Felix Janda
University of Illinois Urbana-Champaign, IL·Mathematics & Statistics·Early-career
Over the past thirty years, pure mathematics and string theory in physics have fed each other in surprising ways. Physics predictions led mathematicians to define invariants that count algebraic curves, shapes defined by polynomial equations, inside geometric spaces.
- Fields
Mathematics & Statistics
Physics
- Topics
algebraic geometry
enumerative geometry
curve counting
- Grants
- 1 known grant, through Jun 2029
What they work on
- Prove the localization formula for the logarithmic gauged linear sigma model (log GLSM), a curve-counting technique, and study the effective invariants that feed into it.
- Apply log GLSM to the tautological ring to establish physics predictions such as the conifold gap condition for the quintic threefold and other one-parameter Calabi–Yau threefolds.
- Establish the Landau–Ginzburg/Calabi–Yau correspondence for the quintic threefold in all genera, linking two physics-inspired ways of counting curves.
- Use quasimaps to compute Gromov–Witten invariants of non-convex complete intersections, and extend log GLSM to allow quasimaps.
More about the research
Studying these counts has in turn advanced string theory. Many physics predictions about these counts have long seemed out of mathematicians' reach. This project develops two curve-counting techniques, and combines them, to make progress on those conjectures.
Why it matters
This is pure mathematics. Proving physics-inspired conjectures about counts of curves in Calabi–Yau spaces would put string theory predictions on rigorous footing and give mathematicians new tools for computing these invariants. The results could eventually inform further work linking algebraic geometry and theoretical physics.
Known grants
From NIH and NSF research grants. Labs often have other funding we can't see.
Closest labs
Jeremy Usatine
Florida State University, FL·Mathematics & Statistics
Use motivic integration for smooth Artin stacks, a class of generalized geometric spaces, to study stringy invariants of singular varieties.
Charles Cifarelli
Stony Brook University, NY·Mathematics & Statistics
Construct new examples of non-compact singularity model geometries, namely Kähler-Ricci solitons and complete non-compact Calabi-Yau metrics, which describe how complex manifolds degenerate.
Motohico Mulase
University of California-Davis, CA·Mathematics & Statistics
Develop complex Lagrangian geometry as a general framework for studying mirror symmetry, the hidden duality between symplectic geometry and complex algebraic geometry, and for studying quantization.
The school
University of Illinois Urbana-Champaign: 41 labs on PI Pages, $907M a year on research, 870 research doctorates a year.
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