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18 results on '"Filip, Simion"'

5. Translation surfaces: Dynamics and Hodge theory.

Author

Filip, Simion

Subjects
HODGE theory, SURFACE dynamics, ALGEBRAIC geometry
Abstract

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. This survey provides an introduction to the subject and describes some developments that make use of Hodge theory to establish algebraization and finiteness statements in moduli spaces of translation surfaces. [ABSTRACT FROM AUTHOR]

Published
2024
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8. Gaps in the support of canonical currents on projective K3 surfaces

Author

Filip, Simion and Tosatti, Valentino

Subjects
Mathematics - Complex Variables, 37F80, 32U40, 14J28, 14J50, 32M18, 20F14, FOS: Mathematics, Dynamical Systems (math.DS), Complex Variables (math.CV), Mathematics - Dynamical Systems
Abstract

We construct examples of canonical closed positive currents on projective K3 surfaces that are not fully supported on the complex points. The currents are the unique positive representatives in their cohomology classes and have vanishing self-intersection. The only previously known such examples were due to McMullen on non-projective K3 surfaces and were constructed using positive entropy automorphisms with a Siegel disk. Our construction is based on a Zassenhaus-type estimate for commutators of automorphisms., 14 pages

Published
2023

10. Uniformization of some weight 3 variations of Hodge structure, Anosov representations, and Lyapunov exponents

Author

Filip, Simion

Subjects
14D07, 34D08, 33C20, 37D20, 14C34, Mathematics - Algebraic Geometry, Mathematics - Geometric Topology, Mathematics::Dynamical Systems, Mathematics - Classical Analysis and ODEs, Condensed Matter::Superconductivity, Classical Analysis and ODEs (math.CA), FOS: Mathematics, Geometric Topology (math.GT), Dynamical Systems (math.DS), Mathematics - Dynamical Systems, Algebraic Geometry (math.AG)
Abstract

We develop a class of uniformizations for certain weight 3 variations of Hodge structure (VHS). The analytic properties of the VHS are used to establish a conjecture of Eskin, Kontsevich, M\"oller, and Zorich on Lyapunov exponents. Additionally, we prove that the monodromy representations are log-Anosov, a dynamical property that has a number of global consequences for the VHS. We establish a strong Torelli theorem for the VHS and describe appropriate domains of discontinuity. Additionally, we classify the hypergeometric differential equations that satisfy our assumptions. We obtain several multi-parameter families of equations, which include the mirror quintic as well as the six other thin cases of Doran--Morgan and Brav--Thomas., Comment: improved exposition; 103 pages, 3 tables, 5 figures

Published
2021

11. KUMMER RIGIDITY FOR K3 SURFACE AUTOMORPHISMS VIA RICCI-FLAT METRICS.

Author

FILIP, SIMION and TOSATTI, VALENTINO

Subjects
*ENTROPY (Information theory), *AUTOMORPHISMS
Abstract

We give an alternative proof of a result of Cantat & Dupont, showing that any automorphism of a K3 surface with measure of maximal entropy in the Lebesgue class must be a Kummer example. Our method exploits the existence of Ricci-flat metrics on K3s and also covers the non-projective case. [ABSTRACT FROM AUTHOR]

Published
2021
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12. S. Filip - K3 surfaces and Dynamics (Part 2)

Author

Girard, Yohan, Filip, Simion, and Bastien, Fanny

Subjects
eem2018, Teichmüller dynamics mapping class groups and applications, [MATH] Mathematics [math], K3 surfaces, Dynamics, Grenoble
Abstract

K3 surfaces provide a meeting ground for geometry (algebraic, differential), arithmetic, and dynamics. I hope to discuss: - Basic definitions and examples - Geometry (algebraic, differential, etc.) of complex surfaces -Torelli theorems for K3 surfaces - Dynamics on K3s (Cantat, McMullen) - Analogies with flat surfaces - (time permitting) Integral-affine structures

Published
2018

13. S. Filip - K3 surfaces and Dynamics (Part 1)

Author

Bastien, Fanny, Filip, Simion, and Bastien, Fanny

Subjects
eem2018, Teichmüller dynamics mapping class groups and applications, [MATH] Mathematics [math], K3 surfaces, Dynamics, Grenoble
Abstract

