Dr. Jake Fillman

Assistant Professor

Texas A&M University

A list of my papers on the arxiv

Google Scholar Profile

ORCID Identifier 0000-0003-4716-710X

My CV (last updated 20 January 2025)

Work supported in part by:
NSF DMS-2513006: 2024-2025 (transfer of DMS 2213196)
NSF  DMS-2213196: 2022-2024
Simons Foundation Collaboration Grant #711663: 2020-2025 (returned in 2022 due to receipt of NSF grant)
Texas State University REP: 2021
AMS-Simons Travel Grant: 2016-2018

Disclaimer: The opinions, findings, conclusions, and recommendations expressed on my website and in my printed work are mine and do not necessarily reflect the views of the National Science Foundation.

Books:

David Damanik, Jake Fillman
One-Dimensional Ergodic Schrödinger Operators, I: General Theory. 
Graduate Studies in Mathematics, 221. American Mathematical Society, 2022.
ISBN-13: 978-1-4704-5606-1
[link]

David Damanik, Jake Fillman
One-Dimensional Ergodic Schrödinger Operators, II: Specific Classes.
Graduate Studies in Mathematics, 249. American Mathematical Society, 2024.
ISBN-13: 978-1-4704-6503-2
[link]

Preprints:

Jake Fillman, Michala N. Gradner, Hannah J. Hendricks
Thin spectra for periodic and ergodic word models
[arxiv]

David Damanik, Íris Emilsdóttir, Jake Fillman
Gap labels and asymptotic gap opening for full shifts
[arxiv]

Christopher Cedzich, Jake Fillman
Mobility edges in pseudo-unitary  quasiperiodic quantum walks
[arxiv]

Matthew J. Colbrook, Mark Embree, Jake Fillman
Optimal algorithms for quantifying spectral size with applications to quasicrystals
[arxiv]

Published papers:

[44] Christopher Cedzich, Jake Fillman, Long Li, Darren C. Ong, Qi Zhou
Exact mobility edges for almost-periodic CMV matrices via gauge symmetries
International Mathematics Research Notices (2024), no. 8, 6906-6941.
[arxiv]

[43] Jake Fillman, Wencai Liu, Rodrigo Matos
Algebraic properties of the Fermi variety for periodic graph operators
Journal of Functional Analysis 286 (2024), no. 4, 110286.
[arxiv]

[42] David Damanik, Mark Embree, Jake Fillman, May Mei
Discontinuities of the integrated density of states for Laplacians associated with Penrose and Amman-Beenker tilings
Experimental Mathematics 33 (2024), no. 4, 588-610.
[arxiv]

[41] Christopher Cedzich, Jake Fillman
Absence of bound states for quantum walks and CMV matrices via reflections
Journal of Spectral Theory 14 (2024), 1513-1536.
[arxiv]

[40] Andrew Arroyo, Faye Castro, Jake Fillman
On the number of closed gaps of discrete periodic one-dimensional operators
Journal of Mathematical Physics  (2024), no. 5, 052101, 19 pp.
[arxiv]

[39] David Damanik, Íris Emilsdóttir, Jake Fillman
The Schwartzman group of an affine transformation
Journal of Spectral Theory 13 (2023), 1281-1296.
[arxiv]

[38] Christopher Cedzich, Jake Fillman, Darren C. Ong
Almost everything about the unitary almost-Mathieu operator
Communications in Mathematical Physics 403 (2023), 745-794.
[arxiv]

[37] David Damanik, Jake Fillman
The almost-sure spectrum of the doubling map model is connected
Communications in Mathematical Physics 400 (2023), 793-804.
[arxiv]

[36] David Damanik, Jake Fillman, Zhenghe Zhang
Johnson-Schwartzman gap labelling for ergodic Jacobi matrices
Journal of Spectral Theory 13 (2023), 297-318.
[arxiv]

[35] Jake Fillman, Sara H. Tidwell
On sums of semibounded Cantor sets
Rocky Mountain  Journal of Mathematics 53 (2023),  737-754.
[arxiv]

[34] David Damanik, Jake Fillman, Chunyi Wang
Thin spectra and singular continuous spectral measures for limit-periodic Jacobi matrices
Mathematische Nachrichten 296 (2023), 4279-4297.
[arxiv]

[33] Benjamin Eichinger, Jake Fillman, Ethan Gwaltney, Milivoje Lukić
Limit-periodic Dirac operators with thin spectra
Journal of Functional Analysis 283 (2022), no. 12, 109711.
[arxiv]

[32] Jake Fillman, Wencai Liu, Rodrigo Matos
Irreducibility of the Bloch variety for finite-range Schrödinger operators
Journal of Functional Analysis 283 (2022), no. 10, 109670.
[arxiv]

