Spectral sequences and orbits of the actions of groups (1967) - Anatolii Fomenko
Below are various notes collected from my time studying mathematics, in the off chance that they might be useful to others.
| 2021-08 | My Ph.D. thesis in mathematical physics, written under the guidance of Ezra Getzler, concerns a new construction of the Batalin-Vilkovisky (BV) Laplacian using the methods of homological perturbation theory. [thesis] [slides] |
| 2019-05 | In a classic paper, Bott computes the differential forms on the classifying space of a compact Lie group G. In this talk I outline this construction and briefly describe how to view this computation as a concrete construction of a shifted symplectic structure (a la Pantev-Toen-Vaquie-Vezzosi) on the classifying stack BG represented by a simplicial smooth manifold. I recommend Ezra Getzler's exposition on simplicial manifolds as a general reference. [talk notes] |
| 2018-xx | Rough notes on derived geometry taken during lectures given by various speakers at the Fields Institute in a summer conference. [lecture notes] |
| 2018-01 | Very unfinished notes on differential cohomology and gerbes, in which I took a concrete and computational approach. Reader assumes responsibility for any and all injuries incurred. [unfinished notes] |
| 2018-xx | Rough notes on Mihnea Popa's course on complex geometry. [notes] |
| 2017-09 | Lightning talk on the Atiyah-Singer index theorem. [notes] |
| 2017-xx | Rough notes from John Francis' course on factorization homology. [notes] [high-level summary] |
| 2017-03 | In this talk (for John Francis' Milnor seminar) I introduce the basics of Chern-Weil theory. [notes] |
| 2017-03 | An informal reading group on WKB methods (led by Aaron Naber) led to this high-level talk on Witten's de Rham approach to Morse theory, and Fukaya's reinterpretation in terms of A-infinity categories. [talk notes] |
| 2017-01 | I gave a talk on the symplectic geometry behind classical mechanics (with an eye towards moment maps and Noether's theorem) for a seminar on the BV formalism, run by Sean Pohorence. [talk notes] |
| 2016-11 | I gave a talk (for John Francis' Kan seminar) sketching Bousfield's construction of the localization of spaces with respect to homology equivalences. I recall John pointing out that I had avoided discussing all the hard parts of the construction. I had it right in middle school: I'm not smart enough to be a mathematician. [talk notes] |
| 2016-01 | For a seminar on Reshetikin-Turaev invariants, led by Theo Johnson-Freyd, I gave a talk on the geometric quantization of Chern-Simons theory (according to Axelrod, della Pietra, and Witten). [talk notes] |
| 2015-12 | I spent a bit of time learning about the basics of symplectic geometry as a first-year graduate student under Eric Zaslow's patient eye. [notes] |