[{"author":[{"last_name":"Hainzl","first_name":"Christian","full_name":"Hainzl, Christian"},{"full_name":"Schlein, Benjamin","last_name":"Schlein","first_name":"Benjamin"},{"first_name":"Robert","orcid":"0000-0002-6781-0521","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","last_name":"Seiringer","full_name":"Seiringer, Robert"},{"first_name":"Simone","last_name":"Warzel","full_name":"Warzel, Simone"}],"_id":"18958","language":[{"iso":"eng"}],"issue":"3","quality_controlled":"1","date_updated":"2025-01-29T13:19:06Z","oa_version":"None","citation":{"ista":"Hainzl C, Schlein B, Seiringer R, Warzel S. 2024. Many-body quantum systems. Oberwolfach Reports. 20(3), 2247–2302.","ieee":"C. Hainzl, B. Schlein, R. Seiringer, and S. Warzel, “Many-body quantum systems,” <i>Oberwolfach Reports</i>, vol. 20, no. 3. EMS Press, pp. 2247–2302, 2024.","mla":"Hainzl, Christian, et al. “Many-Body Quantum Systems.” <i>Oberwolfach Reports</i>, vol. 20, no. 3, EMS Press, 2024, pp. 2247–302, doi:<a href=\"https://doi.org/10.4171/owr/2023/39\">10.4171/owr/2023/39</a>.","ama":"Hainzl C, Schlein B, Seiringer R, Warzel S. Many-body quantum systems. <i>Oberwolfach Reports</i>. 2024;20(3):2247-2302. doi:<a href=\"https://doi.org/10.4171/owr/2023/39\">10.4171/owr/2023/39</a>","apa":"Hainzl, C., Schlein, B., Seiringer, R., &#38; Warzel, S. (2024). Many-body quantum systems. <i>Oberwolfach Reports</i>. EMS Press. <a href=\"https://doi.org/10.4171/owr/2023/39\">https://doi.org/10.4171/owr/2023/39</a>","short":"C. Hainzl, B. Schlein, R. Seiringer, S. Warzel, Oberwolfach Reports 20 (2024) 2247–2302.","chicago":"Hainzl, Christian, Benjamin Schlein, Robert Seiringer, and Simone Warzel. “Many-Body Quantum Systems.” <i>Oberwolfach Reports</i>. EMS Press, 2024. <a href=\"https://doi.org/10.4171/owr/2023/39\">https://doi.org/10.4171/owr/2023/39</a>."},"type":"journal_article","intvolume":"        20","day":"18","publisher":"EMS Press","article_type":"original","title":"Many-body quantum systems","volume":20,"date_published":"2024-04-18T00:00:00Z","status":"public","year":"2024","publication":"Oberwolfach Reports","page":"2247-2302","publication_status":"published","abstract":[{"text":"This workshop brought together experts on the analysis of quantum many-body problems and quantum statistical mechanics, with the goal of discussing the state-of-the-art of the field, recent developments as well as challenges for the future. The main topics of discussion concerned the equilibrium and dynamical behavior of (bosonic or fermionic) quantum gases, quantum spin systems, as well as quantum field theory models like the Nelson or Fröhlich model.","lang":"eng"}],"doi":"10.4171/owr/2023/39","department":[{"_id":"RoSe"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","acknowledgement":"The MFO and the workshop organizers would like to thank the National Science Foundation for supporting the participation of junior researchers in the workshop by the grant DMS-2230648, “US Junior Oberwolfach Fellows”.","date_created":"2025-01-29T13:09:28Z","article_processing_charge":"No","month":"04","publication_identifier":{"eissn":["1660-8941"],"issn":["1660-8933"]}},{"article_type":"original","title":"Arbeitsgemeinschaft: Geometry and representation theory around the P=W conjecture","volume":21,"year":"2024","publication":"Oberwolfach Reports","OA_place":"publisher","page":"949-1004","department":[{"_id":"TaHa"}],"acknowledgement":"The MFO and the workshop organizers would like to thank the\r\nNational Science Foundation for supporting the participation of junior researchers\r\nby the grant DMS-2230648, “US Junior Oberwolfach Fellows”. Moreover, the\r\nMFO and the workshop organizers would like to thank the