Department of Mathematics, UT Austin
Michael Hott
I am currently a mathematics graduate student at UT Austin. My research field is the mathematical analysis of problems arising in physics, especially Statistical Physics, Quantum Field Theory, and Quantum Mechanics. My work merges methods of Renormalization, Functional, Geometric, and Harmonic Analysis, PDEs, and Spectral Theory.
I will be a Postdoc at UMn working with Mitch Luskin in Summer/Fall 2022.
My preferred pronouns are he/him/el or they/them/ellos.
Conference and meetings calendars:
- Mathematical Physics
- Analysis
- mathinstitutes.org
- AMS meetings
- Meetings in Cooperation with AWM
- Grading Conferences
- SIAM PDE
- One World PDE
- IAS Analysis seminar
- MCQM Seminar
- Virtual Analysis and PDE Seminar (VAPS)
- Researchseminars.org
Office: PMA 12.120 (located at 2515 Speedway, Austin, TX 78712)
Office hours: By appointment
E-mail: michael.hott [at] math.utexas.edu
CV
"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
- On the emergence of quantum Boltzmann fluctuation dynamics near a Bose-Einstein Condensate, with Thomas Chen (2021), arXiv.
- Convergence rate towards the fractional Hartree-equation with singular potentials in higher Sobolev norms, Rev. Math. Phys. 33.09, 2150029 (2021), Journal, arXiv.
- Derivation of the Hartree equation for compound Bose gases in the mean field limit, with Ioannis Anapolitanos and Dirk Hundertmark, Rev. Math. Phys. 29.07, 1750022 (2017), Journal, arXiv.
- 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.
- Asymptotic behavior of the ground state energy of a Fermionic Fröhlich multipolaron in the strong coupling limit, with Ioannis Anapolitanos (2016), arXiv.
Theses
- The solution of the 2D Ising model, joint Bachelor thesis in Mathematics and Physics, at Karlsruhe Institute of Technology under supervision of D. Hundertmark and J. Schmalian
- Asymptotic behavior of the ground state energy of a Fermionic multipolaron, joint Master thesis in Mathematics and Physics, at Karlsruhe Institute of Technology under supervision of D. Hundertmark and J. Schmalian
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.
Problem class notes
You can find problem class material for the respective classes listed below.
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.
Junior Analysis seminar talks
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.
- Antiracist Resources for Learning, Teaching, and Assessment
- CRLT UMichigan
- Eberly Center's Strategies for Inclusive Teaching
- Harvard's Guide for Teaching in a Racially Diverse College Classroom
- Stewart, Dafina-Lazarus, "Language of Appeasement"
- reducingstereotypethreat.org
- Free math ressources for students
- International Commision on the History of Mathematics
- DEI commitment of the American Mathematical Society
Local ressources:
- Counseling and Mental Health Center, UT Austin
- Division of Diversity and Community Engagement, UT Austin
- Some context for 'the Eyes of Texas'
Mathematicians seeking Asylum...
Organizations:
- American Association For Advancement of Science
- Association for Women in Mathematics
- The Center for Minorities in the Mathematical Sciences
- The Indian Mathematical Society
- Indigenous Mathematicians
- LATHISMS
- Mac Tutor
- Mathematicians of the African diaspora
- Mathematically gifted and black
- Mathematicians of color alliance of Texas (MOCAT)
- National Association of Mathematicians
- Pride in STEM
- The Southeast Asian Mathematical Society
- laaunch.org
- MΣΣT a Mathematician
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 and types of disability, or degrees and types 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, suppressing entirely or incorrectly attributing scientific contributions. 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 grateful for every single one of you.
It is important to understand the distinction between active allyship and performative saviorism, as explained here. I understand that this a contentious topic, and having a growth mindset rather than a fixed mindset helps further the conversations around it.
There are many misconceptions around the reason of the achievement gap between different groups. I would like to point out this article that addresses the achievement gap found in chess. The article concludes that the achievement gap can be explained by a participation gap. Other reasons are direct and indirect, cultural, structural and systemic discrimination.
Below, I listed only a few members of our diverse community. Each community 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 and reducingstereotypethreat.org. 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 and laaunch.org. 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 the 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, Sinti and Roma, 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, we need to find ways to appreciate each other and let each other know that we appreciate them, and that we 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 providing a nurturing class environment; the interested reader shall take a look at [FT], [T], and other publications by Professor 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/.