Engineering Science Major
Mathematics
tshoda
【Research Topics】1. Geometric analysis on manifolds2. Geometric invariants on submanifolds3. Moduli theory of periodic minimal surfaces
Key Words:Spectral geometry, minimal surfaces, morse index, nullity, signature
afujioka
【Research Topics】1. Differential geometry related to integrable systems2. Geometric variational problems3. Affine differential geometry
Key Words:Harmonic maps, minimal surfaces, surfaces with constant mean curvature, integrable systems, variational problems, affine differential geometry
murabaya
【Research Topics】1. The arithmetic of abelian varieties with complex or quaternionic multiplication2. The relationship between abelian varieties and automorphic forms
Key Words:Abelian variety, complex multiplication, quaternionic multiplication, field of moduli, field of definition, defining equation, rational pointApplications:Crytography theory
yanagawa
【Research Topics】1. Combinatorial commutative algebra2. Application of the derived category and sheaf theory to the above area3. Oriented matroid
Key Words: Stanley-reisner ring, derived category, constructible sheaf, local duality, dualizing complex, poicare- verdier duality, (affine)oriented matroidApplications:Computational algebra
wakui
【Research Topics】1. Quantum invariants of knots and 3-manifolds2. Representation categories of hopf algebras
Key Words:Topology, tensor category, representation, topological field theory, hopf algebra, quantum group, knot, 3-manifold, subfactor, triangulationApplications:Natural science
kanki
【Research Topics】1. Discrete integrable equations2. Cellular automata and ultra-discrete equations
Key Words:Ultra-discrete equations, arithmetic dynamical systems, integrability, discrete integrability
t-uemura
【Research Topics】1. Global path properties for Markov processes2. Regularity problem for dirichlet forms3. Construction of feller semi-groups in terms of integro-differential operators
Key Words:Symmetric stable-like processes, jump-diffusions, dirichlet forms, martingale additive functionals, recurrence, transience, regularities, ergodicity
Applications:Estimates for stationarity of Markov chains, determination of option prices in the discrete model case, foundations of probabilistic risk analysis
mtakeda
【Research Topics】1. Stochastic calculus of symmetric Markov processes2. Spectral properties of symmetric Markov operators3. Large deviations for additive functionals4. Quasi-stationary distribution, penalization problem5. Criticality theory for schrödinger operators
Key Words:Symmetric Markov process, additive functional, large deviation, Dirichlet form
teramoto
【Research Topics】1. Computational algebra2. Applied singularity theory3. Hamiltonian dynamical systems
Key Words:Mixed-module, comprehensive groebner basis, singularity theory, dynamical systems
Applications:Multi-objective optimization, program verification, chemical reaction dynamics
y-uehara
【Research Topics】1. Estimation theory2. Model selection3. Simulation method
Key Words:Lévy process, information criterion, stochastic differential equation, misspecified model
Applications:High frequency data analysis
taguchi
【Research Topics】1. Stochastic calculus
Key Words:Euler-Maruyama scheme, Monte Carlo method, stochastic differential equation, Dyson Brownian motions
Applications:Mathematical finance
