Henrion, Didier (ed.); Kuhlmann, Salma (ed.); Speicher, Roland (ed.); Vinnikov, Victor (ed.) Real algebraic geometry with a view toward hyperbolic programming and free probability. Abstracts from the workshop held March 1–7, 2020. (English) Zbl 1460.00039 Oberwolfach Rep. 17, No. 1, 639-712 (2020). Summary: Continuing the tradition initiated in the MFO workshops held in 2014 and 2017, this workshop was dedicated to the newest developments in real algebraic geometry and polynomial optimization, with a particular emphasis on free non-commutative real algebraic geometry and hyperbolic programming. A particular effort was invested in exploring the interrelations with free probability. This established an interesting dialogue between researchers working in real algebraic geometry and those working in free probability, from which emerged new exciting and promising synergies. MSC: 00B05 Collections of abstracts of lectures 00B25 Proceedings of conferences of miscellaneous specific interest 14-06 Proceedings, conferences, collections, etc. pertaining to algebraic geometry 12-06 Proceedings, conferences, collections, etc. pertaining to field theory 14Pxx Real algebraic and real-analytic geometry 12D15 Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) 14A22 Noncommutative algebraic geometry 46L54 Free probability and free operator algebras 52Axx General convexity 90C23 Polynomial optimization 93B25 Algebraic methods 13Pxx Computational aspects and applications of commutative rings 14Qxx Computational aspects in algebraic geometry 90C22 Semidefinite programming PDFBibTeX XMLCite \textit{D. Henrion} (ed.) et al., Oberwolfach Rep. 17, No. 1, 639--712 (2020; Zbl 1460.00039) Full Text: DOI References: [1] A. Buckley and T. Koˇsir,Determinantal representations of smooth cubic surfaces, Geom. Dedicata125(2007), 115-140. · Zbl 1117.14038 [2] L. G˚arding,An inequality for hyperbolic polynomials, J. Math. Mech.8(1959), 957-965. · Zbl 0090.01603 [3] J. W. Helton and V. Vinnikov,Linear matrix inequality representation of sets, Comm. Pure Appl. Math.60(2007), 654-674. · Zbl 1116.15016 [4] D. Hilbert,Ueber die Darstellung definiter Formen als Summe von Formenquadraten, Math. Ann.32(1888), 342-350. · JFM 20.0198.02 [5] M. Kummer and E. Shamovich,Real fibered morphisms and Ulrich sheaves, J. Algebraic Geom.29(2020), 167-198. · Zbl 1470.14082 [6] E. Shamovic and V. Vinnikov,Livsic-type determinantal representations and hyperbolicity, Adv. Math.329(2018), 487-522 · Zbl 1391.32009 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.