Labs in Waseda University, School of Fundamental Science and Engineering, Department of Mathematics

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The lab studies high-dimensional algebraic varieties through algebraic geometry.

The Nagai Lab studies algebraic geometry, in particular high-dimensional algebraic varieties. The lab focuses on compact holomorphic symplectic Kähler manifolds and the algebro-geometric structures defined on them. As related tools, it also studies moduli of semistable sheaves, geometric invariant theory, toric geometry, and higher-dimensional birational geometry.

#Algebraic geometry #Symplectic Kähler manifolds #Birational geometry

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A lab that uses probability and mathematics to study the motion of random waves.

The Fukuizumi Lab studies, from a mathematical perspective, nonlinear wave phenomena with random fluctuations that arise in statistical physics. The lab's research connects nonlinear dispersive partial differential equations, stochastic partial differential equations, mathematical physics, and probability theory. Applications include random nonlinear waves, Bose-Einstein condensation, and stochastic nonlinear Schrödinger equations.

#Stochastic partial differential equations #Nonlinear waves #Stochastic nonlinear Schrödinger equations

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A lab that explores the essence of geometry and physics through Dirac operators.

The Homma Lab studies spin geometry from the perspectives of differential geometry and global analysis. The lab studies the Dirac operator, a differential operator, from various angles, including differential geometry, global analysis, and representation theory. Specifically, it works on topics such as spin geometry, gauge theory, twistor theory, and index theorems. Another aim of the lab is to understand the geometric and analytic properties of differential operators determined by geometric structures on Riemannian manifolds.

#Spin geometry #Dirac operators #Gauge theory

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A topology lab that studies the shapes of knots and 3-manifolds.

The Murakami Lab studies knot theory and 3-manifolds, which are fields within topology. The lab investigates the shapes of knots and 3-dimensional spaces using algebraic tools. In particular, it uses "quantum invariants" built from quantum groups to study the shapes of knots and their relationship to hyperbolic volume.

#Knot theory #3-manifolds #Quantum invariants

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三竹研究室 (introduction coming soon)

Mitake Lab studies partial differential equations that describe the motion and change of things, from the standpoint of mathematical analysis. At the center of its work are the theory of viscosity solutions, which can handle solutions that are not smooth, and Hamilton-Jacobi equations. The lab also works on problems connected to physics and engineering, such as how solutions settle down as time passes (large-time behavior), optimal control, and crystal growth.

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A lab that studies general relativity using mathematics and computers.

Yoneda Lab studies general relativity from a mathematical perspective. Using tensor algebra and differential geometry to describe relativity, the lab explores new theoretical developments. In particular, it works on the initial value problem for the Einstein equations and the stability of numerical relativity.

#Differential geometry #Lorentzian geometry #Numerical relativity