Mathematics
Our department covers a wide range of research areas—from theorydriven approaches that mainly seek to achieve theoretical sophistication to more empirically oriented approaches that employ computers for calculations on various phenomena. Our research includes diverse fields such as hyperplane arrangements, representation theory, differential geometry, singularity theory, partial differential equations, mathematical physics, chaos, probability theory, and dynamical systems.
Every year, the department sponsors or participates in several research conferences in Sapporo that attract several hundred domestic and foreign researchers. A partial list of the conferences in 2015 gives a sense of the high level of research activity in our department:
The HU and SNU symposium on Mathematics (held annually)
Mathematics Conference for Young Researchers (organized annually by graduate students)
Sapporo Symposium on Partial Differential Equations (held annually)
Northeastan Symposium on Mathematical Analysis (held annually)
These conferences provide students with firsthand glimpses into current research activities as well as opportunities to present their research results to worldrenowned mathematicians. In addition, there are several weekly seminars that students are encouraged to attend. The department has an inhouse library containing about 90,000 books and 525 journals, where students may study in a spacious and quiet environment. Graduate students are provided with their own desks in the department building. Our recent major achievements in receiving large research grants include: (1) the 21st Century Center of Excellence (COE) Program “Mathematics of Nonlinear Structure via Singularity ”from 2003 to 2008, and (2)the Japan Society for the Promotion of Science (JSPS) International Training Program “The international sendingelevating project for young mathematicians based on singularity, topology and mathematical analysis: Hokudai model” from 2008 to 2012. The fruitful success of the COE program resulted in our founding the Research Center for Integrative Mathematics in 2008 which was reformed into Research Center of Mathematics for Social Creativity in RIES, later. Our department provides an advanced integrated education program “Ambitious leader's program” for graduate students from 2014.
Research Fields
Algebra

Masanori Asakura
Professor
PhD
Fields of Specialty:Arithmetic geometry
My research field is arithmetic geometry. I mainly work in Hodge theory, algebraic Ktheory, higher Chow group, mixed motives and regulator.
The classical theory of regulator goes to Dirichlet in the 19th century who showed that it is described by the special values of Lfunctions.
In 1980’s Beilinson gave a vast generalization of Dirichlet’s theorem.
However still it is a widely open question. I study Beilinson’s regulator or its padic counterpart using Hodge theory, padic Hodge theory and so on. 
Mutsumi Saito
Professor
PhD
Fields of Specialty:Algebraic analysis, rings of differential operators
I work on rings of differential operators and their modules, especially the ring of differential operators on an affine toric variety and the system of Ahypergeometric equations whose systematic study was started by Gelfand, Kapranov, and Zelevinsky.
As an algebraic torus acts on these objects, they have some combinatorial descriptions, and they are related to various subjects such as integer programming, hyperplane arrangements, and representation theory. I mostly study them from the combinatorial features. 
Keiji Matsumoto
Professor
PhD
Fields of Specialty:Special functions
There are many special functions defined by integrals or admitting integral representations, such as the gamma function, the beta function, the zeta function, and the hypergeometric function.
We regard these integrals as pairings between elements of some kinds of homology groups and those of cohomology groups. From this point of view, I attempt to find formulas for special functions and to give them geometrical meanings. On the other hand, it is classically known that the elliptic modular function appears as the inverse of the period map for a family of elliptic curves. I study modular forms and modular functions on bounded symmetric domains by the inverses of period maps of families of algebraic varieties. 
Hiroshi Yamashita
Professor
PhD
Fields of Specialty:Representation theory
I am interested in infinitedimensional representation theory of real reductive Lie groups. This is one of the most highly developed, central research areas in modern mathematics. It is connected to various other branches such as number theory, algebraic geometry, combinatorics, differential geometry, harmonic analysis, algebraic analysis, functional analysis, mathematical physics, differential equations, etc. I focus my attention to understand infinitedimensional representations in relation to nilpotent orbits on Lie algebras, by studying geometric invariants and nice realization/model of such representations.

