数理理論物理学ユニット （氷上 忍）

数理理論物理学ユニット

氷上 忍　教授

 

出版物


  E. Brezin and S. Hikami,
  Random Matrix Theory with an External Source,
  SpringerBriefs in Mathematical Physics 19, (2016), Springer Singapore. 

 

概要

物理現象には普遍的な振る舞いが見られます。磁性体での相転移現象では臨界指数と呼ばれる量が対称性や次元数で決まり、どのような原子から出来ているのかには依りません。

また金属・絶縁体転移も普遍的な現象であることが分かっています。このユニットではランダムな不純物散乱やポテンシャルがある無秩序系での普遍的現象を研究しています。

ブラウン運動でのランダムウオークは良く知られていますが、これを多体問題にしたランダム行列模型を研究して、さまざまな普遍現象に応用しています。量子ドットのエネルギー準位や弦理論・ゲージ理論にも応用出来ます。ＤＮＡやたんぱく質の分子配列はランダムな配列に見えますが、その配列には統計的な普遍的性がありランダム行列理論で説明出来るものがあります。生物系は複雑系ですが、それに数理理論物理学からランダム行列理論を使ってアプローチすることを目指しています。

今後のイベント

過去のイベント

Seminar:Khovanov Homology and Its Application to Low-Dimensional Topology

Dates & Venues:

(Day1) Tuesday, June 18, 2024 - 13:00 to 15:00
Venue: L4E01

(Day2) Wednesday, June 19, 2024 - 13:00 to 15:00
Venue: L4E48

(Day3) Thursday, June 20, 2024 - 13:00 to 15:00
Venue: L4E01

Speaker: Prof. Taketo Sano （RIKEN)
Abstract:

Knot homology theories revolutionized the study of knots and links, much like (simplicial or singular) homology theory revolutionized the study of topological spaces. One of the major knot homology theories, Khovanov homology, was introduced by M. Khovanov in 2000 as a "categorification of the Jones polynomial." One notable feature of Khovanov homology is its ability to detect the unknot, a feature not known to be possessed by the Jones polynomial. Recently, it has found notable applications in low-dimensional topology, including the detection of exotic surfaces in the 4-ball.
I will conduct a three-day seminar starting with the basics of Khovanov homology and progressing to my own research. The outline is as follows:
Day 1: Jones polynomial and its categorification.
Day 2: Numerical invariants from Khovanov homology and their applications.
Day 3: Recent developments of Khovanov homology and its applications to low-dimensional topology.

 

Seminar: Origin, evolution, and dynamics of the asteroid Ryugu ~Perspectives from the comprehensive geochemical approach~
 

Date: Friday, March 15, 2024 - 11:00 to 12:00
Location: Lab4 L4E01
Speaker:Katsura Kobayashi (Institute for Planetary Materials, Okayama University)

Abstract:

The asteroid Ryugu is a near-Earth asteroid classified as a C-type asteroid. C-type asteroids have been presumed to have a similar chemical composition to the so-called primordial carbonaceous chondrites that have fallen to Earth. In other words, they are considered to be "fossils" that retain information from the formation of planets in the early solar system, especially organic matter and water, without being exposed to a high-temperature environment after the birth of celestial bodies, melting, or even melting. Based on this scientific background, it was selected as a target for the Hayabusa2 project, an asteroid exploration mission in Japan, and as a result, in December 2021, samples collected from near the surface of Ryugu (total amount of 5.4 g) were successfully brought back to Earth.

The Institute for Planetary Materials, Okayama University, is a higher-level curation facility in charge of the initial analysis of recovered samples. Therefore, 16 particles (~55 mg) of the samples described by JAXA/ISAS, the primary curation facility, were transported to the institute for mineralogical description, elemental concentration, isotope analysis, and dating one particle at a time in our laboratory. In addition, solvent-soluble organic matter (SOM) and poorly soluble organic matter (IOM) in the particles were analyzed, and a variety of organic compounds including 23 kinds of amino acids were successfully detected.

From these basic data, the current asteroid Ryugu originated from an ice planet that existed in the outer solar system ~3 million years after the formation of the solar system (~4.565 Ga). In the interior of the ice planet, it is thought that the minerals observed in the recovered samples were formed by the alteration of the water quality between the fluid mainly water and inorganic minerals at a low temperature (~30°C) formed by the decay heat of the short-lived radiative element, such as 26Al. It is thought that various organic matter, including amino acids, were also formed by reactions mediated by this fluid. We believe that this icy planet was subsequently refrozen and became the current asteroid Ryugu by moving fragments into the solar system that were destroyed by some physical disturbance.

In this seminar, we would like to present the results of the initial analysis of the asteroid Ryugu and introduce our materials science approach used in the analysis.

