[1] For his doctorate, Mustață moved to the United States, obtaining his PhD from UC Berkeley in 2001.
[2] A Clay Research Fellow during 2001–04, Mustață held postdoc positions at the University of Nice Sophia Antipolis (Fall 2001), the Isaac Newton Institute (Spring 2002), and Harvard University (2002–04).
Since 2004, when he became an associate professor, Mustață has been on the faculty of the University of Michigan in Ann Arbor.
[2] Mustață's research deals with a wide range of topics in algebraic geometry, including: various invariants of singularities of algebraic varieties, such as minimal log discrepancies, log canonical thresholds, multiplier ideals, Bernstein–Sato polynomials and F-thresholds ... resolutions of singularities, jet schemes, D-modules or positive characteristic methods ... birational geometry, asymptotic base loci and invariants of divisors, and toric varieties.
[5]Mustață currently resides in Ann Arbor, Michigan, with his wife, Olga, and daughter, Maya.