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Powering Powering the Future AccessAccess to to Ritsumeikan Ritsumeikan RitsumeikanRitsumeikan University University (Kinugasa(Kinugasa Campus) Campus) ToTo Tsuruga Tsuruga Hakubai-choHakubai-cho TojiinTojiin KeifukuKeifuku Line Line LakeLake Biwa Biwa ToTo Kameoka Kameoka JRJR Sagano Sagano Line Line To ToMaibara Maibara NijoNijo ArashiyamaArashiyama ■Suzaku■Suzaku Campus Campus JR JRBiwako Biwako Line Line SaiinSaiin ShijoShijo Karasuma Karasuma Kawara-machiKawara-machi To ToNagoya Nagoya KatsuraKatsura OmiOmi Ohashi Ohashi Bridge Bridge MinamiMinami ShijoShijo Omiya Omiya KusatsuKusatsu HankyuHankyu YamashinaYamashina IshiyamaIshiyama KyotoKyoto To ToRitto Ritto I.C. I.C. LineLine SetaSeta KusatsuKusatsu JRJR kyoto kyoto Line Line tanakamitanakami KyotoKyoto OtsuOtsu I.C. I.C. I.C.I.C. ToTo Osaka Osaka SetaSeta StationStation Nishi/HigashiNishi/Higashi JRJR Shinkansen Shinkansen Line Line I.C.I.C. ToTo Umeda Umeda RitsumeikanRitsumeikan University University (Biwako-Kusatsu(Biwako-Kusatsu Campus) Campus) ToTo Umeda Umeda MeishinMeishin Expressway Expressway SetaSeta River River PPoowweringering tthhee FFututuurree ToTo Get Get to to the the Biwako-Kusatsu Biwako-Kusatsu Campus Campus of of Ritsumeikan Ritsumeikan University University FromFrom Osaka Osaka or or Kyoto Kyoto RRiitstsuummeeikanikan UUnniivversersiityty TakeTake the the JR JR to to Minami Minami Kusatsu Kusatsu Station Station ( 50( 50 minutes minutes from from Osaka, Osaka, 20 20 minutes minutes from from Kyoto). Kyoto). CollegeCollege of of Science Science and and Engineering Engineering ChangeChange from from the the "Shinkaisoku" "Shinkaisoku" Express Express train train to to a alocal local train train at at Ishiyama Ishiyama station station ( 3( 3stops stops afterafter Kyoto Kyoto station). station). Exit Exit the the station station on on the the south south side side ( turning( turning right right after after passing passing through through thethe ticket ticket gates). gates). Take Take an an Omi Omi Railways Railways Bus Bus designated designated as as either either "Ritsumeikan "Ritsumeikan Daigaku Daigaku yuki（立命館大学行き）"yuki（立命館大学行き）" or or "Ritsumeikan "Ritsumeikan Daigaku Daigaku keiyu keiyu Tobishima Tobishima Gurin Gurin Hiru Hiru yuki yuki (立命館大 (立命館大 学経由飛島グリーンヒル行き)"学経由飛島グリーンヒル行き)" and and get get off off at at "Ritsumeikan "Ritsumeikan Daigaku（立命館大学）"( Daigaku（立命館大学）"( 8 8minutes). minutes). ForFor More More Information Information PleasePlease refer refer to to the the homepage homepage for for the the latest latest information information on on scholarships, scholarships, housing housing and and other other assistance.assistance. KYOTOKYOTO TOKYO●TOKYO● OSAKAOSAKA ●● GraduateGraduate School School of of Science Science and and Engineering, Engineering, Ritsumeikan Ritsumeikan University University Biwako-KusatsuBiwako-Kusatsu Campus Campus 1-1-1 1-1-1 Noji Noji Higashi,Kusatsu,Shiga Higashi,Kusatsu,Shiga 525-8577 525-8577, JAPAN, JAPAN Tel:Tel: +81-77-561-2624 +81-77-561-2624 Fax:Fax: +81-77-561-2890 +81-77-561-2890 HP:HP: http://www.ritsumei.ac.jp/gsse/eng/ http://www.ritsumei.ac.jp/gsse/eng/ Ritsumeikan University College of Science and Engineering Powering the Future Department of Mathematical Sciences Department of Mathematical Sciences Research/Development Areas Research/Development Areas INDEX Stochastic process and its application, Structure analysis of von Neumann College of Science and Engineering financial mathematics and its application algebras Department of Mathematical Sciences・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・ 2 Professor / Jiro AKAHORI Associate Professor / Hisashi AOI Department of Physical Sciences・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・ 6 My interest lies in probability theory, financial mathematics and As we live in a three-dimensional world the idea of “four- the various fields that are related to them. This involves various dimensions” can be quite challenging but it is considered quite Department of Electrical and Electronic Engineering・・・・・・・・・・・・・・・・・・・ 10 subjects that include abstract mathematics as well as its appli- routine in mathematics, with well developed arguments for it in cations; stochastic differential equation on topological groups, place. However, contrarily enough five-dimension or six- Department of Electronic and Computer Engineering ・・・・・・・・・・・・・・・・ 16 quadratic Wiener functionals and infinite dimensional Lie alge- dimension worlds appear to have been taken for granted. bras, the pricing of financial derivatives, sustainable economic My interest is in the “infinite dimensional” world that could be Department of Mechanical Engineering・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・ 19 growth problems, and so on. These research projects also in- considered to