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Optimization, Complexity and Invariant Theory (Invited Talk)

Author Peter Bürgisser



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Peter Bürgisser
  • Institut für Mathematik, Technische Universität Berlin, Germany

Acknowledgements

The talk (and this write-up) are mainly based on the joint articles [Peter Bürgisser et al., 2019, https://doi.org/10.1109/FOCS.2019.00055; Peter Bürgisser et al., 2019, https://arxiv.org/abs/1910.12375] with Cole Franks, Ankit Garg, Rafael Oliveira, Michael Walter and Avi Wigderson. I am grateful to my coauthors for inspiration and enlightening discussions and thank Levent Dogan, Yinan Li, Visu Makam, Harold Nieuwboer and Philipp Reichenbach for valuable feedback.

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Peter Bürgisser. Optimization, Complexity and Invariant Theory (Invited Talk). In 38th International Symposium on Theoretical Aspects of Computer Science (STACS 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 187, pp. 1:1-1:20, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2021)
https://doi.org/10.4230/LIPIcs.STACS.2021.1

Abstract

Invariant and representation theory studies symmetries by means of group actions and is a well established source of unifying principles in mathematics and physics. Recent research suggests its relevance for complexity and optimization through quantitative and algorithmic questions. The goal of the talk is to give an introduction to new algorithmic and analysis techniques that extend convex optimization from the classical Euclidean setting to a general geodesic setting. We also point out surprising connections to a diverse set of problems in different areas of mathematics, statistics, computer science, and physics.

Subject Classification

ACM Subject Classification
  • Theory of computation → Continuous optimization
Keywords
  • geometric invariant theory
  • geodesic optimization
  • non-commutative optimization
  • null cone
  • operator scaling
  • moment polytope
  • orbit closure intersection
  • geometric programming

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