personal website
Academic interests
operator algebras, quantum groups, and noncommutative geometry.
Past and upcoming courses
- 2018 Autumn: Representation Theory (MAT4270 / MAT9270)
- 2019 Spring: Advanced Functional Analysis (MAT4450)
- 2019 Autumn: Representation Theory (MAT4270 / MAT9270)
- 2020 Spring: Topics in Operator Algebras (MAT9390)
- 2020 Autumn: Advanced Linear Analysis (MAT4410)
- 2021 Spring: Algebraic Topology I (MAT4530)
- 2021 Autumn: Representation Theory (MAT4270 / MAT9270)
- 2022 Spring: Quantum Computing (MAT3420)
- 2022 Autumn: Topology (MAT3500/MAT4500)
- 2023 Spring: Algebraic Topology I (MAT4530)
- 2024 Spring: Topics in Operator Algebras (MAT9390)
- 2024 Autumn: Linear Algebra (MAT1120)
- 2025 Spring: Groups, Rings and Fields (MAT2200)
Background
- 2011 PhD, the University of Tokyo
- 2011 Postdoc, Cardiff University
- 2011 Postdoc, University of Rome Tor Vergata
- 2012-2018 Assistant / Associate Professor, Ochanomizu University
Awards
- Professor Ingerid Dal og søster Ulrikke Greve Dals pris for humanistisk forskning (August 2025)
- Operator Algebra Prize (November 2024)
- MSJ Takebe Katahiro Prize, The Mathematical Society of Japan (September 2016)
- The Young Scientists’ Prize (Japanese Description), The Commendation for Science and Technology by the Minister of Education, Culture, Sports, Science and Technology (April 2018)
Tags:
Mathematics,
Operator algebras,
Quantum groups,
Noncommutative geometry,
Belgium
Publications
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Jaklitsch, David Alexander & Yamashita, Makoto
(2026).
The braided monoidal structure of tube algebra representations.
Theory and Applications of Categories.
45(49),
p. 2115–2152.
doi:
https:/tac.mta.ca/tac/volumes/45/49/45-49abs.html.
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We consider the tube algebra of a spherical semisimple multitensor category X, and construct a braided monoidal structure with twist for its representations. We further show that this category is braided tensor equivalent with the Drinfeld center of the ind-category of X, extending the well-known linear equivalence.
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Karen, Pavel; Armelao, Lidia; Butler, Ian S.; Tomišić, Vladislav & Yamashita, Makoto
(2025).
Toward a definition of valence as a quantity (IUPAC Technical Report).
Pure and Applied Chemistry.
ISSN 0033-4545.
97(2),
p. 149–187.
doi:
10.1515/pac-2023-0402.
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Valence has a rich history in chemistry, as a bonding concept, in terms of quantitative context, and as a
true quantity. In the latter, a survey preceding this project revealed differing perceptions of valence values
and helped formulate candidate definitions. This IUPAC task group evaluated nine quantities behind eight
alternative definitions on 39 chemical entities of 48 bonding formulas, each giving a set of meaningful values with
mutual relationships. Given the reflection principle of IUPAC normative work, 15 comparative examples with
high variation of these alternative valences for an element were selected, and chemistry articles in English
searched for valence-termed quantities of the compared compounds to imply the definition behind the stated
valence value, the frequency of such use, and the chemistry field. Summarized preferences for the alternative
definitions show two main areas of use. Organic and physical chemists count valence as a number of two-electron
bonds at the atom. Inorganic chemists working with semi-metallic and metallic elements use n-valent as an
adjective for oxidation state. The diverse yet infrequent use cannot be covered by a single definition of the valence
quantity. Clarity in articles that use valence as a quantity is essential and achievable by stating the intended
context.
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Proietti, Valerio & Yamashita, Makoto
(2024).
Homology and K-theory of dynamical systems IV. Further structural results on groupoid homology.
Ergodic Theory and Dynamical Systems.
ISSN 0143-3857.
45(1).
doi:
10.1017/etds.2024.37.
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We consider the homology theory of étale groupoids introduced by Crainic and Moerdijk [A homology theory for étale groupoids. J. Reine Angew. Math. 521 (2000), 25–46], with particular interest to groupoids arising from topological dynamical systems. We prove a Künneth formula for products of groupoids and a Poincaré-duality type result for principal groupoids whose orbits are copies of an Euclidean space. We conclude with a few example computations for systems associated to nilpotent groups such as self-similar actions, and we generalize previous homological calculations by Burke and Putnam for systems which are analogues of solenoids arising from algebraic numbers. For the latter systems, we prove the HK conjecture, even when the resulting groupoid is not ample.
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Proietti, Valerio & Yamashita, Makoto
(2024).
Homology and K-theory of dynamical systems III. Beyond stably disconnected Smale spaces.
Transactions of the American Mathematical Society.
ISSN 0002-9947.
378(3),
p. 2129–2155.
doi:
10.1090/tran/9353.
