Assistant Professor of Mathematics, Montana State Univ, Bozeman, USA (on leave)

Postdoctoral fellow, Perimeter institute for theoretical physics, on, Cn


"
The real problem in speech is not precise language. The problem is clear language. The desire is to have the idea clearly communicated to the other person..."

                                                                           -- RICHARD FEYNMAN


MY RESEARCH IS FOCUSED ON USING PHYSICAL IDEAS TO STUDY TOPOLOGICAL SPACES.  MOTIVATED BY QUESTIONS ABOUT WHAT TYPE OF GEOMETRIES A GIVEN SPACE ADMITS, I STUDY TOPOLOGICAL INVARIANTS OF SPACES BY CONSIDERING QUANTUM FIELD THEORIES ON THE SPACE.  THIS CAN TAKE DIFFERENT FORMS: FROM THE PARADIGM INTRODUCED BY ATIYAH AND SEGAL (AND THE FURTHER CONTRIBUTIONS OF STOLZ AND TEICHNER) TO MORE PERTURBATIVE APPROACHES LIKE THAT OF COSTELLO.