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Graduate Student Homotopy Theory Seminar: Rational Homotopy Theory

Event Type
Seminar/Symposium
Sponsor
n/a
Location
341 Altgeld Hall
Date
Apr 22, 2022   3:00 pm  
Speaker
Langwen Hui
Contact
Doron Grossman-Naples
E-Mail
doronlg2@illinois.edu
Views
33

Rational homotopy theory is homotopy theory modulo torsion. This simplification reduces topology to algebra. More precisely, Quillen proved that the rational homotopy theory of 2-connected spaces is equivalent to that of (1) 1-connected dg Lie algebras (2) 2-connected dg cocommutative coalgebras. This is subsequently augmented by Sullivan, who provides a dg commutative algebra model of rational homotopy theory with computational strength. Time permitting, I will also discuss interesting applications to geometry and local algebra.

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