Dmitri Pavlov

Papers • Texts • Notes • Software • People • Teaching • Resources

Assistant Professor of Mathematics, Department of Mathematics and Statistics, Texas Tech University.

I am currently looking for Ph.D. students. Email me for additional information.

Email: dmitri.pavlov[remove this text]@ttu.edu.

Research interests: functorial field theory, factorization algebras, homotopy theory, higher category theory, higher and derived differential geometry.

Invited talks I have given. A complete list of talks is also available.

Curriculum Vitæ.

Papers

Dmitri Pavlov's articles on arXiv.

Functorial field theory

(with Daniel Grady)
The geometric cobordism hypothesis.
Submitted.

(with Daniel Grady)
Extended field theories are local and have classifying spaces.
Submitted.

(with Daniel Berwick-Evans)
Smooth one-dimensional topological field theories are vector bundles with connection.
Algebraic & Geometric Topology (in press).

Sheaf theory

Projective model structures on diffeological spaces and smooth sets and the smooth Oka principle.
Submitted.

Numerable open covers and representability of topological stacks.
Topology and its Applications 318:108203 (2022), 1–28.
doi:10.1016/j.topol.2022.108203

(with Daniel Berwick-Evans and Pedro Boavida de Brito)
Classifying spaces of infinity-sheaves.
Submitted.

Homotopy theory

The enriched Thomason model structure on 2-categories.
Submitted.

Combinatorial model categories are equivalent to presentable quasicategories.
Submitted.

(with Owen Gwilliam)
Enhancing the filtered derived category.
Journal of Pure and Applied Algebra 222:11 (2018), 3621–3674.
doi:10.1016/j.jpaa.2018.01.004

(with Jakob Scholbach)
Homotopy theory of symmetric powers.
Homology, Homotopy, and Applications 20:1 (2018), 359–397.
doi:10.4310/HHA.2018.v20.n1.a20

(with Jakob Scholbach)
Admissibility and rectification of colored symmetric operads.
Journal of Topology 11:3 (2018), 559–601.
doi:10.1112/topo.12008

(with Jakob Scholbach)
Symmetric operads in abstract symmetric spectra.
Journal of the Institute of Mathematics of Jussieu 18:4 (2019), 707–758.
doi:10.1017/S1474748017000202

von Neumann algebras

Gelfand-type duality for commutative von Neumann algebras.
Journal of Pure and Applied Algebra 226:4 (2022), 106884.
doi:10.1016/j.jpaa.2021.106884.

Algebraic tensor products and internal homs of noncommutative Lp-spaces.
Journal of Mathematical Analysis and Applications 456:1 (2017), 229–244.
doi:10.1016/j.jmaa.2016.11.060

Expository texts

Topology. Notes of a class taught in Fall 2018 and Spring 2019.

Category Theory. Notes of a class taught in Spring 2018.

A very gentle introduction to functorial field theory and Chern–Simons theory via bundle 2-gerbes. Handwritten notes of a series of lectures given at Texas Tech in Fall 2017 and Spring 2018.

Classification of irreducible representations of Heisenberg groups and algebras. Notes of a talk given on December 11, 2007 at QFT Mini Conference at UC Berkeley.

Notes

Lectures on the Atiyah-Singer index theorem, notes for a Spring 2011 course by Peter Teichner.

Notes of Spring 2010 Physics for Topologists Seminar at UC Berkeley.

Scans of papers by other authors.

Software

Scripts for mathematics: automatic downloading of full texts and bibliographic information based on title or repository id.

tspell, a spell checker for TeX files like aspell (using libaspell), but with a much better support for TeX.

jbig2topdf, a program to assemble a bunch of JBIG2 files into a PDF file, which was used to produce the bilevel PDF files on the scans page.

Macros for Knuth's TeX system.

Git tutorial for mathematicians.

