*In this section, Professor Haynes Miller shares the seminal papers featured during math talks, and the order in which students presented them.*

Each participant reports on three seminal papers in algebraic topology over the course of the semester. These talks are generally an hour in length and occur during the regular meeting time for the course (typically 1 hour per session 3 times per week). Each talk is preceded by a student-organized "practice talk," to which the participants are invited but the instructor is not. After the formal talk, the instructor debriefs with the speaker during office hours, discusses the mathematics and the presentation, and helps the speaker decide on his or her next paper.

SES # | PRESENTERS | TOPICS / PAPERS |
---|---|---|

1 | Instructor | Organization |

2 | Instructor | Steenrod Operations (PDF - 1.7MB) |

3 | Student A | Serre, J. -P. "Cohomologie Modulo 2 des Complexes d'Eilenberg–Maclane." Commentarii Mathematici Helvetici 27, no. 1 (1953): 198–232. |

4 | Student B | Milnor, J. W. "The Geometric Realization of a Semi–simplicial Complex." Annals of Mathematics 65, no. 2 (1957): 357–62. |

5 | Student (Auditing) | Milnor, J. W., and J. D. Stasheff. Characteristic Classes (Annals of Mathematics Studies). Vol. 76. Princeton University Press, 1974. ISBN: 9780691081229. [Preview with Google Books] |

6 | Student (Auditing) (cont.) | Thom, R. "Quelques propriétés globales des variétés différentiables." Commentarii Mathematici Helvetici 28 (1954): 17–86. |

7 | Student C | ———. "Quelques propri´et´es globales des vari´et´es diff´erentiables." Commentarii Mathematici Helvetici 28 (1954): 17–86. |

8 | Practice Talk Session | |

9 | Student D | Milnor, J. W., and J. D. Stasheff. "Signature Theorem." In Characteristic Classes (Annals of Mathematics Studies). Vol. 76. Princeton University Press, 1974. ISBN: 9780691081229. [Preview with Google Books] |

10 | Practice Talk Session | |

11 | Student E | Milnor, J. W. "On Manifolds Homeomorphic to the 7–sphere." Annals of Mathematics 64, no. 2 (1956): 399–405. |

12 | Student (Auditing) | Atiyah, M. F. K–theory (Advanced Book Classics). 2nd ed. Notes by D. W. Anderson. Addison Wesley Longman Publishing Company, 1989. ISBN: 9780201093940. |

13 | Student F | Adams, J. F., and M. F. Atiyah. "K–theory and the Hopf Invariant." The Quarterly Journal of Mathematics 17, no. 1 (1966): 31–38. |

14 | Practice Talk Session | |

15 | Student G | Adams, J. F. "Vector Fields on Spheres." Annals of Mathematics 75, no. 3 (1962): 603–32. |

16 | Practice Talk Session | |

17 | Student A | Quillen, D. G. "The Spectrum of an Equivariant Cohomology Ring: I." Annals of Mathematics 94, no. 3 (1971): 549–72. |

18 | Practice Talk Session | |

19 | Student B | Wall, C. T. C. "Finiteness Conditions for CW–complexes." Annals of Mathematics 81, no. 1 (1965): 56–69. |

20 | Practice Talk Session | |

21 | Student C | Adams, J. F. Stable Homotopy and Generalised Homology (Part III) (Chicago Lectures in Mathematics). University of Chicago Press, 1995. ISBN: 9780226005249. [Preview with Google Books] [reprint of the 1974 original] |

22 | Student D | May, J. P. The Geometry of Iterated Loop Spaces (Lectures Notes in Mathematics). Vol. 271. Springer-Verlag, 1972. |

23 | Practice Talk Session | |

24 | Student E | Quillen, D. G. "Algebraic K–theory I." In Vol. 341.Higher K-Theories ( Lecture Notes in Mathematics). Proceedings of the Conference Held at the Seattle Research Center of Battelle Memorial Institute. Springer, 1973, pp. 85–147. ISBN: 9783540064343. |

25 | Student F | Nishida, G. "The Nilpotency of Elements of the Stable Homotopy Groups of Spheres." Journal of the Mathematical Society of Japan 25, no. 4 (1973): 707–32. |

26 | Student G | Atiyah, M. F., and F. Hirzebruch. "Analytic Cycles on Complex Manifolds." Topology 1, no. 1 (1962): 25–45. |

27 | Student A | Quillen, D. G. Homotopical Algebra (Lecture Notes in Mathematics). Vol. 43. Springer, 1967. ISBN: 9783540039143. |

28 | Practice Talk Session | |

29 | Student B | Bousfield, A. K. "The Localization of Spaces with Respect to Homology." Topology 14, no. 2 (1975): 133–50. |

30 | Student C | Griffiths, P. A., and J. W. Morgan. Rational Homotopy Theory and Differential Forms. Birkh ̈auser, 1981. ISBN: 9783764330415. |

31 | Student D | Segal, G. "Categories and Cohomology Theories." Topology 13, no. 3 (1974): 293–312. |

32 | Practice Talk Session | |

33 | Practice Talk Session (cont.) | |

34 | Student E | Tillmann, U. "Mumford's Conjecture—A Topological Outlook." In Handbook of Moduli: Volume III (Advanced Lectures in Mathematics). Vol. 26. International Press of Boston, 2013, pp. 399–429. ISBN: 9781571462596. |

35 | Student F | Adams, J. F. "Quillen's Work on Formal Groups and Complex Cobordism." In Stable Homotopy and Generalised Homology (Chicago Lectures in Mathematics). University of Chicago Press, 1995. ISBN: 9780226005249. [reprint of the 1974 original] |

36 | Practice Talk Session | |

37 | Student G | Goresky, M., and R. MacPherson. "Intersection Homology Theory." Topology 19, no. 2 (1980): 135–62. |