Speakers: Title and Abstract
Noether's Theorem in Classical Dynamics : Continuous Symmetries and Conservation Laws for physical systems -
A pedagogical account of the deep interrelations between continuous symmetries of physical systems described by Action Principles, the associated Constants of Motion, and their role as generators of canonical transformations, will be presented.The application to the theory of Constrained Dynamical Systems as developed by Dirac will also be described.
Emmy Noether in Erlangen and Göttingen -
We give an overview of Emmy Noether's seminal works; and her contribution to the birth of modern algebra. We also give an indication of its influence in present day research.
Noether's works in Topology -
Noether's works in Topology will be described.
Interplay of symmetries and other integrability quantifiers in finite dimensional nonlinear;dynamical systems -
In my talk, I will establish an important interlink between Noether symmetries, Lie point symmetries, contact symmetries, lambda symmetries, adjoint symmetries, null form, inegrating factors, Darboux polynomials, Jacobi last multipliers and generalized lambda symmetries through connection with Prelle - Singer method. I will show the relationship for two, three and nth order nonlinear differential equations.
Noether's theorem and particle physics -
In this talk I will tell the story of the role played by Noether's Theorem in arriving at our current knowledge of quarks and leptons as elementary constituents of matter and the nature of the fundamental interactions among them. I will also like to comment on Emmy Noether's achievements from the point of view of a theoretical physicist who happens to be a woman!
Noether's theorems and their growing physical relevance -
Noether's work on symmetries and conservation laws was far ahead of its time. As a result, Noether's theorems initially had little impact in the physics community. In those days, it was not widely appreciated that the laws of nature were best expressed as variational principles. With the growing realisation that variational principles provide an economical restatement of Nature's Laws and symmetries, the power and generality of Noether's work came to be appreciated. When the signifance of Noether's theorems was finally understood in the middle of the last century, they were seen to contain seeds of many ideas which dominate modern physics: conserved currents, gauge invariance, symplectic geometry, Dirac's theory of contraints and the elusive nature of gravitational energy.
Origin and Development of Valuation Theory -
Emmy Noether played a great role in the development of valuation theory since its inception. She was the first one to provide an axiomatic base for Dedekind rings; she called them F"unf Axiome-Ringe (five axiom rings). She actively participated together with Richard Brauer and Helmut Hasse in the proof of the local global principle for central simple algebras. We go down the memory lane and discuss some significant contributions to Valuation Theory by K"ursch`ak, Ostrowski,Noether, Hasse and others.
Symmetries and Condensed Matter physics -
Noether's formulation of invariance of action (describing the system) under symmetry transformations and understanding the conserved currents (Noether currents) play an important role in describing condensed matter systems. Only recently, we have encountered prototypical systems where interesting physics can emerge even in absence of symmetries. I will give a general outline of how Noether's work have shaped thinking about condensed matter phases in terms of symmetries and also about recent developments where such ideas partially break down in an important way.
Emmy Noether’s ideas in Gravity, Black holes and AdS/CFT -
The phenomenal ideas that Emmy Noether pioneered a century ago continue to guide us in theoretical physics in diverse ways. My talk will be focused on the original problem that instigated her famous theorems - the problem of gravity and its geometric description in general relativity. I will describe how about fifty years ago, the quest to define Noether charges for space-time geometries led to the ADM formalism named after Richard Arnowitt, Charles Misner and Stanley Deser. This in turn led to the Blackhole thermodynamics and then to holography. Emmy Noether's ideas again made a curious reappearance in Robert Wald's work on casting Black hole entropy as a Noether charge. This long list of applications continues to grow with AdS/CFT duality where the two theorems of Noether get unified and are seen to be dual to each other.