Oberwolfach Foundation for supporting the participation of junior researchers in the Arbeitsgemeinschaft.","date_created":"2025-01-29T15:34:22Z","article_processing_charge":"No","publication_identifier":{"eissn":["1660-8941"],"issn":["1660-8933"]},"author":[{"full_name":"Hausel, Tamás","first_name":"Tamás","orcid":"0000-0002-9582-2634","id":"4A0666D8-F248-11E8-B48F-1D18A9856A87","last_name":"Hausel"},{"last_name":"Maulik","first_name":"Davesh","full_name":"Maulik, Davesh"},{"full_name":"Mellit, Anton","first_name":"Anton","last_name":"Mellit"},{"last_name":"Schiffmann","first_name":"Olivier","full_name":"Schiffmann, Olivier"},{"last_name":"Shen","first_name":"Junliang","full_name":"Shen, Junliang"}],"_id":"18970","has_accepted_license":"1","quality_controlled":"1","citation":{"ama":"Hausel T, Maulik D, Mellit A, Schiffmann O, Shen J. Arbeitsgemeinschaft: Geometry and representation theory around the P=W conjecture. <i>Oberwolfach Reports</i>. 2024;21(2):949-1004. doi:<a href=\"https://doi.org/10.4171/owr/2024/16\">10.4171/owr/2024/16</a>","ieee":"T. Hausel, D. Maulik, A. Mellit, O. Schiffmann, and J. Shen, “Arbeitsgemeinschaft: Geometry and representation theory around the P=W conjecture,” <i>Oberwolfach Reports</i>, vol. 21, no. 2. EMS Press, pp. 949–1004, 2024.","ista":"Hausel T, Maulik D, Mellit A, Schiffmann O, Shen J. 2024. Arbeitsgemeinschaft: Geometry and representation theory around the P=W conjecture. Oberwolfach Reports. 21(2), 949–1004.","mla":"Hausel, Tamás, et al. “Arbeitsgemeinschaft: Geometry and Representation Theory around the P=W Conjecture.” <i>Oberwolfach Reports</i>, vol. 21, no. 2, EMS Press, 2024, pp. 949–1004, doi:<a href=\"https://doi.org/10.4171/owr/2024/16\">10.4171/owr/2024/16</a>.","chicago":"Hausel, Tamás, Davesh Maulik, Anton Mellit, Olivier Schiffmann, and Junliang Shen. “Arbeitsgemeinschaft: Geometry and Representation Theory around the P=W Conjecture.” <i>Oberwolfach Reports</i>. EMS Press, 2024. <a href=\"https://doi.org/10.4171/owr/2024/16\">https://doi.org/10.4171/owr/2024/16</a>.","short":"T. Hausel, D. Maulik, A. Mellit, O. Schiffmann, J. Shen, Oberwolfach Reports 21 (2024) 949–1004.","apa":"Hausel, T., Maulik, D., Mellit, A., Schiffmann, O., &#38; Shen, J. (2024). Arbeitsgemeinschaft: Geometry and representation theory around the P=W conjecture. <i>Oberwolfach Reports</i>. EMS Press. <a href=\"https://doi.org/10.4171/owr/2024/16\">https://doi.org/10.4171/owr/2024/16</a>"},"type":"journal_article","intvolume":"        21","publisher":"EMS Press","date_published":"2024-05-05T00:00:00Z","status":"public","abstract":[{"text":"Given a smooth projective curve C, nonabelian Hodge theory gives a diffeomorphism between two different moduli spaces associated to C. The first is the moduli space of Higgs bundles on C of rank n, which is equipped with the structure of an algebraic completely integrable Hamiltonian system. The second is the character variety of representations of the fundamental group of C into GL(n). In 2012, de Cataldo, Hausel, and Migliorini [1] proposed the P=W conjecture which identifies the perverse filtration on the cohomology of the Higgs moduli space with the weight filtration on the cohomology of the character variety. Recently, in 2022, two independent proofs of the P=W Conjecture appeared, in work of Maulik &Shen [2] and Hausel, Mellit, Minets &Schiffmann [6]. The aim of the Arbeitsgemeinschaft was to understand the P=W Conjecture and these two recent proofs.","lang":"eng"}],"publication_status":"published","ddc":["500"],"doi":"10.4171/owr/2024/16","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","name":"Creative Commons Attribution-ShareAlike 4.0 International Public License (CC BY-SA 