Christoph Fischbacher, Ph.D.

Education

Ph. D., Mathematics, University of Kent, United Kingdom, 2017.

M.Sc., Theoretical and Mathematical Physics, Ludwig-Maximilians University, Munich, Germany, 2013.

B.A., Philosophy, Munich School of Philosophy, Munich, Germany, 2012.

B.Sc., Physics, Ludwig-Maximilians University, Munich, Germany, 2010.

Biography

Prior to joining Baylor's Mathematics department in 2022, Christoph Fischbacher was a Visiting Assistant Professor at the University of California, Irvine (working with Abel Klein)  and the University of Alabama at Birmingham (working with Gunter Stolz). 

Research Interests

Spin Systems, Many Particle Schroedinger Operators, Many Body Localization, Functional Analysis, Spectral Theory, Dissipative Operators.

Publications

• C. Fischbacher, F. Gesztesy, P. Hagelstein, and L. Littlejohn: Abstract Left-Definite Theory: A Model Operator Approach, Examples, Fratcional Sobolev Spaces, and Interpolation Theory, submitted, https://arxiv.org/abs/2408.01514
• H. Abdul-Rahman, M. Darras, C. Fischbacher, and G. Stolz: Slow Propagation Velocities in Schrödinger operators with large periodic potential, https://arxiv.org/abs/2401.11508
• C. Fischbacher, F. Gesztesy, and R. Nichols: A Bessel Analog of the Riesz Composition Formula, Computational Methods and Function Theory. 1-27. 10.1007/s40315-024-00539-2. 
• C. Fischbacher and L. Fisher: Entanglement Entropy Bounds for Droplet States of the XXZ Model on the Strip, J. Math. Phys. 65, 021901 (2024)
• C. Fischbacher and R. Schulte: Lower bound to the entanglement entropy of the XXZ spin ring, Ann. Henri Poincaré (2023). https://doi.org/10.1007/s00023-023-01318-w
• C. Fischbacher, S.N.Naboko, and I. Wood: Complete nonselfadjointness for Schrödinger operators on the semi-axis, St. Petersburg Math Journal/Algebra i Analiz, 35:1 (2023), 283–303
• C. Fischbacher and O. Ogunkoya: Entanglement Entropy Bounds in the Higher Spin XXZ Chain, Journal of Mathematical Physics 62 (2021), 101901.
• C. Fischbacher: Extensions of dissipative operators with closable imaginary part, Opuscula Math., 41, no. 3 (2021), 381-393.
• H. Abdul-Rahman, C. Fischbacher, and G. Stolz: Entanglement Bounds in the XXZ Quantum Spin Chain, Ann. Henri Poincaré 21 (2020), 2327-2366.
•  C. Fischbacher: A Schrödinger Operator Approach to Higher Spin XXZ Systems on General Graphs, Analytic Trends in Mathematical Physics 741 (2020): 83-103.
• C. Fischbacher: The Closed Extensions of a Closed Operator, Integr. Equ. Oper. Theory (2019) 91, 33.  https://doi.org/10.1007/s00020-019-2531-5
• C. Fischbacher: A Birman-Krein-Vishik-Grubb Theory for Sectorial Operators, Complex Anal. Oper. Theory, 13, 3623–3658 (2019).
• C. Fischbacher: The Non-Proper Dissipative Extensions of a Dual Pair, Trans. Amer. Math. Soc. 370 (2018), pp. 8895-8920.
• C. Fischbacher and G. Stolz: Droplet States in Quantum XXZ Spin Systems on General Graphs, J. Math. Phys. 59 (2018), 051901.
• C. Fischbacher, S. Naboko and I. Wood: The Proper Dissipative Extensions of a Dual Pair, Integ. Equ. Oper. Th., Vol. 85, 04 (2016), 573-599.
• C. Fischbacher and G. Stolz: The Infinite XXZ Quantum Spin Chain Revisited: Structure of Low Lying Spectral Bands and Gaps, Mathematical Modelling of Natural Phenomena, Vol.\ 9, 05 (2014), 44-72.