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Seminar information archive
Seminar information archive ～04/26｜Today's seminar 04/27 | Future seminars 04/28～
thesis presentations
13:00-14:15 Room #126 (Graduate School of Math. Sci. Bldg.)
UEDA Kento (Graduate School of Mathematical Sciences University of Tokyo)
Error Distribution for One-Dimensional Stochastic Differential Equation Driven By Fractional Brownian motion
（非整数ブラウン運動で駆動される1次元確率微分方程式の誤差分布）
UEDA Kento (Graduate School of Mathematical Sciences University of Tokyo)
Error Distribution for One-Dimensional Stochastic Differential Equation Driven By Fractional Brownian motion
（非整数ブラウン運動で駆動される1次元確率微分方程式の誤差分布）
thesis presentations
14:45-16:00 Room #128 (Graduate School of Math. Sci. Bldg.)
HU XIN (Graduate School of Mathematical Sciences University of Tokyo)
On the hydrodynamic limit of the Boltzmann equation and its numerical computation
（ボルツマン方程式の流体力学極限とその数値計算について）
HU XIN (Graduate School of Mathematical Sciences University of Tokyo)
On the hydrodynamic limit of the Boltzmann equation and its numerical computation
（ボルツマン方程式の流体力学極限とその数値計算について）
2024/01/24
Classical Analysis
10:30-12:00 Room #122 (Graduate School of Math. Sci. Bldg.)
Gergő Nemes (Tokyo Metropolitan University)
On the Borel summability of formal solutions of certain higher-order linear ordinary differential equations (English)
Gergő Nemes (Tokyo Metropolitan University)
On the Borel summability of formal solutions of certain higher-order linear ordinary differential equations (English)
[ Abstract ]
We will consider a class of $n$th-order linear ordinary differential equations with a large parameter $u$. Analytic solutions of these equations can be described by (divergent) formal series in
descending powers of $u$. We shall demonstrate that, given mild conditions on the potential functions of the equation, the formal solutions are Borel summable with respect to the parameter $u$ in large, unbounded domains of the independent variable. We will establish that the formal series expansions serve as asymptotic expansions, uniform with respect to the independent variable, for the Borel re-summed exact solutions. Additionally, the exact solutions can be expressed using factorial series in the parameter, and these expansions converge in half-planes, uniformly with respect to the independent variable. To illustrate our theory, we apply it to an $n$th-order Airy-type equation.
Related preprint: https://arxiv.org/abs/2312.14449
We will consider a class of $n$th-order linear ordinary differential equations with a large parameter $u$. Analytic solutions of these equations can be described by (divergent) formal series in
descending powers of $u$. We shall demonstrate that, given mild conditions on the potential functions of the equation, the formal solutions are Borel summable with respect to the parameter $u$ in large, unbounded domains of the independent variable. We will establish that the formal series expansions serve as asymptotic expansions, uniform with respect to the independent variable, for the Borel re-summed exact solutions. Additionally, the exact solutions can be expressed using factorial series in the parameter, and these expansions converge in half-planes, uniformly with respect to the independent variable. To illustrate our theory, we apply it to an $n$th-order Airy-type equation.
Related preprint: https://arxiv.org/abs/2312.14449
Number Theory Seminar
17:00-18:00 Room #056 (Graduate School of Math. Sci. Bldg.)
Yong Suk Moon (BIMSA)
Purity for p-adic Galois representations (English)
Yong Suk Moon (BIMSA)
Purity for p-adic Galois representations (English)
[ Abstract ]
Given a smooth p-adic formal scheme, Tsuji proved a purity result for crystalline local systems on its generic fiber. In this talk, we will discuss a generalization for log-crystalline local systems on the generic fiber of a semistable p-adic formal scheme. This is based on a joint work with Du, Liu, and Shimizu.
Given a smooth p-adic formal scheme, Tsuji proved a purity result for crystalline local systems on its generic fiber. In this talk, we will discuss a generalization for log-crystalline local systems on the generic fiber of a semistable p-adic formal scheme. This is based on a joint work with Du, Liu, and Shimizu.
2024/01/23
Tuesday Seminar on Topology
17:00-18:00 Room #ハイブリッド開催/056 (Graduate School of Math. Sci. Bldg.)
Pre-registration required. See our seminar webpage.
Gefei Wang (The University of Tokyo)
On the rational cohomology of spin hyperelliptic mapping class groups (JAPANESE)
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
Pre-registration required. See our seminar webpage.
