[phys4phys] TopArtGravity visit and lectures on Topological quantum matter

[Dusan Djordjevic]

Dear colleagues,

The last email about the minicourse on topological quantum matter, to be
delivered by Prof. Juricic from 21.10. to 24.10, has a strange-looking
attachment. Therefore, we are sending here the detailed plan of the
lectures.



   1. *Foundations: Berry phase & Chern number. *


   - Bloch bands and Bloch bundle
   - Berry connection, curvature, and Zak phase
   - Chern number/TKNN invariant. Hall conductivity.
   - Bulk–boundary correspondence.
   - Minimal models: Su-Schrieffer-Heeger, Bernevig-Hughes-Zhang, Haldane



   - *2. Time-Reversal Topological Insulators & Superconductors. Tenfold
   way. *


   - Altland–Zirnbauer symmetry classes (TRS, PHS, chiral)
   - Fu–Kane parity criterion and Pfaffian formulation
   - 3D topological insulators.. 3D TI surface Dirac cone
   - Kitaev chain and Majorana bound state



   - *3. **Crystalline Topology & Higher-Order Phases*


   - Symmetry indicators and topological quantum chemistry.
   - Wannier obstruction and symmetry-protected topology.
   - Mirror/rotation/inversion invariants.
   - Higher-order TIs: hinge/corner states; fragile topology



   -  4.*Quantum Geometry & Responses*


   - Quantum geometric tensor: Berry curvature + Fubini–Study metric
   - Modern theory of polarization and orbital magnetization
   - Anomalous Hall effect. Berry-curvature dipole and nonlinear Hall
   conductivity.
   - Superfluid weight and geometric contributions
   - Flat/near-flat Chern bands; moiré miniband geometry (overview)



   - *5. Non-Hermitian Topology: NH Dirac fermions, Interactions, and flat
   bands.*


   - Biorthogonal formalism. NH Bloch bands.
   - NH Dirac fermions.
   - Interaction effects.
   - Exceptional flat bands.

Best wishes,
Dušan Đorđević
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