KANSAI UNIVERSITY

Kansai University

Engineering Science Major
Mathematics

Cohomological Aspects in Mathematics

ProfessorSHODA Toshihiro

tshoda @kansai-u.ac.jp

Research Topics

① Geometric analysis on manifolds
② Geometric invariants on submanifolds
③ Moduli Theory of periodic minimal surfaces

Key Words

Spectral Geometry, Minimal surfaces, Morse index, Nullity, Signature

Cohomological Aspects in Mathematics

ProfessorFUJIOKA Atsushi

website

afujioka @kansai-u.ac.jp

Research Topics

① Differential geometry related to integrable systems
② Geometric variational problems
③ Affine differential geometry

Key Words

Harmonic maps, Minimal surfaces, Surfaces with constant mean curvature, Integrable systems, Variational problems, Affine differential geometry

Cohomological Aspects in Mathematics

ProfessorMURABAYASHI Naoki

murabaya @kansai-u.ac.jp

Research Topics

① The arithmetic of abelian varieties with complex or quaternionic multiplication
② 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 Point

Applications

Crytography Theory

Cohomological Aspects in Mathematics

ProfessorYANAGAWA Kohji

yanagawa @kansai-u.ac.jp

Research Topics

① Combinatorial commutative algebra
② Application of the derived category and sheaf theory to the above area
③ Oriented Matroid

Key Words

Stanley-Reisner Ring, Derived Category, Constructible Sheaf, Local Duality, Dualizing Complex, Poicare- Verdier Duality, (Affine)Oriented Matroid

Applications

Computational Algebra

Cohomological Aspects in Mathematics

ProfessorWAKUI Michihisa

wakui @kansai-u.ac.jp

Research Topics

① Quantum invariants of knots and 3-manifolds
② Representation categories of Hopf algebras

Key Words

Topology, Tensor Category, Representation, Topological Field Theory, Hopf Algebra, Quantum Group, Knot, 3-Manifold, Subfactor, Triangulation

Applications

Natural Science

Cohomological Aspects in Mathematics

Associate ProfessorKANKI Masataka

Research Topics

① Discrete dynamical systems and their integrability criteria
② Cellular automata and ultra-discrete equations

Key Words

Algebraic entropy, Ultra-discrete equations, Arithmetic dynamical systems, Singularity confinement

Probability and Statistics

ProfessorUEMURA Toshihiro

website

t-uemura @kansai-u.ac.jp

Research Topics

① Global path properties for Markov Processes
② Regularity problem for Dirichlet forms
③ 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

Probability and Statistics

ProfessorTAKEDA Masayoshi

mtakeda@kansai-u.ac.jp

Research Topics

① Stochastic calculus of symmetric Markov processes
② Spectral properties of symmetric Markov operators
③ Large deviations for additive functionals
④ Quasi-stationary distribution, penalization problem
⑤ Criticality theory for Schrödinger operators

Key Words

Symmetric Markov process, Additive functional, Large deviation, Dirichlet form

Probability and Statistics

Associate ProfessorUEHARA Yuma

website

y-uehara @kansai-u.ac.jp

Research Topics

① Estimation theory
② Model Selection
③ Simulation method

Key Words

Lévy process,information criterion,stochastic differential equation,misspecified model

Applications

High frequency data analysis

Probability and Statistics

Associate ProfessorTAGUCHI Dai

Research Topics

① Stochastic calculus

Key Words

Euler-Maruyama scheme, Monte Carlo method, stochastic differential equation, Dyson Brownian motions

Applications

Mathematical finance

Probability and Statistics

Associate ProfessorTERAMOTO Hiroshi

Research Topics

① Computational Algebra
② Applied Singularity Theory
③ Hamiltonian Dynamical Systems

Key Words

mixed-module, comprehensive Groebner basis, singularity theory, dynamical systems

Applications

multi-objective optimization, program verification, chemical reaction dynamics

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