 

Workshop: Knot theory, LMO invariants and related topics

Date: Mar. 9-11, 2024

Venue: OIST Lab.4, E48

Organized by Xiaobing Sheng (OIST), Masaaki Suzuki (Meiji Univ.), Shinobu Hikami (OIST)

Titles&Abstracts

Program:

 

10:00-10:30

10:45-11:15

11:30-12:00

13:30-14:15

14:30-15:00

15:15-15:45

9th (Sat)

Suzuki

Bao

Ishikawa

Nozaki

Kitano

Ozawa

10th (Sun)

Nozaki(10:00-10:45)

  Cha (11:00-11:45)

 

 

 

 

11th (Mon)

Kitayama

Sheng

Petrou

Cha

Sakasai

Morifuji

 

Talk:

  1. Yuanyuan Bao (Tohoku University): (1|1) Alexander polynomial, Reidemeister torsion and lens space
  2. Jae Choon Cha (POSTECH): Minicourse: “Topological = smooth” in dimension 4
  3. Katsumi Ishikawa (Kyoto Univesity): The trapezoidal conjecture for knots and links of braid index 3
  4. Teruaki Kitano (Soka University): Some applications of a twisted Alexander polynomial to a symmetric union presentation of a knot
  5. Takahiro Kitayama (University of Tokyo) : Blanchfield pairings and Gordian distance
  6. Takayuki Morifuji (Keio University): A volume presentation of a hyperbolic fibered knot
  7. Yuta Nozaki (Yokohama National University) : Mini course: On the LMO invariant of 3-manifolds
  8. Yuko Ozawa (Meiji University): Epimorphisms between genus two handlebody-knot groups
  9. Andreani Petrou (OIST): Factorisation of the Harer-Zagier transform of the HOMFLY-PT polynomial
  10. Takuya Sakasai (University of Tokyo) : Invariants of homologically fibered knots
  11. Xiaobing Sheng (OIST): On sequences of alternating links constructed from elements of Thompson’s group F
  12. Massaki Suzuki (Meiji University): Twisted Alexander polynomials of knots associated to the regular representations of finite groups

 

University of Tokyo and OIST Joint Symposium of Knot theory

Date: Sep. 11 (Monday), 2023
Venue: Graduate School of Mathematical Sciences, University of Tokyo.  Room123.
Schedule: 13:00-17:30, (each talk is 40min).
Participants: Yuanyuan Bao (Univ. Tokyo), Dror Bar-Natan (Toronto Univ.), Mai Katada (Univ. Tokyo), Andreani Petrou (OIST)
Contact: hikami@oist.jp

 

Titles & Abstracts

 

 

 

 

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)
Program
Speakers:
  • Laurent Baulieu (LPTHE)
  • Timothy Budd (Rudboud Univ.)
  • Severin Charbonnier (Geneve Univ.) (online)
  • Bertrand Duplantier (IPhT, U Paris Saclay)
  • Nina Holden (Courant Inst.)　(online)
  • Motoko Kato (Ryukyu Univ.)
  • Makoto Katori (Chuo Univ.)
  • Shota Komatsu (CERN)
  • Wenliang Li (Sun Yat Sen Univ.)
  • Eveliina Peltola (Aalto Univ.)
  • Kazuhiro Sakai (Meiji Gakuin)
  • Xiaobing Sheng (OIST)
  • Hirohiko Shimada (Tsuyama Nat. Col. Tech.)
  • Hidehiko Shimada (Yukawa Institute Kyoto)
  • Yiling Wang (IHES)
  • Noriko Yui (Queen’s Univ.)
Titles & Abstracts
Contributing talks and participation: TBA

Registration deadline is postponed. 　Please register from the webform.
 

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

miwako.tokuda@oist.jp

Silver workshop V I  : Complex Geometry and related topics

  • Date:  Aug. 7-9th , 2023
  • Venue:Lab.4, F01, OIST
  • Program
  • Organizers: N. Yui (Queen’s Univ.), K. Saito (RIMS, Kyoto) and S. Hikami(OIST)

This 6th workshop is a continuation of the previous workshop in a series. 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.

- Sponsorship: Kaken-hi and OIST(Mathematical and Theoretical Physics Unit).

  • Registration for participation: dead line on June 30, 2023. Webform

Please contact to organizers or conference secretary: Miwako Tokuda (OIST, RUA), miwako.tokuda@oist.jp

 

Mini workshop of singularities

  • Date: March 30 and 31, 2023
  • Venue: The University of Tokyo, Math. Department, Room 002 (Onsite only)
  • Titles and abstracts : PDF
  • 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).
  • Lecture notes/slides

 

Seminar

Title: Drone observation reveals a multilevel society of feral horses

  • Date: Tuesday, March 7, 2023
  • Time: 13:30-14:30
  • Venue: Lab4 F01
  • Speaker: Tamao Maeda (Wildlife Research Center, Kyoto University)
  • Abstract: PDF

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)