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

"μάλα γὰρ φιλοσόφου τοῦτο τὸ πάθος, τὸ θαυμάζειν: οὐ γὰρ ἄλλη ἀρχὴ φιλοσοφίας ἢ αὕτη [...]" Translation: "For this feeling of wonder shows that you are a philosopher, since wonder is the only beginning of philosophy [...]" - Plato, Theaetetus 155d. Translation: Plato. Plato in Twelve Volumes, Vol. 12 translated by Harold N. Fowler. Cambridge, MA, Harvard University Press; London, William Heinemann Ltd. 1921, see Tufts university

"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. On the emergence of quantum Boltzmann fluctuation dynamics near a Bose-Einstein Condensate, with Thomas Chen (2021), arXiv.
  2. Convergence rate towards the fractional Hartree-equation with singular potentials in higher Sobolev norms, to be published in Rev. Math. Phys. (2018), arXiv, Journal.
  3. Derivation of the Hartree equation for compound Bose gases in the mean field limit, with Ioannis Anapolitanos and Dirk Hundertmark, Rev. Math. Phys. 29, 1750022 (2017), Journal, arXiv.
  4. A simple proof of convergence to the Hartree dynamics in Sobolev trace norms, with Ioannis Anapolitanos, Journal of Mathematical Physics 57.12: 122108 (2016), Journal, arXiv.
  5. Asymptotic behavior of the ground state energy of a Fermionic Fröhlich multipolaron in the strong coupling limit, with Ioannis Anapolitanos (2016), arXiv.

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 held by Alexis Vasseur in Spring 2019
  • Geometric harmonic maps part 1, part 2 held by Salvatore Stuvard in Fall 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 part 1, part 2 held by Philipp Isett in Spring 2020.
  • Problem class notes

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

  • M427 J (Differential Equations+Linear Algebra) Spring 2020
  • M340 L (Linear Algebra+Matrix Calculus) Fall 2019
  • M427 J (Differential Equations+Linear Algebra) Spring 2019
  • 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.
  • Geometric topology based on this paper by Lewin.
  • Stability of materials under the influence of periodic potentials
  • Intro to scattering theory, based on Reed and Simon III: Scattering Theory, for a course I gave in summer 2018.
  • Sharp inequalities via flows, based on works by G. Toscani, Dolbeaut, Esteban, Loss, Carlen, Carrillo, Loss.
  • The ionization problem, based on a minicourse by Rupert Frank at MCQM 2018.
  • Uniqueness of radial solutions, based on this work by Frank, Lenzmann, Silvestre.
  • A method dual to stationary phase.

