Simion Filip

About

Simion Filip is a professor in the Department of Mathematics at the University of Chicago. His research spans several areas in mathematics, including dynamics, geometry, and algebraic geometry, with a particular focus on the study of K3 surfaces, translation surfaces, and variations of Hodge structure. Filip's work often involves the interplay between dynamical systems and geometric structures, as evidenced by his contributions to measure rigidity for stationary measures of random walks generated by diffeomorphisms and actions of SL(2,R) on smooth manifolds. He has developed new techniques in the theory of normal forms for non-uniformly contracting dynamics and has explored the geometric and dynamical properties of hyperbolic manifolds and Calabi-Yau varieties.

Research topics

• Mathematical analysis
• Pure mathematics
• Mathematics

Selected publications

• On pseudo-Anosov autoequivalences

  Advances in Mathematics · 2021 · 10 citations

  PublisherOA PDFDOI

• Translation surfaces: Dynamics and Hodge theory

  EMS Surveys in Mathematical Sciences · 2024-05-02 · 6 citations

  articleOpen access1st authorCorresponding

  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.

  PublisherOA PDFDOI

• Canonical currents and heights for K3 surfaces

  Cambridge Journal of Mathematics · 2023-01-01 · 6 citations

  articleOpen access1st authorCorresponding

  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, defined over an enlarged boundary of the ample cone. Along the way, we construct preferred representatives for certain height functions and currents on elliptically fibered surfaces.

  PublisherOA PDFDOI

• Asymptotic shifting numbers in triangulated categories

  arXiv (Cornell University) · 2020-08-14 · 4 citations

  preprintOpen accessSenior author

  We introduce invariants, called shifting numbers, that measure the asymptotic amount by which an autoequivalence of a triangulated category translates inside the category. The invariants are analogous to Poincare translation numbers that are widely used in dynamical systems. We additionally establish that in some examples the shifting numbers provide a quasimorphism on the group of autoequivalences. Additionally, we relate our shifting numbers to the entropy function introduced by Dimitrov, Haid…

  PublisherOA PDFDOI

• Asymptotic shifting numbers in triangulated categories

  Advances in Mathematics · 2023-06-15 · 3 citations

  articleSenior author
  PublisherDOI

Recent grants

• Geometry and Dynamics of K3 Surfaces

  NSF · $216k · 2020–2024

Frequent coauthors

• Valentino Tosatti

  16 shared

• Alexander I. Bufetov

  7 shared

• Carlos Matheus

  Heilbronn Institute for Mathematical Research

  5 shared

• Charles Fougeron

  Université Sorbonne Paris Nord

  5 shared

• Giovanni Forni

  Istituti Clinici Scientifici Maugeri

  3 shared

• Alex Eskin

  University of Chicago

  3 shared

• Alex Wright

  University of Michigan–Ann Arbor

  3 shared

• Fabian Haiden

  2 shared

Education

• Ph.D.

  University of Chicago

  2016

Awards & honors

• 2020 EMS Prize

Similar researchers at University of Chicago

• Jiajie Chenh-98
• Vladimir Drinfeldh-39
• Victor Ginzburgh-38