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

Silver Workshop : Complex geometry and related topics VII (Series final)

(List updated on January 14, 2025)

Organizer: N. Yui (Queen’s Univ.), K. Saito (RIMS, Kyoto), S. Hikami (OIST)
Local organizer: N. Kawazumi (Univ. Tokyo)
Support: OIST funding
Date: March 11-13, 2025
Venue: Room123, The University of Tokyo, Math. Department.

Silver Workshop VII (2025, March) Tentative Program

	9:30-10:20	10:30-11:20	11:30-12:20	12:20-14:00	14:00-14:50	15:00-15:50	16:00-16:50	17:00-17:50	18:00-20:00
^11th		*Kyoji Saito	*Sekiguchi	lunch	*Suwa	*Sakasai	*Motoko Kato	*Aleshkin
^12th	*Noriko Yui	*Andreani Petrou	*Hikami	lunch	*Oka	*Watanabe	*Shihoko Ishii	*Fujiwara	Dinner
13^th	*Takahiro Saito	*Makiko Mase	*Milanov	*Tajima (12:30-13:20)

*Confirmed talker

Conference dinner: March12, 2025 18:00-20:00
Organized by S.Ishii, M.Oka , K.Watanabe
Venue: Lever Son Verre (Komaba Campus)
Registration : Attendants for this dinner is required for registration. Dead line on March 1, 2025.
Talkers of Silver workshop VII are invited to this dinner with free charge. Takers are also required for registration of dinner.

Title and abstract :

Kyoji Saito (RIMS Kyoto University)
Title: Semi-infinite Hodge structure for hyperbolic root systems
Abstract: We construct semi-infinite Hodge structure associated with hyperbolic root systems of rank 2. As its consequences, we determine
(1) its associated flat structure (the Frobenius manifold structure) and
(2) the period map associated with the primitive form, both defined on the extended orbit space of the hyperbolic Weyl group action on a tube domain.

Mutsuo Oka (Tokyo University of Science)
Title:Almost non-degenerate functions and some applications
Abstract: We first introduce a class of functions "Almost Newton non-degenerate functions" which include Newton non-degenerate functions but it contains much wider class of functions.
We give a generalization of Varchenko formula for the zeta functions and then we present two applications.

Takuya Sakasai (The University of Tokyo)
Title: On structures of groups of Kim-Manturov

Makiko Mase (Tokyo Metropolitan University）
Title: On K3 surfaces admitting finite symplectic automorphisms
Abstract: We consider an algebraic K3 surface X admitting a finite automorphism group G that symplectically acts on X. It is known that the quotient space X/G contains at most simple singularities, and is birational to a K3 surface Y. Denote by L the lattice generated by all the classes of the irreducible components of the exceptional divisor in Y obtained by resolving the singularities in X/G. Despite the fact that the lattice L, which is a disjoint union of lattices of type ADE, is a sublattice of the K3 lattice, the embedding is not necessarily primitive. We post a problem to determine whether or not there exists a unique primitive sublattice of the K3 lattice that contains the lattice L. If the group G is abelian, then, V.V.Nikulin gives an affirmative answer to the problem as well as presenting the explicit primitive sublattice for each group. In case the group G is simple, U.Whitcher investigates the problem and gives the answers.
In our study, we analyse the problem in all the remaining cases. In the talk, we discuss how to attack the problem, and show how much we have sorted it out.
This is based on an on-going joint work with Kenji Hashimoto.

Todor Milanov (IPMU, University of Tokyo)
Title: Dubrovin conjecture and the second structure connection
Abstract: My talk will be based on my recent paper with John Alexander Cruz Morales. The theory of Frobenius manifolds was preceded by Saito's theory of flat structures in singularity theory. In particular,
many constructions in singularity theory are straightforward to import in the theory of Frobenius manifolds too. In my talk, I would like first to explain how one can introduce the ingredients of twisted
Picard--Lefschetz theory for an arbitrary semi-simple Frobenius manifold. Our main result with Alex is a reformulation of the so-called refined Dubrovin conjecture in terms of the monodromy data for the
second structure connection of quantum cohomology.

