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Valmir Bucaj

Thesis title: Anderson localization for discrete one dimensional random operators
Adviser: David Damanik

Research Interests

Spectral theory of random Jacobi operators
Anderson localization

Publications

The Kunz-Souillard approach to localization for Jacobi operators. Oper. Matrices. (To Appear)

Preprints

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)
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) rice (dot) edu

Office 40
Department of Mathematics
Rice University
6100 Main St. Ms-136
Houston, TX 77005