Faculty

Institution

Unit

Venue

Yusheng Luo

Assistant Professor

Cornell University

Affiliations

College of Arts and Sciences

Department of Mathematics

Yusheng Luo is currently serving as a College Of Arts And Sciences Assistant Professor at Cornell University.

Honors

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Experiences

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Education

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Yusheng Luo

Cornell University

Assistant Professor

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mathematics mathematical sciences geometry and topology geometric topology applied mathematics topology real algebraic geometry algebraic geometry geometry combinatorial theory quasiconformal mappings algebraic topology discrete geometry complex geometry geometric group theory rational maps combinatorics mathematical analysis julia set function spaces global analysis algebraic combinatorics integral geometry finite degenerations julia sets polyhedron convex analysis lie group topological combinatorics coxeter group enumerative geometry topological properties hyperbolic components finite degenerations ii shadow problem circle packings entropy planar graphs geometric graph theory applied algebra geometry of numbers symbolic dynamics extremal combinatorics lower bounds geometric algorithms topological invariants global geometry computational topology entropy production topological dynamics complex dynamics set-theoretic topology riemann-hilbert problem schubert calculus algebraic analysis reflection groups anti-rational maps math xmlns barycentric extension bounded multipliers annotation encoding= hyperbolic rational maps local conformal symmetries differential geometry dynamical systems

Video Presentations

Notable Scholarly Works

Notable Federal Grants

Collaborators

On Quasiconformal Non-Equivalence of Gasket Julia Sets and Limit Sets. Ergodic Theory and Dynamical Systems (2025)

YUSHENG LUOYONGQUAN ZHANG

real algebraic geometrytopologyjulia setquasiconformal mappingsgeometric topologygasket julia setsjulia setsmathematicsgeometry and topologyalgebraic geometrymathematical sciences

A General Dynamical Theory of Schwarz Reflections, B-Involutions, and Algebraic Correspondences. arXiv (Cornell University) (2024)

Luo, YushengLyubich, MikhailMukherjee, Sabyasachi

real algebraic geometryapplied mathematicsmathematicscomplex geometryalgebraic combinatoricsgeneral dynamical theorygeometric topologyalgebraschwarz reflectionsparameter spacesalgebraic geometrymathematical sciences

Disk Patterns, Quasi-Duality and the Uniform Bounded Diameter Conjecture. arXiv (Cornell University) (2024)

Luo, YushengZhang, Yongquan

applied mathematicsdisk patternscoxeter grouptopologygeometric group theorygeometryskinning imagediameter conjecturegeometric topologycombinatorial theorydiscrete geometrymathematicsgeometry and topologymathematical sciences

On Quasiconformal Non-Equivalence of Gasket Julia Sets and Limit Sets. arXiv (Cornell University) (2024)

Luo, YushengZhang, Yongquan

real algebraic geometrytopologyjulia setquasiconformal mappingsgeometric topologygasket julia setsjulia setsmathematicsset theorygeometry and topologyalgebraic geometrymathematical sciences

Piecewise Quasiconformal Dynamical Systems of the Unit Circle. arXiv (Cornell University) (2024)

Luo, YushengNtalampekos, Dimitrios

unit circlegeometric analysiscomplex geometrycomplex analysistopologygeometryparabolic basinsdavid extensionquasiconformal mappingsgeometric topologymathematicsdifferential geometrygeometry and topologymathematical sciences

Uniformization of Gasket Julia Sets. arXiv (Cornell University) (2024)

Luo, YushengNtalampekos, Dimitrios

topological propertiesfat gasketapplied mathematicstopologyjulia setquasiconformal mappingsgeometric topologygasket julia setsset-theoretic topologymathematicsgeometry and topologymathematical sciences

Circle Packings, Renormalizations and Subdivision Rules. arXiv (Cornell University) (2023)

Luo, YushengZhang, Yongquan

computational topologymathematical sciencescircle packingstopologygeometric measure theorydiscrete geometryrenormalization theoryintegral geometrytopological propertiesgeometric analysisgeometry and topologyapplied mathematicsgeometric group theorygeometrytopological combinatoricsgeometric topologycombinatorial theorymathematicsrenormalization operator

