Šverák obtained his doctorate from the Charles University in Prague in 1986, under supervision of Jindřich Nečas. He worked on problems in the theory of non-linear elasticity. In 1992 he won an EMS Prize for producing a counterexample to a problem first posed by Charles B. Morrey, Jr. in 1950, whether rank-one convexity implies quasiconvexity.
- Joseph, Anthony, ed. (1994). First European Congress of Mathematics: Invited lectures. Nelson Thornes. ISBN 3-7643-2798-7.
- ——— (1992). "Rank-one convexity does not imply quasiconvexity". Proceedings of the Royal Society of Edinburgh. Section A. Mathematics. 120 (1–2): 185–189. ISSN 0308-2105.