# Gunter Stolz

Professor

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(205) 934-2154

Campbell Hall 483A

**Research and Teaching Interests: **Analysis, Operator and spectral theory, Mathematical physics, Quantum mechanics

**Office Hours:** By appointment

**Education:**

- Diploma (M.S.), Goethe University Frankfurt, Germany, Mathematics
- Dr. Phil. Nat. (Ph.D.), Goethe University Frankfurt, Germany, Mathematics
- Dr. habil. (Honorary Professor), Goethe University Frankfurt, Germany, Mathematics

I joined the Mathematics Department at UAB in 1994, after completing my academic education in Germany, including a postdoc year at University of California at Los Angeles. At UAB I have taught classes mostly in the areas of analysis, linear algebra, and probability. Since 2005 I have served as Graduate Recruiting Coordinator and have successfully advised seven Ph.D. students.

Throughout my career I have been fascinated by the near miraculous fact that the laws of physics can be described by mathematical formulas. Accordingly, my research interests tend to alternate between physics, which provides me with motivation, and mathematics, which often provides the solutions after years of stubborn attempts and hard work.

### Research Interests

My main research interest lies in mathematical physics and, in particular, in understanding the effects of disorder on quantum systems. Specifically, I have done extensive work on the question of Anderson localization for random Schrodinger operators.

A topic of much current research, by both physicists and mathematicians, is the investigation of the combined effect of disorder and particle interactions on quantum many-body systems. Quantum spin systems such as the Heisenberg model A are a particularly important class of models that allow us to study the central questions. These models are central in areas ranging from condensed matter physics to quantum information theory and electrical engineering.

Several of my recent works with collaborators and Ph.D. students have contributed to describing the phenomenon of many-body localization in disordered spin systems — such as its implications for quantum transport — as well as for correlations and entanglement of quantum states. We have succeeded in rigorously proving many-body localization for some models such as the disordered XY and XXZ spin chains. But a wide range of questions remain open for future research.

### Recent Courses

- EGR/MA 265: Math Tools for Engineering Problem Solving (team taught with faculty at the School of Engineering)
- MA 485/585 Introduction to Probability
- MA 645/646: Real Analysis I/II (Measure Theory and Lebesgue Integration)

### Select Publications

- Gunter Stolz with S. Jitomirskaya, and H. Schulz-Baldes. Delocalization in random polymer models, Commun. Math. Phys. 233, (2003), 27-48.
- Gunter Stolz with M. Aizenman, A. Elgart, S. Naboko and J. Schenker. Moment Analysis for Localization in Random Schrodinger Operators, Invent. Math. 163 (2006), 343-413.
- Gunter Stolz with J. Baker and M. Loss. Minimizing the ground state energy of an electron in a randomly deformed lattice, Commun. Math. Phys. 283 (2008), 397-415.
- Gunter Stolz with F. Klopp, M. Loss and S. Nakamura. Localization for the Random Displacement Model, Duke Math. J. 161 (2012), 587-621.
- Gunter Stolz with E. Hamza and R. Sims. Dynamical localization in disordered quantum spin systems, Commun. Math. Phys. 315 (2012), 215-39.
- Gunter Stolz with B. Nachtergaele and R. Sims. An area law for the bipartite entanglement of disordered oscillator systems, J. Math. Phys. 54 (2013), 042110, 24 pp.
- Gunter Stolz with R. Froese, D. Lee, C. Sadel and W. Spitzer. Localization for transversally periodic random potentials on binary trees, J. Spectr. Theory 6 (2016), 557-600.
- Gunter Stolz with H. Abdul-Rahman, B. Nachtergaele and R. Sims. Entanglement dynamics of disordered quantum XY chains. Lett. Math. Phys. 106 (2016), 649-74.
- Gunter Stolz with Y. Karpeshina, Y.-R. Lee and R. Shterenberg. Ballistic transport for the Schrodinger operator with limit-periodic or quasi-periodic potential in dimension two, Commun. Math. Phys. 354 (2017), 85-113.

### Academic Distinctions & Professional Memberships

- American Mathematical Society
- Deutsche Mathematiker Vereinigung
- International Association of Mathematical Physics