On Geometrically Finite Degenerations I: Boundaries of Main Hyperbolic Components. Journal of the European Mathematical Society (2023)

Yusheng Luo

real algebraic geometryhyperbolic componentsapplied mathematicsmain hyperbolic componentscomplex geometrytopologyalgebraic topologygeometric topologycombinatorial theorymathematicsfinite degenerationsgeometry and topologyalgebraic geometrymathematical sciences

Circle Packings, Kissing Reflection Groups and Critically Fixed Anti-Rational Maps. Forum of Mathematics Sigma (2022)

Russell LodgeYusheng LuoSabyasachi Mukherjee

circle packingsalgebraic combinatoricscombinatoricsgeometric group theorygeometrytopologyplanar graphsreflection groupstopological combinatoricsgeometric topologycombinatorial theorydiscrete geometrygeometric graph theorymathematicsanti-rational mapsgeometry and topologymathematical sciences

On Deformation Space Analogies Between Kleinian Reflection Groups and Antiholomorphic Rational Maps. Geometric and Functional Analysis (2022)

Russell LodgeYusheng LuoSabyasachi Mukherjee

lie groupreal algebraic geometrytopological invariantscomplex geometrygeometric group theoryantiholomorphic rational mapskleinian reflection groupsalgebraic topologygeometric topologymathematicsdeformation space analogiesgeometry and topologymathematical sciences

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Yusheng Luo

Assistant Professor

Cornell University

Affiliations

College of Arts and Sciences

Department of Mathematics

Yusheng Luo is currently serving as a College Of Arts And Sciences Assistant Professor at Cornell University.

Honors

Create free account to unlock more features

Experiences

Create free account to unlock more features

Education

Create free account to unlock more features

Yusheng Luo

Cornell University

Assistant Professor

You can click a keyword to filter the displayed items

Video Presentations

Notable Scholarly Works

Notable Federal Grants

Collaborators

On Quasiconformal Non-Equivalence of Gasket Julia Sets and Limit Sets. Ergodic Theory and Dynamical Systems (2025)

YUSHENG LUOYONGQUAN ZHANG

real algebraic geometrytopologyjulia setquasiconformal mappingsgeometric topologygasket julia setsjulia setsmathematicsgeometry and topologyalgebraic geometrymathematical sciences

A General Dynamical Theory of Schwarz Reflections, B-Involutions, and Algebraic Correspondences. arXiv (Cornell University) (2024)

Luo, YushengLyubich, MikhailMukherjee, Sabyasachi

Disk Patterns, Quasi-Duality and the Uniform Bounded Diameter Conjecture. arXiv (Cornell University) (2024)

Luo, YushengZhang, Yongquan

On Quasiconformal Non-Equivalence of Gasket Julia Sets and Limit Sets. arXiv (Cornell University) (2024)

Luo, YushengZhang, Yongquan

real algebraic geometrytopologyjulia setquasiconformal mappingsgeometric topologygasket julia setsjulia setsmathematicsset theorygeometry and topologyalgebraic geometrymathematical sciences

Piecewise Quasiconformal Dynamical Systems of the Unit Circle. arXiv (Cornell University) (2024)

Luo, YushengNtalampekos, Dimitrios

Uniformization of Gasket Julia Sets. arXiv (Cornell University) (2024)

Luo, YushengNtalampekos, Dimitrios

Circle Packings, Renormalizations and Subdivision Rules. arXiv (Cornell University) (2023)

Luo, YushengZhang, Yongquan

On Geometrically Finite Degenerations I: Boundaries of Main Hyperbolic Components. Journal of the European Mathematical Society (2023)

Yusheng Luo

Circle Packings, Kissing Reflection Groups and Critically Fixed Anti-Rational Maps. Forum of Mathematics Sigma (2022)

Russell LodgeYusheng LuoSabyasachi Mukherjee

On Deformation Space Analogies Between Kleinian Reflection Groups and Antiholomorphic Rational Maps. Geometric and Functional Analysis (2022)

Russell LodgeYusheng LuoSabyasachi Mukherjee

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