Mathematical and Theoretical Physics Unit (Shinobu Hikami)
Mathematical and Theoretical Physics Unit
Professor Shinobu Hikami
Book
E. Brezin and S. Hikami,
Random Matrix Theory with an External Source,
SpringerBriefs in Mathematical Physics 19, (2016), Springer Singapore.
Abstract
Universal behaviors can be observed in various physical phenomena. For instance, a magnet shows a phase transition with critical indices, which are determined by the symmetry and the space dimensions. They do not depend on the details of the materials. In our unit, we study the universal phenomena of the disordered systems which are typically described by random scatterings and random potentials. The random walk in Brown motion is one of the wellknown problems in this field. The aim of our study is to generalize these approaches through the random matrix model and to discuss the universal phenomena.
The random matrix model can be applied to low dimensional electronic system such as a quantum dot, and also to the string theory and gauge theory. The molecularsequence of DNA or protein seems randomly distributed, but some of these sequences can be explained by random matrix theory. The biological system is an extremely complex system. Our research project is an approach to the biological system from the mathematical and theoretical physics by the use of the random matrix theory.
Upcoming Events
Mini workshop of singularities
 Date: March 30 and 31, 2023
 Venue: The University of Tokyo, Math. Department, Room 002
 Program:
 March 30: (1) S. Yokura, (2) H.Hauser,(3) Ki. Yoshida (4) T. Okuma (5) M. Enokizono
 March 31 (1) K. Shibata (2) C. Chiu, (3) M.Tomari & T.Tomaru, (4) K.Sato (5) S.Hikami
(1) 9:30–10:30, (2) 11:00–12:00, (3) 13:30–14:30, (4) 15:00–16:00 (5) 16:30–17:30
 Organizers:
Toru Ohmoto, Hiraku Kawanoue, Keiichi Watanabe, Shihoko Ishii  Sponsorship: Kakenhi and OIST(Mathematical and Theoretical Physics Unit).
 Online Registration
OIST workshop 2023: New trends of conformal theory from probability to gravity
The study of conformal theory connects the theoretical physics and mathematics, which has been closely related to the representation theory of Lie group, algebraic geometry, topology and number theory.
Recently the random matrix models have been discussed for quantum chaos of the black hole entropy, through a universal spectral form factor. This probabilistic study of the random matrix model and random tensor model may reveal the cases of the central charge c greater than one. The rational CFT for central charge c is less than one, are well known as minimal models and as SchrammLoewner evolution in the probability theory. The gravity coupled to matter fields may be related to exotic random geometries.
In this workshop, we focus a new relation between theoretical physics and mathematics: gravity and probability by new theoretical methods, such as conformal bootstrap methods and the studies of the eigenvalues of CalabiYau manifolds etc. Algebraic geometric structures like Thomson group and Moonshine will be also included for the study of complicated exotic geometries, which are related to CFT. The number theory related to padic group and modular form, and higher dimensional knots are topics of this workshop.
Organizers: Nicolas Delporte, Reiko Toriumi, Shinobu Hikami (OIST)
Date: July 31 August 4, 2023
Venue: OIST lecture rooms
Fundings: OIST workshop and JSPS (Kakenhi)
Speakers:
 Nina Holden (Courant Inst.) (on line)
 Motoko Kato (Ryukyu Univ.)
 Noriko Yui, (Queen’s Univ)
 Hirohiko Shimada (Tsuyama College)
 Hidehiko Shimada(Yukawa Inst.Kyoto Univ.)
 Shota Komatsu (CERN)
 Xiaobing Sheng (Univ. Tokyo)
 Kazuhiro Sakai (Meiji Gakuin)
 Makoto Katori, (Chuo Univ.)
 Eveliina Peltola (Aalto)
 Timothy Budd(Rudboud Univ.)
 Luca Lionni (Heidelberg Univ)
 Wenliang Li ( Sun YatSen Univ)
 Severin Charbonnier (Max Planck Inst. Bonn)
Contributing talks and participation:
Application Deadline:
20230402 23:45
Please contact to organizers or conference secretary: Miwako Tokuda (OIST, RUA),
Past Events
Silver workshop V : Complex Geometry and related topics
This 5th workshop is a continuation of the previous workshop in a series. In the occasion of Prof. Kyoji Saito’s visting OIST as TSVP, we include the special topics of the representation theory and category theory on the third day. This workshop discuss the modularity and duality, geometric group, cohomological theory, singularity theory, and knot theory. All talks on the black board are expected. The online participation of Zoom will be possible by the registration in advance.
 Organizers: Noriko Yui, Kyoji Saito, Shinobu Hikami
 Date: 9 11th, November 2022
 Venue: OISTL4E01
 Participants:
Noriko Yui (Queen’s University), Kyoji Saito (TSVPOIST, RIMS), George Elliott(Toronto Univ.), Shihoko Ishii (The Univ. of Tokyo), Motoko Kato (Ryukyu Univ.), Shinichi Tajima (Niigata Univ.), Makiko Mase (Tokyo Metropolitan Univ.), Mutsuo Oka ( Tokyo Science Univ.), Yoshihisa Saito (Rikkyo Univ.), Andreani Petrou(OIST), Xiaobing Sheng (Univ.of Tokyo), Christine Vespa(AixMarseille Univ.), Liron Speyer (OIST), Martin Forsberg Conde(OIST),Todor Milanov (IPMU), Takahiro Saito (RIMS), Shinobu Hikami (OIST)
 Titles and Abstracts: PDF
Seminar:
Title: Superconductivity, magnetism and nematicity in thin films of Fe chalcogenides
 Date: Monday, June 13, 2022
 Time: 17:0018:00
 Zoom
 Speaker: A. Maeda, and F. Nabeshima (University of Tokyo)
 Abstract: PDF
Silver workshop 2022 : “Complex geometry and related topics”
Hybrid of onsite & online (zoom) conference
 Organizers: Noriko Yui (Queen’s University at Kingston), Kyoji Saito (RIMS), Shinobu Hikami (OIST)
 Dates: January 1112, 2022
 Venue: International House of Japan (IHJ), (Roppongi 51116/Tokyo) https://www.ihouse.or.jp/

Schedule
11th January (room 404)9:0010:00 George Elliott, zoom talk (19:00 EST 10th Toronto)
“The classification of wellbehaved simple amenable C*algebras, and applications”
10:0011:00 Yasuyuki Kawahigashi,
"Tensor networks and operator algebras”
11:0012:00 Mutsuo Oka,
"Generalization of A'CampoVarchenko formula for almost nondegenerate functions"
12:0013:30 Lunch (The Garden)
13:3014:30 Shinichi Tajima,
“Grothendieck residue mappings and holonomic Dmodules”
12th January (room 404 (morning)& room D(afternoon))
9:00 (JST)10:00 Noriko Yui, zoom talk (19:00 EST 11th Toronto),
“Siegel modularity of certain CalabiYau threefolds over Q”
10:0011:00 Shinobu Hikami,
“Modularity and links in the intersection theory of pspin curves”
11:0012:00 Shihoko Ishii,
“Ideals in positive characteristic and fractional ideals in characteristic 0“
12:0013:30 Lunch (The Garden)
13:3014:30 Makiko Mase,
Orlik’s conjecture and the Milnor lattice of isolated hypersurface singularities“