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UID:www.tcs.tifr.res.in/event/818
DTSTAMP:20230914T125939Z
SUMMARY:The Critical Exponent: A Novel Graph Invariant
DESCRIPTION:Speaker: Apoorva Khare (Indian Institute of Science\nDepartment
  of Mathematics\nBangalore 560012)\n\nAbstract: \nGiven a graph $G$\, let 
 $\\mathbb{P}_G$ denote the cone of positive semidefinite (psd) matrices\, 
 with non-negative entries\, and zeros according to $G$. Which powers prese
 rve psd-ness when applied entrywise to all matrices in $\\mathbb{P}_G$?\n\
 nIn recent work\, joint with D. Guillot and B. Rajaratnam\, we show how pr
 eserving positivity relates to the geometry of the graph $G$. This leads u
 s to propose a novel graph invariant: the "critical exponent" of $G$. Our 
 main result shows how this combinatorial invariant resolves the problem fo
 r all chordal graphs. We also report on progress for several families of n
 on-chordal graphs.\n\n \n
URL:https://www.tcs.tifr.res.in/web/events/818
DTSTART;TZID=Asia/Kolkata:20171017T160000
DTEND;TZID=Asia/Kolkata:20171017T170000
LOCATION:A-201 (STCS Seminar Room)
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