4.0)","image":"/images/cc_by_sa.png","short":"CC BY-SA (4.0)"},"OA_type":"hybrid","month":"05","main_file_link":[{"url":"https://doi.org/10.4171/owr/2024/16","open_access":"1"}],"oa":1,"language":[{"iso":"eng"}],"issue":"2","date_updated":"2025-01-29T15:39:55Z","oa_version":"Published Version","license":"https://creativecommons.org/licenses/by-sa/4.0/","day":"05"},{"citation":{"chicago":"Arnaud, Marie-Claude, Michael Hutchings, and Vadim Kaloshin. “Dynamische Systeme.” <i>Oberwolfach Reports</i>. EMS Press, 2023. <a href=\"https://doi.org/10.4171/owr/2023/30\">https://doi.org/10.4171/owr/2023/30</a>.","short":"M.-C. Arnaud, M. Hutchings, V. Kaloshin, Oberwolfach Reports 20 (2023) 1671–1730.","apa":"Arnaud, M.-C., Hutchings, M., &#38; Kaloshin, V. (2023). Dynamische Systeme. <i>Oberwolfach Reports</i>. EMS Press. <a href=\"https://doi.org/10.4171/owr/2023/30\">https://doi.org/10.4171/owr/2023/30</a>","ama":"Arnaud M-C, Hutchings M, Kaloshin V. Dynamische Systeme. <i>Oberwolfach Reports</i>. 2023;20(3):1671-1730. doi:<a href=\"https://doi.org/10.4171/owr/2023/30\">10.4171/owr/2023/30</a>","mla":"Arnaud, Marie-Claude, et al. “Dynamische Systeme.” <i>Oberwolfach Reports</i>, vol. 20, no. 3, EMS Press, 2023, pp. 1671–730, doi:<a href=\"https://doi.org/10.4171/owr/2023/30\">10.4171/owr/2023/30</a>.","ieee":"M.-C. Arnaud, M. Hutchings, and V. Kaloshin, “Dynamische Systeme,” <i>Oberwolfach Reports</i>, vol. 20, no. 3. EMS Press, pp. 1671–1730, 2023.","ista":"Arnaud M-C, Hutchings M, Kaloshin V. 2023. Dynamische Systeme. Oberwolfach Reports. 20(3), 1671–1730."},"quality_controlled":"1","date_updated":"2025-01-29T13:23:15Z","oa_version":"None","issue":"3","_id":"18959","language":[{"iso":"eng"}],"author":[{"last_name":"Arnaud","first_name":"Marie-Claude","full_name":"Arnaud, Marie-Claude"},{"full_name":"Hutchings, Michael","first_name":"Michael","last_name":"Hutchings"},{"full_name":"Kaloshin, Vadim","first_name":"Vadim","id":"FE553552-CDE8-11E9-B324-C0EBE5697425","last_name":"Kaloshin","orcid":"0000-0002-6051-2628"}],"publisher":"EMS Press","day":"09","intvolume":"        20","type":"journal_article","page":"1671-1730","abstract":[{"lang":"eng","text":"This workshop continues a series of workshops whose current format originated in 1981 under then-organizers Moser and Zehnder, and whose latest iteration took place in July 2023. The general goal of this series of workshops is to discuss the latest developments in the field of dynamical systems, broadly construed, and its connections with neighboring areas of mathematics such as differential geometry, partial differential equations, and more recently contact and symplectic geometry. We continued this tradition, bringing in new participants working in areas of dynamical systems and its connections with other areas of mathematics that are currently highly active and/or showing great promise for future development. Key focus areas for the 2023 workshop include spectral rigidity for planar domains, chaotic and oscillatory motions in celestial mechanics, conformal symplectic dynamics, and relations between dynamics.he workshop by the grant DMS-2230648, “US Junior Oberwolfach Fellows”."}],"publication_status":"published","publication":"Oberwolfach Reports","status":"public","year":"2023","date_published":"2023-07-09T00:00:00Z","volume":20,"article_type":"original","title":"Dynamische Systeme","publication_identifier":{"eissn":["1660-8941"],"issn":["1660-8933"]},"month":"07","article_processing_charge":"No","date_created":"2025-01-29T13:19:15Z","acknowledgement":"The MFO and the workshop organizers would like to thank the National Science Foundation for supporting the participation of junior researchers in the workshop by the grant DMS-2230648, “US Junior Oberwolfach Fellows”.","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","department":[{"_id":"VaKa"}],"doi":"10.4171/owr/2023/30"},{"scopus_import":"1","quality_controlled":"1","citation":{"chicago":"Arnaud, Marie-Claude, Helmut W. Hofer, Michael Hutchings, and Vadim Kaloshin. “Dynamische Systeme.” <i>Oberwolfach Reports</i>. European Mathematical Society, 2022. <a href=\"https://doi.org/10.4171/owr/2021/33\">https://doi.org/10.4171/owr/2021/33</a>.","apa":"Arnaud, M.