[1] Her dissertation "Statistical properties of elements in infinite group" was directed by Benson Farb.
Dani joined the tenure stream faculty at Louisiana State University in 2009.
Dani delivered a series of invited lectures on geometric group theory at the Mathematical Sciences Research Institute in Berkeley, California in June 2015.
[4] In 2016, the Association for Women in Mathematics awarded Dani the Ruth I. Michler Memorial Prize.
The prize, awarded annually to a recently promoted associate professor, allows the recipient to spend a semester in the mathematics department at Cornell University in Ithaca, New York without teaching obligations.