Gefei Wang (The University of Tokyo)
On the rational cohomology of spin hyperelliptic mapping class groups (JAPANESE)
[ Abstract ]
Let $G$ be the subgroup $S_{n−q} \times S_q$ of the $n$-th symmetric group $S_n$ for $n-q \ge q$. In this talk, we study the $G$-invariant part of the rational cohomology group of the pure braid group $P_n$. The invariant part $H^*(P_n)^G$ includes the rational cohomology of a spin hyperelliptic mapping class group of genus $g$ as a subalgebra when $n=2g+2$. Based on the study of Lehrer-Solomon, we prove that they are independent of n and q in degree $* \le q-1$. We also give a formula to calculate the dimension of $H^* (P_n)^G$ and calculate it in all degree for $q \le 3$.
[ Reference URL ]Let $G$ be the subgroup $S_{n−q} \times S_q$ of the $n$-th symmetric group $S_n$ for $n-q \ge q$. In this talk, we study the $G$-invariant part of the rational cohomology group of the pure braid group $P_n$. The invariant part $H^*(P_n)^G$ includes the rational cohomology of a spin hyperelliptic mapping class group of genus $g$ as a subalgebra when $n=2g+2$. Based on the study of Lehrer-Solomon, we prove that they are independent of n and q in degree $* \le q-1$. We also give a formula to calculate the dimension of $H^* (P_n)^G$ and calculate it in all degree for $q \le 3$.
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
FJ-LMI Seminar
13:30-14:40 Room #118 (Graduate School of Math. Sci. Bldg.)
Antoine DIEZ (京都大学, Kyoto University, ASHBi)
Particle systems with geometrical constraints and applications (英語)
https://fj-lmi.cnrs.fr/seminars/
Antoine DIEZ (京都大学, Kyoto University, ASHBi)
Particle systems with geometrical constraints and applications (英語)
[ Abstract ]
Since the pioneering work of Boltzmann, statistical physics has moti-vated the mathematical study or large systems of interacting particles, especially at the interface between stochastic analysis and PDE. More recently, there has been a surge of interest to consider applications to life sciences, where particles can be seen as convenient modeling entities to represent e.g. cell aggregates, bacterial swarms or animal societies. An important question in this context is the link between the microscopic agent-based description and the macroscopic continuum PDE description. Unlike physical systems which generally obey conservation laws, biological systems are rather subjects to constraints which are more geometrical in nature: volume constraints, shape or internal structure for instance. This poses a number of challenges on the modeling, analytical and numerical aspects. In this talk, I will first review earlier works on the study of particle systems with geometrical constraints. Then I will introduce a new framework, based on optimal transport theory, to model particles with arbitrary shapes and deformability properties. I will discuss potential applications in biology and compare this novel approach to other more classical methods.
[ Reference URL ]Since the pioneering work of Boltzmann, statistical physics has moti-vated the mathematical study or large systems of interacting particles, especially at the interface between stochastic analysis and PDE. More recently, there has been a surge of interest to consider applications to life sciences, where particles can be seen as convenient modeling entities to represent e.g. cell aggregates, bacterial swarms or animal societies. An important question in this context is the link between the microscopic agent-based description and the macroscopic continuum PDE description. Unlike physical systems which generally obey conservation laws, biological systems are rather subjects to constraints which are more geometrical in nature: volume constraints, shape or internal structure for instance. This poses a number of challenges on the modeling, analytical and numerical aspects. In this talk, I will first review earlier works on the study of particle systems with geometrical constraints. Then I will introduce a new framework, based on optimal transport theory, to model particles with arbitrary shapes and deformability properties. I will discuss potential applications in biology and compare this novel approach to other more classical methods.
https://fj-lmi.cnrs.fr/seminars/
2024/01/19
Colloquium
15:30-16:30 Room #大講義室(auditorium) (Graduate School of Math. Sci. Bldg.)
If you do not belong to Graduate School of Mathematical Sciences, the University of Tokyo, please apply from the form at [Reference URL].
Kenji Fukaya (Simons Center for Geometry and Physics)
Lagrangian correspondence and Floer theory (JAPANESE)
https://forms.gle/7T6ewXWtrVEKM9dY7
If you do not belong to Graduate School of Mathematical Sciences, the University of Tokyo, please apply from the form at [Reference URL].