-C., Hofer, H. W., Hutchings, M., &#38; Kaloshin, V. (2022). Dynamische Systeme. <i>Oberwolfach Reports</i>. European Mathematical Society. <a href=\"https://doi.org/10.4171/owr/2021/33\">https://doi.org/10.4171/owr/2021/33</a>","short":"M.-C. Arnaud, H.W. Hofer, M. Hutchings, V. Kaloshin, Oberwolfach Reports 18 (2022) 1735–1803.","ama":"Arnaud M-C, Hofer HW, Hutchings M, Kaloshin V. Dynamische Systeme. <i>Oberwolfach Reports</i>. 2022;18(3):1735-1803. doi:<a href=\"https://doi.org/10.4171/owr/2021/33\">10.4171/owr/2021/33</a>","ieee":"M.-C. Arnaud, H. W. Hofer, M. Hutchings, and V. Kaloshin, “Dynamische Systeme,” <i>Oberwolfach Reports</i>, vol. 18, no. 3. European Mathematical Society, pp. 1735–1803, 2022.","mla":"Arnaud, Marie-Claude, et al. “Dynamische Systeme.” <i>Oberwolfach Reports</i>, vol. 18, no. 3, European Mathematical Society, 2022, pp. 1735–803, doi:<a href=\"https://doi.org/10.4171/owr/2021/33\">10.4171/owr/2021/33</a>.","ista":"Arnaud M-C, Hofer HW, Hutchings M, Kaloshin V. 2022. Dynamische Systeme. Oberwolfach Reports. 18(3), 1735–1803."},"_id":"17063","author":[{"full_name":"Arnaud, Marie-Claude","first_name":"Marie-Claude","last_name":"Arnaud"},{"full_name":"Hofer, Helmut W.","first_name":"Helmut W.","last_name":"Hofer"},{"full_name":"Hutchings, Michael","first_name":"Michael","last_name":"Hutchings"},{"full_name":"Kaloshin, Vadim","first_name":"Vadim","orcid":"0000-0002-6051-2628","last_name":"Kaloshin","id":"FE553552-CDE8-11E9-B324-C0EBE5697425"}],"intvolume":"        18","publisher":"European Mathematical Society","type":"journal_article","page":"1735-1803","volume":18,"title":"Dynamische Systeme","article_type":"original","publication":"Oberwolfach Reports","year":"2022","article_processing_charge":"No","date_created":"2024-05-29T06:01:19Z","publication_identifier":{"eissn":["1660-8941"],"issn":["1660-8933"]},"department":[{"_id":"VaKa"}],"date_updated":"2024-08-06T07:28:50Z","oa_version":"Published Version","issue":"3","language":[{"iso":"eng"}],"oa":1,"day":"26","corr_author":"1","publication_status":"published","abstract":[{"text":"This workshop continued a biannual series of workshops at Oberwolfach on dynamical systems that started with a meeting organized by Moser and Zehnder in 1981. Workshops in this series focus on new results and developments in dynamical systems and related areas of mathematics, with symplectic geometry playing an important role in recent years in connection with Hamiltonian dynamics. In this year special emphasis was placed on various kinds of spectra (in contact geometry, in Riemannian geometry, in dynamical systems and in symplectic topology) and their applications to dynamics.","lang":"eng"}],"date_published":"2022-11-26T00:00:00Z","status":"public","month":"11","main_file_link":[{"url":"https://www.doi.org/10.4171/OWR/2021/33","open_access":"1"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","doi":"10.4171/owr/2021/33"},{"intvolume":"        16","day":"04","publisher":"European Mathematical Society","type":"journal_article","oa_version":"None","quality_controlled":"1","date_updated":"2024-03-11T09:20:34Z","issue":"2","keyword":["Organic Chemistry","Biochemistry"],"citation":{"mla":"Anderson, Lara, et al. “Geometry and Physics of Higgs Bundles.” <i>Oberwolfach Reports</i>, vol. 16, no. 2, European Mathematical Society, 2020, pp. 1357–417, doi:<a href=\"https://doi.org/10.4171/owr/2019/23\">10.4171/owr/2019/23</a>.","ista":"Anderson L, Hausel T, Mazzeo R, Schaposnik L. 2020. Geometry and physics of Higgs bundles. Oberwolfach Reports. 