Department of Mathematics Faculty Members & Research Themes

・Global path properties for Markov Processes
・Regularity problem for Dirichlet forms
・Construction of Feller semi-groups in terms of integro-differential operators

Trajectory of two-dimensional Brownian motion

・Geometric analysis on manifolds
・Geometric invariants on submanifolds Moduli
・Theory of periodic minimal surfaces

Can you see it as a surface with two points removed from a torus?

・Stochastic calculus of symmetric Markov processes
・Spectral properties of symmetric Markov operators
・Large deviations for additive functionals

Markov chain (queue)

・Computational Algebra
・Applied Singularity Theory
・Hamiltonian Dynamical Systems

Conceptual diagram of the novel chemical reaction mechanism "reaction coordinate switching" (Phys. Rev. Lett. 115, 093003 (2015))

・FDifferential geometry related to integrable systems
・Geometric variational problems
・Affine differential geometry

Even the genius Gauss would be surprised!!

・The arithmetic of abelian varieties with complex or quaternionic multiplication
・The relationship between abelian varieties and automorphic forms

Fundamental domain of SL(Z). By gluing the boundaries, it becomes the moduli space of one-dimensional abelian varieties (= elliptic curves).

・Combinatorial commutative algebra
・Application of the derived category and sheaf theory to the above area
・Oriented Matroid

From "Combinatorial Commutative Algebra" by Miller-Sturmfels.

・Quantum invariants of knots and 3-manifolds
・Representation categories of Hopf algebras

2cocycle

・Estimation theory
・Model　Selection
・Simulation　method

Stochastic differential equation model and sample path of solution process

・Discrete integrable equations
・Cellular automata and ultra-discrete equations

Discrete KdV equation and its soliton solution

・Stochastic calculus

Simulation of stochastic processes