Kenji Fukaya (Simons Center for Geometry and Physics)
Lagrangian correspondence and Floer theory (JAPANESE)
[ Abstract ]
It was proposed by Weinstein that the morphism of the `category’ of symplectic manifold should be a Lagrangian correspondence (a Lagrangian submanifold of the direct product).
Gromov-Witten invariant is not functorial for this functor.
However Lagrangian Floer theory is functorial.
I will explain present status of the study of this functoriality and a few of its applications.
[ Reference URL ]It was proposed by Weinstein that the morphism of the `category’ of symplectic manifold should be a Lagrangian correspondence (a Lagrangian submanifold of the direct product).
Gromov-Witten invariant is not functorial for this functor.
However Lagrangian Floer theory is functorial.
I will explain present status of the study of this functoriality and a few of its applications.
https://forms.gle/7T6ewXWtrVEKM9dY7
2024/01/16
Operator Algebra Seminars
16:45-18:15 Room #128 (Graduate School of Math. Sci. Bldg.)
Miho Mukohara (Univ. Tokyo)
Inclusions of simple C$^*$-algebras arising from isometrically shift absorbing actions
[ Reference URL ]
https://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm
Miho Mukohara (Univ. Tokyo)
Inclusions of simple C$^*$-algebras arising from isometrically shift absorbing actions
[ Reference URL ]
https://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm
Tuesday Seminar on Topology
17:00-18:00 Room #ハイブリッド開催/056 (Graduate School of Math. Sci. Bldg.)
Pre-registration required. See our seminar webpage.
Jin Miyazawa (The University of Tokyo)
A gauge theoretic invariant of embedded surfaces in 4-manifolds and exotic P2-knots (JAPANESE)
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
Pre-registration required. See our seminar webpage.
Jin Miyazawa (The University of Tokyo)
A gauge theoretic invariant of embedded surfaces in 4-manifolds and exotic P2-knots (JAPANESE)
[ Abstract ]
When two embeddings of surfaces on a 4-dimensional manifold are given, if they are topologically isotopic but not smoothly isotopic, we call them a pair of exotic surfaces. While there is a great deal of study of exotic surfaces in 4-manifolds, studies of closed exotic surfaces in S4 are limited. In particular, the existence of orientable exotic surfaces in S4 remains unknown to date. There are some examples of non-orientable exotic surfaces in S4, including the initial example given by Finashin-Kreck-Viro in 1988, but all such cases have genus greater than or equal to 5. The difficulty in detecting exotic surfaces in S4 is to prove that two embeddings of surfaces are not smoothly isotopic. All examples of exotic non-orientable surfaces in S4 have been detected by proving the 4-manifolds obtained by the double branched covers are exotic. If we attempt to apply this technique to low-genus non-orientable surfaces in S4, we have to discover exotic small 4-manifolds, which is known to be difficult. In this seminar, we construct an invariant for embedded surfaces in 4-manifolds using Real Seiberg-Witten theory. As an application, we give an infinite family of exotic embeddings into S4 for the real projective plane.
[ Reference URL ]When two embeddings of surfaces on a 4-dimensional manifold are given, if they are topologically isotopic but not smoothly isotopic, we call them a pair of exotic surfaces. While there is a great deal of study of exotic surfaces in 4-manifolds, studies of closed exotic surfaces in S4 are limited. In particular, the existence of orientable exotic surfaces in S4 remains unknown to date. There are some examples of non-orientable exotic surfaces in S4, including the initial example given by Finashin-Kreck-Viro in 1988, but all such cases have genus greater than or equal to 5. The difficulty in detecting exotic surfaces in S4 is to prove that two embeddings of surfaces are not smoothly isotopic. All examples of exotic non-orientable surfaces in S4 have been detected by proving the 4-manifolds obtained by the double branched covers are exotic. If we attempt to apply this technique to low-genus non-orientable surfaces in S4, we have to discover exotic small 4-manifolds, which is known to be difficult. In this seminar, we construct an invariant for embedded surfaces in 4-manifolds using Real Seiberg-Witten theory. As an application, we give an infinite family of exotic embeddings into S4 for the real projective plane.
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
2024/01/11
Information Mathematics Seminar
16:50-18:35 Room #128 (Graduate School of Math. Sci. Bldg.)
