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SUMMARY:Systems of forms of the same degree - Simon Leo Rydin Myerson (Uni
 versity of Oxford)
DTSTART:20160503T131500Z
DTEND:20160503T141500Z
UID:TALK64194@talks.cam.ac.uk
CONTACT:G. Rosso
DESCRIPTION:Let f = (f_1\,...\,f_R) be a system of forms of degree d in n 
 variables. A classic result of Birch estimates the number of integral zero
 es of f of bounded height\, when  n >>_{d\,R} 1 is large and the variety  
 f = 0  is smooth. We give an improvement when R >>_d 1 is large\, and an e
 xtension to systems of Diophantine inequalities | f_i | < 1  with real coe
 fficients. Our strategy reduces the problem to an upper bound for the numb
 er of solutions to a multilinear auxiliary inequality\, comparable to an a
 uxiliary equation introduced by Dietmann and Schindler.
LOCATION:MR13
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