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UID:142dcd7cab48a4b40adae7330632328e
CATEGORIES:Special Colloquium
CREATED:20230405T110120
SUMMARY:Sign patterns of the Mobius function. 
LOCATION:CORE   431
DESCRIPTION:<p><strong style="color: #222222; font-family: Arial, Helvetica, sans-serif
 ; font-size: small; letter-spacing: normal; orphans: 2; text-align: start; 
 text-indent: 0px; text-transform: none; white-space: normal; widows: 2; wor
 d-spacing: 0px;">Abstract:</strong>&nbsp;The Mobius function is one of the 
 most important arithmetic functions. There is a vague yet well known princi
 ple regarding its randomness properties called the “Mobius randomness law".
  It basically states that the Mobius function should be orthogonal to any "
 structured" sequence. P. Sarnak suggested a far reaching conjecture as a po
 ssible formalization of this principle. He conjectured that "structured seq
 uences" should correspond to sequences arising from deterministic dynamical
  systems. Sarnak’s conjecture follows from Chowla’s conjecture - which is t
 he mobius version of the prime tuple conjecture. I will describe progress i
 n recent years towards these conjectures, building on major advances dynami
 cs, additive combinatorics, and analytic number theory.</p>
CONTACT:Speaker: Tamar Ziegler (Hebrew University and IAS)
DTSTAMP:20260827T141829
DTSTART;TZID=America/New_York:20230413T153000
DTEND;TZID=America/New_York:20230413T163000
SEQUENCE:0
TRANSP:OPAQUE
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