Gustav Roch
Gustav Adolph Roch (born December 9, 1839 in Dresden , † November 21, 1866 in Venice ) was a German mathematician . He is known for the Riemann-Roch theorem .
Life
Gustav Roch was the son of Gustav Adolf Roch (royal kitchen assistant) and Auguste Caroline Roch born. Buttner. He attended schools in Dresden and Dresden-Neustadt and initially studied chemistry at the Dresden Polytechnic . His mathematics professor there, Oskar Schlömilch , recognized his mathematical talent and moved him to switch to mathematics and physics. In 1859 he published a work on electrodynamics according to André-Marie Ampère in the magazine for mathematics and physics published by Schlömilch, which was followed by further publications on electrodynamics and magnetism as a student. In 1859 he continued his studies at the University of Leipzig , where the mathematicians August Ferdinand Möbius , Moritz Wilhelm Drobisch , Wilhelm Scheibner and Wilhelm Hankel were among his professors. He also attended lectures on botany, philology and history ( Heinrich von Treitschke ). Because of his achievements, he received the Kregel-Sternbach scholarship, which enabled him to continue his studies in Göttingen and Berlin. From 1861 he studied at the Georg-August University in Göttingen with the physicists Wilhelm Eduard Weber , Ernst Christian Julius Schering and Alfred Enneper and the philosopher Hermann Lotze . He was particularly impressed by the mathematician Bernhard Riemann . In 1862 he was reciprocated in the Corps Teutonia Göttingen . He went to Berlin, where he did not enroll as a student, but maintained contacts with Leopold Kronecker , Karl Weierstrass , Ernst Eduard Kummer and Karl Wilhelm Borchardt and was accepted into the German Physical Society .
In 1862 he completed his studies at the University of Leipzig with a master's degree. In the same year he was promoted to Dr. with Moritz Drobisch and Wilhelm Hankel and (since Drobisch felt unable to assess the dissertation) Wilhelm Scheibner in Leipzig. phil. PhD. After that he stayed at the University of Leipzig. In 1862 he attended lectures on economics ( Wilhelm Roscher ), archeology ( Johannes Overbeck ) and history (but not on mathematics and physics).
In 1863 he completed his habilitation at the Friedrichs University in Halle with a thesis on Abelian functions. After that he held several lectures in Halle as a private lecturer. In 1865 he published the work “About the number of arbitrary constants in algebraic functions” , which contained the Riemann-Roch theorem, which relates the topological properties (gender) of a Riemann surface with properties of the body of the meromorphic functions defined on the surface brought. The theorem was named after Riemann and Roch in 1874 by Max Noether and Alexander Brill (Riemann's contribution was the Riemann inequality). He had previously published several papers on function theory in Crelle's Journal.
On August 21, 1866 he became associate professor in Halle after a positive opinion from Eduard Heine and Otto August Rosenberger . He was on leave in the winter semester of 1866/67 because of his tuberculosis and sought healing in the milder climate of Italy. In November 1866 he died of tuberculosis at the age of 26.
The Riemann-Roch theorem played an important role in algebraic geometry and was generalized in the 1920s to algebraic curves and in the 1950s to higher dimensions.The Hirzebruch-Riemann-Roch theorem was generalized by Friedrich Hirzebruch and by Alexander Grothendieck to morphisms between algebraic varieties.
Works
- About the number of arbitrary constants in algebraic functions. in Crelle J. Math. 64 (1865) 372-376.
- About integrals of the second kind and the averaging of the value of theta functions. in Schlömilch's Ztschr. Math. Phys. 11 (1866) 53-63.
Web links
- Life and works of Gustav Roch (M. Goebel, H. Schlosser, M. Sekatzek, University of Halle)
- John J. O'Connor, Edmund F. Robertson : Gustav Roch. In: MacTutor History of Mathematics archive .
- Jeremy Gray, The Riemann-Roch theorem and geometry, 1854-1914 , ICM Berlin 1998, Documenta Mathematica, 1998, pp. 811-822
Individual evidence
- ↑ Kösener Corpslisten 1930, 48/106.
- ↑ Gustav Roch in the Mathematics Genealogy Project (English)
- ^ Habilitation thesis: De theoremate quodam circa functiones Abelianas .
| personal data | |
|---|---|
| SURNAME | Roch, Gustav |
| ALTERNATIVE NAMES | Roch, Gustav Adolph (full name) |
| BRIEF DESCRIPTION | German mathematician |
| DATE OF BIRTH | December 9, 1839 |
| PLACE OF BIRTH | Dresden |
| DATE OF DEATH | November 21, 1866 |
| Place of death | Venice |