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DTSTART:20240310T070000
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URL:https://uwaterloo.ca/combinatorics-and-optimization/events/tutte-colloq
 uium-akash-sengupta
SUMMARY:Tutte Colloquium - Akash Sengupta
CLASS:PUBLIC
DESCRIPTION:TITLE: Sylvester-Gallai type configurations and Polynomial Ide
 ntity\nTesting\n\nSPEAKER:\n Akash Sengupta\n\nAFFILIATION:\n University o
 f Waterloo\n\nLOCATION:\n MC 5501\n\nABSTRACT: The classical Sylvester-Ga
 llai theorem in combinatorial\ngeometry says the following:\n\nIf a finite
  set of points in the Euclidean plane has the property that\nthe line join
 ing any two points contains a third point from the set\,\nthen all the poi
 nts must be collinear. \n\nMore generally\, a Sylvester-Gallai (SG)-type 
 configuration is a finite\nset of geometric objects with certain local dep
 endencies. A remarkable\nphenomenon is that the local constraints give ris
 e to global dimension\nbounds for linear SG-type configurations\, and such
  results have found\nfar reaching applications to complexity theory and co
 ding theory. In\nparticular\, SG-type configurations have been extremely u
 seful in\napplications to Polynomial Identity Testing (PIT)\, a central pr
 oblem\nin algebraic complexity theory.\n\nIn this talk\, we will discuss n
 on-linear generalizations of SG-type\nconfigurations which consist of poly
 nomials. We will discuss how\nuniform bounds on SG-configurations give ris
 e to deterministic\npoly-time algorithms for the PIT problem. I’ll talk 
 about results\nshowing that these non-linear SG-type configurations are in
 deed\nlow-dimensional as conjectured by Gupta in 2014. This is based on\nj
 oint works with A. Garg\, R. Oliveira and S. Peleg.
DTSTAMP:20260403T014524Z
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