Mathematical Genealogy of Pramod N. Achar Ph.D., Universit¨at Leipzig, 1665–66 Otto Mencke Ex Theologia naturali—De Absoluta Dei Simplicitate, Micropolitiam, id est Rempubli- cam In Microcosmo Conspicuam Ph.D., Universit¨at Leipzig, 1685 Johann Wichmannshausen Disputationem Moralem De Divortiis Secundum Jus Naturae Dr. Phil., Martin-Luther-Universit¨atHalle-Wittenberg, 1713 Christian Hausen De corpore scissuris figurisque non cruetando ductu Ph.D., Universit¨at Leipzig, 1739 Abraham K¨astner Theoria radicum in aequationibus Georg Lichtenberg Dr. Phil., Georg-August-Universit¨atG¨ottingen, 1765 Unknown Dr. Phil., Georg-August-Universit¨atG¨ottingen, 1786 Johann Pfaff Commentatio de ortibus et occasibus siderum apud auctores classicos commemoratis Ph.D., Universit¨at Helmstedt, 1799 Carl Gauß Demonstratio nova theorematis omnem functionem algebraicam rationalem integram unius variabilis in factores reales primi vel secundi gradus resolvi posse Dr. Phil., Georg-August-Universit¨atG¨ottingen, 1800 Heinrich Brandes Unknown Dr. Phil., Georg-August-Universit¨atG¨ottingen, 1810 Friedrich Bessel Unknown Ph.D., Universit¨at Berlin, 1823 Heinrich Scherk De evolvenda functione . disquisitiones nonnullae analyticae Ph.D., Martin-Luther-Universit¨atHalle-Wittenberg, 1831 Ernst Kummer De cosinuum et sinuum potestatibus secundum cosinus et sinus arcuum multiplicium evolvendis Christoph Gudermann Ph.D., Georg-August-Universit¨atG¨ottingen, 1841 Uber¨ die Entwicklung der Modularfunctionen Ph.D., Universit¨at K¨onigsberg, 1854 Karl Weierstraß Unknown Ph.D., Universit¨at Berlin, 1864 Hermann Schwartz De superficiebus in planum explicabilibus primorum septem ordinum Leopold Fej´er Ph.D., E¨otv¨osLor´andUniversity, 1902 Unknown Ph.D., E¨otv¨osLor´andUniversity, 1912 Marcel Riesz Unknown Ph.D., Stockholm University, 1918 C. Einar Hille Some Problems Concerning Spherical Harmonics Ph.D., Yale University, 1940 Irving Segal Ring Properties of Certain Classes of Functions Ph.D., University of Chicago, 1954 Bertram Kostant Representations of a Lie Algebra and its Enveloping Algebra on Hilbert Space Ph.D., Massachusetts Institute of Technology, 1976 David Vogan Lie Algebra Cohomology and the Representations of Semisimple Lie Groups Ph.D., Massachusetts Institute of Technology, 2001 Pramod Achar Equivariant Coherent Sheaves on the Nilpotent Cone for Complex Reductive Lie Groups.