Alexis Drouot
 
Assistant Professor,
Department of Mathematics,
University of Washington
 

email: adrouot at uw dot edu

Research interests: Partial differential equations, mathematical physics, dynamical systems.
Supported by DMS 1800086 and DMS 2054589
 
CV

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Papers
 
    Dirac operators and topological insulators

• Topological insulators in semiclassical regime. Preprint, submitted, 2022.
• (With G. Bal and S. Becker) Magnetic slowdown of topological edge states. Preprint, submitted, 2022. 
• (With G. Bal, S. Becker, C. Fermanian-Kamerrer, J. Lu and A. Watson) Edge state dynamics along curved interfaces. Preprint, submitted 2021.  

    Mathematical aspects of topological insulators

• Ubiquity of conical points in topological insulators. Journal de l’École polytechnique—Mathématiques 8(2021), 507-532 
• Microlocal analysis of the bulk edge correspondence. Communications in Mathematical Physics 383(2021), 2069-2112 
• The bulk-edge correspondence for continuous dislocated systems. Annales de l'Institut Fourier, 71(2021), 1185-1239. 
• The bulk-edge correspondence for continuous honeycomb lattices. Communications in PDEs 44(2019), 1406–1430.  

    Edge states in graphene and related materials

• (With M. Weinstein) Edge states and the Valley Hall Effect. Advances in Mathematics 368(2020), 107142.
• Characterization of edge states in perturbed honeycomb structures. Pure and Applied Analysis (3) 1(2019), 385–445. 
• (With C. Fefferman and M. Weinstein) Defect states for dislocated periodic media. Comm. Math. Physics 377(2020), 3, 1637-1680. 

        Homogenization of Schrodinger operators

• Resonances for random highly oscillatory potentials. Journal of Mathematical Physics 59(2018), 101506, 34 pp.
• Scattering resonances for highly oscillatory potentials. Annales Scientifiques de l'Ecole Normale Supérieure (4) 51(2018), no. 4, 865–925.  
• Bound states for rapidly oscillatory Schrödinger operators in dimension 2. SIAM Journal of Mathematical Analysis 50(2018), 1471–1484. 

      Semiclassical analysis and Quantum chaos

• Pollicott-Ruelle resonances via kinetic Brownian motion. Communications in Mathematical Physics 356(2017), No. 2, 357–396. 
• (With M. Zworski) A quantitative version of the Catlin-D'Angelo-Quillen theorem. Analysis and Mathematical Physics 3(2013), No. 1, 1–19. 

       General relativity

• A quantitative version of Hawking radiation. Annales Henri Poincaré 18(2017), No. 3, 757–806.

 
   Optimal bounds for the k-plane tranform

• Quantitative form of certain k-plane transform inequalities. Journal of Functional Analysis 268(2015), No. 5, 1241–1276. 
• Best constant for a k-plane transform inequality. Analysis and PDE 7(2014), No. 6, 1237–1252. 
• Existence and non-existence of extremizers for k-plane transform inequalities. Unpublished note, 2014. 

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Selected talks

• Dirac operators and topological insulators
• Microlocal analysis of the bulk-edge correspondence 
• Edge states in near honeycomb structures  
•  A quantitative version of Hawking radiation   
• Topologically protected edge states via highly oscillatory potentials   
• Resonances for stochastic, highly oscilltory potentials    
• Pollicott-Ruelle resonances via kinetic Brownian motion    
• Scattering resonances for highly oscillatory potentials   
• Existence and non-existence of extremizers for a k-plane transform inequality   
• The principle of concentration-compactness and an application    

 

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Teaching
Measure theory (Spring 2022) 
Semiclassical Analysis (Winter 2022) 
Complex Analysis (Winter 2021) 
Linear Algebra (Spring 2020, Winter 2022)  
 Real Analysis (Fall 2018, Spring 2021)  
 Analysis and Optimization (Spring 2018)