Labs in Waseda University, School of Fundamental Science and Engineering

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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

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A lab that uses mathematics to understand the singularities that appear in shapes and maps.

Ohmoto Lab studies the properties of singularities that appear in shapes and maps from a mathematical perspective. Singularities are the places where things stop being smooth, such as where a surface folds or has a sharp point, and the lab classifies them using methods from topology and geometry. The research covers a wide range of fields, including persistent homology for studying the shape of data, information geometry related to machine learning, and differential line geometry related to robotics.

#Singularity theory #Topology #Applied singularity theory

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The lab studies how to compute with mathematically guaranteed bounds on the errors hidden in computer calculations.

Ogita Lab mainly studies verified numerical computation. In numerical computation on computers, errors arise from sources such as the rounding of numbers. The lab studies methods that compute while mathematically guaranteeing the bounds within which those errors lie.

#Verified numerical computation #Numerical computation

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The lab uses differential equations to explain territorial competition among organisms and the formation of patterns.

Kuto Lab uses differential equations to study curious phenomena that appear in living things and materials. Centered on equations called “reaction-diffusion systems,” which describe territorial competition between organisms and pattern formation, the lab theoretically investigates the behavior of their solutions. Pattern formation in chemistry and physics, such as the stripe and spiral patterns formed by molecules moving on a platinum surface, is also a subject of research. The lab values both the appeal of pure theory and the appeal of mathematical models that explain phenomena.

#Reaction-diffusion systems #Pattern formation #Partial differential equations

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The lab studies mathematical models such as the "box-ball system," which is described by the movement of balls.

Takahashi Lab studies difference equations and a mathematical technique called ultradiscretization. The lab conducts research using cellular automata, including a model called the "box-ball system," which is described by the movement of balls. The lab publishes its research results through presentations at academic conferences in Japan and abroad, and as papers.

#Box-ball systems #Cellular automata #Ultradiscretization

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The lab uses probability to interpret familiar phenomena such as networks and sports.

Toyoizumi Lab studies how to represent a wide variety of probabilistic phenomena in the world with mathematical models. It covers a broad range of subjects, including networks, sports, the ecology of living things, genes, financial engineering, and how companies and projects progress. The lab also studies the mathematical properties of probability theory and stochastic process theory themselves, which are needed to understand uncertain phenomena.

#Probabilistic models #Stochastic processes #Financial engineering