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Complex Analysis Lab
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The lab develops single-variable complex analysis into several complex variables and complex manifolds.
AboutAbout the lab
Extending single-variable complex analysis to several variables and manifolds.
The lab builds on single-variable complex analysis (function theory), which students study as undergraduates, by considering several variables and carrying out analysis on complex manifolds.
Professor Yutaka Ishii works on complex dynamical systems and fractals, and Professor Joe Kamimoto works on several complex variables and partial differential equations.
Associate Professor Yuta Kusakabe studies the Oka principle, the homotopy principle of complex analysis, from the standpoint of several complex variables and complex geometry.
Key terms
- Several complex variables
- The field that takes single-variable complex analysis (function theory), as studied at the undergraduate level, and considers it with more variables
- Complex Hénon map
- A map studied as an example of a two-dimensional complex dynamical system
- Oka principle
- The homotopy principle of complex analysis; the heuristic principle that analytic problems on Stein manifolds face only topological obstructions
ResearchResearch themes
The lab develops single-variable complex analysis (function theory), which students study as undergraduates, by considering several variables and carrying out analysis on complex manifolds. The faculty's research covers complex dynamical systems, fractals, the Oka principle, partial differential equations, and more.
*Illustrative imageDynamics of Complex Hénon Maps
The lab analyzes complex Hénon maps, which are two-dimensional complex dynamical systems, from a combinatorial perspective. This work includes establishing criteria for hyperbolicity and analyzing the structure of Julia sets and of the parameter space.
*Illustrative imageThe Oka Principle and Gromov Ellipticity
The lab studies the Oka principle, the homotopy principle in complex analysis, and its surroundings, including Gromov ellipticity, which is the exact opposite of Kobayashi hyperbolicity. Current work examines the Oka principle from a broader perspective that includes algebraic geometry and differential geometry.
MembersFaculty
- ProfessorYutaka Ishii
- ProfessorJoe Kamimoto
- Associate ProfessorYuta Kusakabe
VoicesStudent voices
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Report an errorAbout the images
The top and research theme images are illustrative and were not taken at the lab. They are cropped from Wikimedia Commons images. Cropped CC BY-SA images are provided under the same CC BY-SA license as the original (version shown on each line).
- Top image: “Msltoe - Julia Bulb Mod4 OpenCL HQ 16K 20201222” PantheraLeo1359531 / CC0 (cropped)
- Dynamics of Complex Hénon Maps: “Julia set (highres 01)” Solkoll / Public domain (cropped)
- The Oka Principle and Gromov Ellipticity: “Riemann sqrt” Wlongqi / CC BY-SA 3.0 (cropped)
- Related lab (Algebraic Geometry Lab): “Heike Kamerlingh Onnes - 29 - Plaster model of a Ψ surface of a mixture of two substances” 作者不詳 / Public domain (cropped)
- Related lab (Number Theory Lab): “SinRiemannSiegelTheta” Chrgue / CC BY-SA 3.0 (cropped)
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- Related lab (Dynamical Systems Lab): “Lorenz caos3” António Miguel de Campos / Public domain (cropped)
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