16(2), 1357–1417.","ieee":"L. Anderson, T. Hausel, R. Mazzeo, and L. Schaposnik, “Geometry and physics of Higgs bundles,” <i>Oberwolfach Reports</i>, vol. 16, no. 2. European Mathematical Society, pp. 1357–1417, 2020.","ama":"Anderson L, Hausel T, Mazzeo R, Schaposnik L. Geometry and physics of Higgs bundles. <i>Oberwolfach Reports</i>. 2020;16(2):1357-1417. doi:<a href=\"https://doi.org/10.4171/owr/2019/23\">10.4171/owr/2019/23</a>","short":"L. Anderson, T. Hausel, R. Mazzeo, L. Schaposnik, Oberwolfach Reports 16 (2020) 1357–1417.","apa":"Anderson, L., Hausel, T., Mazzeo, R., &#38; Schaposnik, L. (2020). Geometry and physics of Higgs bundles. <i>Oberwolfach Reports</i>. European Mathematical Society. <a href=\"https://doi.org/10.4171/owr/2019/23\">https://doi.org/10.4171/owr/2019/23</a>","chicago":"Anderson, Lara, Tamás Hausel, Rafe Mazzeo, and Laura Schaposnik. “Geometry and Physics of Higgs Bundles.” <i>Oberwolfach Reports</i>. European Mathematical Society, 2020. <a href=\"https://doi.org/10.4171/owr/2019/23\">https://doi.org/10.4171/owr/2019/23</a>."},"language":[{"iso":"eng"}],"_id":"15070","author":[{"full_name":"Anderson, Lara","first_name":"Lara","last_name":"Anderson"},{"full_name":"Hausel, Tamás","first_name":"Tamás","id":"4A0666D8-F248-11E8-B48F-1D18A9856A87","last_name":"Hausel"},{"first_name":"Rafe","last_name":"Mazzeo","full_name":"Mazzeo, Rafe"},{"first_name":"Laura","last_name":"Schaposnik","full_name":"Schaposnik, Laura"}],"month":"06","article_processing_charge":"No","date_created":"2024-03-04T11:36:31Z","publication_identifier":{"issn":["1660-8933"]},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","department":[{"_id":"TaHa"}],"doi":"10.4171/owr/2019/23","page":"1357-1417","publication_status":"published","abstract":[{"text":"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.","lang":"eng"}],"volume":16,"date_published":"2020-06-04T00:00:00Z","title":"Geometry and physics of Higgs bundles","article_type":"original","publication":"Oberwolfach Reports","year":"2020","status":"public"},{"type":"journal_article","day":"10","intvolume":"        16","publisher":"European Mathematical Society","language":[{"iso":"eng"}],"_id":"15072","author":[{"full_name":"Hainzl, Christian","last_name":"Hainzl","first_name":"Christian"},{"full_name":"Schlein, Benjamin","last_name":"Schlein","first_name":"Benjamin"},{"full_name":"Seiringer, Robert","first_name":"Robert","orcid":"0000-0002-6781-0521","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","last_name":"Seiringer"},{"full_name":"Warzel, Simone","last_name":"Warzel","first_name":"Simone"}],"date_updated":"2024-03-12T12:02:00Z","oa_version":"None","quality_controlled":"1","issue":"3","citation":{"ama":"Hainzl C, Schlein B, Seiringer R, Warzel S. Many-body quantum systems. <i>Oberwolfach Reports</i>. 2020;16(3):2541-2603. doi:<a href=\"https://doi.org/10.4171/owr/2019/41\">10.4171/owr/2019/41</a>","mla":"Hainzl, Christian, et al. “Many-Body Quantum Systems.” <i>Oberwolfach Reports</i>, vol. 16, no. 3, European Mathematical Society, 2020, pp. 2541–603, doi:<a href=\"https://doi.org/10.4171/owr/2019/41\">10.4171/owr/2019/41</a>.","ista":"Hainzl C, Schlein B, Seiringer R, Warzel S. 2020. Many-body quantum systems. Oberwolfach Reports. 