[Quantum-ms] Fwd: Mathematics of Waves and Quantum Materials

[Gil Zussman]

> Begin forwarded message:
> 
> From: Henry Yuen <hyuen at CS.COLUMBIA.EDU <mailto:hyuen at CS.COLUMBIA.EDU>>
> Subject: Fwd: Mathematics of Waves and Quantum Materials
> Date: August 27, 2025 at 8:07:32 PM EDT
> To: QUANTUM at LISTS.COLUMBIA.EDU <mailto:QUANTUM at LISTS.COLUMBIA.EDU>
> Reply-To: Quantum <QUANTUM at LISTS.COLUMBIA.EDU <mailto:QUANTUM at LISTS.COLUMBIA.EDU>>
> 
> Course announcement for this Fall.
> 
> ---------- Forwarded message ---------
> From: Michael I. Weinstein <miw2103 at columbia.edu <mailto:miw2103 at columbia.edu>>
> Date: Wed, Aug 27, 2025 at 10:33 AM
> Subject: Mathematics of Waves and Quantum Materials
> To: <henry.yuen at columbia.edu <mailto:henry.yuen at columbia.edu>>
> Cc: Michael I Weinstein <miw2103 at columbia.edu <mailto:miw2103 at columbia.edu>>
> 
> 
> Dear Henry, I hope all is well with you.
> Below is information on an Applied Math course I’m teaching this semester. 
> Please forward to anyone you think may be interested. 
> Best wishes, Michael
> 
> Michael I. Weinstein
> Department of Applied Physics 
>     & Applied Mathematics, and
> Department of Mathematics
> Columbia University
> New York, New York 10027
> 
> http://www.columbia.edu/~miw2103/  <http://www.columbia.edu/~miw2103/ >
> 
> 
> 
> Fall 2025, Applied Mathematics E4990, Section 001
> Tuesday and Thursdays 10:10-11:25am
> Location: 253 Engineering Terrace (SW Mudd Building)
> Special Topics in Applied Mathematics
> Instructor: Michael I Weinstein
>> Course Title: Mathematics of Waves and Quantum Materials
>> 
> Course description: In this course we will study mathematical aspects of wave phenomena in classical and quantum
> physics, with a view toward models (PDE, discrete,..) of quantum materials, and their metamaterial analogues.
> Topics include: Wave phenomena (non-dispersive and dispersive);
> wave, Schroedinger, Dirac equations, 
> Spectral theory of periodic operators (Floquet-Bloch) and the band structure of crystals.
> Multiple scale methods and applications to wave-packets and their dynamics.
> Effective Hamiltonians arising in homogenization and strong binding (high contrast) regimes.
> Case study of quantum materials: graphene.  2D materials in a magnetic field.
> Basics of symmetries, band structure degeneracies, symmetry breaking perturbations,
> and topological wave phenomena in 2D materials.
> 
> Prerequisites: The following courses or equivalents: 
> Applied Analysis APMA 4100, Applied Functional Analysis APMA 4150,  Partial Differential Equations APMA 4200,
> or permission of the instructor.


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