After teacher training in mathematics and chemistry, Kalmbach obtained a PhD at the University of Göttingen under the supervision of Hans Grauert on the topic of low-dimensional CW complexes in non-compact manifolds.

Kalmbach's research deals with manifolds, lattice theory and quantum structures.

[3] In addition to her research career, Kalmbach invented in 1985 the talent program in STEM subjects (called MINT in Germany).

[4][5] Part of this is the yearly mathematics competition at the University of Ulm.

[7] She was a founder of European Women in Mathematics,[8] and a member and chair of the Emmy Noether Verein which supports female mathematicians.