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<td>14.</td> | <td>14.</td> | ||
<td>July</td> | <td>July</td> | ||
− | <td> | + | <td>E-infinity coalgebras and a generalized Segal conjecture</td> |
− | <td></td> | + | <td>Allen Yuan</td> |
</tr> | </tr> | ||
</table> | </table> |
Latest revision as of 20:34, 29 June 2020
[edit] Online Seminar: Integral Homotopy Theory
Given a simply connected topological space, its rational and p-adic homotopy types can be understood in terms of the algebras of its cochains. In more detail, rational homotopy theory, due to Sullivan and Quillen, states that associating to a space its cochain algebra with rational coefficients induces a fully faithful embedding from simply connected rational spaces to rational commutative dgas. Later, an analogous statement for the p-adic case was proved by Mandell, with cdgas replaced by $E_\infty$-algebras. However, there was no known way to "glue" the information about rational and p-adic cochains together, in order to reconstruct the integral homotopy type. In his recent paper "Integral models for spaces via the higher Frobenius", Yuan solves this problem by refining the p-adic model, using Nikolaus-Scholze Frobenius map on $E_\infty$-rings as one of the main instruments. In this seminar, we will study the paper by Yuan. We will use the language of modern homotopy theory, the necessary notions from the Nikolaus-Scholze paper will be recalled.
[edit] Dates and location
SS 2020, Tuesdays, 14-16, Online Seminar via Zoom.
In order to get access to the Zoom meetings, please contact Marc Hoyois or Maria Yakerson.
[edit] Program
Here you may find the extended program.
[edit] Talks
If you are interested in giving a talk in this seminar, please contact Marc Hoyois or Maria Yakerson.
Talk | Date | Title | Speaker | |
1 | 5. | May | Overview | Marc Hoyois |
2 | 12. | May | Tate construction and Tate diagonal | Harry Gindi |
3 | 19. | May | Equivariant stable homotopy theory | Marc Hoyois |
4 | 26. | May (at 16:00) | The $E_\infty$ Frobenius | Martin Speirs |
5 | 2. | June | Borel global algebras | Peter Haine |
6 | 9. | June | Partial algebraic K-theory: $S_\bullet$-construction | Maria Yakerson |
7 | 16. | June | Partial algebraic K-theory: Q-construction | Denis-Charles Cisinski |
8 | 23. | June | The partial algebraic K-theory of $F_p$ | Denis Nardin |
9 | 30. | June | The p-complete Frobenius and the action of $B\Z_{\geqslant 0}$ | Milton Lin |
10 | 7. | July | Integral models for the unstable homotopy category | Georgios Raptis |
11 | 14. | July | E-infinity coalgebras and a generalized Segal conjecture | Allen Yuan |