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UID:www.tcs.tifr.res.in/event/1553
DTSTAMP:20250515T092022Z
SUMMARY:Algebraic Independence Testing
DESCRIPTION:Speaker: Shanthanu  Suresh Rai (TIFR)\n\nAbstract: \nQuestion: 
 Are the given set of multivariate polynomials f_1\, ...\, f_k algebraicall
 y dependent? In other words\, is there a non-zero polynomial g such that g
 (f_1\, ...\, f_k) = 0?\nWe will see that algebraic independence shares the
  matroid structure of linear independence. We show this connection with th
 e help of partial derivatives of f_i (in particular\, using the Jacobian m
 atrix). From the Jacobian criteria\, we can show that algebraic independen
 ce testing is in RP.\nBut the above Jacobian criteria is valid over fields
  of characteristic 0\, like the complex numbers. In particular\, it is not
  valid over finite fields. Thus the problem of algebraic independence test
 ing over finite fields is wide open.\nWe will see that over finite fields\
 , algebraic independence testing is in AM ∩ coAM.\nLink to paper: https
 ://arxiv.org/abs/1801.09275\n
URL:https://www.tcs.tifr.res.in/web/events/1553
DTSTART;TZID=Asia/Kolkata:20250516T160000
DTEND;TZID=Asia/Kolkata:20250516T170000
LOCATION:A-201 (STCS Seminar Room)
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