Tatsuo Suwa (Hokkaido University)
Title:Localized intersection product for maps and applications
Abstract: In his celebrated book, W. Fulton defines intersection products, in the algebraic category, using normal cones. We define the notions in combinatorial topology. In particular, the localized intersection product corresponds to the cup product in relative cohomology via the Alexander duality. This may be extended to the localized intersection product for maps. Combined with the relative Čech-de Rham cohomology, it is effectively used in the residue theory of vector bundles and coherent sheaves. As an application, we have the functoriality of Baum-Bott residues of singular holomorphic foliations under certain conditions, which yields an answer to an existing problem.
This includes a joint work with M. Corrêa.
References:
[1] W. Fulton, Intersection Theory, Springer, 1984.
[2] T. Suwa, Complex Analytic Geometry - From the Localization Viewpoint,
World Scientific, 2024.
[3] M. Corrêa and T. Suwa, On functoriality of Baum-Bott residues, in preparation.

Andreani Petrou (OIST)
Title: Knots, links and Harer-Zagier factorisability
Abstract: The focus of this talk will be the HOMFLY-PT polynomial and its Harer-Zagier (HZ) transform, a discrete Laplace transform, which maps it into a rational function. For some special families of knots and links, generated by full twists and Jucys–Murphy braids, the latter has a simple factorised form and hence their HOMFLY-PT polynomial is fully encoded in two sets of integers, corresponding to the numerator and denominator exponents. These exponents turn out to be related to the Khovanov homology and its Euler characteristics. We conjecture that the HZ factorisability is in 1-1 correspondence with a relation between the HOMFLY-PT and Kauffman polynomials, which is proven in some specific cases. The latter is equivalent to the vanishing of the two-crosscap BPS invariants of topological strings.

Shinichi Tajima (Niigata University)
Title: Holonomic D-modules associated to a hypersurface with non-isolated singularities
Abstract: We consider a method for analyzing holonomic D-modules associated to a hypersurface with non-isolated singularities. We start by recalling some basics on solution sheaves to holonomic D-modules and b-functions. Then, we give a method for computing local cohomology solutions to holonomic D-modules associated to roots of b-functions. The key idea is the use of the concept of Noetherian differential operators for local cohomology classes. We study, as an application of our approach, Whitney equisingular deformations of isolated hypersurface singularity. We examine two typical cases, (1) semi-quasi homogeneous singularity and (2) Newton non-degenerate singularity. We show, by using examples, a method to determine the structure of holonomic D-modules associated to the deformations. We consider, as another application, Kashiwara operator by looking at s-parametric annihilators.
Reference:
J. Alvarez Montaner and F. Planas Vilanova, Divisors of expected Jacobian type, Math. Scand. 127 (2021), 161-184.

Shinobu Hikami (OIST)
Title: Decomposition of Harer-Zagier (Laplace) transform for HOMFLY-PT polynomial
Abstract: We show that the Harer-Zagier transform (HZ) of HOMFLY-PT polynomial is decomposed into the sum of factorised forms. The character expansion for HOMFLY-PT polynomial is well suited for HZ. We decompose HZ of character expansion into the sum of factorised forms, similar to Plucker decomposition of KP τ- function. By putting the parameter λ in HZ, as λ= \(q^m\) , a new knot invariants polynomial is obtained, which reduces to a factorised form of HZ in one variable q. This polynomial is similar to Molien series of the singularity theory. The knot invariant polynomial is known to be a generating function of BPS invariant. We remark that Schwinger effect in topological strings appears in the knot invariants, notably for factorised HZ family of knots (2-crosscap invariants are zero; torus knot family and 1-crosscap invariant is -1; figure eight family), which are related to the complete screening of the spin and charge. This is a joint work with Andreani Petrou.

Past Events

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
9^th(Sat)	Suzuki	Bao	Ishikawa	Nozaki	Kitano	Ozawa
10^th(Sun)	Nozaki(10:00-10:45)	Cha (11:00-11:45)
11^th(Mon)	Kitayama	Sheng	Petrou	Cha	Sakasai	Morifuji

Talk:

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

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)
Yilin Wang (IHES)
Noriko Yui (Queen’s Univ.)

Titles & Abstracts

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 / Zoom
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“

Mathematical and Theoretical Physics Unit (Shinobu Hikami)