Primary Research Area
- High Energy Physics
- Ph.D., Mathematics, Princeton, 1980
Professor Katz is an internationally renowned mathematician with strong interests in physics who holds a joint appointment in Physics and Mathematics at the University of Illinois. He received his bachelor's degree in mathematics from Massachusetts Institute of Technology in 1976 and his Ph.D in mathematics from Princeton University in 1980.
A Regents Professor of Mathematics at Oklahoma State University, Professor Katz joined the faculty at the University of Illinois in 2001. His research interests interests include algebraic geometry and mathematical physics, particularly string theory and supersymmetric quantum field theories. Professor Katz is the author (with D. Cox) of the influential book Mirror Symmetry and Algebraic Geometry (Providence RI, American Mathematical Society, 1999).
String theory seeks to unify quantum field theory and general relativity. Current research in this area focuses on duality, which relates different formulations of string theory in various regimes. This allows the moduli space of these theories to be explored in greater detail. This is expected to provide hints for the sought-for complete formulation of string theory. String and M-theory dualities also lead to dualities of supersymmetric quantum field theories and deep connections to geometry.
Algebraic geometry is the geometric study of systems of algebraic equations. Current research in this area focuses on the study of algebraic curves on three complex dimensional algebraic varieties. These are identified with world-sheet instantons in string theory. Specific topics include Gromov-Witten theory, which is identified with topological string amplitudes, and toric varieties, which are closely related to Witten's gauged linear sigma model.
Selected Articles in Journals
- S Katz, DR Morrison, S Schafer-Nameki, J Sully. Tate's algorithm and F-theory. Journal Of High Energy Physics Issue: 8, 094, Aug 2011.
- Josh Guffin, Sheldon Katz. Deformed quantum cohomology and (0,2) mirror symmetry. Journal of High Energy Physics (8): Art. No. 109 (Aug. 2010).
Recent Courses Taught
- MATH 416 - Abstract Linear Algebra
- MATH 425 - Honors Advanced Analysis
- MATH 502 - Commutative Algebra
- MATH 511 - Intro to Algebraic Geometry
- MATH 512 - Modern Algebraic Geometry
- MATH 514 - Complex Algebraic Geometry
- MATH 595 - Moduli of Curves
- MATH 597 - Reading Course