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
Silver Workshop : Complex geometry and related topics VII (Series final)
(List updated on February 16, 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
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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 |
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*Kyoji Saito |
*Sekiguchi |
lunch |
*Suwa |
*Sakasai |
*Motoko Kato |
*Aleshkin |
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12th |
*Noriko Yui |
*Andreani Petrou |
*Hikami |
lunch |
*Oka |
*Watanabe |
*Shihoko Ishii |
*Fujiwara |
Dinner |
13th |
*Takahiro Saito |
*Makiko Mase |
*Milanov |
*Tajima (12:30-13:20) |
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*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. Talkers 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.
Jiro Sekiguchi (Tokyo University of Agriculture and Technology)
Title: A family of del Pezzo surfaces of degree one and the reflection group W(H4)
Abstract: In this talk, we treat a family of surfaces of C3which is a deformation of simple singularity of type E8 related with the root system of type H4. We define F(x,y,z;τ)=t15+x5+5t26x+5t6x3+y(10t1t6x+5t1x3+t10)+5t21xy2+y3−z2,
where τ=(t1,t6,t10,t15). Then F(x,y,z;τ)=0 defines a surface S(t1,t6,t10,t15) in C3. The parameters t1,t6,t10,t15 are regarded as basic invariants of W(H4). Let C:y=φ(x),z=ψ(x) be a curve in C3, where
φ(x)=m1x2+a1x+b1,ψ(x)=n1x3+c1x2+d1x+e1
and m1,a1,b1,n1,c1,d1,e1 are constants depending on t1,t6,t10,t15. We discuss the problem of determining m1,a1,b1,n1,c1,d1,e1 so that C is contained in S(t1,t6,t10,t15) following the theory on Mordell-Weil lattices by T. Shioda.
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.
Takuya Sakasai (The University of Tokyo)
Title: On structures of groups of Kim-Manturov
Motoko Kato (Ryukyu University)
Title: On certain generalizations of Thompson’s group T
Abstract: Thompson’s groups F and T are finitely presented groups consisting of homeomorphisms of the unit interval and the circle, respectively. T is known as one of the first examples of finitely presented infinite simple groups. There are various generalizations of F and T, for example, the Higman-Thompson groups F_n and T_n. In this talk, we discuss certain generalizations of T. These groups, called ring groups, are generated by finitely many orientation preserving homeomorphisms of the circle and are a further generalization of T_n. These groups seem to have some properties similar to T_n, but have not been studied in detail. In this talk, we give a condition for ring groups to have finitely generated simple commutator subgroups. This is motivated by a study on Thompson’s group F and chain groups of homeomorphisms of the interval by Kim, Koberda and Lodha.
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.
Shinobu Hikami (OIST)
Title: The HOMFLY-PT Polynomial from Residues and Duality
Abstract: We consider the HOMFLY-PT polynomial with Harer-Zagier (HZ) transform in the character expansion. HZ yields a rational polynomial with the numerator described by determinants, which is expressed in the sum of the factorised multiplets. By the insertion of the parameter λ as λ= qm in this decomposition, a factorisation appears in a single variable q, similar to Molien series of the singularity theory. This is a joint work with Andreani Petrou.
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.
Shihoko Ishii (Unversity of Tokyo)
Title: Lifting of ideals in positive characteristic to those in characteristic 0
Abstract: In this talk, I will demonstrate how an appropriate lifting of an ideal serves as a bridge between the singularities in positive characteristic and those in characteristic zero. This method is effective for dimensions of three or less. As applications of this approach, we find that the set of log discrepancies in positive characteristic is contained within the set in characteristic zero. Additionally, the set of log canonical thresholds (lct) in positive characteristic is also contained within the set in characteristic zero.
Takahiro Saito
Title: Monodromic mixed Hodge modules and Hodge microsheaves on plumbings
Abstract: This talk is about an application of my previous talk at Silver workshop V in 2022. Mixed Hodge modules on complex manifolds are objects defined as a tuple of D-modules, perverse sheaves, Hodge and weight filtrations on them, for Hodge theory on constructible sheaves. In general, it is difficult to answer the questions like "What kind of objects exists?" and "What forms do they take?". In this talk, I will present a result that describes mixed Hodge modules under the assumption of being "monodromic" in terms of linear algebraic data. And I will explain that it leads a natural definition of the "Fourier-Laplace transform of monodromic mixed Hodge modules". On the other hand, the category of microsheaves on a plumbing plays an important role for a description of the Fukaya category in the study of mirror symmetry. As an application of the above result, I will introduce a "mixed Hodge structure" on microsheaves. Furthermore, I will discuss an observation that the weight on the Hodge-microlocal skyscrapers on the $A_n$-plumbing induces a certain grading called the Koszul grading of an algebra, which appears in the formulation of "Koszul duality" for the catgeory of microsheaves (or the Fukaya category).
This is a joint work with Tatsuki Kuwagaki (Kyoto University).
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.
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.
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)
Program:
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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) |
|
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|
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11th (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), 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),
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/
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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“