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DTSTART:20240310T070000
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URL:https://uwaterloo.ca/pure-mathematics/events/logic-seminar-72
SUMMARY:Logic Seminar
CLASS:PUBLIC
DESCRIPTION:ARISTOMENIS PAPADOPOULOS\, UNIVERSITY OF MARYLAND\n\nZarankiewi
 cz's Problem and Model Theory\n\n\"A shower thought that anyone interested
  in graph theory must have had\nat some point in their lives is the follow
 ing: 'How \"\"sparse\"\" must a\ngiven graph be\, if I know that it has no
  \"\"dense\"\" subgraphs?'. This\ncuriosity definitely crossed the mind of
  Polish mathematician K.\nZarankiewicz\, who asked a version of this quest
 ion formally in 1951.\nIn the years that followed\, many central figures i
 n the development of\nextremal combinatorics contemplated this problem\, g
 iving various kinds\nof answers. Some of these will be surveyed in the fir
 st part of my\ntalk.\n\nSo far so good\, but this is a logic seminar and t
 he title says the\nwords \"\"Model Theory\"\"… In the second part of my 
 talk\, I will\ndiscuss how the celebrated Szemerédi-Trotter theorem gave 
 a starting\npoint to the study of Zarankiewicz's problem in \"\"geometric\
 "\"\ncontexts\, and how the language of model theory has been able to\ncap
 ture exactly what these contexts are. I will then ramble about\nimprovemen
 ts to the classical answers to Zarankiewicz's problem\, when\nwe restrict 
 our attention to semilinear/semibounded o-minimal\nstructures\, Presburger
  arithmetic\, and various kinds of Hrushovski\nconstructions. \n\nThe new 
 results that will appear in the talk were obtained jointly\nwith Pantelis 
 Eleftheriou.\"\n\nMC 5479
DTSTAMP:20260504T224345Z
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