I am Assistant Professor of Mathematical Physics at Virginia Tech in Blacksburg, Virginia. Previously, I was an independent research fellow and lecturer at the Institute of Mathematics, University of Zurich, funded by an Ambizione Grant from the Swiss National Science Foundation and a Marie Skłodowska-Curie individual fellowship of the European Union. From October 2016 to September 2019, I was a postdoctoral researcher in the group of Prof. Dr. Robert Seiringer at the Institute of Science and Technology Austria (ISTA). I obtained my doctoral degree in mathematics in 2016 from the University of Tübingen, with a thesis in analysis and mathematical physics under the supervision of Prof. Dr. Christian Hainzl.
My main research interests are mathematical quantum mechanics and quantum statistical mechanics. In my work, I develop analytic, functional-analytic, and probabilistic methods to study mathematical problems arising from solid-state physics. Currently, I am primarily interested in developing new mathematical tools to study bosonic many-particle systems at positive temperature. Another important theme of my work are mathematical aspects of the BCS theory of superconductivity (formulated as a non-commutative variational problem). I have also been interested in the physics of the angulon quasi-particle.
For more information, see my CV.
I will give an invited talk at the conference Operator Theory in Quantum Physics – OTQP 2026 that will be held at the Institute of Matematics of the Polish Academy of Sciences in Będlewo, Poland, June 14-19, 2026.
Together with Tobias Ried (Georgia Tech) I am organizing a special session on Mathematical Physics, Nonlinear Partial Differential Equations, and Optimal Transportation at the AMS Fall Eastern Sectional Meeting hosted by George Washington University, Washington, DC on October 3-4, 2026.
My research group currently includes Drake Woosley (PhD student), Amitabha Roy (PhD student), Xuanyu Li (Master’s student), and Benjamin Denson (undergraduate researcher).
If you are interested in writing a Bachelor's, Master's, or PhD thesis in quantum statistical mechanics from a mathematical perspective, I would be happy to hear from you. I also supervise undergraduate research.
I am currently teaching Matrix Theory (Math 5524). If you have questions regarding the class please send me an email. Here is a brief description: Topics to be covered in the course include spectral theory for Hermitian matrices, the Jordan normal form, singular value decomposition, variational characterizations of eigenvalues, eigenvalue perturbation theory, nonnegative matrices and Perron–Frobenius theory, functions of matrices, traces of functions of matrices (von Neumann entropy, relative entropy), and trace inequalities. We will also provide a brief introduction to quantum mechanics and illustrate the material with applications to quantum mechanics and quantum information theory. The topics covered in this class are fundamental and therefore relevant for students interested in a variety of areas, such as matrix analysis, numerical analysis, quantum information theory, dynamical systems, and probability theory.
Participants are expected to have an undergraduate-level background in linear algebra and some familiarity with complex numbers.
arXiv:2507.20877 [math-ph] (2025), 83 pagesarXiv:2505.13170 [math-ph] (2025), 27 pagesarXiv:2501.19402 [math-ph], doi.org/10.1007/s11005-025-01996-z.arXiv:2501.19396 [math-ph] (2025), 102 pagesarXiv:2310.12314 [math-ph], doi.org/10.1007/s00023-024-01505-3.arXiv:2305.19173 [math-ph], doi.org/10.1137/23M1580930.arXiv:2210.09356 [math-ph], doi.org/10.1007/s00526-023-02539-x.arXiv:2203.17204 [math-ph], doi.org/10.4171/AIHPC/93.arXiv:2105.05623 [math-ph], doi.org/10.2140/pmp.2023.4.1.arXiv:2009.00992 [math-ph], doi.org/10.1016/j.jfa.2021.109096. arXiv:1912.02658 [cond-mat.mes-hall], doi.org/10.1063/1.5144759.arXiv:1910.03372 [math-ph], doi.org/10.1017/fms.2020.17.arXiv:1901.11363 [math-ph], doi.org/10.1007/s00205-020-01489-4. arXiv:1809.01204 [cond-mat.quant-gas], doi.org/10.1103/PhysRevB.98.224506.arXiv:1803.05180 [math-ph], doi.org/10.1007/s00220-018-3239-0.arXiv:1705.05162 [cond-mat.quant-gas], doi.org/10.1103, arXiv:1703.04616 [math-ph], doi:10.1063/1.4996580.arXiv:1612.03303 [math-ph], doi.org/10.1007.arXiv:1502.07205 [math-ph], doi:10.1007/s11005-015-0787-5.arXiv:1202.4111 [cond-mat.quant-gas], doi:10.1103/PhysRevA.86.013618.Three page summary of publication no. 6.
Three page summary of publication no. 13.
Publication no. 16 has been covered e.g. in (english) Gizmodo, Phys.org, (german) Der Standard.
CIRM Library. Youtube. YouTube. Youtube.40 min50 min50 min60 min45 min25 min50 min50 min30 min20 min50 min20 min50 min20 minIn March 2024 I gave a lecture series (4 75 min) on mathematical aspects of the BCS theory of superconductivity at the Winter School of the SFB TRR 352 Mathematics of Many-Body Quantum Systems and Their Collective Phenomena that took place in Kochl am See. The lecture notes can be found here: part1, part2.
Functional Analysis (Math 6625, Fall term 2025)(1) Introduction, (2) Four important PDEs, (3) Fourier Series, (4) Separation of variables(The lecture notes can be found on the course webpages. Just follow the links.)
Introduction to the statistical mechanics of lattice systems (Summer term 2023)Variational methods in analysis (Summer term 2022, joint with Dr. Alessandro Olgiati)Advanced topics in analysis (Summer term 2022, joint with Dr. Alessandro Olgiati) (first half of Variational methods in analysis that could be booked independently by Bachelor students)Mathematical statistical mechanics (Summer term 2021)The mathematics of dilute quantum gases (Summer term 2020)andreas.deuchert@vt.edu>