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Seminar information archive
Seminar information archive ～12/08｜Today's seminar 12/09 | Future seminars 12/10～
Applied Analysis
16:00-17:00 Online
Xingzhi Bian (Shanghai University)
A brief introduction to a class of new phase field models (English)
https://forms.gle/esc7Y6KGASwbFro97
Xingzhi Bian (Shanghai University)
A brief introduction to a class of new phase field models (English)
[ Abstract ]
Existence of weak solutions for a type of new phase field models, which are the system consisting of a degenerate parabolic equation of order parameter coupled to a linear elasticity sub-system. The models are applied to describe the phase transitions in elastically deformable solids.
[ Reference URL ]Existence of weak solutions for a type of new phase field models, which are the system consisting of a degenerate parabolic equation of order parameter coupled to a linear elasticity sub-system. The models are applied to describe the phase transitions in elastically deformable solids.
https://forms.gle/esc7Y6KGASwbFro97
2022/06/29
Tokyo-Nagoya Algebra Seminar
10:30-12:00 Online
Please see the reference URL for details on the online seminar.
Nicholas Williams (The University of Tokyo)
Cyclic polytopes and higher Auslander--Reiten theory 2 (English)
https://www.math.nagoya-u.ac.jp/~aaron.chan/TNAseminar.html
Please see the reference URL for details on the online seminar.
Nicholas Williams (The University of Tokyo)
Cyclic polytopes and higher Auslander--Reiten theory 2 (English)
[ Abstract ]
This continues part 1. In the second talk, we focus on higher Auslander--Reiten theory. We survey the basic setting of this theory, starting with d-cluster-tilting subcategories of module categories. We then move on to d-cluster-tilting subcategories of derived categories in the case of d-representation-finite d-hereditary algebras. We explain how one can construct (d + 2)-angulated cluster categories for such algebras, generalising classical cluster categories. We finally consider the d-almost positive category, which is the higher generalisation of the category of two-term complexes. Throughout, we illustrate the results using the higher Auslander algebras of type A, and explain how the different categories can be interpreted combinatorially for these algebras.
[ Reference URL ]This continues part 1. In the second talk, we focus on higher Auslander--Reiten theory. We survey the basic setting of this theory, starting with d-cluster-tilting subcategories of module categories. We then move on to d-cluster-tilting subcategories of derived categories in the case of d-representation-finite d-hereditary algebras. We explain how one can construct (d + 2)-angulated cluster categories for such algebras, generalising classical cluster categories. We finally consider the d-almost positive category, which is the higher generalisation of the category of two-term complexes. Throughout, we illustrate the results using the higher Auslander algebras of type A, and explain how the different categories can be interpreted combinatorially for these algebras.
https://www.math.nagoya-u.ac.jp/~aaron.chan/TNAseminar.html
2022/06/28
Tuesday Seminar of Analysis
16:00-17:30 Room #126 (Graduate School of Math. Sci. Bldg.)
ISHIDA Atsuhide (Tokyo University of Science)
Mourre inequality for non-local Schödinger operators (Japanese)
https://forms.gle/sBSeNH9AYFNypNBk9
ISHIDA Atsuhide (Tokyo University of Science)
Mourre inequality for non-local Schödinger operators (Japanese)
[ Abstract ]
We consider the Mourre inequality for the following self-adjoint operator $H=\Psi(-\Delta/2)+V$ acting on $L^2(\mathbb{R}^d)$, where $\Psi: [0,\infty)\rightarrow\mathbb{R}$ is an increasing function, $\Delta$ is Laplacian and $V: \mathbb{R}^d\rightarrow\mathbb{R}$ is an interaction potential. Mourre inequality immediately yields the discreteness and finite multiplicity of the eigenvalues. Moreover, Mourre inequality has the application to the absence of the singular continuous spectrum by combining the limiting absorption principle and, in addition, Mourre inequality is also used for proof of the minimal velocity estimate that plays an important role in the scattering theory. In this talk, we report that Mourre inequality holds under the general $\Psi$ and $V$ by choosing the conjugate operator $A=(p\cdot x+x\cdot p)/2$ with $p=-\sqrt{-1}\nabla$, and that the discreteness and finite multiplicity of the eigenvalues hold. This talk is a joint work with J. Lőrinczi (Hungarian Academy of Sciences) and I. Sasaki (Shinshu University).
[ Reference URL ]We consider the Mourre inequality for the following self-adjoint operator $H=\Psi(-\Delta/2)+V$ acting on $L^2(\mathbb{R}^d)$, where $\Psi: [0,\infty)\rightarrow\mathbb{R}$ is an increasing function, $\Delta$ is Laplacian and $V: \mathbb{R}^d\rightarrow\mathbb{R}$ is an interaction potential. Mourre inequality immediately yields the discreteness and finite multiplicity of the eigenvalues. Moreover, Mourre inequality has the application to the absence of the singular continuous spectrum by combining the limiting absorption principle and, in addition, Mourre inequality is also used for proof of the minimal velocity estimate that plays an important role in the scattering theory. In this talk, we report that Mourre inequality holds under the general $\Psi$ and $V$ by choosing the conjugate operator $A=(p\cdot x+x\cdot p)/2$ with $p=-\sqrt{-1}\nabla$, and that the discreteness and finite multiplicity of the eigenvalues hold. This talk is a joint work with J. Lőrinczi (Hungarian Academy of Sciences) and I. Sasaki (Shinshu University).
https://forms.gle/sBSeNH9AYFNypNBk9
Lie Groups and Representation Theory
17:00-18:00 Room #online (Graduate School of Math. Sci. Bldg.)
