Department of

# Mathematics

Seminar Calendar
for events the day of Friday, April 22, 2022.

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Questions regarding events or the calendar should be directed to Tori Corkery.
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Friday, April 22, 2022

3:00 pm in 341 Altgeld Hall,Friday, April 22, 2022

#### Rational Homotopy Theory

###### Langwen Hui (UIUC Math)

Abstract: 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.