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We study homological invariants of étale groupoids arising from Smale spaces, continuing our previous work, but going beyond the stably disconnected case by incorporating resolutions in the space direction. We show that the homology groups defined by Putnam are isomorphic to the Crainic–Moerdijk groupoid homology with integer coefficients.
We also show that the K-groups of C*-algebras of stable and unstable equivalence relations have finite rank. For unstably disconnected Smale spaces, we provide a cohomological spectral sequence whose second page shows Putnam’s (stable) homology groups, and converges to the K-groups of the unstable C*-algebra.
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Brannan, Michael; Elzinga, Floris Eelke; Harris, Samuel J & Yamashita, Makoto
(2023).
Crossed Product Equivalence of Quantum Automorphism Groups of Finite Dimensional C*-Algebras.
International Mathematics Research Notices (IMRN).
ISSN 1073-7928.
2023(20),
p. 17749–17787.
doi:
10.1093/imrn/rnad060.
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Commer, Kenny De; Neshveyev, Sergiy; Tuset, Lars & Yamashita, Makoto
(2023).
Comparison of quantizations of symmetric spaces: cyclotomic Knizhnik-Zamolodchikov equations and Letzter-Kolb coideals.
Forum of Mathematics, Pi.
11.
doi:
10.1017/fmp.2023.11.
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We establish an equivalence between two approaches to quantization of irreducible symmetric spaces of compact type within the framework of quasi-coactions, one based on the Enriquez–Etingof cyclotomic Knizhnik–
Zamolodchikov (KZ) equations and the other on the Letzter–Kolb coideals. This equivalence can be upgraded to
that of ribbon braided quasi-coactions, and then the associated reflection operators (K-matrices) become a tangible
invariant of the quantization. As an application we obtain a Kohno–Drinfeld type theorem on type B braid group
representations defined by the monodromy of KZ-equations and by the Balagović–Kolb universal K-matrices. The
cases of Hermitian and non-Hermitian symmetric spaces are significantly different. In particular, in the latter case
a quasi-coaction is essentially uniq
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Proietti, Valerio & Yamashita, Makoto
(2023).
Homology and K-theory of dynamical systems II. Smale spaces with totally disconnected transversal.
Journal of Noncommutative Geometry.
ISSN 1661-6952.
17(3),
p. 957–998.
doi:
10.4171/JNCG/494.
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We apply our previous work on the relation between groupoid homology and K-theory to Smale spaces. More precisely, we consider the unstable equivalence relation of a Smale space with totally disconnected stable sets and prove that the associated spectral sequence shows Putnam's stable homology groups on the second sheet. Moreover, this homology is in fact isomorphic to the groupoid homology of the unstable equivalence relation.
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Yamashita, Makoto
(2023).
Deformation of algebras associated with group cocycles.
Journal of Noncommutative Geometry.
ISSN 1661-6952.
17(4),
p. 1145–1166.
doi:
10.4171/JNCG/522.
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We study deformation of algebras with coaction symmetry of reduced algebras of discrete groups, where the deformation parameter is givenby a continuous family of group 2-cocycles. When the group satisfies the Baum–Connes conjecture with coefficients, we obtain an isomorphism of K-groups of the deformed algebras. This extends both the θ-deformation of Rieffel on Tn-actions, and a recent result of Echterhoff, Lück, Phillips, and Walters on the K-groups on the twisted group algebras.
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Elzinga, Floris & Yamashita, Makoto
(2023).
Poisson–Lie group structures on semidirect products.
Journal of Noncommutative Geometry.
ISSN 1661-6952.
18(2),
p. 631–655.
doi:
10.4171/JNCG/538.
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We look at the Poisson structure on the total space of the dual bundle to the Lie algebroid arising from a matched pair of Lie groups. This dual bundle, with the natural semidirect product group structure, becomes a Poisson–Lie group as suggested by a recent work of Stachura. Moreover, when we start from the matched pairs given by the Iwasawa decomposition of simple Lie groups, we find that the associated Lie bialgebra is coboundary.
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Neumann, Hans Henrich & Yamashita, Makoto
(2022).
Lieb type convexity for positive operator monotone decreasing functions.
Linear and multilinear algebra.
ISSN 0308-1087.
doi:
10.1080/03081087.2022.2042476.
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We prove Lieb type convexity and concavity results for trace functionals associated with positive operator monotone (decreasing) functions and certain monotone concave functions, together with strictly positive linear maps of matrices. This gives a partial generalization of Hiai's recent work on trace functionals associated with power functions, by allowing positive operator monotone decreasing functions instead of power maps.Our proof is based on variational formula for trace functionals based on the Legendre transform, and a strengthened convexity of positive operator monotone decreasing functions in a previous work of Kirihata and the second named author. We also provide the generalization to the framework of unital tracial C -algebras based on Petz's work.
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Proietti, Valerio & Yamashita, Makoto
(2021).
Homology and K-theory of dynamical systems I. Torsion-free ample groupoids.
Ergodic Theory and Dynamical Systems.