Yasunari Suzuki (MTT)
Introduction to quantum computation and quantum error correction (Japanese)
Yasunari Suzuki (MTT)
Introduction to quantum computation and quantum error correction (Japanese)
[ Abstract ]
To demonstrate quantum computational advantage, we need quantum error-correction technology to reduce effective error rates to a small value. In this talk, we introduce the basic theory of quantum computation and quantum error-correcting codes.
To demonstrate quantum computational advantage, we need quantum error-correction technology to reduce effective error rates to a small value. In this talk, we introduce the basic theory of quantum computation and quantum error-correcting codes.
Tokyo-Nagoya Algebra Seminar
10:30-12:00 Online
Ryo Fujita (RIMS)
量子Grothendieck環とその量子団代数構造について (Japanese)
[ Reference URL ]
http://www.math.nagoya-u.ac.jp/~aaron.chan/TNAseminar.html
Ryo Fujita (RIMS)
量子Grothendieck環とその量子団代数構造について (Japanese)
[ Reference URL ]
http://www.math.nagoya-u.ac.jp/~aaron.chan/TNAseminar.html
2024/01/10
Number Theory Seminar
17:00-18:00 Room #117 (Graduate School of Math. Sci. Bldg.)
Yuri Yatagawa (Tokyo Institute of Technology)
Characteristic cycle and partially logarithmic characteristic cycle of a rank 1 sheaf (Japanese)
Yuri Yatagawa (Tokyo Institute of Technology)
Characteristic cycle and partially logarithmic characteristic cycle of a rank 1 sheaf (Japanese)
2024/01/09
Numerical Analysis Seminar
16:30-18:00 Room #002 (Graduate School of Math. Sci. Bldg.)
Takashi Matsubara (Osaka University)
Deep learning that learns from, becomes part of, or replaces numerical methods for differential equations (Japanese)
[ Reference URL ]
https://sites.google.com/g.ecc.u-tokyo.ac.jp/utnas-bulletin-board/
Takashi Matsubara (Osaka University)
Deep learning that learns from, becomes part of, or replaces numerical methods for differential equations (Japanese)
[ Reference URL ]
https://sites.google.com/g.ecc.u-tokyo.ac.jp/utnas-bulletin-board/
Tuesday Seminar on Topology
17:00-18:00 Room #ハイブリッド開催/056 (Graduate School of Math. Sci. Bldg.)
Pre-registration required. See our seminar webpage.
Akihiro Takano (The University of Tokyo)
Stabilizer subgroups of Thompson's group F in Thompson knot theory (JAPANESE)
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
Pre-registration required. See our seminar webpage.
Akihiro Takano (The University of Tokyo)
Stabilizer subgroups of Thompson's group F in Thompson knot theory (JAPANESE)
[ Abstract ]
Thompson knot theory, introduced by Vaughan Jones, is a study of knot theory using Thompson's group F.
More specifically, he defined a method of constructing a knot from an element of F, and proved that any knot can be realized in his way. This fact is called Alexander’s theorem, which is an analogy of the braid group. In this talk, we consider Thompson knot theory in terms of a relation between subgroups of F and knots obtained from their elements. In particular, we focus on stabilizer subgroups of F with respect to the natural action on the unit interval. This talk is based on joint work with Yuya Kodama (Tokyo Metropolitan University).
[ Reference URL ]Thompson knot theory, introduced by Vaughan Jones, is a study of knot theory using Thompson's group F.
More specifically, he defined a method of constructing a knot from an element of F, and proved that any knot can be realized in his way. This fact is called Alexander’s theorem, which is an analogy of the braid group. In this talk, we consider Thompson knot theory in terms of a relation between subgroups of F and knots obtained from their elements. In particular, we focus on stabilizer subgroups of F with respect to the natural action on the unit interval. This talk is based on joint work with Yuya Kodama (Tokyo Metropolitan University).
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
2023/12/26
Tokyo-Nagoya Algebra Seminar
15:00-16:30 Room #ハイブリッド・002 (Graduate School of Math. Sci. Bldg.)
Ivan Losev (Yale University)
t-structures on the equivariant derived category of the Steinberg scheme (English)
http://www.math.nagoya-u.ac.jp/~aaron.chan/TNAseminar.html
Ivan Losev (Yale University)
t-structures on the equivariant derived category of the Steinberg scheme (English)
[ Abstract ]
The Steinberg scheme and the equivariant coherent sheaves on it play a very important role in Geometric Representation theory. In this talk we will discuss various t-structures on the equivariant derived category of the Steinberg of importance for Representation theory in positive characteristics. Based on arXiv:2302.05782.
