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Geometric recursion Permalink

Integer points in polyhedra Permalink

Donaldson–Thomas invariants Permalink

Recent advances on moduli spaces of curves Permalink

TR Salento 2022 Permalink

Moduli spaces: theory and coding Permalink

Topological recursion and integrability Permalink

Quantum Geometry Permalink

Refinement in Enumerative Geometry and Physics Permalink

Topological recursion for Masur–Veech volumes

with J. E. Andersen, G. Borot, S. Charbonnier, V. Delecroix, D. Lewański, C. Wheeler
J. London Math. Soc. 107.1 (2023)

We study the Masur–Veech volumes of quadratic differentials, showing they correspond to constant terms of polynomials determined by topological recursion/Virasoro constraints.

Masur–Veech volumes and intersection theory, the principal strata of quadratic differentials

with G. Borot, D. Lewański
Appendix in Duke Math. J. 172.9 (2023)

We prove that the descendant integrals of the Segre class of the quadratic Hodge bundle are computed by topological recursion.

On the Kontsevich geometry of the combinatorial Teichmüller space

with J. E. Andersen, G. Borot, S. Charbonnier, D. Lewański, C. Wheeler
(2020)

We study the geometry of the combinatorial moduli spaces, providing a completely geometric proof of Witten’s conjecture.

A new spin on Hurwitz theory and ELSV via theta characteristics

with R. Kramer, D. Lewański
Accepted in in Selecta Math. (2025)

We study spin Hurwitz numbers, which count ramified covers of the Riemann sphere with a sign coming from a theta characteristic. We conjecture a topological recursion governing these counts, and prove equivalence with an ELSV formula.

Around the combinatorial unit ball of measured foliations on bordered surfaces

with G. Borot, S. Charbonnier, V. Delecroix, C. Wheeler
Int. Math. Res. Not. 2023.17 (2023)

We study the \(L^p\)-integrability of the volume of the unit ball in the space of measured foliations.

An intersection-theoretic proof of the Harer–Zagier formula

with D. Lewański, P. Norbury
Algebraic Geom. 10.2 (2023)

We compute the Euler charcteristic of the moduli space of curves via Chern–Gauss–Bonnet and Hodge integrals.

Shifted Witten classes and topological recursion

with S. Charbonnier, N. K. Chidambaram, E. Garcia-Failde
Trans. Amer. Math. Soc. 377.2 (2024)

We deduce Witten’s \(r\)-spin conjecture from the connection between Givental’s formalism and topological recursion.

Relations on \({\overline{\mathcal{M}}}_{g,n}\) and the negative \(r\)-spin Witten conjecture

with N. K. Chidambaram, E. Garcia-Failde
Accepted in Invent. Math. (2025)

We construct a negative \(r\)-spin cohomological field theory, the \(r\)-spin \({\Theta}\)-class, prove topological recursion and \({\mathcal{W}}\)-constraints, and derive tautological relations via Teleman’s classification.

The spin Gromov–Witten/Hurwitz correspondence for \({\mathbb{P}}^1\)

with R. Kramer, D. Lewański, A. Sauvaget
J. Eur. Math. Soc. (2025)

We prove the GW/H correspondence for the spin projective line, a first step toward the computation of GW invariants of surfaces of general type.

Resurgent large genus asymptotics of intersection numbers

with B. Eynard, E. Garcia-Failde, P. Gregori, D. Lewański
(2023)

We prove the large genus asymptotics for Witten–Kontsevich, Norbury’s, and \(r\)-spin intersection numbers.

Length spectrum of large genus random metric maps

with S. Barazer, M. Liu
Forum Math. Sigma 13 (2025)

We prove that the lenght spectrum of random metric maps converges to a Poisson point process in the large genus limit.

Symmetries of F-cohomological field theories and F-topological recursion

with G. Borot, G. Umer
Accepted in Commun. Math. Phys. (2025)

We introduce F-topological recursion and show that the descendant theory of F-CohFTs in the Givental orbit are compute by F-topological recursion.

Can transformers do enumerative geometry?

with B. Hashemi, R. G. Corominas
13th Int. Conf. Learn. Represent. (2025)

We use transformer to compute and understand recursive patterns in \(\psi\)-class intersection numbers, showing that the model learns key mathematical features from the data.

The factorial growth of topological recursions

with G. Borot, B. Eynard
Lett. Math. Phys. 115.62 (2025)

We prove that topological recursion is Gevrey-2.

Les Houches lecture notes on moduli spaces of Riemann surfaces

with D. Lewański
In: Les Houches Summer School Lecture Notes - 2024-08: Quantum Geometry
SciPost Phys. Lect. Notes (2025)

Lecture notes on the moduli space of curves, cohomological field theories, and topological recursion.

Theta classes: generalized topological recursion, integrability and \({\mathcal{W}}\)-constraints

with V. Bouchard, N. K. Chidambaram, S. Shadrin
(2025)

We introduce a new collection of CohFTs, the \({\Theta}^{r,s}\)-classes, and show that their descendant potential is an \(r\)-KdV tau function, is computed by topological recursion, and satisfies \({\mathcal{W}}\)-constraints.

Riemann Surfaces

Undergraduate course, ETHZ, Spring 2024

A first introduction to the theory of Riemann surfaces. These are beautiful objects that sit at the intersection of algebra, geometry, and analysis. We covered the theorems of Riemann–Hurwitz, Riemann–Roch, and Abeli–Jacobi, as well as the basics of Hurwitz theory.

Toric Geometry

Undergraduate course, ETHZ, Spring 2025

Toric varieties provide a rich class of examples in algebraic geometry that bridge combinatorics and geometry, making them an ideal starting point for exploring the interplay between these fields. We will introduce toric varieties, study their combinatorial and abstract structures, and examine their basic geometry, including Picard groups, cohomology, and singularities.