# Counting special lagrangian fibrations in twistor families of K3 surfaces

@article{Filip2016CountingSL, title={Counting special lagrangian fibrations in twistor families of K3 surfaces}, author={Simion Filip}, journal={Annales scientifiques de l'{\'E}cole normale sup{\'e}rieure}, year={2016} }

The number of closed billiard trajectories in a rational-angled polygon grows quadratically in the length. This paper gives an analogue on K3 surfaces, by considering special Lagrangian tori. The analogue of the angle of a billiard trajectory is a point on a twistor sphere, and the number of directions admitting a special Lagrangian torus fibration with volume bounded by $ V $ grows like $ V^{20} $ with a power-saving term. Bergeron--Matheus have explicitly estimated the exponent of the error…

## 11 Citations

### Recounting special Lagrangian cycles in twistor families of K3 surfaces (or: How I learned to stop worrying and count BPS states)

- MathematicsAdvances in Theoretical and Mathematical Physics
- 2020

We consider asymptotics of certain BPS state counts in M-theory compactified on a K3 surface. Our investigation is parallel to (and was inspired by) recent work in the mathematics literature by…

### Counting special Lagrangian classes and semistable Mukai vectors for K3 surfaces

- Mathematics
- 2021

Motivated by the study of growth rate of the number of geodesics in flat surfaces with bounded lengths, we study generalizations of such problems for K3 surfaces. In one generalization, we give an…

### Semiclassical Entropy of BPS States in 4d $\mathcal{N}=2$ Theories and Counts of Geodesics

- Mathematics
- 2019

We relate a number of results in the theory of flat surfaces to BPS spectra of a class of 4d $\mathcal{N}=2$ supersymmetric quantum field theories arising from M5 branes wrapped on Riemann surfaces…

### Masur's Divergence for Tori and Kummer Surfaces

- Mathematics
- 2021

Masur’s divergence states that the horizontal foliation of translation surfaces is uniquely ergodic if the geodesic flow is recurrent on the moduli space. This established a relationship between…

### On the equidistribution of some Hodge loci

- MathematicsJournal für die reine und angewandte Mathematik (Crelles Journal)
- 2020

Abstract We prove the equidistribution of the Hodge locus for certain non-isotrivial, polarized variations of Hodge structure of weight 2 with h 2 , 0 = 1 {h^{2,0}=1} over complex, quasi-projective…

### Semiclassical Entropy of BPS States in 4d N = 2 Theories and Counts of Geodesics

- Mathematics
- 2019

We relate a number of results in the theory of flat surfaces to BPS spectra of a class of 4d N = 2 supersymmetric quantum field theories arising from M5 branes wrapped on Riemann surfaces – A1 class…

### Canonical currents and heights for K3 surfaces

- Mathematics
- 2021

We construct canonical positive currents and heights on the boundary of the ample cone of a K3 surface. These are equivariant for the automorphism group and fit together into a continuous family,…

### TRANSLATION SURFACES: DYNAMICS AND HODGE THEORY

- Mathematics
- 2022

A translation surface is a multifaceted object that can be studied with the tools of dynamics, analysis, or algebraic geometry. Moduli spaces of translation surfaces exhibit equally rich features.…

### Tropical dynamics of area-preserving maps

- MathematicsJournal of Modern Dynamics
- 2019

We consider a class of area-preserving, piecewise affine maps on the 2-sphere. These maps encode degenerating families of K3 surface automorphisms and are profitably studied using techniques from…

### AN INTRODUCTION TO K3 SURFACES AND THEIR DYNAMICS

- Mathematics
- 2019

These notes provide an introduction to the geometry of K3 surfaces and the dynamics of their automorphisms. They are based on lectures delivered in Grenoble in July 2018, and in Beijing in July 2019.

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