BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Mokshay Madiman (University of Delaware) DTSTART:20231122T160000Z DTEND:20231122T171500Z DTSTAMP:20260423T035956Z UID:AAIT/25 DESCRIPTION:Title: An alogies between entropy\, volume\, and cardinality inequalities for projec tions.\nby Mokshay Madiman (University of Delaware) as part of Seminar on Algorithmic Aspects of Information Theory\n\n\nAbstract\nIt is well kn own that entropy inequalities are a quick way of obtaining volume inequali ties for projections of sets in a Euclidean space (or cardinality inequali ties for projections of subsets of the integer lattice) - for example\, th e Loomis-Whitney inequality follows easily from the classical Han’s ineq uality. There is also a well known connection with integral inequalities. We will review more such analogies\, as well as their limitations. For exa mple\, we will observe that volume of projections to coordinate subspaces is not submodular (though entropy is)\, and discuss general dualities betw een entropy and integral inequalities. We will also discuss some particula rly useful classes of Shannon-type inequalities that may be new to the AAI T audience - these also have applications to volume or cardinality. Most o f this talk will be tutorial - it will be based on the work of many people in the geometry\, combinatorics\, probability\, and information theory co mmunities\, rather than just the work of the speaker.\n LOCATION:https://researchseminars.org/talk/AAIT/25/ END:VEVENT END:VCALENDAR