DATES: Monday 29 Aug, 2016 - Tuesday 30 Aug, 2016
VENUE: Madhava Lecture Hall, ICTS Bangalore
Emmy Noether (1882-1935) is well known for her famous contributions to abstract algebra and theoretical physics. Noether’s mathematical work has been divided into three ”epochs”. In the first (1908-19), she made contributions to the theories of algebraic invariants and number fields. Her work on differential invariants in the calculus of variations, Noether’s theorem, has been called ”one of the most important mathematical theorems ever proved in guiding the development of modern physics”. In the second epoch (1920-26), she began work that changed the face of abstract algebra. In her classic paper Idealtheorie in Ringbereichen (Theory of Ideals in Ring Domains, 1921) Noether developed the theory of ideals in commutative rings into a tool with wideranging applications. She made elegant use of the ascending chain condition, and objects satisfying it are named Noetherian in her honor. In the third epoch (1927-35), she published works on noncommutative algebras and hypercomplex numbers and united the representation theory of groups with the theory of modules and ideals. In addition to her own publications, Noether was generous with her ideas and is credited with several lines of research published by other mathematicians, even in fields far removed from her main work, such as algebraic topology.
In ICTS-TIFR, we shall celebrate the work of this remarkable mathematician and physicist in this two day discussion meet.
The topics will include the following:
Noether's Theorem in Classical Dynamics: Continuous Symmetries and Conservation Laws for physical systems.
Applications of Noether theorem in particle physics, condensed matter physics, gravity and string theory.
Noether's pioneering contributions to Commutative Algebra and other fields of pure mathematics.
Application deadline: 01 July, 2016
Support for train travel by students and postdocs will be provided as per rules. Due to limited funds, faculty applicants are requested to find an alternative travel support.
For more information, contact program@icts.res.in
PROGRAM LINK: [ Ссылка ]
Table of Contents (powered by [ Ссылка ])
0:00:00 Start
0:00:11 Emmy Noether in Erlangen and Gottingen
0:00:31 Abstract
0:01:46 Her name
0:02:16 Erlangen
0:03:51 Noether's thesis
0:05:17 Noether invited to Gottingen
0:06:42 Privatdozent in Gottingen
0:08:18 Noether's work
0:09:59 Contd.
0:11:25 Steinitz paper on field theory
0:12:37 Invariant Theory
0:15:59 The ring of invariants
0:16:49 Noether's degree bound
0:19:14 Noether's thesis work
0:21:32 Gordan's work
0:22:52 Hilbert transforms Invariant Theory
0:24:12 Contd.
0:25:28 Noether's thesis
0:26:55 The Inverse Galois Problem
0:28:46 Fischer's work on Inv Gal Problem
0:29:46 Noether's work on Inv Gal Prob
0:30:34 Noether's proof
0:32:47 Noether's problem
0:34:01 Present day status
0:34:58 Noether Normalization
0:42:33 Consequences
0:43:34 Krull Dimension
0:44:04 Applications of Noether Normalization
0:44:46 Elimination, Hilbert Nullstellensatz, Density
0:44:59 Projective version of Hilbert's Nullstellensatz
0:45:42 Birational correspondences between projective varieties
0:46:25 Generic Flatness Lemma
0:46:49 Fibre dimension: Upper semi-continuous
0:47:11 Reciprocity and Fermat: Genesis of Algebraic Number Theory
0:49:33 Contd.
0:51:06 Ideal vs real
0:53:26 Roots of Commutative Algebra
0:56:11 Rings and ideals
0:56:58 Ascending Chain Conditions (ACC)
0:57:55 First Year course in T.I.F.R.
1:01:14 Papers on Dedekind rings and orders
1:01:19 Different ideal, tensor products, etc.
1:02:51 Non-commutative algebra and Representation theory
1:08:55 Nilpotent ideals
1:09:01 Semi-simple rings and modules
1:16:20 Her ICM address in Zurich, 1932
