Publications

Preprints

Fabert, O., & Straat, J. (2026). Hamiltonian Floer Theory for Quantum Electrodynamics up to First Order in \(\hbar\).

arXiv
```
@online{fabertHamiltonianFloerTheory2026,
  author = {Fabert, Oliver and Straat, Jesse},
  date = {2026-08-20},
  eprint = {2608.19996},
  eprinttype = {arXiv},
  eprintclass = {math.SG},
  pubstate = {prepublished},
  title = {Hamiltonian Floer Theory for Quantum Electrodynamics up to First Order in \(\hbar\)}
}
```
We use Hamiltonian Floer theory to prove a cuplength result about the existence of periodic solutions of particle-field systems with a Gaussian random field. As a concrete model we study stochastic electrodynamics, which approximates quantum electrodynamics up to first order in \(\hbar\), and is even exact in the case of low-order Hamiltonians or when the particles are treated classically.

Journal articles

Theses (available upon request)

Straat, J. (2025). Gromov–Witten Invariants, Topological Strings and Mirror Symmetry.

DOI
```
@thesis{straatGromovWittenInvariants2025,
  title = {Gromov–Witten Invariants, Topological Strings and Mirror Symmetry},
  author = {Straat, Jesse},
  date = {2025},
  doi = {20.500.12932/49915}
}
```
Gromov–Witten invariants count the number of holomorphic maps into some projective variety. We introduce moduli stacks and follow Kontsevich’s construction of Gromov–Witten invariants by doing a Deligne–Mumford compactification on the relevant moduli space. We then define quantum cohomology and show how it gives the Witten–Dijkgraaf–Verlinde–Verlinde equations, and review contemporary research on finding Gromov–Witten invariants on products and blowups. In the second half, we consider the Landau–Ginzburg model, which, when twisted and promoted to a string theory, has correlators which correspond to Gromov–Witten invariants. Finally, we discuss mirror symmetry, a physical tool that can be used to compute Gromov–Witten invariants.
Straat, J. (2022). From Electrodynamics to Grand Unified Theories: A Mathematical Analysis of Gauge Theories.
```
@thesis{straatElectrodynamicsGrandUnified2022,
  title = {From Electrodynamics to Grand Unified Theories: A Mathematical Analysis of Gauge Theories},
  author = {Straat, Jesse},
  date = {2022}
}
```
Gauge theories are mathematical structures that form an integral part of modern physics, particularly through the standard model. It is therefore profitable for the modern physicist to gain a deeper knowledge of the mathematics that lie at the foundation of gauge theories. In this thesis, we develop the general notion of a gauge theory using principal bundles and connection forms thereon. We furthermore define fermions using spinor bundles that are twisted in order to interact with the gauge potential. We develop the Yang–Mills–Dirac Lagrangian, which is usable for all gauge theories with a compact structure group. Finally, we discuss further developments of gauge theories, with a focus on grand unified theories such as the Georgi–Glashow model and \(SO(10)\), and their flaws and virtues.