[31] David Damanik, Jake Fillman, Philipp Gohlke
Spectral characteristics of Schrödinger operators generated by product systems
Journal of Spectral Theory 12 (2022), 1659-1718.
[arxiv]

[30] Jon Chaika, David Damanik, Jake Fillman, Philipp Gohlke
Zero-measure spectrum for multi-frequency Schrödinger operators
Journal of Spectral Theory 12 (2022), no. 2, 573-590.
[arxiv]

[29] David Damanik, Jake Fillman, Anton Gorodetski
Multidimensional Schrödinger operators whose spectrum features a half-line and a Cantor set
Journal of Functional Analysis 280 (2021), no. 7, 108911.
[arxiv]

[28] Michael Boshernitzan, David Damanik, Jake Fillman, Milivoje Lukić
Ergodic Schrödinger operators in the infinite-measure setting
Journal of Spectral Theory 11 (2021), no. 2, 873-902.
[arxiv]

[27] David Damanik, Jake Fillman, Mark Helman, Jacob Kesten, Selim Sukhtaiev
Random Hamiltonians with arbitrary point interactions
Journal of Differential Equations 282 (2021),  104-126.
[arxiv]

[26] David Damanik, Jake Fillman, Selim Sukhtaiev
Localization for Anderson models on metric and discrete tree graphs
Mathematische Annalen 376 (2020), 1337–1393.
[arxiv]

[25] Jake Fillman, Rui Han
Discrete Bethe–Sommerfeld conjecture for triangular, square, and hexagonal lattices
Journal d'Analyse Mathématique 142 (2020), no. 1,  271-321.
[arxiv]

[24] Christopher Cedzich, Jake Fillman, Tobias Geib, Albert Werner
Singular continuous Cantor spectrum for magnetic quantum walks
Letters in Mathematical Physics 110 (2020), 1141-1158.
[arxiv] 

[23] Mark Embree, Jake Fillman
Spectra of discrete two-dimensional periodic Schrödinger operators with small potentials
Journal of Spectral Theory 9 (2019), no. 3,1063–1087.
[arxiv]

[22] Valmir Bucaj, David Damanik, Jake Fillman, Vitaly Gerbuz, Tom VandenBoom, Fengpeng Wang, Zhenghe Zhang
Localization for the one-dimensional Anderson model via positivity and large deviations for the Lyapunov exponent
Transactions of the American Mathematical Society 372 (2019), no. 5, 3619–3667.
[arxiv] 

[21] Valmir Bucaj, David Damanik, Jake Fillman, Vitaly Gerbuz, Tom VandenBoom, Fengpeng Wang, Zhenghe Zhang
Positive Lyapunov exponents and a large deviation theorem for continuum Anderson models, briefly
Journal of Functional Analysis 277 (2019), no. 9, 3179–3186.
[arxiv] ] 

[20] David Damanik, Jake Fillman, Anton Gorodetski
Multidimensional almost-periodic Schrödinger operators with Cantor spectrum
Annales Henri Poincaré 20 (2019), no. 4, 1393–1402.
[arxiv]  

[19] David Damanik, Jake Fillman
Limit-periodic Schrödinger operators with Lipschitz continuous IDS
Proceedings of the American Mathematical Society 147 (2019), no. 4, 1531–1539.
[arxiv]  

[18] Jake Fillman, Darren C. Ong, Tom VandenBoom
Spectral approximation for ergodic CMV matrices with an application to quantum walks
Journal of Mathematical Analysis and Applications 467 (2018), no. 1, 132–147.
[arxiv]  

[17] Jake Fillman, May Mei
Spectral properties of continuum Fibonacci Schrödinger operators
Annales Henri Poincaré 19 (2018), no. 1, 237–247.
[arxiv]  

[16] Jake Fillman, Darren C. Ong
A condition for purely absolutely continuous spectrum for CMV operators using the density of states
Proceedings of the American Mathematical Society 146 (2018), no. 2, 571–580.
[arxiv]  

[15] Jake Fillman, Darren C. Ong, Zhenghe Zhang
Spectral characteristics of the unitary critical almost-Mathieu operator
Communications in Mathematical Physics 351 (2017), no. 2, 525–561.
[arxiv]  

[14] Jake Fillman
Ballistic transport for limit-periodic Jacobi matrices with applications to quantum many-body problems
Communications in Mathematical Physics 350 (2017), no. 3, 1275–1297.
[arxiv]  

[13] David Damanik, Jake Fillman, Milivoje Lukić
Limit-periodic continuum Schrödinger operators with zero-measure Cantor spectrum
Journal of Spectral Theory 7 (2017), no. 4, 1101–1118.
[arxiv]  

