BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Stanislaw Szarek (Case Western Reserve University/Sorbonne Univers ite) DTSTART:20210412T190000Z DTEND:20210412T200000Z DTSTAMP:20260423T021336Z UID:paw/31 DESCRIPTION:Title: Gen eralized probabilistic theories and tensor products of normed spaces\n by Stanislaw Szarek (Case Western Reserve University/Sorbonne Universite) as part of Probability and Analysis Webinar\n\n\nAbstract\nGeneralized Pro babilistic Theories (GPTs) form an abstract framework to describe theories of nature that have probabilistic features. A GPT must specify the set of states purporting to represent the physical reality\, the allowable measu rements\, the rules for outcome statistics of the latter\, and the composi tion rules describing what happens when we merge subsystems and create a l arger system. Examples include classical probability and quantum theory.\ nThe composition rules alluded to above usually involve tensor products an d\, in some formulations\, normed spaces. Among tensor products of normed spaces that have operational meaning in the GPT context\, the projective and the injective product are the extreme ones\, which leads to the natura l question "How much do they differ?" considered already by Grothendieck and Pisier (in the 1950s and 1980s). Surprisingly\, no systematic quanti tative analysis of the finite-dimensional case seems to have ever been mad e. We show that the projective/injective discrepancy is always lower-bound ed by the power of the (smaller) dimension\, with the exponent depending o n the generality of the setup. Some of the results are essentially optimal \, but others can be likely improved. The methods involve a wide range of techniques from geometry of Banach spaces and random matrices.\nJoint work with G. Aubrun\, L. Lami\, C. Palazuelos\, A. Winter.\n LOCATION:https://researchseminars.org/talk/paw/31/ END:VEVENT END:VCALENDAR