[ Reference URL ]The Steinberg scheme and the equivariant coherent sheaves on it play a very important role in Geometric Representation theory. In this talk we will discuss various t-structures on the equivariant derived category of the Steinberg of importance for Representation theory in positive characteristics. Based on arXiv:2302.05782.
http://www.math.nagoya-u.ac.jp/~aaron.chan/TNAseminar.html
2023/12/21
Information Mathematics Seminar
16:50-18:35 Room #128 (Graduate School of Math. Sci. Bldg.)
Takashi Yamakawa (NTT)
Quantum Computing and Cryptography (Japanese)
Takashi Yamakawa (NTT)
Quantum Computing and Cryptography (Japanese)
[ Abstract ]
I explain several topics on quantum computing and cryptography including quantum money and verification of quantum computation based on cryptography.
I explain several topics on quantum computing and cryptography including quantum money and verification of quantum computation based on cryptography.
2023/12/20
Number Theory Seminar
17:00-18:00 Room #117 (Graduate School of Math. Sci. Bldg.)
Jinhyun Park (KAIST)
Accessing the big de Rham-Witt complex via algebraic cycles with a vanishing condition (English)
Jinhyun Park (KAIST)
Accessing the big de Rham-Witt complex via algebraic cycles with a vanishing condition (English)
[ Abstract ]
The big de Rham-Witt complexes of certain good rings over a field are known to admit certain motivic descriptions, namely via cycles with a modulus condition, e.g. additive higher Chow groups. This allowed us to define the trace maps on the de Rham-Witt forms in geometric terms, for instance.
Inspired by a lemma of Kato-Saito on the class field theory and Milnor K-groups, in this talk I would introduce a recent attempt in progress, where a version of “vanishing algebraic cycles” is defined over the formal power series k[[t]]. Using these cycles, I would sketch an alternative cycle-theoretic description of the big de Rham-Witt forms.
The big de Rham-Witt complexes of certain good rings over a field are known to admit certain motivic descriptions, namely via cycles with a modulus condition, e.g. additive higher Chow groups. This allowed us to define the trace maps on the de Rham-Witt forms in geometric terms, for instance.
Inspired by a lemma of Kato-Saito on the class field theory and Milnor K-groups, in this talk I would introduce a recent attempt in progress, where a version of “vanishing algebraic cycles” is defined over the formal power series k[[t]]. Using these cycles, I would sketch an alternative cycle-theoretic description of the big de Rham-Witt forms.
2023/12/19
Tuesday Seminar on Topology
17:00-18:30 Room #ハイブリッド開催/056 (Graduate School of Math. Sci. Bldg.)
Pre-registration required. See our seminar webpage.
Yasuyuki Kawahigashi (The University of Tokyo)
Topological quantum computing, tensor networks and operator algebras (JAPANESE)
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
Pre-registration required. See our seminar webpage.
Yasuyuki Kawahigashi (The University of Tokyo)
Topological quantum computing, tensor networks and operator algebras (JAPANESE)
[ Abstract ]
Modular tensor categories have caught much attention in connection to topological quantum computing based on anyons recently. Condensed matter physicists recently try to understand structures of modular tensor categories appearing in two-dimensional topological order using tensor networks. We present understanding of their tools in terms of operator algebras. For example, 4-tensors they use are exactly bi-unitary connections in the Jones theory of subfactors and their sequence of finite dimensional Hilbert spaces on which their gapped Hamiltonians act is given by the so-called higher relative commutants of a subfactor. No knowledge on operator algebras are assumed.
[ Reference URL ]Modular tensor categories have caught much attention in connection to topological quantum computing based on anyons recently. Condensed matter physicists recently try to understand structures of modular tensor categories appearing in two-dimensional topological order using tensor networks. We present understanding of their tools in terms of operator algebras. For example, 4-tensors they use are exactly bi-unitary connections in the Jones theory of subfactors and their sequence of finite dimensional Hilbert spaces on which their gapped Hamiltonians act is given by the so-called higher relative commutants of a subfactor. No knowledge on operator algebras are assumed.
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
2023/12/15
Algebraic Geometry Seminar
13:30-15:00 Room #118 (Graduate School of Math. Sci. Bldg.)