Noriyuki Abe
Associate Professor
PhD
Fields of Specialty:Representation theory
I am interested in the representation theory of reductive groups. Such groups appear in many other branches, such as number theory, physics etc. They also have a precise combinatorial description and many representation theoretic invariants can be calculated explicitely. I study the representation theory of reductive groups over local fields mainly using algebraic methods.

Youichi Shibukawa
Associate Professor
PhD
Fields of Specialty:YangBaxter equations and quantum groups
My research areas are: representation theory of quantum groups; elliptic Roperators; and dynamical YangBaxter maps. The dynamical YangBaxter map is a solution to the YangBaxter equation on a suitable tensor category. This concept induces bialgebroids and tensor categories of their dynamical representations. My interest is to clarify relations between them.

Simona Settepanella
Associate Professor
PhD
Fields of Specialty:Singularity theory, combinatorics
Arrangements of hyperplanes are mathematical objects that can be approached by many different point of view such as algebrogeometric, combinatorial and topological ones. Moreover they are related to Artin Groups and the algebra connected with them.
I’m mainly interested in the cohomology of the complement of hyperplane arrangements with local coefficients which is related to the cohomology of the Milnor Fiber of the arrangement. I’m also interested in toric arrangements, i.e. arrangements of hypersurfaces in a complex torus. Recently I also started research in social choice, economics and organizational studies. In particular, jointly with some economists, we modeled and studied problems related to these disciplines using arrangements of hyperplanes. 
Kenichiro Tanabe
Associate Professor
PhD
Fields of Specialty:Vertex algebras, algebraic combinatorics
I study vertex algebras and algebraic combinatorics for the purpose of understanding finite groups appeared in these mathematical objects. Now I am working on the representation theory of fixed point vertex subalgebras of a vertex algebra.

Daisuke Matsushita
Associate Professor
PhD
Fields of Specialty:Algebraic geometry
A holomorphic symplectic manifold is a Kahler manifold which is endowed a holomorphic symplectic form. Together with a CalabiYau manifold and a complex torus, they form building blocks of a compact Kahler manifold whose first Chern class is zero. I am working a fibration structure of a holomorphic symplectic manifold.

Kazuma Morita
Assistant Professor
PhD
Fields of Specialty:Arithmetic geometry
My research interest is Number Theory. I have studied the padic aspects of this theory (called padic Hodge theory). In particular, by using the padic differential operators, I proved the padic monodromy conjecture of Fontaine in the relative case. The method of the proof is a strange one and I am proud of this petty method.
Recently, however, I am hoping that I can prove the problems in a more dignified way, possibly from a grander perspective.
Geometry

Toshiyuki Akita
Professor
PhD
Fields of Specialty:algebraic topology, group cohomology, discrete groups
I’m working on group cohomology, the subject arose from both topological and algebraic sources. My main subject is the cohomology of Coxeter groups and mapping class groups of closed oriented surfaces.

Goo Ishikawa
Professor
PhD
Fields of Specialty:Real algebraic geometry, singularity theory
By singularity theory, we treat singularities of various objects and study their mathematical structures. In particular we investigate the structures on the subspace consisting of singular objects, so called the bifurcation set.
In the 16th problem of Hilbert, we study the topological structure of the zeroset of a real polynomial. Naturally we apply complex algebraic geometry, manifold theory, algebraic topology and singularity theory etc for the solution of the problem.
One of my themes is to develop the singularity theory in symplectic geometry which is related to classical mechanics and quantum mechanics. Moreover I am interested in unknown area, such as quantum topology, quantum singularity theory etc.
I was involved in various mathematical works and then recently I have noticed that my interests tend to be gravitated more strongly towards “topology on solution spaces of differential systems” and now I take great delight in working on them. 
Katsunori Iwasaki
Professor
PhD
Fields of Specialty:Complex geometry, dynamical systems, Painleve systems
I am interested in dynamical systems theory and ergodic theory of holomorphic maps on complex manifolds or on algebraic varieties. Complex manifolds and algebraic varieties are known to have very beautiful geometric structures. On the other hand, dynamical systems theory and ergodic theory deal with very complicated figures, chaos and fractals, created by iterations of a mapping. The fusion of these two fields enables us to feel the double joy of drawing an extremely complicated figure on a space of extremely simple beauty. As applications of these, I am working on the complex dynamics of nonlinear differenatial equations called Painlev? equations. Painlev? equations are nonlinear analogues of hypergeometric equations which are classically wellknown linear equations. Because of their nonlinearity, Painlev? equations exhibit chaotic behaviors which cannot be observed in hypergeometric equations, a feature that interests me very much!

