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| Sheldon Katz | |
|---|---|
| Name | Sheldon Katz |
| Birth date | 1949 |
| Birth place | New York City |
| Nationality | United States |
| Fields | Mathematics |
| Workplaces | University of Illinois at Urbana–Champaign; University of Massachusetts Amherst; Rutgers University |
| Alma mater | Stony Brook University; Harvard University |
| Doctoral advisor | Phillip Griffiths |
| Known for | Algebraic geometry; String theory; Mirror symmetry |
Sheldon Katz is an American mathematician noted for work at the intersection of algebraic geometry and theoretical physics, particularly in topics related to mirror symmetry, Calabi–Yau manifolds, and D-branes. His career spans faculty appointments at major research universities and collaborations with leading figures in mathematical physics and complex geometry. Katz has contributed to the mathematical formalism underlying aspects of string theory and has published influential expositions and research monographs used in graduate instruction.
Katz was born in New York City and raised in a period marked by rapid expansion of American research in mathematics and physics. He completed undergraduate studies at Stony Brook University before entering graduate study at Harvard University, where he was supervised by Phillip Griffiths, a prominent figure in complex geometry and Hodge theory. Katz's doctoral work was situated within the tradition of algebraic geometry influenced by the Italian school of algebraic geometry revival and modern developments stemming from Alexander Grothendieck's reformulations.
Katz held faculty positions at institutions including Rutgers University, University of Massachusetts Amherst, and University of Illinois at Urbana–Champaign, engaging with departments that were centers for algebraic geometry and mathematical physics. He collaborated with scholars affiliated with research centers such as the Institute for Advanced Study and participated in programs at the Mathematical Sciences Research Institute. Katz supervised doctoral students who went on to positions at research universities and national laboratories, and served on editorial boards of journals bridging geometry and theoretical physics communities.
Katz's research spans multiple interlinked areas: rigorous aspects of mirror symmetry, enumerative geometry of Calabi–Yau manifolds, and mathematical descriptions of D-brane moduli spaces. He worked on counts of holomorphic curves using techniques related to Gromov–Witten theory and coherent sheaf theory, connecting classical problems in enumerative geometry with predictions from string theory dualities involving Type II string theory and M-theory. Katz contributed to the study of Pandharipande–Thomas invariants and their relation to Donaldson–Thomas theory, exploring how moduli of sheaves and stable pairs correspond to physical BPS state counts as proposed in conjectures by researchers at institutions like Princeton University and Harvard University.
His analyses elucidated aspects of stability conditions on derived categories in the sense of Tom Bridgeland and examined implications for derived equivalences in Calabi–Yau settings. Katz investigated singularity resolutions and flops in threefolds, linking geometric transitions to phenomena in Seiberg–Witten theory and wall-crossing behavior formalized by Kontsevich–Soibelman wall-crossing formulas. He collaborated with physicists and mathematicians from groups at CERN and national institutes to translate physical intuition from quantum field theory into rigorous statements in algebraic geometry.
Katz authored and coauthored numerous peer-reviewed articles and monographs. He contributed chapters and lecture notes to volumes produced by the American Mathematical Society and edited collections from programs at the Clay Mathematics Institute and Mathematical Sciences Research Institute. Selected topics in his bibliography include enumerative predictions for curve counts on Calabi–Yau threefolds, rigorous treatments of D-brane categories, and expository surveys on mirror symmetry suitable for graduate study. Katz also coedited proceedings from conferences that brought together researchers from geometry and string theory communities.
Representative papers were published in journals associated with societies such as the American Mathematical Society and the London Mathematical Society, and he presented invited talks at meetings of the International Congress of Mathematicians and at symposia organized by the Institute for Advanced Study and the Perimeter Institute.
Katz received recognition from professional organizations for contributions bridging mathematics and physics. He held research fellowships and visiting positions at institutions including the Institute for Advanced Study and was awarded grants from agencies like the National Science Foundation. His work featured in invited sessions of the American Mathematical Society and he served on panels and committees for scientific programs at research institutes such as the Mathematical Sciences Research Institute.
Katz's mentorship influenced cohorts of researchers who continue work at the interface of algebraic geometry and theoretical physics. His expository style and collaborative projects fostered interactions among mathematicians at universities such as Princeton University, Massachusetts Institute of Technology, and University of California, Berkeley and physicists at laboratories including CERN and Fermilab. Katz's legacy persists in graduate curricula that incorporate his surveys and in mathematical frameworks that remain central to ongoing research in mirror symmetry and enumerative geometry.
Category:American mathematicians Category:Algebraic geometers Category:Mathematical physicists Category:Living people