Higher differential geometry seminar (Summer 2020)

HDG seminar continues this summer. The references list can be found here. Topics include:

1. Iterated integrals, superconnections, and higher holonomy;
2. Higher Riemann-Hilbert correspondance;
3. Lie groupoids, higher groupoids and stacks.

We are meeting each Tuesday at 3:00pm. Please let me know if you want to join the mail list.

Higher differential geometry seminar (Summer 2019)

Together with Darrick, I am running the Homotopy theory seminar continuing in summer 2019 (mainly in June). We are mainly focusing on higher structure in differential geometry and topology. Topics includes: higher holonomy/parallel transport, superconnections/representations up to homotopy, dg manifolds/$L_\infty$ algebroids, simplicial (pre)sheaves, $(\infty,1)$-sheaves/$\infty$-stacks, and string topology.

Meeting time: Each Tuesday and Friday 1:30pm at 4N30.

References:

Simplicial sheaves:

1. Sheaves and homotopy theory by Daniel Dugger

2. Simplicial presheaves and derived algebraic geometry by Bertrand Toen

3. Local homotopy theory by John F. Jardine

Differential graded manifolds:

4. Introduction to graded geometry by Maxime Fairon

5. Differential graded manifolds and associated stacks: an overview by Dmitry Roytenberg

6. Superconnections and Parallel Transport by Florin Dumitrescu

Stacks, derived geometry

7. Differentiable stacks and gerbes by Kai Behrend and Ping Xu

8. Derived smooth manifolds by David I. Spivak

9. The universal property of derived geometry by Andrew W. Macpherson

10. An introduction to d-manifolds and derived differential geometry by Dominic Joyce

Iterated integrals

11. Iterated path integrals by K. T. Chen

12. Iterated integrals of superconnections by K. Igusa

13. The $A_\infty$ de Rham theorem and integration of representations up to homotopy by C. A. Abad and F. Schatz

14. "Parallel" transport - revisited by J. Stasheff

Chen's $\pi_1$ de Rham Theorem

15. Iterated integrals of differential forms and loop space homology by K. T. Chen

16. [* Algebras of iterated path integrals and fundamental groups by K. T. Chen

17. Iterated integrals, fundamental groups and covering spaces by K. T. Chen](https://www.jstor.org/stable/1995617?seq=1#metadata_info_tab_contents)

18. On Chen's iterated integrals by V. K. A. M. Gugenheim

Parallel Transport

19. Connections, holonomy and path space homology by K. T. Chen

20. Extension of $C^\infty$ function algebra by integrals and Malcev completion of $\pi_1$ by K. T. Chen