Toru Ohmoto
Professor
PhD
Fields of Specialty:Singularity theory, topology
I’m working on singularity theory and topology. My main subject is the theory of characteristic classes for singular spaces and singular maps, which is deeply connected with the enumerative geometry from classic to modern times. It includes, e.g., CSM class , (singular) Todd class, Hirzebruch class, Schubert calculus, Thom polynomials for singularities of maps. I’m also interested in its applications and real counterpart.

Shyuichi Izumiya
Specially Appointed Professor
PhD
Fields of Specialty:Geometry, singularity theory
I am interested in the following subjects:
1)Applications of the theory of singularities to classical differential Geometries (i.e., Euclidean Geometry, Hyperbolic Geometry, Lorentz geometry etc)
2)Singularities appearing in the various models of horizon in General relativity theory
3)Caustics appearing in the brane world scenario
4)Singularities of special surfaces (i.e., flat surfaces, ruled surfaces etc) in space forms (i.e., Euclidean space, Sphere, Hyperbolic space, Minkowski space, de Sitter space or anti de Sitter space)
5)Gravitaional lensings
6)Singularities of solutions for nonlinear partial differential equations I applied the theory of Legendrian or Lagrangian singularities to the above subjects and have discovered some interesting geometric invariants 
Shimpei Kobayashi
Associate Professor
PhD
Fields of Specialty:Differential geometry
Constant mean curvature surfaces are given by solutions of a variational problem and have been studied for long time.
On the one hand, it is known that the structure equation of the constant mean curvature surface is an integrable equation.
I am working on these constant mean curvature surfaces and their generalization, harmonic maps, using theory of integrable systems. 
Masao Jinzenji
Associate Professor
PhD
Fields of Specialty:Mathematical physics
I’m now studying the relation between GaussManin systems and Quantum Cohomology Rings of complex manifolds from the point of view of mirror symmetry. I’m also interested in mathematical physics arising from string theory.

Hitoshi Furuhata
Associate Professor
PhD
Fields of Specialty:Differential geometry
Curves and surfaces in a Euclidean space are approachable research topics. Numerous and indepth studies on them are the centuryold traditions of geometry, and at the very foundation of it. Differential geometry of submanifolds is a direct generalization of this research field. At present, I am particularly interested in two specific areas. One is geometry of submanifolds in a vector space, socalled centroaffine differential geometry. The other is geometry of statistical manifolds. It’s an important concept in information geometry, an emerging research domain, and is also closely related to affine differential geometry and Hessian geometry. Let’s enjoy exploring the world of forms and shapes together.

Masahiko Yoshinaga
Associate Professor
PhD
Fields of Specialty:Algebraic geometry, combinatorics
Hyperplane arrangements relate several branches of mathematics, topology, representation theory, combinatorics, and so on. I am working in two aspects of hyperplane arrangements. The first is around logarithmic vector fields.
It is a reflexive sheaf on the projective space, which controls combinatorial structures of arrangements. The other is minimality of the homotopy types of the complements. Recently I am also interested in computational complexity of periods. 
Yutaka Kanda
Assistant Professor
PhD
Fields of Specialty:Differential topology
My research interests are mainly in mapping class groups and related topics to them. My goal for the time being is to construct cocycles of the MoritaMumford classes in various ways and to get a concrete estimate for the Gromov seminorm.

