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 well-known 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 molecular-sequence 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) K-i. 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, Kei-ichi Watanabe, Shihoko Ishii
  • Sponsorship: Kaken-hi 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 Schramm-Loewner 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 Calabi-Yau 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 p-adic 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 Yat-Sen Univ) 
  • Severin Charbonnier (Max Planck Inst. Bonn)
Contributing talks and participation:

Application Deadline:

2023-04-02 23:45

Please contact to organizers or conference secretary: Miwako Tokuda (OIST, RUA),

miwako.tokuda@oist.jp

 

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: OIST-L4E01
  • Participants:

Noriko Yui (Queen’s University), Kyoji Saito (TSVP-OIST, 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(Aix-Marseille 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: 17:00-18:00
  • Zoom
  • Speaker: A. Maeda, and F. Nabeshima (University of Tokyo)
  • Abstract: PDF

Silver workshop 2022   :  “Complex geometry and related topics”

Hybrid of on-site & on-line (zoom) conference

  • Organizers: Noriko Yui (Queen’s University at Kingston), Kyoji Saito (RIMS), Shinobu Hikami (OIST)
  • Dates:  January 11-12, 2022
  • Venue: International House of Japan (IHJ), (Roppongi 5-11-16/Tokyo) https://www.i-house.or.jp/
  • Schedule
    11th January (room 404)

    9:00-10:00 George Elliott, zoom talk (19:00 EST 10th Toronto)

     “The classification of well-behaved simple amenable C*-algebras, and applications”

    10:00-11:00 Yasuyuki Kawahigashi, 

    "Tensor networks and operator algebras”

    11:00-12:00 Mutsuo Oka, 

    "Generalization of A'Campo-Varchenko formula for almost non-degenerate functions"

    12:00-13:30 Lunch (The Garden)

    13:30-14:30 Shinichi Tajima, 

    “Grothendieck residue mappings and holonomic D-modules”

     

    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 Calabi-Yau threefolds over Q”

    10:00-11:00 Shinobu Hikami, 

    “Modularity and links in the intersection theory of p-spin curves”

    11:00-12:00 Shihoko Ishii,

    “Ideals in positive characteristic and fractional ideals in characteristic 0“

    12:00-13:30 Lunch (The Garden) 

    13:30-14:30 Makiko Mase,

    Orlik’s conjecture and the Milnor lattice of isolated hypersurface singularities“

 

Events (2012-2021)