People

Academic ancestors:
Peter Teichner • Matthias Kreck • Friedrich Hirzebruch • Heinz Hopf / Heinrich Behnke • Erhard Schmidt / Erich Hecke • David Hilbert • Ferdinand von Lindemann • Felix Klein • Julius Plücker • Christian Ludwig Gerling • Carl Friedrich Gauß • Johann Friedrich Pfaff

Collaborators:
Daniel Berwick-Evans • Pedro Boavida de Brito • Daniel Grady • Owen Gwilliam • Alex Kahle • Jakob Scholbach • Stephan Stolz • Peter Teichner • Peter Ulrickson

Graduated PhD students:

2022
Stephen Peña: Geometric factorization algebras.
2021
Nilan Manoj Chathuranga Kasisetti Mudalige: Equivalence of complete distributive inverse semigroups and étale localic groupoids, and a characterization of topological orbifolds.
2021
(Co-advisor; advisor: Răzvan Gelca) Rachel Harris: Algorithms for skein manipulation and automation of skein computations.

Teaching

Topology and Geometry Seminar.

Quantum Homotopy Seminar.

Summer Seminar and Winter Seminar.

Fall 2022: Mathematics 6325 (Category Theory), TuTh 11–12:30 in CMLL 119. Homework: 12.

Fall 2022: Mathematics 4362 (Theory of Numbers), TuTh 2–3:30 in MA 12.

Spring 2022: Mathematics 4351 (Advanced Calculus II), TuTh 2–3:20 in MA 109. Blackboard.

Fall 2021: Mathematics 2450.021 (Calculus III), TuTh 9:30–11:30 in MA 16. Syllabus, WeBWorK.

Fall 2021: Mathematics 6330 (Manifold Theory), TuTh 2–3:30 in MA 114. Syllabus, notes, homework.

Spring 2021: Mathematics 5399.002 (Introduction to Modern Algebra II), TuTh 9:30–11 in MA 17. Syllabus, handwritten notes by Jack Weiland, homework 12.

Spring 2021: Mathematics 2360.022 (Linear Algebra), TuTh 11–12:30 in HUMSCI 63. Syllabus, digest, WeBWorK, Blackboard.

Fall 2020: Mathematics 5317 (Introduction to Modern Algebra), TuTh 9:30–11 in MA 109. Syllabus, handwritten notes by Jack Weiland, homework 123456789.

Fall 2020: Mathematics 2360.121 (Linear Algebra), online. Syllabus, study guide, digest, review 123, WeBWorK, Blackboard.

Spring 2020: Mathematics 6322 (Homological Algebra II), TuTh 9:30–11 in MA 113 and online. Syllabus, handwritten notes by Rachel Harris, midterm, projects.

Spring 2020: Mathematics 6332 (Geometric Mechanics), TuTh 11–12:30 in MA 17 and online. Syllabus, projects.

Fall 2019: Mathematics 6321 (Homological Algebra I), TuTh 9:30–11 in MA 109. Syllabus, notes, handwritten notes by Rachel Harris, homework, projects.

Fall 2019: Mathematics 6333 (Lie Groups), TuTh 11–12:30 in MA 113. Syllabus, handwritten notes by Rachel Harris, homework, projects.

Summer 2019: Topology Doctoral Preliminary Examination. Practice problems, supplement, May 2019, August 2019, August 2020.

Spring 2019: Mathematics 5325 (Topology II), TuTh 11–12:30 in MA 113. Syllabus, notes, handwritten notes by Rachel Harris, midterm 12, final.

Fall 2018: Mathematics 5324 (Topology I), TuTh 11–12:30 in MA 113. Syllabus, notes, midterm 12final.

Fall 2018: Mathematics 5365 (Analysis of Algorithms), TuTh 12:30–2 in MA 113. Syllabus, homework: 123, midterm 12final.

Spring 2018: Mathematics 6325 (Category Theory), MWF 9–10 in MA 10. Syllabus, notes, handwritten notes by Nilan Manoj Chathuranga, homework: 123.

Fall 2017: Mathematics 2360.002 (Linear Algebra), MWF 2–3 in MA 110. Syllabus.

Resources

MathSciNet (profile) • zbMATH (profile) • Google Scholar (profile)

MathOverflow (profile) • nLab (profile) • Kerodon (PDF) ∙ Stacks (PDF)

arXiv (profile) • Library Genesis • Sci-Hub 1 • 2 • 3

MathMeetings.net • researchseminars.org

Cycling in Lubbock: city map with traffic lights • heat map • thoroughfare plan

My sister's paintings