Michele Torielli
Assistant Professor
PhD
Fields of Specialty:Algebraic geometry, Combinatorics
My area of interest is singularity theory, and in particular hyperplane arrangements. I am interested in understanding the links between the topological and combinatorial aspects of these objects.
Analysis

Hiroaki Aikawa
Professor
PhD
Fields of Specialty:Potential theory, real analysis
I have been studying potential theory. The main theme of potential theory is the investigation of fundamental functions such as (super)harmonic functions, subharmonic functions, plurisubharmonic functions. The importance of the deep analysis of these functions has been recognized as they play crucial role in analysis, geometry, probability, applied mathematics and so on. On the other hand, methods, notions and aims of real and complex analysis, functional analysis and probabilistic analysis have enriched potential theory. Generally speaking, the interior properties of solutions to partial differential equations have been exploited even though the equations are complicated; if the domain is sufficiently smooth, the boundary behavior of the solutions can be studied to some extent. Nevertheless the boundary behavior of harmonic functions has many open problems if the domain is not smooth. My research interest is the boundary behavior of these functions in a wide sense. More specifically, I have been studying the Fatou theorem, minimal fine topology, the integrability of super harmonic functions, the additivity of capacity, the norm estimate of the Green operator, Martin boundary and the boundary Harnack principle.

Akihito Hora
Professor
PhD
Fields of Specialty:Functional analysis, probability theory
I have made random walks around the frontier of probability and group representations. Having the notion of measures as the navigator, my walk often digresses in a random way. I am interested in bridging finite and infinite objects. The latest and biggest concerns of mine are analyzing probabilistic phenomena caused by the actions of huge groups.

Naofumi Honda
Professor
PhD
Fields of Specialty:Algebraic analysis
I am mainly studying subjects related to “Algebraic Analysis”, in particular, microlocal aspects of asymptotic analysis and exact WKB analysis. The microlocal analysis, which was initiated by Mikio Sato in 70’s, is a quite powerful tool to study solutions of systems of linear partial differential equations, and I am now trying to extend this method to the area of asymptotic analysis.

Jun Masamune
Professor
PhD
Fields of Specialty:Global Analysis
My research interest is to investigate the relationships between the analytical and geometric properties of spaces such as Riemannian manifolds and graphs by analyzing the Laplacian, head kernels, Green functions, and Brownian motion on the spaces. The problems currently I am working on are to determine the selfadjoint extensions of the Laplacians, longterm behaviors of Brownian motion such as conservation ad recurrent property, and the Liouville property of harmonic functions applying the techniques from PDEs and Functional Analysis.

Asao Arai
Specially Appointed Professor
PhD
Fields of Specialty:Mathematical physics, functional analysis
Searches and investigations, from all possible aspects, of mathematical ideas and laws which govern quantum phenomena. Subjects that have been considered in recent years include the following:
Mathematical analysis of quantum systems interacting with quantum fields, mathematical theory of time operator, representation theory of canonical commutation relations, mathematical foundations of quantum electrodynamics, mathematical construction of supersymmetric quantum field theory and a theory of infinitedimensional Dirac operators. 
Masaharu Kobayashi
Associate Professor
PhD
Fields of Specialty:Harmonic Analysis
My research field is analysis. Especially, I am interested in topics called harmonic analysis and real analysis. Roughly speaking, to study boundedness, continuity, differentiability and integrability of functions, we measure “quantitative properties” of functions. We also study how these “quantitative properties” change when we apply various operators. To measure “quantitative properties”, we use various norms (and we also use function spaces defined by these norms). Recently, I am interested in the theory of modulation spaces which were introduced by H.Feichtinger, and I’m trying to study pseudodifferential operators and partial differential equations in the framework of modulation spaces.

Reiji Tomatsu
Associate Professor
PhD
Fields of Specialty:Operator algebras
I am mainly studying von Neumann algebras and (quantum) group actions on them. My recent interest has been focused on the classification of Rohlin flows on injective factors and the characterization of the Rohlin property for flows.

Takahiro Hasebe
Associate Professor
PhD
Fields of Specialty:Probability theory, complex analysis, functional analysis
Free probability was discovered in the context of operator algebras to study free groups. By regarding the generators of a free group (algebra) as “independent random variables”, a probabilistic structure appears. Thus free probability comes up. Later, applications to the eigenvalue distributions of random matrices were discovered, and then probabilistic research started to increase. Now free probability is a field that involves operator algebras, probability theory, combinatorics, complex analysis and representation theory. I am working in particular on the aspects combinatorics of set partitions and complex analysis.