Shihoko Ishii (University of Tokyo)
On a pair of a smooth variety and a multi-ideal with a real exponent in positive characteristic (日本語)
Shihoko Ishii (University of Tokyo)
On a pair of a smooth variety and a multi-ideal with a real exponent in positive characteristic (日本語)
[ Abstract ]
In birational geometry, the behaviors of the invariants, mld (minimal log discrepancy) and lct (log canonical threshold), play important roles. These invariants are studied well in case the base field is characteristic zero, but not so in positive characteristic case. In this talk, I work on a pair consisting of smooth variety and a multi-ideal with a real exponent over an algebraically closed field of positive characteristic. We reduce some behaviors of the invariants for such pairs in positive characteristic case into characteristic zero.
In birational geometry, the behaviors of the invariants, mld (minimal log discrepancy) and lct (log canonical threshold), play important roles. These invariants are studied well in case the base field is characteristic zero, but not so in positive characteristic case. In this talk, I work on a pair consisting of smooth variety and a multi-ideal with a real exponent over an algebraically closed field of positive characteristic. We reduce some behaviors of the invariants for such pairs in positive characteristic case into characteristic zero.
Colloquium
15:30-16:30 Room #大講義室(auditorium) (Graduate School of Math. Sci. Bldg.)
If you do not belong to Graduate School of Mathematical Sciences, the University of Tokyo, please apply from the form at [Reference URL].
Mikiya Masuda (Osaka Central Advanced Mathematical Institute, Osaka Metropolitan University)
Hessenberg varieties and Stanley-Stembridge conjecture in graph theory (JAPANESE)
https://forms.gle/42wEF5c2pqsqrHqR7
If you do not belong to Graduate School of Mathematical Sciences, the University of Tokyo, please apply from the form at [Reference URL].
Mikiya Masuda (Osaka Central Advanced Mathematical Institute, Osaka Metropolitan University)
Hessenberg varieties and Stanley-Stembridge conjecture in graph theory (JAPANESE)
[ Abstract ]
Hessenberg varieties, a family of subvarieties of flag varieties, includes Springer fibers in geometric representation theory, Peterson varieties related to the quantum cohomology of flag varieties, and permutohedral varieties which are nonsingular toric varieties. Hessenberg varieties are also related to the QR algorithm for matrix eigenvalues and to hyperplane arrangements. Recently, Hessenberg varieties have attracted attention because of their connection to the Stanley-Stembridge conjecture on symmetric functions in graph theory. In this talk, I will explain how Hessenberg varieties are related to this conjecture.
[ Reference URL ]Hessenberg varieties, a family of subvarieties of flag varieties, includes Springer fibers in geometric representation theory, Peterson varieties related to the quantum cohomology of flag varieties, and permutohedral varieties which are nonsingular toric varieties. Hessenberg varieties are also related to the QR algorithm for matrix eigenvalues and to hyperplane arrangements. Recently, Hessenberg varieties have attracted attention because of their connection to the Stanley-Stembridge conjecture on symmetric functions in graph theory. In this talk, I will explain how Hessenberg varieties are related to this conjecture.
https://forms.gle/42wEF5c2pqsqrHqR7
Infinite Analysis Seminar Tokyo
13:00-14:30 Room #056 (Graduate School of Math. Sci. Bldg.)
Laszlo Feher (University of Szeged, Hungary)
Bi-Hamiltonian structures of integrable many-body models from Poisson reduction (ENGLISH)
Laszlo Feher (University of Szeged, Hungary)
Bi-Hamiltonian structures of integrable many-body models from Poisson reduction (ENGLISH)
[ Abstract ]
We review our results on bi-Hamiltonian structures of trigonometric spin Sutherland models
built on collective spin variables.
Our basic observation was that the cotangent bundle $T^*\mathrm{U}(n)$ and its holomorphic analogue $T^* \mathrm{GL}(n,{\mathbb C})$,
as well as $T^*\mathrm{GL}(n,{\mathbb C})_{\mathbb R}$, carry a natural quadratic Poisson bracket,
which is compatible with the canonical linear one. The quadratic bracket arises by change of variables and analytic continuation
from an associated Heisenberg double.
Then, the reductions of $T^*{\mathrm{U}}(n)$ and $T^*{\mathrm{GL}}(n,{\mathbb C})$ by the conjugation actions of the
corresponding groups lead to the real and holomorphic spin Sutherland models, respectively, equipped
with a bi-Hamiltonian structure. The reduction of $T^*{\mathrm{GL}}(n,{\mathbb C})_{\mathbb R}$ by the group $\mathrm{U}(n) \times \mathrm{U}(n)$ gives
a generalized Sutherland model coupled to two ${\mathfrak u}(n)^*$-valued spins.
