Renato Vianna

activity

20142025

most citedInfinitely many exotic monotone Lagrangian tori in CP^2

44 citations · 62 across the 8 of their papers we have counts for

collaborators

9 papers

math.SG2025

On singular Lagrangian fibrations and applications to symplectic embeddings I

Santiago Achig-Andrango, Renato Vianna, Alejandro Vicente

In this paper, we construct singular Lagrangian fibrations on some examples of disk cotangent bundles in dimensions 4 and 6. As an application, we show how this construction can be…

math.SG2020★ 4 cited

Algebraic and symplectic viewpoint on compactifications of two-dimensional cluster varieties of finite type

Man-Wai Mandy Cheung, Renato Vianna

In this article we explore compactifications of cluster varieties of finite type in complex dimension two. Cluster varieties can be viewed as the spec of a ring generated by theta…

math.SG2020

Full Ellipsoid Embeddings and Toric Mutations

Roger Casals, Renato Vianna

This article introduces a new method to construct volume-filling symplectic embeddings of 4-dimensional ellipsoids by employing polytope mutations in toric and almost-toric varieti…

math.SG2019

Asymptotic behavior of Vianna's exotic Lagrangian tori $T_{a, b, c}$ in $CP^{2}$ as $a + b + c \to \infty$

Weonmo Lee, Yong-Geun Oh, Renato Vianna

In this paper, we study various asymptotic behavior of the infinite family of monotone Lagrangian tori $T_{a, b, c}$ in $CP^{2}$ associated to Markov triples $(a, b, c)$ describ…

math.SG2018

Geometry of symplectic flux and Lagrangian torus fibrations

Egor Shelukhin, Dmitry Tonkonog, Renato Vianna

Symplectic flux measures the areas of cylinders swept in the process of a Lagrangian isotopy. We study flux via a numerical invariant of a Lagrangian submanifold that we define usi…

math.SG2016

Continuum families of non-displaceable Lagrangian tori in $(C P^{1})^{2 m}$

Renato Vianna

We construct a family of Lagrangian tori $Θ_{s}^{n}$ $\subset$ $(C P^{1})^{n}$ , $s \in (0, 1)$ , where $Θ_{1/2}^{n} = Θ^{n}$ , is the monotone twist Lagrangian torus described by Chekanov…

math.SG2016★ 5 cited

Infinitely many monotone Lagrangian tori in del Pezzo surfaces

Renato Vianna

We construct almost toric fibrations (ATFs) on all del Pezzo surfaces, endowed with a monotone symplectic form. Except for $C P^{2} #1 C P^{2}$ and $\mathb…

math.SG2015★ 9 cited

Low-area Floer theory and non-displaceability

Dmitry Tonkonog, Renato Vianna

We introduce a new version of Floer theory of a non-monotone Lagrangian submanifold which only uses least area holomorphic disks with boundary on it. We use this theory to prove no…

math.SG2014★ 44 cited

Infinitely many exotic monotone Lagrangian tori in CP^2

Renato Vianna

Related to each degeneration from CP^2 to CP(a^2,b^2,c^2), for (a,b,c) a Markov triple - positive integers satisfying a^2 + b^2 + c^2 = 3abc - there is a monotone Lagrangian torus,…

On singular Lagrangian fibrations and applications to symplectic embeddings I

Algebraic and symplectic viewpoint on compactifications of two-dimensional cluster varieties of finite type

Full Ellipsoid Embeddings and Toric Mutations

Asymptotic behavior of Vianna's exotic Lagrangian tori Ta,b,c​ in CP2 as a+b+c→∞

Geometry of symplectic flux and Lagrangian torus fibrations

Continuum families of non-displaceable Lagrangian tori in (CP1)2m

Infinitely many monotone Lagrangian tori in del Pezzo surfaces

Low-area Floer theory and non-displaceability

Infinitely many exotic monotone Lagrangian tori in CP^2

Asymptotic behavior of Vianna's exotic Lagrangian tori $T_{a, b, c}$ in $CP^{2}$ as $a + b + c \to \infty$

Continuum families of non-displaceable Lagrangian tori in $(C P^{1})^{2 m}$