., 2015], which analyzes a related graphical allocation process. In this paper, we provide an upper bound of 𝒪 (√n log n) on the expected gap of the above process for cycles of length n. We introduce a new potential analysis technique, which enables us to bound the difference in load between k-hop neighbors on the cycle, for any k ≤ n/2. We complement this with a "gap covering" argument, which bounds the maximum value of the gap by bounding its value across all possible subsets of a certain structure, and recursively bounding the gaps within each subset. We provide analytical and experimental evidence that our upper bound on the gap is tight up to a logarithmic factor.}, author = {Alistarh, Dan-Adrian and Nadiradze, Giorgi and Sabour, Amirmojtaba}, booktitle = {47th International Colloquium on Automata, Languages, and Programming}, location = {Saarbrücken, Germany, Virtual}, publisher = {Schloss Dagstuhl - Leibniz-Zentrum für Informatik}, title = {{Dynamic averaging load balancing on cycles}}, doi = {10.4230/LIPIcs.ICALP.2020.7}, volume = {168}, year = {2020}, } @article{15079, abstract = {Large complex systems tend to develop universal patterns that often represent their essential characteristics. For example, the cumulative effects of independent or weakly dependent random variables often yield the Gaussian universality class via the central limit theorem. For non-commutative random variables, e.g. matrices, the Gaussian behavior is often replaced by another universality class, commonly called random matrix statistics. Nearby eigenvalues are strongly correlated, and, remarkably, their correlation structure is universal, depending only on the symmetry type of the matrix. Even more surprisingly, this feature is not restricted to matrices; in fact Eugene Wigner, the pioneer of the field, discovered in the 1950s that distributions of the gaps between energy levels of complicated quantum systems universally follow the same random matrix statistics. This claim has never been rigorously proved for any realistic physical system but experimental data and extensive numerics leave no doubt as to its correctness. Since then random matrices have proved to be extremely useful phenomenological models in a wide range of applications beyond quantum physics that include number theory, statistics, neuroscience, population dynamics, wireless communication and mathematical finance. The ubiquity of random matrices in natural sciences is still a mystery, but recent years have witnessed a breakthrough in the mathematical description of the statistical structure of their spectrum. Random matrices and closely related areas such as log-gases have become an extremely active research area in probability theory. This workshop brought together outstanding researchers from a variety of mathematical backgrounds whose areas of research are linked to random matrices. While there are strong links between their motivations, the techniques used by these researchers span a large swath of mathematics, ranging from purely algebraic techniques to stochastic analysis, classical probability theory, operator algebra, supersymmetry, orthogonal polynomials, etc.}, author = {Erdös, László and Götze, Friedrich and Guionnet, Alice}, issn = {1660-8933}, journal = {Oberwolfach Reports}, number = {4}, pages = {3459--3527}, publisher = {European Mathematical Society}, title = {{Random matrices}}, doi = {10.4171/owr/2019/56}, volume = {16}, year = {2020}, }