We also show that
a bi-Hamiltonian structure on the associative algebra ${\mathfrak{gl}}(n,{\mathbb R})$ that appeared in the context
of Toda models can be interpreted as the quotient of compatible Poisson brackets on $T^*{\mathrm{GL}}(n,{\mathbb R})$.
Before our work, all these reductions were studied using the canonical Poisson structures of the cotangent bundles,
without realizing the bi-Hamiltonian aspect.
Finally, if time permits, the degenerate integrability of some of the reduced systems
will be explained as well.
[1] L. Feher, Reduction of a bi-Hamiltonian hierarchy on $T^*\mathrm{U}(n)$
to spin Ruijsenaars--Sutherland models, Lett. Math. Phys. 110, 1057-1079 (2020).
[2] L. Feher, Bi-Hamiltonian structure of spin Sutherland models: the holomorphic case, Ann. Henri Poincar\'e 22, 4063-4085 (2021).
[3] L. Feher, Bi-Hamiltonian structure of Sutherland models coupled to two $\mathfrak{u}(n)^*$-valued spins from Poisson reduction,
Nonlinearity 35, 2971-3003 (2022).
[4] L. Feher and B. Juhasz,
A note on quadratic Poisson brackets on $\mathfrak{gl}(n,\mathbb{R})$ related to Toda lattices,
Lett. Math. Phys. 112:45 (2022).
[5] L. Feher,
Notes on the degenerate integrability of reduced systems obtained from the master systems of free motion on cotangent bundles of
compact Lie groups, arXiv:2309.16245
We review our results on bi-Hamiltonian structures of trigonometric spin Sutherland models
built on collective spin variables.
Our basic observation was that the cotangent bundle $T^*\mathrm{U}(n)$ and its holomorphic analogue $T^* \mathrm{GL}(n,{\mathbb C})$,
as well as $T^*\mathrm{GL}(n,{\mathbb C})_{\mathbb R}$, carry a natural quadratic Poisson bracket,
which is compatible with the canonical linear one. The quadratic bracket arises by change of variables and analytic continuation
from an associated Heisenberg double.
Then, the reductions of $T^*{\mathrm{U}}(n)$ and $T^*{\mathrm{GL}}(n,{\mathbb C})$ by the conjugation actions of the
corresponding groups lead to the real and holomorphic spin Sutherland models, respectively, equipped
with a bi-Hamiltonian structure. The reduction of $T^*{\mathrm{GL}}(n,{\mathbb C})_{\mathbb R}$ by the group $\mathrm{U}(n) \times \mathrm{U}(n)$ gives
a generalized Sutherland model coupled to two ${\mathfrak u}(n)^*$-valued spins.
We also show that
a bi-Hamiltonian structure on the associative algebra ${\mathfrak{gl}}(n,{\mathbb R})$ that appeared in the context
of Toda models can be interpreted as the quotient of compatible Poisson brackets on $T^*{\mathrm{GL}}(n,{\mathbb R})$.
Before our work, all these reductions were studied using the canonical Poisson structures of the cotangent bundles,
without realizing the bi-Hamiltonian aspect.
Finally, if time permits, the degenerate integrability of some of the reduced systems
will be explained as well.
[1] L. Feher, Reduction of a bi-Hamiltonian hierarchy on $T^*\mathrm{U}(n)$
to spin Ruijsenaars--Sutherland models, Lett. Math. Phys. 110, 1057-1079 (2020).
[2] L. Feher, Bi-Hamiltonian structure of spin Sutherland models: the holomorphic case, Ann. Henri Poincar\'e 22, 4063-4085 (2021).
[3] L. Feher, Bi-Hamiltonian structure of Sutherland models coupled to two $\mathfrak{u}(n)^*$-valued spins from Poisson reduction,
Nonlinearity 35, 2971-3003 (2022).
[4] L. Feher and B. Juhasz,
A note on quadratic Poisson brackets on $\mathfrak{gl}(n,\mathbb{R})$ related to Toda lattices,
Lett. Math. Phys. 112:45 (2022).