ISSN 0143-3857.
doi:
10.1017/etds.2021.50.
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Given an ample groupoid, we construct a spectral sequence with groupoid homology with integer coefficients on the second sheet, converging to the K-groups of the (reduced) groupoid C∗-algebra, provided the groupoid has torsion-free stabilizers and satisfies a strong form of the Baum–Connes conjecture. The construction is based on the triangulated category approach to the Baum–Connes conjecture developed by Meyer and Nest. We also present a few applications to topological dynamics and discuss the HK conjecture of Matui.
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Kirihata, Megumi & Yamashita, Makoto
(2020).
Strengthened convexity of positive operator monotone decreasing functions.
Mathematica Scandinavica.
ISSN 0025-5521.
126(3),
p. 559–567.
doi:
10.7146/math.scand.a-120579.
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We prove a strengthened form of convexity for operator monotone decreasing positive functions defined on the positive real numbers. This extends Ando and Hiai's work to allow arbitrary positive maps instead of states (or the identity map), and functional calculus by operator monotone functions defined on the positive real numbers instead of the logarithmic function.
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Commer, Kenny De; Neshveyev, Sergey; Tuset, Lars & Yamashita, Makoto
(2019).
Ribbon braided module categories, quantum symmetric pairs and Knizhnik-Zamolodchikov equations.
Communications in Mathematical Physics.
ISSN 0010-3616.
367(3),
p. 717–769.
doi:
10.1007/s00220-019-03317-7.
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Let u be a compact semisimple Lie algebra, and σ be a Lie algebra involution of u. Let Repq(u) be the ribbon braided tensor C∗-category of admissible Uq(u)-representations for 0 < q < 1. We introduce three module C∗-categories over Repq(u) starting from the input data (u,σ). The first construction is based on the theory of 2-cyclotomic KZ-equations. The second construction uses the notion of quantum symmetric pair as developed by G. Letzter. The third construction uses a variation of Drinfeld twisting. In all three cases the module C∗-category is ribbon twist-braided in the sense of A. Brochier—this is essentially due to B. Enriquez in the first case, is proved by S. Kolb in the second case, and is closely related to work of J. Donin, P. Kulish, and A. Mudrov in the third case. We formulate a conjecture concerning equivalence of these ribbon twist-braided module C∗-categories, and confirm it in the rank one case.
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Chakraborty, Sayan & Yamashita, Makoto
(2019).
Tracing cyclic homology pairings under twisting of graded algebras.
Letters in Mathematical Physics.
ISSN 0377-9017.
109(7),
p. 1625–1664.
doi:
10.1007/s11005-018-01147-7.
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We give a description of cyclic cohomology and its pairing with K-groups for 2-cocycle deformation of algebras graded over discrete groups. The proof relies on a realization of monodromy for the Gauss–Manin connection on periodic cyclic cohomology in terms of the cup product action of group cohomology.
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Neshveyev, Sergey & Yamashita, Makoto
(2018).
A Few Remarks on the Tube Algebra of a Monoidal Category.
Proceedings of the Edinburgh Mathematical Society.
ISSN 0013-0915.
61(3),
p. 735–758.
doi:
10.1017/S0013091517000426.
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We prove two results on the tube algebras of rigid C*-tensor categories. The first is that the tube algebra of the representation category of a compact quantum group G is a full corner of the Drinfeld double of G. As an application, we obtain some information on the structure of the tube algebras of the Temperley–Lieb categories 𝒯ℒ(d) for d > 2. The second result is that the tube algebras of weakly Morita equivalent C*-tensor categories are strongly Morita equivalent. The corresponding linking algebra is described as the tube algebra of the 2-category defining the Morita context.
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Bhowmick, Jyotishman; Ghosh, Shamindra; Rakshit, Narayan & Yamashita, Makoto
(2018).
Tube representations and twisting of graded categories.
Theory and Applications of Categories.
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Commer, Kenny De & Yamashita, Makoto
(2015).
Tannaka–Kreĭn duality for compact quantum homogeneous spaces. II. Classification of quantum homogeneous spaces for quantum SU(2).
Journal für die Reine und Angewandte Mathematik.
ISSN 0075-4102.
2015(708),
p. 143–171.
doi:
10.1515/crelle-2013-0074.
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Commer, Kenny De & Yamashita, Makoto
(2013).
A construction of finite index C*-algebra inclusions from free actions of compact quantum groups.
Publications of the Research Institute for Mathematical Sciences.
ISSN 0034-5318.
49(4),
p. 709–735.
doi:
10.4171/PRIMS/117.
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Yamashita, Makoto
(2013).
Operator algebra of foliations with projectively invariant transverse measure.
Publications of the Research Institute for Mathematical Sciences.
ISSN 0034-5318.
49(4),
p. 679–708.
doi:
10.4171/PRIMS/116.
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View all works in NVA
Published
Aug. 29, 2018 4:07 PM
- Last modified
Oct. 14, 2025 1:56 PM
