Autumn 2025

• • Nov 042025

  Natalia Pacheco-Tallaj (MIT)

  Twisted string bordism in $7$ dimensions with applications to anomaly cancellation

  In upcoming joint work with I. Basile, C. Krulewski and G. Leone, we use homotopic and topological techniques to study anomaly cancellation in 6d supergravity theories. In this talk, I will give a quick overview of anomalies of quantum field theories and their classification using twisted bordism groups. Then, I will overview how we leverage the unstable classification of vector bundles over $\mathbb{CP}^2$ to construct explicit generators for $7$-dimensional twisted string bordism groups, and I will show how to construct a complete family of index-theoretic invariants to detect the torsion in these groups.

  Slides

• • Oct 282025

  Natalie Stewart (Harvard)

  Norms for compact Lie groups

  This talk is 3:30pm-4:30pm

  Hill-Hopkins-Ravanel norms give a lift of tensor-induction from the category of $H$-spectra to $G$-spectra for $H \subseteq G$ a subgroup of a finite group, and they were crucial to their resolution of the Kervaire Invariant one problem in all but one dimension; analogously, the influential Angelveit-Blumberg-Gerhardt-Hill-Lawson-Mandell perspective on (twisted) topological Hochschild homology expresses it as a norm from finite subgroups of the circle group. Following this, Blumberg-Hill-Mandell issued a series of conjectures concerning equivariant factorization homology as a technique for constructing norms along closed subgroup inclusions between compact Lie groups (extending the above examples) and computing their geometric fixed points. Following work-in-progress with Juran, I will sketch a resolution of these conjectures.

• • Oct 212025

  Daniel Pomerleano (UMB)

  A Fontaine-Lafaille structure in symplectic topology

  The small quantum connection on a Fano manifold is one of the simplest objects in enumerative geometry. Nevertheless, the poles of the connection have a very rich structure. I will sketch the construction of a (mod $p$) Fontaine-Lafaille structure on its Fourier-Laplace dual and explain some implications of this structure for the monodromy of this connection (e.g. bounds on the size of the Jordan blocks of the connection). This is joint work with Paul Seidel.

• • Oct 142025

  Francis Baer (Wayne State University)

  Composition methods in the unstable Adams spectral sequence

  The stem-wise computation of unstable homotopy groups of spheres is a foundational problem in algebraic topology which has seen little progress in the past several decades. In this talk we will discuss an approach to the problem which combines the composition methods of Toda with the unstable Adams spectral sequence via computer automation. A survey will be given of our results as well as their applications to more tangible problems of a geometric nature.

• • Oct 072025

  Sarah Petersen (University of Colorado Boulder)

  Splittings of equivariant and motivic truncated Brown-Peterson cooperations algebras

  In the 1980's, Mahowald and Kane used integral Brown-Gitler spectra to decompose $BP \langle 1 \rangle \wedge BP \langle 1 \rangle$ as a sum of finitely generated $BP \langle 1 \rangle$-module spectra. This splitting, along with an analogous decomposition of $ko \wedge ko$, led to a great deal of progress in stable homotopy computations and a complete understanding of $v_1$-periodicity in the stable homotopy groups of spheres. In this talk, I will discuss joint work with Guchuan Li, Jackson Morris, and Elizabeth Tatum in which we construct analogues of Mahowald and Kane's splittings in equivariant and motivic homotopy theory. I will then describe the $E_1$-pages of the analogous $BP \langle 1 \rangle$-based Adams spectral sequences in these settings and how this approach gives excellent access to $v_1$-periodicity in equivariant and motivic stable stems.