Michael Hott

I am currently a mathematics graduate student at UT Austin. My research interests lie in Mathematical Physics and Analysis.

Conferences and Meetings on Mathematical Physics

Office: PMA 12.120 (located at 2515 Speedway, Austin, TX 78712)
Office hours: By appointment
E-mail: michael.hott [at] math.utexas.edu

"Alles was überhaupt gedacht werden kann, kann klar gedacht werden. Alles was sich aussprechen läßt, läßt sich klar aussprechen." Translation: "What can be thought at all, can be thought clearly. What can be said, can be said clearly." - Ludwig Wittgenstein, Tractatus logico-philosophicus 4.116


"I think I can safely say that nobody understands quantum mechanics." - Richard P. Feynman, “Probability and Uncertainty — the Quantum Mechanical View of Nature”, chapter 6, p. 129


An anecdote attributed to Marie Curie: Instead of asking her kids about how school was, Marie asked them about whether they had asked a good question.


"Aber meine Herren, wir sind doch in einer Universität und nicht in einer Badeanstalt." Translation: "After all, we are a university, not a bathhouse." - David Hilbert in 1915 when trying to hire Emmy Noether as a faculty member. Other faculty members described it as humiliating to have a woman teach soldiers coming home from war.



Publications

  1. "Convergence rate towards the fractional Hartree-equation with singular potentials in higher Sobolev norms", arXiv preprint: arXiv:1805.01807 (2018).
  2. "Derivation of the Hartree equation for compound Bose gases in the mean field limit", joint work with Ioannis Anapolitanos and Dirk Hundertmark, Rev. Math. Phys. 29, 1750022 (2017).
  3. "A simple proof of convergence to the Hartree dynamics in Sobolev trace norms", joint work with Ioannis Anapolitanos, Journal of Mathematical Physics 57.12: 122108 (2016).
  4. "Asymptotic behavior of the ground state energy of a Fermionic Froehlich multipolaron in the strong coupling limit", joint work with Ioannis Anapolitanos, arXiv preprint: arXiv:1601.05272 (2016).

Selected Lecture notes

Here you can find a selection of handwritten notes I took for some of my classes. These notes are not complete and I sometimes paraphrased, shortened or changed parts of the notes. Personal comments are written in grey.

  • Diffusion processes held by Luis Caffarelli in Spring 2018
  • Fluid dynamics being held by Alexis Vasseur in Spring 2019
  • Mathematical Physics held by Thomas Chen in Fall 2017
  • PDE 1 held by Alexis Vasseur in Fall 2017
  • PDE 2 held by Nataša Pavlović in Spring 2017
  • Application of QFT to Geometry held by Andy Neitzke in Fall 2017
  • Weak solutions and Convex Integration being held by Philipp Isett in Spring 2020 (in progress)
  • Problem class notes

    You can find problem class material for the respective classes listed below.

  • M427 J (Differential Equations+Linear Algebra) Spring 2019
  • M340 L (Linear Algebra+Matrix Calculus) Fall 2019
  • M427 J (Differential Equations+Linear Algebra) Spring 2020
  • Additional material

    Over the years, I gave seminar talks on several topics where I worked out the details of some papers. The notes and slides may contain minor mistakes but should provide the general idea.

  • Positive part of Onsager's conjecture based on this paper by Cheskidov, Constantin, Friedlander, Shvydkoy.
  • Derivation of the Quantum Boltzmann equation based on this paper by Erdős, Salmhofer, Yau.
  • Geometric topology based on this paper by Lewin.
  • Stability of materials under the influence of periodic potentials
  • Intro to scattering theory, based on a course I gave in summer 2018

    Theses

  • My bachelor's thesis at KIT under supervision of D. Hundertmark and J. Schmalian
  • My master's thesis at KIT under supervision of D. Hundertmark and J. Schmalian
  • A word on inclusivity


    Knowledge is not the merit of a few famous scientists over the course of human existence; it is rather the result of collected contributions of countless, unfortunately, some of them even unknown, scientists across the globe, across all nations, across all ethno-racial groups, gender, gender identifications, sexual orientations, and religious beliefs. Unfortunately, many important scientists have remained and remain unknown also due to hostile societal structures, see, e.g., this Guardian article on the subject. Oppression has come from within the scientific community, e.g. when German scientists tried to undermine, what they called, "Jewish science", see, e.g., this Scientific American article, as well as oppression from outside, see, e.g., this interview with J. L. Lebowitz. This has led to undermining the significance of scientific contributions and even suppressing scientific contributions entirely. The oppression of scientists and sciences have or have almost caused catastrophic events, e.g., in the case of Alan Turing cracking the Enigma. Regardless of being a scientist or not, the result of oppression on the individual is devestating, as seen, e.g., in Turing's case. Many of us suffer oppression and being marginalized on a daily or otherwise very frequent basis.
    We may also not dismiss the fact that sciences have been pursued on the back of oppressed groups as, e.g., in the case of experiments of female slaves for the sake of developing gynaecolgical tools, and there arise serious ethical questions in the use of knowledge gained in an unethical way. It is thus among our responsibilities as a scientific community to nurture a friendly, healthy environment for everyone so that we can thrive as individuals and drive scientific progress together, and to hold each other accountable.
    At this point, I would like to address my students: If you at any point face any struggle, please feel free to share it with me. I also welcome and encourage you to share any helpful feedback with me. I will listen to you and I will try to guide you to the correct ressources and I will give my best to amplify your voice in case you seek assistance; and I will try to implement your suggestions as good as possible. I am fully committed to accommodating my teaching to your individual needs; the interested reader shall take a look at [FT], [T], and other publications by our own Uri Treisman. Moreover, you might be interested in attending lectures by Leonard Moore. Rest assured that you deserve to be here at UT and that you make this world more wonderful just by being you. We at UT value your contributions and wish you best health and success for your personal and professional life.