[5] L. Feher,
Notes on the degenerate integrability of reduced systems obtained from the master systems of free motion on cotangent bundles of
compact Lie groups, arXiv:2309.16245
2023/12/14
Tuesday Seminar on Topology
17:00-18:30 Room #ハイブリッド開催/056 (Graduate School of Math. Sci. Bldg.)
Pre-registration required. See our seminar webpage.
Mikiya Masuda (Osaka City University)
Torus orbit closures in the flag variety (JAPANESE)
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
Pre-registration required. See our seminar webpage.
Mikiya Masuda (Osaka City University)
Torus orbit closures in the flag variety (JAPANESE)
[ Abstract ]
The study of torus orbit closures in the flag variety was initiated by Gelfand-Serganova and Klyachko in 1980’s but has not been studied much since then. Recently, I have studied its geometry and topology jointly with Eunjeong Lee, Seonjeong Park, Jongbaek Song in connection with combinatorics of polytopes, Coxeter matroids, and polygonal triangulations. In this talk I will report on the development of this subject.
[ Reference URL ]The study of torus orbit closures in the flag variety was initiated by Gelfand-Serganova and Klyachko in 1980’s but has not been studied much since then. Recently, I have studied its geometry and topology jointly with Eunjeong Lee, Seonjeong Park, Jongbaek Song in connection with combinatorics of polytopes, Coxeter matroids, and polygonal triangulations. In this talk I will report on the development of this subject.
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
Information Mathematics Seminar
16:50-18:35 Room #128 (Graduate School of Math. Sci. Bldg.)
Junichi Tomida (NTT)
Functional encryption and attribute-based encryption (Japanese)
Junichi Tomida (NTT)
Functional encryption and attribute-based encryption (Japanese)
[ Abstract ]
I will explain the basics and the recent progress of functional encryption and attribute-based encryption.
I will explain the basics and the recent progress of functional encryption and attribute-based encryption.
Tokyo-Nagoya Algebra Seminar
10:30-12:00 Online
Xiaofa Chen (University of Science and Technology of China)
On exact dg categories (English)
http://www.math.nagoya-u.ac.jp/~aaron.chan/TNAseminar.html
Xiaofa Chen (University of Science and Technology of China)
On exact dg categories (English)
[ Abstract ]
In this talk, I will give an introduction to exact dg categories and then explore their application to various correspondences in representation theory. We will generalize the Auslander–Iyama correspondence, the Iyama–Solberg correspondence, and a correspondence considered in a paper by Iyama in 2005 to the setting of exact dg categories. The slogan is that solving correspondence-type problems becomes easier using dg categories, and interesting phenomena emerge when the dg category is concentrated in degree zero or is abelian.
[ Reference URL ]In this talk, I will give an introduction to exact dg categories and then explore their application to various correspondences in representation theory. We will generalize the Auslander–Iyama correspondence, the Iyama–Solberg correspondence, and a correspondence considered in a paper by Iyama in 2005 to the setting of exact dg categories. The slogan is that solving correspondence-type problems becomes easier using dg categories, and interesting phenomena emerge when the dg category is concentrated in degree zero or is abelian.
http://www.math.nagoya-u.ac.jp/~aaron.chan/TNAseminar.html
2023/12/12
Tuesday Seminar on Topology
17:00-18:30 Room #ハイブリッド開催/056 (Graduate School of Math. Sci. Bldg.)
Pre-registration required. See our seminar webpage.
Stavros Garoufalidis (Southern University of Science and Technology)
Multivariable knot polynomials from braided Hopf algebras with automorphisms (ENGLISH)
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
Pre-registration required. See our seminar webpage.
Stavros Garoufalidis (Southern University of Science and Technology)
Multivariable knot polynomials from braided Hopf algebras with automorphisms (ENGLISH)
[ Abstract ]
We will discuss a unified approach to define multivariable polynomial invariants of knots that include the colored Jones polynomials, the ADO polynomials and the invariants defined using the theory of quantum groups. Our construction uses braided Hopf algebras with automorphisms. We will give examples of 2-variable invariants, and discuss their structural properties. Joint work with Rinat Kashaev.
[ Reference URL ]We will discuss a unified approach to define multivariable polynomial invariants of knots that include the colored Jones polynomials, the ADO polynomials and the invariants defined using the theory of quantum groups. Our construction uses braided Hopf algebras with automorphisms. We will give examples of 2-variable invariants, and discuss their structural properties. Joint work with Rinat Kashaev.
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
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