Dr Parth Shimpi

College positions: Junior Research Fellow

Dr Parth Shimpi is a Nevile Research Fellow in Pure Mathematics at Magdalene, and studies homological phenomena in algebraic geometry and representation theory.

Sometimes, objects in algebraic geometry and representation theory share equivalent homological theories -- that is to say, upon squinting your eyes, some manifolds appear just like a non-commutative algebra. Parth's research has revolved around answering exactly how often this happens, and in how many ways.

The simplest equivalence of this sort formed the subject of his Part III essay, completed in 2022 as a part of the Mathematical tripos in the University of Cambridge. Parth then did a PhD at the University of Glasgow, studying three-dimensional singularities and associated algebro-geometric structures. His thesis furnishes a complete description of the derived symmetries of irreducible flops -- showing that a handful of geometric and algebraic models in fact form an exhaustive list of equivalent structures in this case -- and sets up a programme to answer analogous questions in broader generalities.

Parth continues to study derived categories and associated structures in their various guises; in practice he spends his time drawing triangulations of blackboards and looking for patterns in the tilings.

Research Interests

  • Derived categories of sheaves and modules
  • Torsion theories
  • Stability conditions
  • Hall algebras
  • Coxeter--Artin groups and root systems

Qualifications

  • 2026: PhD in Mathematics, University of Glasgow
  • 2022: MMath, University of Cambridge
  • 2021: BA in Mathematics, University of Cambridge

Career / Research Highlights

2022: European Research Council Scholarship, Award towards doctoral education
2021: Stephen Hawking Award, Gonville and Caius College, Cambridge
2019, 2021: Examination Prize, Gonville and Caius College, Cambridge
2018: Cambridge Trust Scholarship, Cambridge Trust, Award towards undergraduate education
2018: Overseas scholarship, Gonville and Caius College, Award towards undergraduate education

KEY PUBLICATIONS

Bricks and Stones in the Homological Minimal Model Programme. PhD thesis.

Torsion pairs and 3-fold flops. Preprint [arXiv:2502.05146].

Simple complexes on a flopped curve. Preprint [arXiv:2508.06437].

Kleinian orbifolds, cohomological Hall algebras, and Yangians. F. Sala, O. Schiffmann. Preprint [arXiv:2511.08576].