About the Seminar
Information about the 2026–2027 academic year will be announced here. All times are in Beijing time (UTC +8).
Schedule
| Date | Speaker | Title |
|---|---|---|
| Fall 2025 | ||
| Oct 18, 4 pm | Sven van Nigtevecht (University of Bonn) | Synthetic modular forms |
| Nov 2, 4 pm | William Balderrama (University of Bonn) | Smooth knots in the metastable range via orthogonal calculus |
| Nov 16, 4 pm | Yingxin Li (Nankai University） | - |
| Nov 30, 4 pm | Rin Ray (University of Münster) | - |
| Dec 15, 10 am | Ben Knudsen (Colorado State University) | - |
Sven van Nigtevecht: Synthetic modular forms
Topological modular forms play an essential role in modern homotopy theory, in particular in computations of the homotopy groups of spheres. This requires an understanding of the homotopy groups of tmf. In this talk, I will explain a longstanding circularity in the literature on this computation, and a resolution of it through the use of a synthetic spectrum called Smf (synthetic modular forms). The construction of Smf is part of a larger result that lifts spectral sequences to synthetic spectra, allowing for comparisons to Adams-Novikov spectral sequences as well as a host of computational techniques to be applied. This is joint work with Christian Carrick and Jack Davies.
Resources: [Video: YouTube] · [Video: Bilibili]
William Balderrama: Smooth knots in the metastable range via orthogonal calculus
The homotopy groups of spheres are closely tied to classification problems in differential topology. Seminal work of Haefliger gave a homotopy classification of the smooth knot group \( C_n^q = \pi_0 \mathrm{Emb}(S^n,S^{n+q}) \) in codimension \( q\geq 3 \) in terms of the fiber of the unstable \(J \)-homomorphism. I will describe how this classification may be combined with the methods of Weiss's orthogonal calculus to identify the groups \( C_n^q \) in the metastable range \( n \leq 3(q-2) \) with the homotopy groups of a certain Thom spectrum over \( BO(2) \).