exist at the beyond of “finite-dimensional” worlds volve a number of postgraduate students. International ex- where phenomena considered impossible in a finite-dimensional Department of Robotics・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・ 24 changes take active place with guests frequently visiting my world could occur. The subject of “operator algebras” can be laboratory from all over the world, from whom we can all learn a considered something that “acts” on this marvelous world. The Department of Civil Engineering・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・ 27 lot. The number of foreign students at our laboratory is also in- study of this is classified as “analysis”; however, it is also closely creasing while some of our students occasionally get sent to related to algebra and geometry. In the real world quantum Department of Environmental Systems Engineering・・・・・・・・・・・・・・・・・・・ 30 foreign universities. We also frequently have the opportunity to mechanics and knot theory etc are also related to it. travel overseas to attend academic society meetings. Gradu- This field is comparatively new in mathematics and has a lot of Department of Architecture and Urban Design・・・・・・・・・・・・・・・・・・・・・・・・・・・・ 33 ates from our laboratory unknown problems, thus making it a challenging research often enter professions subject. in the banking industry. ■Commemorative laboratory photo Research/Development Areas Research/Development Areas Semi-classical Analysis of Schrödinger Application of gauge theory to V-manifolds Equations and its three-dimensional manifold in the same boundary Professor / Setsuro FUJIIE Professor / Yoshihiro FUKUMOTO Semi-classical analysis is an asymptotic analysis where the Homologically the same boundary groups configured with Planck constant appearing in the Schrödinger equation is re- whole three-dimensional homological spheres are an important garded as a small parameter. Under certain conditions, quan- subject of research related to the unsolved expectation of trian- tum mechanics is expected to approach classical mechanics in gles being divisible by high-dimensional manifolds, however, the semi-classical limit (Bohr’s correspondence principle). The very little is known about the structure except the fact that it is asymptotic distribution of eigenvalues or resonances created by a finitely generated Abelian group. My research involves homo- a bound or semi-bound state, respectively, is closely related to logically the same boundary invariants in seeking structures that the existence and the geometry of “trapped” trajectories of the particularly include the integer lifting of classic Rochlin invariants corresponding classical dynamics. by applying gauge theory to V-manifolds. Gauge theory can be This problem is an extension of the famous question “Can one used to extract topology information from nonlinear partial dif- hear the shape of the drum?” (M. Kac), which examines the re- ferential equations describing the field (particle) on the manifold. lationship between the geometry of a bounded domain and the I focus on the contribution made by the singular point of a V- asymptotic distribution of eigenvalues of its Dirichlet Laplacian. manifold and configure the integer lift of an Ochanine invariant The useful WKB method consists of constructing an asymptotic based on elliptic genus and unbound algebra related to the power series solution globally with respect to the Planck con- same boundary of the stant. This power series diverges and the asymptotic form three-dimensional mani- changes discontinuously when passing through turning points fold and the functor in a or caustics. This so-called Stokes phenomenon is a key to certain type of zone solve the above problem. with a commutative ring in order to consider the relationship between basic group, homologi- cal algebra and gauge theory more. ■Application of gauge theory to topology Ritsumeikan University Powering the Future 2 Ritsumeikan University College of Science and Engineering Department of Mathematical Sciences Research/Development Areas Research/Development Areas Research/Development Areas Research/Development Areas Number theory, network algorithms, and Amusing number theory Operator Algebras and Operator Theory Algebra centering on commutativering cryptosystems theory/algebraic geometry Professor / Hidenori ISHII Professor / Takaaki KAGAWA Professor / Hiroyuki OSAKA Professor / Yukihide TAKAYAMA Research within the number theory field undertaken at our I specialize in number theory, and recently in particular Functional analysis of the abstraction of mathematical models Dr Takayama’s main research interest is algebraic geometry in laboratory involves the overall aim of researching automorphic L classifying elliptic curves found in real quadratic
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