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DTSTART:20240310T070000
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DTSTART:20241103T060000
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DTSTART;TZID=America/Toronto:20250224T143000
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URL:https://uwaterloo.ca/pure-mathematics/events/pure-math-department-collo
 quium-6
SUMMARY:Pure Math Department Colloquium
CLASS:PUBLIC
DESCRIPTION:CARLO PAGANO\, CONCORDIA UNIVERSITY \n\nHilbert 10 via additive
  combinatorics\n\nIn 1900 Hilbert proposed a list of problems that have be
 en very\ninfluential throughout the last century. In 1970 Matiyasevich\,\n
 building on earlier work of Davis—Putnam—Robinson\, proved that\nHilbe
 rt's 10th problem is undecidable for Z. The problem of extending\nthis res
 ult to any ring that is finitely generated over Z (eg ring of\nintegers in
  number fields) has attracted significant attention since\n1970 and\, than
 ks to the efforts of many mathematicians\, the task has\nbeen reduced to a
 n arithmetic problem about elliptic curves. This\nproblem so far had been 
 solved only conditional on the BSD conjecture\n(one of the Millenium probl
 ems) by Mazur—Rubin. \n\nIn joint work with Peter Koymans we have combin
 ed additive\ncombinatorics (Green—Tao’s celebrated theorem) with 2-des
 cent (an\nold technique dating back to Fermat) to solve this problem about
 \nelliptic curves unconditionally. This shows that Hilbert 10 is\nundecida
 ble over any finitely generated infinite commutative ring. \n\nIn this col
 loquium I will provide a gentle introduction to this\nundecidability resul
 t\, giving a glimpse of how mathematical logic\,\nnumber theory and additi
 ve combinatorics meet into one story. \n\nMC 5501
DTSTAMP:20260504T224031Z
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