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<!DOCTYPE html>
<html>
<header>
<h1> Daniel Mitropolsky</h1>
</header>
<p>
<i>mitropolsky</i> @ <i>cs</i> . <i>columbia</i> . <i>edu</i>
</p>
<img src="academic_photo.jpeg" alt="A photo." width=256>
<p>
I also go by: Danny, Dan, Dani, Mito, Даня, Даниил Всеволодович Митропольский, <ruby>水戸<rt>みと</rt>智<rt>さとし</rt></ruby>, 刘智龙
</p>
<p>
I am a PhD student at Columbia University in the <a href="https://theory.cs.columbia.edu/">Theory of Computation</a> group and the <a href="http://www1.cs.columbia.edu/nlp/index.cgi">NLP group</a>.
</p>
<p>
I have the pleasure of being advised by <a href="https://www.engineering.columbia.edu/faculty/christos-papadimitriou">Christos Papadimitriou</a> and <a href="https://www.cs.columbia.edu/~tal/">Tal Malkin</a>. I am interested in everything, but my main research interests are:
<ul>
<li> neurally-plausible, mathematical models of the brain
<li> complexity theory, including total complexity and foundational cryptography
<li> language; computational linguistics, NLP
</ul>
</p>
<h2> About</h2>
<p>
Before starting my PhD, I lived in San Francisco and worked as a Software Engineer at <a href="https://www.google.com">Google</a> on the <a href="https://www.google.com">Search</a> team.
<br>
Before that, I did my undergrad at <a href="https://www.yale.edu/">Yale University</a> where I graduated summa cum laude with an intensive B.S. in Mathematics and a B.S. in Computer Science.
</p>
<h2> Languages</h2>
Languages are one of my greatest passions. I love to use them, so do not be shy if you know any of these.
I plan to update this section with my favorite resources, poems, and thoughts about languages.
<ul>
<li> Fluent (C1-C2) in English, French, Spanish, Portuguese, Italian, Russian, Polish, Chinese (Mandarin), Japanese, German, American Sign Language (ASL)
<li> Advanced / Conversational (B2+) in Korean, Vietnamese
<li> Working on (B1+) Greek, Arabic
</ul>
<h2> Publications</h2>
<ul>
<li> D. Mitropolsky, C. Papadimitriou, "The Architecture of a Biologically Plausible Language Organ", 2023, in submission, <a href=https://arxiv.org/abs/2306.15364>Arxiv</a>
<li> P. Harsha, D. Mitropolsky, A. Rosen, "Downward Self-Reducibility in TFNP", 14th Innovations in Theoretical Computer Science Conference (<b>ITCS</b>), 2023, <a href=https://arxiv.org/abs/2209.10509>Arxiv</a>
<li> D. Mitropolsky, A. Ejaz, M. Shi, M. Yannakakis, C. Papadimitriou, "Center-Embedding and Constituency in the Brain and a New Characterization of Context-Free Languages", Natural Logic Meets Machine Learning (NALOMA), 2022
<li> F. d'Amore, D. Mitropolsky, P. Creszenzi, E. Natale, C. Papadimitriou, "Planning with Biological Neurons and Synapses", (<b>AAAI</b>), 2022, <a href=https://arxiv.org/abs/2112.08186>Arxiv</a>
<li> D. Mitropolsky, M. Collins, C. Papadimitriou, "A Biologically Plausible Parser", Transactions of the Association for Computational Linguistics (<b>TACL</b>), 2021, <a href=https://arxiv.org/abs/2108.02189>Arxiv</a>
<li> R. Kleinberg, D. Mitropolsky, C. Papadimitriou, “Total Functions in the Polynomial Hierarchy”, 12th Innovations in Theoretical Computer Science Conference (<b>ITCS</b>), 2021, <a href=https://eccc.weizmann.ac.il/report/2020/153/>ECCC</a>
<li> C. Papadimitriou, S. Vempala, D. Mitropolsky, M. Collins, W. Maass, “Brain Computation by Assemblies of Neurons”, in <b>PNAS</b>, vol. 117, no. 25, June 2020
<li> C. Papadimitriou, S. Vempala, D. Mitropolsky, M. Collins, W. Maass, L. Abbott, “A Calculus for Brain Computation”, in <b>CCNeuro</b>, Berlin, Germany, 2019.
<li> D. Jensen, A. Deveau, J. Kainic, D. Mitropolsky, “Gonality of Random Graphs”, in <b>Involve</b>, vol. 9, no 4, 715-720, 2016
</ul>
<h2> Selected Talks</h2>
<ul>
<li> Invited talk on my brain research at the MIT CBMM (Center for Brains, Minds and Machines), Dec. 2023, <a href=https://cbmm.mit.edu/video/simplest-neural-model-and-hypothesis-language>Link (recording of in-person talk)</a>
<li> Talk on my brain research at the Brown Theoretical Computer Science Seminar (this one is more CS-oriented) , Dec. 2023 <a href=https://www.youtube.com/watch?v=FIVWf1wTOlM&t=477s>Link (recording of in-person talk)</a>
<li> Talk on my brain research at Tufts, Dec. 2023 <a href=http://www.cs.tufts.edu/t/colloquia/current/?event=1570>Announcement link</a>
<li> Talk on downward self-reducibility in TFNP (and the unlikelihood of recursive algorithms for factoring!), Jan 2023 <a href=https://www.youtube.com/watch?v=5gk2O8v2HZA&t=339s>Link (Zoom talk)</a>
<li> Talk on total functions and the polynomial hierarchy (a new area of complexity theory!), Jan 2021, <a href=https://www.youtube.com/watch?v=cwd5uPWYBEk&t=7s> Link (Zoom talk)</a>
</ul>
<h2> Errata for Computational Complexity (Arora Barak)</h2>
<ul>
<li> <a href="arora-barak-errata.html">List of errata in advanced chapters of Computational Complexity: A Modern Approach, by Arora and Barak</a>
<li> Please send me an email if you find anything new. Please include page number and an explanation (it might be a while since I read that particular chapter)!
</ul>
<h2> Teaching</h2>
<ul>
<li> <b>Course Instructor</b>, <a href="teaching/6261/">COMS E6261: Advanced Cryptography, Crypto ∩ TFNP, Spring 2019</a>
<li> <b>Course Instructor</b>, <a href="http://www.cs.columbia.edu/~mcollins/cs4705-spring2019/">COMS W4705: Natural Language Processing, Spring 2019</a>
<li> <b>Teaching Assistant</b>, <a href="https://computationandbrain.github.io/about/">COMS 6998-004: Computation and Brain, Fall 2019</a>
<li> <b>Teaching Assistant</b>, COMS 6998-004: Computation and Brain, Fall 2018
</ul>
<h2> Industry research </h2>
<ul>
<li>Research Intern, <a href="https://research.google/teams/language/">Google AI Language</a> with Ankur Parikh, Summer 2019
<li> Student Researcher, <a href="https://research.google/teams/language/">Google AI Language</a> with Ankur Parikh, Fall 2019
</ul>
</html>