Dmitri Pavlov

Papers • Drafts • 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: homotopy theory, higher differential geometry, factorization algebras, functorial quantum field theory, derived manifolds, synthetic differential geometry, Tomita–Takesaki theory, locales and toposes.

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

Curriculum Vitæ: DVI, PostScript, PDF.

Papers

Dmitri Pavlov's articles on arXiv.

arXiv:2005.05284

Gelfand-type duality for commutative von Neumann algebras.

arXiv:1912.10544

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

arXiv:1602.01515

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

arXiv:1510.04969

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

arXiv:1501.00967

(with Daniel Berwick-Evans) Smooth one-dimensional topological field theories are vector bundles with connection.
Submitted.

arXiv:1410.5699

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

arXiv:1410.5675

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

arXiv:1309.7856

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

Drafts

Brown representability via concordance. Manuscript in preparation.

(with Stephan Stolz and Peter Teichner) Differential cohomology via smooth topological field theories. Manuscript in preparation.

Noncommutative L_p-spaces of W*-categories and their applications to L_p-modules. Draft: PDF.

Jones index as a bicategorical trace. Draft: PDF.

Expository texts

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: TeX, DVI, PostScript, PDF.

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.

jpegtopdf and jbig2topdf, programs to assemble a bunch of JPEG/JBIG2 files into a PDF file. The latter 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

Teaching

Topology and Geometry Seminar.

Quantum Homotopy Seminar.

Spring 2020: Mathematics 6322 (Homological Algebra II), TuTh 9:30–11 in MA 113 and online. Syllabus, 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.

Spring 2019: Mathematics 5325 (Topology II), TuTh 11–12:30 in MA 113. Syllabus, notes, handwritten notes by Rachel Harris, midterm 1, 2, final.

Fall 2018: Mathematics 5324 (Topology I), TuTh 11–12:30 in MA 113. Syllabus, notes, midterm 1, 2, final.

Fall 2018: Mathematics 5365 (Analysis of Algorithms), TuTh 12:30–2 in MA 113. Syllabus, homework: 1, 2, 3, midterm 1, 2, final.

Spring 2018: Mathematics 6325 (Category Theory), MWF 9–10 in MA 10. Syllabus, notes, homework: 1, 2, 3.

Fall 2017: Mathematics 2360 (Linear Algebra), Section 002, MWF 2–3 in MA 110. Syllabus.