Ayodeji Lindblad

Research | Expository | Talks | Organization | Figures

Welcome to my website.

I’m a third-year PhD student of Tom Mrowka at MIT with interests in low-dimensional topology, gauge theory, and discrete geometry. Previously, I graduated from MIT with a BS in mathematics. You can reach me at my_first_name@mit.edu and can find my CV at this link.

Research:

• Designs related through projective and Hopf maps. Discrete & Computational Geometry, 2025.
  Formalizes a construction that builds a spherical $t$-design by placing a spherical $t$-design on each projective or Hopf fiber associated to the points of a $\lfloor t/2\rfloor$-design on a quotient projective space or sphere, generalizing work of König, Kuperberg, and Okuda (who was inspired by work of Cohn, Conway, Elkies, and Kumar).

• Asymptotically optimal $t$-design curves on $S^3$. arXiv:2408.04044, submitted for publication, 2025.
  Solves the problem posed by Ehler and Gröchenig of proving that there exist asymptotically optimal sequences of $t$-design curves on the 3-sphere.

• Asymptotically short generalizations of $t$-design curves. arXiv:2505.03056, to be submitted for publication, 2025.
  Proves existence of asymptotically optimal approximate and weighted $t$-design curves satisfying certain desirable properties on the $d$-sphere for all odd $d$ in the approximate setting and all $d$ in the weighted setting, solving analogues of a problem posed by Ehler and Gröchenig. Explicit constructions are provided and formulas for such weighted $t$-design curves on the 2-sphere and 3-sphere are given for all $t$.

• Dynamical stability of translators under mean curvature flow. Posted to MIT SPUR website, 2022.
  Joint with Carlos Alvarado, supported by Tang-Kai Lee. Investigates whether certain classes of perturbations of mean curvature flow translators converge to translators under the flow.

• Abelianized boundary Dehn twists on connected sums of complete intersections. In preparation, to be submitted for publication, 2026.

• Lifting design curves. In preparation, to be submitted for publication, 2026.

• A note on $t$-designs of minimal harmonic strength. In preparation, to be submitted for publication, 2026.

• Harmonic strength related through geometric maps. In preparation, to be submitted for publication, 2026.

Expository:

• Instanton Floer homology and applications. In New Structures in Low-Dimensional Topology, Bolyai Society Mathematical Studies 1, Springer, Cham, 2026.
  Joint with John Baldwin, Joye Chen, Nathan Geist, Tomasz Mrowka, Ollie Thakar. These notes, which follow a mini-course presented by John Baldwin and Tomasz Mrowka at the meeting New Structures in Low-Dimensional Topology in Budapest, define instanton Floer homology–a powerful 3-manifold invariant–and discuss applications to sutured manifolds and knot theory.

• Khovanov Skein lasagna modules for the working topologist. In preparation, 2026.
  Joint with Enrico Colón, Gage Martin, Mira Wattal. These notes present Khovanov skein lasagna modules and their impacts from the perspective of low-dimensional topology.

Invited talks:

• Boundary Dehn twists after abelianization. London Low-Dimensional Topology Seminar, 2026.
  I discussed my forthcoming work on abelianized boundary Dehn twists on connected sums of complete intersections, which proves that notable boundary Dehn twists known to be non-trivial by work of Kronheimer-Mrowka, Jianfeng Lin, Baraglia-Konno, and Tilton become trivial after abelianization.

Contributed talks:

• Skein lasagna modules and handle attachments. Scottish Talbot On Algebra and Topology, 2026.
  I discussed work of Manolescu and Neithalath describing how 4- and 3-handle attachments respectively don’t change and don’t enlargen the skein lasagna module of a 4-manifold and establishing an isomorphism between the skein lasagna module of a 2-handlebody and cabled Khovanov-Rozansky homology.

• Designs related through projective and Hopf maps. AMS Eastern Sectional Meeting FRACTals section, 2024.
  I discussed my paper of the same name.

Department talks:

• Geometrically designing geometric designs. MIT PuMaGraSS, 2025.
  I discussed geometric constructions of spherical $t$-designs and $t$-design curves.

• Monopole Floer homology and a refinement of Manolescu. MIT Juvitop, 2024.
  I gave an overview of the construction of monopole Floer homology (as in Ch. 22 of Tom and Peter’s book) and discussed a refinement due to Manolescu involving finite-dimensional approximations of the Seiberg-Witten map which produces a space whose homotopy groups are the monopole Floer homology groups.

• In case you’re curious what your local low-dimensional topologists do all day. MIT PuMaGraSS, 2024.
  I provided an introduction to Morse theory and Floer theories.

Organization:

• The Low-dimensional Cambridge-Organized Student Topology Gathering (the Low COST Gathering). MIT and Harvard, 2026.
  Joint with Ollie Thakar. A meeting on low-dimensional topology which we plan to organize in Fall 2026. Please feel free to e-mail me if you’d be interested in speaking at or attending the event and I’ll be in contact when it is becoming a reality (though note, as is to be expected with the name, we likely won’t have too much funding available for travel or lodging).

• The Low-dimensional Princeton-Cambridge Exchange Gathering (the Low PriCE Gathering). MIT and Harvard, 2025.
  Joint with Ollie Thakar. A meeting on low-dimensional topology which we organized. Abstracts from the event can be found here.

Fun:

Coming soon!

This page has been loaded — total times since its creation at the end of 2025.

Many thanks to my good friend Torque, who helped greatly to set up the site!