Nao Hamamuki
Associate Professor
PhD
Fields of Specialty:Nonlinear partial differential equations?Theory of viscosity solutions
My major research topic is the study of nonlinear partial differential equations, especially evolution equations such as HamiltonJacobi equations and curvature flow equations which appear in materials science and describe a motion of a surface (an interface) separated by two different phases of matter.
On the basis of the theory of viscosity solutions, which is a notion of weak solutions for differential equations, I aim at introducing a suitable notion of solutions, establishing unique existence of solutions to the initial value problem and tracking the large time behavior of solutions to give mathematical foundations to such nonlinear equations.
My current interests include a multifaceted understanding of phenomena via the limit process; for instance, finding a connection between a discrete/continuum problem and a microscopic/macroscopic model (homogenization).
I will be glad if we could make links among various research fields through mathematics and find applications to new fields. 
Tadahiro Miyao
Associate Professor
PhD
Fields of Specialty:Mathematical physics, functional analysis, condensed matter physics
I am trying to clarify various mathematical structures behind physical phenomena in the condensed matter physics by applying and cultivating methods of functional analysis.
Applied Mathematics

Shinichiro Ei
Professor
PhD
Fields of Specialty:Nonlinear analysis, nonlinear partial differential equations
The understanding of various patterns such as snow crystal, combustion, spot patterns of groups of plankton, and other kinds of chemical patterns appearing in nature are one of the most attractive objects of
study in natural science. My interest is to theoretically study the structure and mechnism of such phenomena. To do it, I use description through model equations, which is one of the most theoretical methods, well known since Newton.
The model equations which I have studied so far lie in the framework of partial differential equations which describe evolutional processes of certain materials with two mechanisms: (1) the diffusion process in space, and (2) the production and/or extinction of materials. Such model equations are generally called “reactiondiffusion systems” and their use has been well recognized in physics, chemistry, biology and other fields from a mathematical modelling point of view.
It is important to have interests in patterns appearing in nature, which give a strong motivation and conatus for learning in our laboratory. I welcome such students. 
Hideo Kubo
Professor
PhD
Fields of Specialty:Partial Differential Equations associated with Nonlinear Dynamics
The wave equation is one of the typical partial differential equations and has a long history. Although the wave equation looks like so simple, its mathematical structure is quite rich. In my research the effect from some perturbation such as the nonlinear perturbation, the presence of an obstacle, and so on are analyzed. The main issue is to compare the leading term of a solution to the unperturbed system and that to the perturbed system. For instance, the scattering theory is nothing else but the comparison between the behavior of solutions to these systems as time goes to infinity. We use functional analysis and real analysis for studying the scattering theory. But heavy computations based on calculus are the core of our analysis. It is of special interest to consider the case where the effect from the perturbation is balanced with that from the unperturbed system, because such consideration enables us to see the essential feature of the unperturbed and perturbed systems. Recently, I’m also interested in systems appeared in mathematical physics which are reduced to the wave equation and in the noncommutative structure of some partial differential equations.

Shuichi Jimbo
Professor
PhD
Fields of Specialty:Applied analysis, Partial differential equations, Spectral theory
Singular deformation of domains and spectral analysis: I enjoy walking on mountains in summer and skiing in winter. I walk around the woods, look at trees and feel the atmosphere. It is quite a joyful and comfortable experience. From physical point of view, this can be well simulated and demonstrated by receiving sound waves, light waves or mechanical vibrations induced by natural phenomena. They are the objects which I like to understand very well. These phenomena are written mathematically in terms of PDEs, which are several kinds of wave equations depending on the situations. Elliptic operators appear in these equations. My research interest is to study and analyze the spectra of these operators, centered around their dependence on the geometric properties and several other environmentoriented features.

Masaharu Nagayama
Professor
PhD
Fields of Specialty:Reactiondiffusion systems, mathematical modeling, numerical simulation
The goal of our study is to understand the mechanism of nonlinear phenomena from the mathematical viewpoint, using mathematical modeling, numerical simulation and mathematical analysis. For example, we are studying on the motion of droplets and particles, a chemical reaction and a cell dynamics.

