Simon Brendle has solved major open problems regarding the Yamabe equation in conformal geometry.

In 2012, he proved the Hsiang–Lawson's conjecture, a longstanding problem in minimal surface theory.

For his contributions to differential geometry he was awarded an EMS Prize in 2012.

He was named as the recipient of the 2014 Bôcher Prize[3] of the American Mathematical Society.

In 2017, he received a Simons Investigator Award[4] and the Fermat Prize.