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Inequalities in Operator Algebras

MA5930A1.3 Mathematics Modules on Special Topics3 ECTSEnglishEinmaligDepartment Mathematics
AI-edited module sheet. Based on the TUMonline module description, edited for readability.Original in TUMonline

What it is about

You learn the fundamentals of operator algebras and deepen key inequalities and structures that play a role in quantum mechanics. In the end you will be able to apply and understand important concepts such as complete positivity, operator monotonicity/-convexity, Tomita–Takesaki theory, as well as central results on entropy and relaxation in noncommutative systems.

What you will be able to do

  • Understanding of fundamental concepts of operator algebras
  • Mastery of completely positive maps
  • Insight into operator monotonicity and operator convexity
  • Familiarity with Tomita–Takesaki theory and Araki's relative modular operator
  • Knowledge and application of Lieb's Concavity Theorem and Lindblad's Monotonicity Theorem
  • Understanding of strong subadditivity of quantum entropy and related inequalities
  • Insight into entropy dissipation, noncommutative logarithmic Sobolev inequalities and relaxation rates of Lindblad equations
  • Foundations of noncommutative optimal transport inequalities

What the module consists of

  • LecturePresentation and discussion of theory at the board; central role in conveying the content

Teaching method

  • Board lectureExplanation of the theory and derivations during lectures
  • Discussion in plenaryQuestions and discussions to deepen and clarify the content
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Official page in TUMonline · Details are not binding.