K3 surfaces provide a meeting ground for geometry (algebraic, differential), arithmetic, and dynamics. I hope to discuss: - Basic definitions and examples - Geometry (algebraic, differential, etc.) of complex surfaces -Torelli theorems for K3 surfaces - Dynamics on K3s (Cantat, McMullen) - Analogies with flat surfaces - (time permitting) Integral-affine structures

Published
2018

14. S. Filip - K3 surfaces and Dynamics (Part 3)

Author

Girard, Yohan, Filip, Simion, and Bastien, Fanny

Subjects
eem2018, Teichmüller dynamics mapping class groups and applications, [MATH] Mathematics [math], K3 surfaces, Dynamics, Grenoble
Abstract

K3 surfaces provide a meeting ground for geometry (algebraic, differential), arithmetic, and dynamics. I hope to discuss: - Basic definitions and examples - Geometry (algebraic, differential, etc.) of complex surfaces -Torelli theorems for K3 surfaces - Dynamics on K3s (Cantat, McMullen) - Analogies with flat surfaces - (time permitting) Integral-affine structures

Published
2018

15. The algebraic hull of the Kontsevich-Zorich cocycle

Author

Eskin, Alex, Filip, Simion, and Wright, Alex

Subjects
Mathematics - Algebraic Geometry, Mathematics - Geometric Topology, Mathematics::Dynamical Systems, Mathematics::Algebraic Geometry, Mathematics::K-Theory and Homology, Mathematics::Complex Variables, Mathematics::Quantum Algebra, FOS: Mathematics, Geometric Topology (math.GT), Dynamical Systems (math.DS), Mathematics - Dynamical Systems, Algebraic Geometry (math.AG)
Abstract

We compute the algebraic hull of the Kontsevich-Zorich cocycle over any GL^+_2(R) invariant subvariety of the Hodge bundle, and derive from this finiteness results on such subvarieties.

Published
2017

16. Notes on the multiplicative ergodic theorem.

Author

FILIP, SIMION

Abstract

The Oseledets multiplicative ergodic theorem is a basic result with numerous applications throughout dynamical systems. These notes provide an introduction to this theorem, as well as subsequent generalizations. They are based on lectures at summer schools in Brazil, France, and Russia. [ABSTRACT FROM AUTHOR]

Published
2019
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17. Quaternionic covers and monodromy of the Kontsevich-Zorich cocycle in orthogonal groups.

Author

Filip, Simion, Forni, Giovanni, and Matheus, Carlos

Subjects
*MONODROMY groups, *TEICHMULLER spaces, *COHOMOLOGY theory, *ABELIAN groups, *MUMFORD-Tate groups
Abstract

We give an example of a Teichmüller curve which contains, in a factor of its monodromy, a group which was not observed before. Namely, it has Zariski closure equal to the group SO-.6/in its standard representation; up to finite index, this is the same as SU.3; 1/in its second exterior power representation. The example is constructed using origamis (i.e. square-tiled surfaces). It can be generalized to give monodromy inside the group SO-.2n/for all n, but in the general case the monodromy might split further inside the group. Also, we take the opportunity to compute the multiplicities of representations in the .0; 1/part of the cohomology of regular origamis, answering a question of Matheus-Yoccoz-Zmiaikou. [ABSTRACT FROM AUTHOR]

Published
2018
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18. On Hölder-continuity of Oseledets subspaces.

Author

Araújo, Vítor, Bufetov, Alexander I., and Filip, Simion

Subjects
LIPSCHITZ spaces, FUNCTION spaces, MATHEMATICAL transformations, DIFFERENTIAL geometry, MATHEMATICAL functions
Abstract

For Hölder cocycles over a Lipschitz base transformation, possibly non-invertible, we show that the subbundles given by the Oseledets Theorem are Hölder-continuous on compact sets of measure arbitrarily close to 1. The results extend to vector bundle automorphisms, as well as to the Kontsevich-Zorich cocycle over the Teichmüller flow on the moduli space of abelian differentials. Following a recent result of Chaika-Eskin, our results also extend to any given Teichmüller disk. [ABSTRACT FROM AUTHOR]

Published
2016
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