[12] Jake Fillman, Milivoje Lukić
Spectral homogeneity of limit-periodic Schrödinger operators
Journal of Spectral Theory 7 (2017), no. 2, 387–406.
[arxiv]  

[11] Jake Fillman, Darren C. Ong
Purely singular continuous spectrum for limit-periodic CMV operators with applications to quantum walks
Journal of Functional Analysis 272 (2017), no. 12, 5107–5143.
[arxiv]  

[10] Jake Fillman
Purely singular continuous spectrum for Sturmian CMV matrices via strengthened Gordon Lemmas
Proceedings of the American Mathematical Society 145 (2017), no. 1, 225–239.
[arxiv]  

[9] Jake Fillman
Spectral homogeneity of discrete one-dimensional limit-periodic operators
Journal of Spectral Theory 7 (2017), no. 1, 201–226.
[arxiv]  

[8] David Damanik, Jake Fillman, Darren C. Ong
Spreading estimates for quantum walks on the integer lattice via power-law bounds on transfer matrices
Journal de Mathématiques Pures et Appliquées (9) 105 (2016), no. 3, 293–341.
[ arxiv ]  

[7] David Damanik, Jon Erickson, Jake Fillman, Gerhardt Hinkle, Alan Vu
Quantum intermittency for sparse CMV matrices with an application to quantum walks on the half-line
Journal of Approximation Theory 208 (2016), 59–84.
[ arxiv ]  

[6] Jake Fillman, Yuki Takahashi, William Yessen
Mixed spectral regimes for square Fibonacci Hamiltonians
Journal of Fractal Geometry , 3 (2016), no. 4, 377–405.
[arxiv] 

[5] David Damanik, Jake Fillman, Milivoje Lukić, William Yessen
Characterizations of uniform hyperbolicity and spectra of CMV matrices
Discrete and Continuous Dynamical Systems – Series S 9 (2016), no. 4, 1009–1023.
[arxiv] 

[4] David Damanik, Jake Fillman, Milivoje Lukić, William Yessen
Uniform hyperbolicity for Szegő cocycles and applications to random CMV matrices and the Ising model
International Mathematics Research Notices (2015), no. 16, 7110–7129.
[arxiv]  

[3] Charles Puelz, Mark Embree, Jake Fillman
Spectral approximation for quasiperiodic Jacobi operators
Integral Equations and Operator Theory 82 (2015), no. 4, 533–554.
[arxiv]  

[2] David Damanik, Jake Fillman, Robert Vance
Dynamics of unitary operators
Journal of Fractal Geometry 1 (2014), no. 4, 391–425.
[arxiv] 

[1] David Damanik, Jake Fillman, Anton Gorodetski
Continuum Schrödinger operators associated with aperiodic subshifts
Annales Henri Poincaré 15 (2014), 1123–1144.
*This paper was awarded the 2014 Annales Henri Poincaré Prize
[arxiv]  

Expository writing:

David Damanik, Mark Embree, Jake Fillman
Gap labels for zeros of the partition function of the 1D Ising model via the Schwartzman homomorphism
Indagationes Mathematicae 35 (2024), 813-836.
[arxiv]

David Damanik, Jake Fillman
Gap labelling for discrete one-dimensional ergodic Schrödinger operators
In:  From Complex Analysis to Operator Theory: A Panorama
(Eds. M. Brown, F. Gesztesy, P. Kurasov, A. Laptev, B. Simon, G. Stolz, I. Wood)
[arxiv]

David Damanik, Jake Fillman, Shuzheng Guo, Darren C. Ong
On Simon's Hausdorff dimension conjecture
In: From Operator Theory to Orthogonal Polynomials, Combinatorics, and Number Theory
(Eds. Fritz Gesztesy and Andrei Martinez-Finkelshtein)
[arxiv]

Jake Fillman
Ballistic transport for periodic Jacobi operators on Z^d
In: From Operator Theory to Orthogonal Polynomials, Combinatorics, and Number Theory
(Eds. Fritz Gesztesy and Andrei Martinez-Finkelshtein)
[arxiv]

David Damanik, Jake Fillman
Schrodinger operators with thin spectra
IAMP News Bulletin
[link]

David Damanik, Jake Fillman
Spectral properties of limit-periodic operators
In: Analysis and Geometry on Graphs and Manifolds
(Eds. Matthias Keller, Daniel Lenz, and Radoslaw Wojciechowski)
[arxiv]

Jake Fillman, Tom VandenBoom
A surprising connection between quantum mechanics and shallow water waves
Snapshots of Modern Mathematics from Oberwolfach
[link]

Jake Fillman
Resolvent methods for quantum walks with an application to a Thue-Morse quantum walk
Interdisciplinary Information Sciences 23 (2017), 27–32.
[arxiv]