Michiko Yuri
Professor
PhD
Fields of Specialty:Ergodic theory, dynamical systems, complex systems
The purpose of our project is to present mathematical ideas and methods?which are useful in?predicting asymptotic behavior of complex systems.
In particular, we are interested in dynamics of complex systems exhibiting “nonhyperbolic” phenomena and in applying our results to a number of the applied sciences, (e.g., in neuroscience, physics, chemistry and economics).
Our techniques are based on ergodic theory arising from equilibrium statistical physics. We develop a new concept that may be adapted to nonequilibrium steady states exhibiting dissipative phenomena producing nonstationary processes. This allows us to study statistical properties of complex systems admitting both chaotic and fractal structures. 
Akira Sakai
Associate Professor
PhD
Fields of Specialty:Probability theory, statistical mechanics, mathematical physics
My major research field is mathematical physics (probability and statistical mechanics). The topics I have been most fascinated with are phase transitions and critical phenomena, and associated scaling limits. For example, the Ising model exhibits a magnetic phase transition; it takes on positive spontaneous magnetization when the temperature of the system is turned down below its critical value. Various other observables also exhibit singular behavior around the critical point, due to cooperation of infinitely many interacting variables. To fully understand such phenomena, it would require development of a theory beyond the standard probability theory. This is a challenging and intriguing problem, towards which I would love to make even a tiny contribution. The mathematical models I have been studying are the Ising model, selfavoiding walk, percolation, the contact process (a model for the spread of an infection) and random walk with reinforcement.

Yuzuru Sato
Associate Professor
PhD
Fields of Specialty:Complex systems, chaotic dynamical systems
I study nonlinear dynamical systems and complex systems with interest in complexity of spatiotemporal chaotic dynamics. My current research are focused on random dynamical systems approaches to noiseinduced phenomena, timeseries analysis of dynamical systems with large degrees of freedom, and information theoretic analysis of spatiotemporal chaos. Applications of nonlinear dynamical systems theory to problems in information theory, computation theory, prediction and control, are also put in perspective.

Takao Namiki
Associate Professor
PhD
Fields of Specialty:Ergodic theory, dynamical systems, complex systems
I study complex system, especially cellular automata and quantum walks. First, we can observe fascinating dynamical behavior of cellular automata, typical complex system like the Game of Life, on their configuration space. Though the definition of cellular automata is various, my interest is the orbit structure of such behavior from the viewpoint of dynamical system and ergodic theory. Second, quantum walk, quantum version of random walk, shows different behavior from normal random walk. In the definition of quantum walk, a unitary operator on given Hilbert space is required and I study the features of quantum walks defined by the pair induced with measure preserving dynamical system. Now, relative to quantum information, the study of quantum walk is so important.

Kenji Matsumoto
Associate Professor
PhD
Fields of Specialty:Biophysical complex systems, chaotic dynamical systems
My main research interest lies in the analysis of time series from complex systems. I focus on analysis of the movement of microorganisms, developments of data acquisition programs for recording the movements of organisms including image processing and numerical simulation of highdimensional dynamical systems.

Masakazu Akiyama
Assistant Professor
PhD
Fields of Specialty:Mathematical modeling, mathematical and theoretical biology, numerical calculation
A mathematical model of cleavage
Mathematical analysis of Physarum
A mathematical model of planar cell polarity
A mathematical study of cell division model
Mathematical analysis of gait transitions in quadrupeds.
A mathematical model for locomotion of the amoeba cell.
A mathematical model of rivers 
Marko Jusup
Assistant Professor
PhD
Fields of Specialty:Mathematical Biology, Ecological Modelling, Biophysics
Research based on an integrative global perspective has the potential to address the problems of practical significance for societies. The specific problems addressed in my research have quite diverse origins, ranging from ecology to biology to social sciences and even economics. Yet, when translated into the universal language of mathematics, the principles and processes underlying all these problems attain a similar form. Recognizing this form by means of the mathematical translations (i.e. models) of complex realworld phenomena and inferring the consequent dynamic properties is at the heart of analyses that I am conducting at Research Institute for Electronic Science (RIES) in collaboration with colleagues from Japan and internationally.
In summary, the overall aim of my research is to formulate the mathematical models of complex ecological, biological, social, and economic phenomena and analyze their dynamic properties. Special emphasis is put on finding the solutions of practical significance for society and global community.