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SUMMARY:Why Condensed Mathematics is Better Than Topology - Jiacheng Tang\
 , University of Manchester
DTSTART:20241206T160000Z
DTEND:20241206T170000Z
UID:TALK220645@talks.cam.ac.uk
CONTACT:Julian Wykowski
DESCRIPTION:The classic way to study algebra and topology together is thro
 ugh topological groups: groups with a compatible topology. However\, topol
 ogical abelian groups do not have nice categorical properties\, nor is the
 re a satisfactory theory of tensor products. Condensed mathematics was dev
 eloped recently as an attempt to combine algebra and topology in a nicer w
 ay. I will explain the problems with classic topology and how condensed ma
 thematics (partially) solves them. As an example\, we will see that many c
 ondensed notions (Ext\, tensor products\, group rings...) generalise the c
 orresponding notions for profinite modules\, suggesting that the condensed
  world is a better place to study profinite modules than the topological w
 orld.
LOCATION:MR13
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