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UID:www.tcs.tifr.res.in/event/1124
DTSTAMP:20230914T125951Z
SUMMARY:Two-and-a-half proofs of "the duality trick"
DESCRIPTION:Speaker: Anamay Tengse\n\nAbstract: \nThe fact that the polynom
 ial (x1+...+xn)^d can be written as a poly(n\,d)-sum of products of univar
 iates is a consequence of what is popularly known as 'the duality trick' i
 n the algebraic complexity circles. The actual identity is much more gener
 al\, and in particular\, applies to any linear form raised to an arbitrary
  power. Saxena (2008) famously used this duality to derive identity testin
 g algorithms for polynomials that are poly(n\,d)-sums of powers of linear 
 forms. This model (AKA sum-power-sum) coincides with the well-studied noti
 on of Waring rank in mathematics.\n\nIn this talk\, we will see two proofs
  of the duality trick due to Saxena and Shpilka respectively. Both these p
 roofs use fairly elementary ideas about polynomials. We shall then see a d
 ifferent proof of correctness of Saxena's construction that uses mildly no
 n-elementary algebraic geometry.\n\nZoom link: https://zoom.us/j/981322275
 53?pwd=K2cyQllKVjExdUhlRm0vc0ZHcEt0Zz09\n
URL:https://www.tcs.tifr.res.in/web/events/1124
DTSTART;TZID=Asia/Kolkata:20210409T171500
DTEND;TZID=Asia/Kolkata:20210409T181500
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