Phases to Phases - An Invitation to Topological Phases of Many Particles by Vijay Shenoy

Explore the fascinating world of topological phases in many-particle systems through this comprehensive lecture from the International Centre for Theoretical Sciences. Delve into the foundations of quantum condensed matter physics, examining electronic phases and their topological properties. Discover the Tenfold Way classification, understand the concept of topological insulators, and learn about their potential technological applications. Gain insights into cutting-edge research topics such as amorphous topological insulators and tunable topology. Suitable for graduate students and researchers in physics, this nearly two-hour talk covers essential quantum ideas, symmetries in fermionic systems, and the interplay between topology and ground states, providing a solid foundation for understanding the current state and future directions of research in topological phases of matter.

Acknowledgements
Overview: Phases to Phases
Topological Matter Matters
Phases of Electrons- Matter... and its phases
Whence Phases?
Atomic Theory...to Theory of Phases
Electrons... and Electronic Phases
Quantum Condensed Matter Physics - Bird's Eye View
Taking Stock...
Summary of a Grad Course!
Current Status
Electronic Phases.... What and Why Topology?
Essential Quantum Ideas
Warm Up: Atomic Structure - Few Electrons
Electronic Liquid Phase - Metal
...and Insulators
Insulators: "Electronic Solid Phase"
Topology of Electrons Phases - Whetting the Appetite
Topology...Revealed in a Finite Chain
Topology...on the Edge
Phases Distinguished by Topology... and Phase Transitions
Topology of Electron Phases
Gapped Phases of Electrons
Topology of Ground States
The Tenfold Way-Bird's-Eye View
Beginnings...
Beginnings...II
Symmetries...Recap
Symmops of Fermionic Systems
Symmops - Summary
Non-ordinary Symmops: Properties
Tenfold Way-Another View
Grotesque" Fermionic Systems GFS
Further Properties of Non-Ordinary Symmetries of a GFS
Ten Classes
Canonical Representation of Symmetries
Tenfold Way - A Group Cohomological View
Tenfold Way: Noninteracting Systems
Interacting Systems
From GFS to Lattice
Bands etc.
Ground state.. and Topology
Periodic Table
Periodic Table...for Human beings
Topological Insulators
Topology Insulator for Technology
Topological Insulators in Amorphous Systems
Motivating Clues...
Edge States
....with Quantized Transport
Topological Invariant
Phase Diagram
Experimental Realization!
Tunable Topology?
Things Not Discussed...and Open Issues
Key Takeaway
Summary