    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
  • 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, religious beliefs, degrees of disability, or degrees of neurodiversity or neurodivergence. 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. MacTutor is a project created and maintained by Edmund Robertson, and John O'Connor, of the School of Mathematics and Statistics at the University of St Andrews. It is dedicated to giving a more complete history of the development of mathematics than the one that is given in standard mathematics books. It includes some of the important contributions attributed to non-European mathematicians, and it is a constant work in progress.
    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. These are traumatic experiences.
    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. The oppressive structures of today were created by some priviliged of the past, and are maintained by some priviliged of today. Contrary to some beliefs, oppression does not drive individuals to thrive, but only contributes to an achievement gap, see this medium article.
    It is thus among our responsibilities as a scientific community to nurture a friendly, healthy, and safe environment for everyone so that we can thrive as individuals and drive scientific progress together, and to hold each other accountable. Excellence in STEM does not require stereotypes. Instead, everyone with a desire to drive progress in STEM deserves to do so. And we are greatful for every single one of you.
    Below, I listed only a few members of our diverse community. Each community belonging to a different minority group faces different, sometimes similar discrimination and oppression. It is important for us to not treat eachother as monoliths representing a group we are assigned to, see also stereotype threat. In order to elevate eachother and ourselves, I would like to point out a few initiatives that already exist. I am fully committed to support every single one of you and to amplify your voices. There are a few websites highlighting excellence in diverse communities. For our black community and everyone interested, please take a look at Mathematicians of the African diaspora, mathematically gifted and black, and NAM. There is also the student run organization MoCAT at UT. Scott Williams at the Mathematics Department of the State University of New York at Buffalo created a list of links for more resources for black students and students from other underrepresented groups. Among these links, there are special scholarship opportunities. Scholly is another place to find scholarships suited for you. For our LatinX and Hispanic community and everyone interested, I recommend looking at LATHISMS. I want to refer our southeast Asian community and everyone interested to SEAMS. Our Indian community and everyone interested can find support at IMS. For our LGBTQIA+ community and everyone interested, please check out PrideInStem. For our female community and everyone interested, please check out AWM and contact our wonderful and very supportive Jennifer Austin for its local chapter. Our indigenous community and everyone interested can find useful resources here. Unfortunately, I could not find resources specifically for our disabled, Arabic or Muslim, Jewish, neurodivergent or neurodiverse community, but you will find a community interested in your personal struggles at CMMS. If I ommited a group or did not mention helpful resources, please let me know about it as I did not intentionally ommit anyone. Any member of these groups deserve our attention for their shared and, more importantly, individual needs.
    It is important to emphasize that diversity has to be intersectional, i.e., we need to work on uplifting each and everyone, and abondon cultural norms that prevent us from doing so. There is no common good in engaging in oppression olympics. Instead, find ways to appreciate each other and let each other know that you appreciate them, and acknowledge their struggle. For that, it is also important that we continue to educate ourselves on existing struggle. Apart from the mentioned factors, there also exists discrimination based on arbitrary cultural beauty standards and perceived level of intelligence as well as other factors. Discrimination creates abusive environments and impedes us from striving for serendipity. When you can, absolve yourself from abusive environments and, instead, surround yourself with people you love and that love you. Diversity is not just a tag that can be obtained but a culture that allows all of us to achieve our personal goals.
    Personally, I have started to overcome past trauma by seeing a therapist. It has helped me to recognize and not engage in past bad learned behavioral patterns, and helped me seek happiness instead. Neil Pasricha wrote a couple of excellent books on happiness. The four agreements are also a fantastic source to address past struggles on an emotional level. I am interested in all of your stories and I will see and hear how I can help.
    At this point, I would like to address my students: If you at any point face struggle of any kind, please feel free but not obligated 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 implement your suggestions as good as possible. I am fully committed to accommodating my teaching to your individual needs and to provide a nurturing class environment; 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.

    Land Acknowledgement

    I would like to acknowledge that we are meeting on the Indigenous lands of Turtle Island, the ancestral name for what now is called North America. Moreover, I would like to acknowledge the Alabama-Coushatta, Caddo, Carrizo/Comecrudo, Coahuiltecan, Comanche, Kickapoo, Lipan Apache, Tonkawa and Ysleta Del Sur Pueblo, and all the American Indian and Indigenous Peoples and communities who have been or have become a part of these lands and territories in Texas.
    Since some of our classes are online, you may be contributing from other tribal lands. Here is a map that may help you in identifying the indigenous peoples of the land on which you study: https://native-land.ca/.
    Mathematics is a beautiful language we as humans developed to assign meaning to our empirical surroundings and to express our thoughts accurately. Contrary to most school curricula, mathematics is not the competition on who can solve a certain set of canonized exercises in a given time. Instead, requiring only a few agreed upon principles from logic, it allows us to formulate problems, solve problems and develop language to formulate and solve problems. Whenever we plan our shopping trips, we tackle a brachistochrone problem. Modern technology is built on numerical solutions of mathematical problems. Traffic light rules rely on Network Theory, a subfield of Graph Theory. Maximizing cellular coverage can be tackled with tools from Algebraic Topology. Tsunamis and hurricanes are modelled with the help of Fluid Dynamics. Arts often are inspired by Geometry and Topology. Mathematics also lives of its symbiosis with fields of applications. I personally enjoy finding out which mathematical rules can be applied to nature, developing a true understanding of those rules, and studying the implications of those rules. If you want to know more about what mathematicians do, do not hesitate to talk to me.