16(3), 2541–2603.","ieee":"C. Hainzl, B. Schlein, R. Seiringer, and S. Warzel, “Many-body quantum systems,” <i>Oberwolfach Reports</i>, vol. 16, no. 3. European Mathematical Society, pp. 2541–2603, 2020.","chicago":"Hainzl, Christian, Benjamin Schlein, Robert Seiringer, and Simone Warzel. “Many-Body Quantum Systems.” <i>Oberwolfach Reports</i>. European Mathematical Society, 2020. <a href=\"https://doi.org/10.4171/owr/2019/41\">https://doi.org/10.4171/owr/2019/41</a>.","apa":"Hainzl, C., Schlein, B., Seiringer, R., &#38; Warzel, S. (2020). Many-body quantum systems. <i>Oberwolfach Reports</i>. European Mathematical Society. <a href=\"https://doi.org/10.4171/owr/2019/41\">https://doi.org/10.4171/owr/2019/41</a>","short":"C. Hainzl, B. Schlein, R. Seiringer, S. Warzel, Oberwolfach Reports 16 (2020) 2541–2603."},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","department":[{"_id":"RoSe"}],"doi":"10.4171/owr/2019/41","article_processing_charge":"No","month":"09","date_created":"2024-03-04T11:46:12Z","publication_identifier":{"issn":["1660-8933"]},"date_published":"2020-09-10T00:00:00Z","volume":16,"article_type":"original","title":"Many-body quantum systems","publication":"Oberwolfach Reports","status":"public","year":"2020","abstract":[{"lang":"eng","text":"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."}],"publication_status":"published","page":"2541-2603"},{"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","department":[{"_id":"LaEr"}],"doi":"10.4171/owr/2019/56","publication_identifier":{"issn":["1660-8933"]},"month":"11","article_processing_charge":"No","date_created":"2024-03-05T07:54:44Z","publication":"Oberwolfach Reports","year":"2020","status":"public","volume":16,"date_published":"2020-11-19T00:00:00Z","title":"Random matrices","article_type":"original","publication_status":"published","page":"3459-3527","abstract":[{"text":"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.\r\nThis 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.","lang":"eng"}],"type":"journal_article","publisher":"European Mathematical Society","day":"19","intvolume":"        16","_id":"15079","language":[{"iso":"eng"}],"author":[{"first_name":"László","orcid":"0000-0001-5366-9603","last_name":"Erdös","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","full_name":"Erdös, László"},{"first_name":"Friedrich","last_name":"Götze","full_name":"Götze, Friedrich"},{"last_name":"Guionnet","first_name":"Alice","full_name":"Guionnet, Alice"}],"citation":{"short":"L. Erdös, F. Götze, A. Guionnet, Oberwolfach Reports 16 (2020) 3459–3527.","apa":"Erdös, L., Götze, F., &#38; Guionnet, A. (2020). Random matrices. <i>Oberwolfach Reports</i>. European Mathematical Society. <a href=\"https://doi.org/10.4171/owr/2019/56\">https://doi.org/10.4171/owr/2019/56</a>","chicago":"Erdös, László, Friedrich Götze, and Alice Guionnet. “Random Matrices.” <i>Oberwolfach Reports</i>. European Mathematical Society, 2020. <a href=\"https://doi.org/10.4171/owr/2019/56\">https://doi.org/10.4171/owr/2019/56</a>.","ieee":"L. Erdös, F. Götze, and A. Guionnet, “Random matrices,” <i>Oberwolfach Reports</i>, vol. 16, no. 4. European Mathematical Society, pp. 3459–3527, 2020.","mla":"Erdös, László, et al. “Random Matrices.” <i>Oberwolfach Reports</i>, vol. 16, no. 4, European Mathematical Society, 2020, pp. 3459–527, doi:<a href=\"https://doi.org/10.4171/owr/2019/56\">10.4171/owr/2019/56</a>.","ista":"Erdös L, Götze F, Guionnet A. 2020. Random matrices. Oberwolfach Reports. 16(4), 3459–3527.","ama":"Erdös L, Götze F, Guionnet A. Random matrices. <i>Oberwolfach Reports</i>. 2020;16(4):3459-3527. doi:<a href=\"https://doi.org/10.4171/owr/2019/56\">10.4171/owr/2019/56</a>"},"quality_controlled":"1","date_updated":"2024-03-12T12:25:18Z","oa_version":"None","issue":"4"}]