[1] She specializes in differential geometry and was awarded the 2020-2021 Joan and Joseph Birman Fellowship for Women Scholars by the American Mathematical Society.
[2] Melnick also has research interests in conformal pseudo-Riemannian structures, parabolic Cartan geometries in general, and smooth dynamics.
[4] Prior to her graduate studies, Melnick received her Bachelor of Arts, also in Mathematics, from Reed College in 1999.
Before working at UMD, Melnick held the position of Gibbs Assistant Professor at Yale University while on an NSF Postdoctoral Research Fellowship.
[2][5] Melnick was awarded the 2020-2021 Joan and Joseph Birman Fellowship for Women Scholars by the American Mathematical Society for her research on differential-geometric aspects of rigidity.