Valmir Bucaj
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Valmir Bucaj

2018-Present:
​Assistant Professor of Mathematics
United States Military Academy
West Point​

PhD, Rice University
​​
  • Thesis title:  Anderson localization for discrete one dimensional random operators​​
  • Adviser: David Damanik 

 Research Interests
  • Spectral theory of random Jacobi operators
  • Anderson localization​
Related Interests
  • Machine Learning
  • Deep Learning
  • Sentiment Analysis

Publications​
  1. The Kunz-Souillard approach to localization for Jacobi operators. Oper. Matrices.Volume 12, Number 4(2018), 1099-1127

Preprints

​
  1. Localization for the one-dimensional Anderson model via positivity and large deviations of the Lyapunov exponent (with D. Damanik, J. Fillman, V. Gerbuz, T. VandenBoom, and Z. Zhang) arXiv:1706.06135v2(2017) (Submitted)
  2. ​On the Kunz-Souillard approach to localization for the discrete one dimensional generalized Anderson model. arXiv:1608.01379. Aug. 3, 2016​​ (Submitted)​

Undergraduate and REU publications
  • Finding Factors of Factor Rings over Eisenstein Integers. Int. Math. Forum.Vol. 9, 2014, no. 31, 1521 - 1537 
  • Embeddedness for singly periodic Scherk surfaces with higher dihedral symmetry. Involve, 6 (2013) 383-392 (with Sarah Cannon, Michael Dorff, Jamal Lawson, and Ryan Viertel)


Invited Talks
  • Lyapunov exponent for the generalized discrete Anderson model. AMS Special Session on Spectral Theory, Disorder, and Quantum Physics. JMM, January 11th, 2018. San Diego.
  • Localization for the 1D Anderson model via positivity and LDT of the Lyapunov exponent. TexAMP, UT Austin, Nov. 4th, 2017
  •  On the Kunz-Souillard approach to Anderson localization for Schr\"odinger operators. University of Alabama at Birmingham. Sept 22nd, 2016.
  • Localization for the discrete generalized Anderson model via Kunz-Souillard method. PDE/Analysis Mini-school. UNC, Chapel Hill, Oct 27-28, 2016

Selected Conferences and Workshops Attended

  • Analysis and Geometry on Graphs and Manifolds, University of Potsdam, Germany, Aug. 2017
  • Great Lakes Mathematical Physics Meeting, Michigan State University, June 2017.
  • PDE/Analysis Mini-School. Random Schrödinger operators: Basic properties, localization, and spectral statistics. UNC Chapel Hill, Oct. 27-28, 2016
  • Frontiers in Mathematical Physics, Centre de Recherches Mathématiques, Université de Montréal, Aug. 28-Sept 2nd. 2016.   
  • Methods of Modern Mathematical Physics--A Young Researcher's Symposium. Fields Institute, Toronto. Aug. 22-26. 2016. 
  • The Texas Analysis and Mathematical Physics Symposium, UT Dallas, TX (Nov. 2015)
  • Workshop in Periodic and Ergodic Spectral Problems, Issac Newton Institute for Mathematical Sciences, Cambridge, UK (Jan. 5th-16th).
  • The Texas Analysis and Mathematical Physics Symposium, UT Austin, TX (Nov. 2014)

Contact Info:

Email: valmir (dot) bucaj (at) usma (dot) edu
​

Office 218
Department of Mathematical Sciences
United States Military Academy
West Point, NY
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