Toni Annala

I'm a member at the Institute for Advanced Study. Most of my research focuses on constructing and studying various cohomology theories in algebraic geometry, but I'm also interested in mathematical questions coming from physics.

Math

Here are my peer-reviewed publications (appeared or to appear):

Topologically protected vortex knots and links (joint with Roberto Zamora-Zamora and Mikko Möttönen), Communications Physics.
Bivariant algebraic cobordism with bundles (joint with Shoji Yokura), Algebraic Geometry (Foundation Compositio Mathematica).
Cohomology of the moduli stack of algebraic vector bundles (joint with Ryomei Iwasa), Advances in Mathematics.
Charge ambiguity and splitting of monopoles, (joint with Mikko Möttönen), Physical Review Research.
Base independent algebraic cobordism, Journal of Pure and Applied Algebra.
Algebraic Spivak's theorem and applications, Geometry & Topology.
Chern classes in precobordism theories, Journal of the European Mathematical Society.
Precobordism and cobordism, Algebra & Number Theory.
Oriented Borel-Moore homologies of toric varieties, Annales de l'Institut Fourier.
On line bundles in derived algebraic geometry, Annals of K-theory.
Bivariant derived algebraic cobordism, Journal of Algebraic Geometry.

and preprints:

Algebraic cobordism and a Conner-Floyd isomorphism for algebraic K-theory (joint with Marc Hoyois and Ryomei Iwasa).
Bordism invariants of colored links and topologically protected tricolorings (joint with Hermanni Rajamäki and Mikko Möttönen).
Motivic spectra and universality of K-theory (joint with Ryomei Iwasa).

Here is my doctoral thesis:

Derived algebraic cobordism.

Here are slide(s) of talks I have given:

Topologically protected vortex knots and links.
Derived algebraic cobordism --- Towards bivariant Conner--Floyd (Motives and What Not, 17th of June, 2020).

Here are some of my older writings. Several people seem to have found my notes on resolutions of singularities; this makes me uncomfortable. However, I will keep everything online, at least for now.