Mark A. Stern
- Professor of Mathematics
Research Areas and Keywords
Geometry: Differential & Algebraic
PDE & Dynamical Systems
The focus of Professor Stern's research is the study of analytic problems arising in geometry, topology, and physics.
In recent work, Professor Stern has studied analytical, geometric, and topological questions arising from Yang-Mills theory, string theory, and Hodge theory. These have led for example to a study of (i) stability questions arising in Yang Mills theory and harmonic maps, (ii) energy minimizing connections and instantons, (iii) new Hodge structures on vector bundles, (iv) the analysis of harmonic spinors on singular spin structures, and (v) non fredholm index theories and exotic fixed point theorems.
Stern, MA. "Mechanical D Branes and B Fields."
Sethi, S, and Stern, M. "Invariance Theorems for Supersymmetric Yang-Mills Theories." Adv.Theor.Math.Phys. 4: 487-501. Open Access Copy
Degeratu, A, and Stern, M. "The Positive Mass Conjecture for Non-spin Manifolds."
Paban, S, Sethi, S, and Stern, M. "Summing Up Instantons in Three-Dimensional Yang-Mills Theories." Adv.Theor.Math.Phys. 3: 343-361.