Mark A. Stern
- Professor of Mathematics
Monday and Tuesday 2-3
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, physics, and number theory.
In recent work, Professor Stern has studied analytical, geometric, and topological questions arising from Yang-Mills theory, Hodge theory, and number 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) new bounds for eigenvalues of Laplace Beltrami operators, and (v) new bounds for betti numbers.
"Fixed point theorems from a de Rham perspective." Asian Journal of Mathematics 13.1 (October 26, 2009): 065-088.
"I. Non-commutativity and supersymmetry." Journal of High Energy Physics 6.3 (March 1, 2002): 183-200.
Stern, MA. "Quantum Mechanical Mirror Symmetry, D Branes, and B fields." Eprint (2002). (Academic Article)
"Pure hodge structure on the L2-cohomology of varieties with isolated singularities." Journal Fur Die Reine Und Angewandte Mathematik 533 (December 1, 2001): 55-80.
"Spinning bound states of two and three black holes." Journal of High Energy Physics 5.11 (January 1, 2001): 1-19. Full Text
"Invariance theorems for supersymmetric Yang-Mills theories." Advances in Theoretical and Mathematical Physics 4.2 (March 1, 2000): 1-12. Open Access Copy
"Supersymmetry and the Yang-Mills effective action at finite N." Journal of High Energy Physics 3.6 (December 1, 1999).