Ryosuke Nakahama (Kyushu University)
Computation of weighted Bergman inner products on bounded symmetric domains and Plancherel-type formulas for $(Sp(2r,\mathbb{R}),Sp(r,\mathbb{R})\times Sp(r,\mathbb{R}))$ (Japanese)
Ryosuke Nakahama (Kyushu University)
Computation of weighted Bergman inner products on bounded symmetric domains and Plancherel-type formulas for $(Sp(2r,\mathbb{R}),Sp(r,\mathbb{R})\times Sp(r,\mathbb{R}))$ (Japanese)
[ Abstract ]
Let $(G,G_1)=(G,(G^\sigma)_0)$ be a symmetric pair of holomorphic type, and we consider a pair of Hermitian symmetric spaces $D_1=G_1/K_1\subset D=G/K$, realized as bounded symmetric domains in complex vector spaces $\mathfrak{p}^+_1:=(\mathfrak{p}^+)^\sigma\subset\mathfrak{p}^+$ respectively. Then the universal covering group $\widetilde{G}$ of $G$ acts unitarily on the weighted Bergman space $\mathcal{H}_\lambda(D)\subset\mathcal{O}(D)=\mathcal{O}_\lambda(D)$ on $D$ for sufficiently large $\lambda$. Its restriction to the subgroup $\widetilde{G}_1$ decomposes discretely and multiplicity-freely, and its branching law is given explicitly by Hua--Kostant--Schmid--Kobayashi's formula in terms of the $\widetilde{K}_1$-decomposition of the space $\mathcal{P}(\mathfrak{p}^+_2)$ of polynomials on $\mathfrak{p}^+_2:=(\mathfrak{p}^+)^{-\sigma}\subset\mathfrak{p}^+$. Our goal is to understand the decomposition of the restriction $\mathcal{H}_\lambda(D)|_{\widetilde{G}_1}$ by studying the weighted Bergman inner product on each $\widetilde{K}_1$-type in $\mathcal{P}(\mathfrak{p}^+_2)\subset\mathcal{H}_\lambda(D)$.
Today we mainly deal with the symmetric pair $(G,G_1)=(Sp(2r,\mathbb{R}),Sp(r,\mathbb{R})\times Sp(r,\mathbb{R}))$.
Let $(G,G_1)=(G,(G^\sigma)_0)$ be a symmetric pair of holomorphic type, and we consider a pair of Hermitian symmetric spaces $D_1=G_1/K_1\subset D=G/K$, realized as bounded symmetric domains in complex vector spaces $\mathfrak{p}^+_1:=(\mathfrak{p}^+)^\sigma\subset\mathfrak{p}^+$ respectively. Then the universal covering group $\widetilde{G}$ of $G$ acts unitarily on the weighted Bergman space $\mathcal{H}_\lambda(D)\subset\mathcal{O}(D)=\mathcal{O}_\lambda(D)$ on $D$ for sufficiently large $\lambda$. Its restriction to the subgroup $\widetilde{G}_1$ decomposes discretely and multiplicity-freely, and its branching law is given explicitly by Hua--Kostant--Schmid--Kobayashi's formula in terms of the $\widetilde{K}_1$-decomposition of the space $\mathcal{P}(\mathfrak{p}^+_2)$ of polynomials on $\mathfrak{p}^+_2:=(\mathfrak{p}^+)^{-\sigma}\subset\mathfrak{p}^+$. Our goal is to understand the decomposition of the restriction $\mathcal{H}_\lambda(D)|_{\widetilde{G}_1}$ by studying the weighted Bergman inner product on each $\widetilde{K}_1$-type in $\mathcal{P}(\mathfrak{p}^+_2)\subset\mathcal{H}_\lambda(D)$.
Today we mainly deal with the symmetric pair $(G,G_1)=(Sp(2r,\mathbb{R}),Sp(r,\mathbb{R})\times Sp(r,\mathbb{R}))$.
2022/06/24
Colloquium
15:30-16:30 Hybrid
If you do not belong to Graduate School of Mathematical Sciences, the University of Tokyo, please take part online [Reference URL].
Yoshiki Oshima (Graduate School of Mathematical Sciences, the University of Tokyo)
Unitary representations of real reductive Lie groups and the method of coadjoint orbits (JAPANESE)
https://u-tokyo-ac-jp.zoom.us/meeting/register/tZIldu-vqD8tHtE0Vyl29MXHFfzp2NcC0MzR
If you do not belong to Graduate School of Mathematical Sciences, the University of Tokyo, please take part online [Reference URL].
Yoshiki Oshima (Graduate School of Mathematical Sciences, the University of Tokyo)
Unitary representations of real reductive Lie groups and the method of coadjoint orbits (JAPANESE)
[ Abstract ]
The orbit method aims to study unitary representations of Lie groups by relating them to coadjoint actions. It is known that for unipotent groups there exists a one-to-one correspondence between the unitary representations and the coadjoint orbits. For reductive groups it has been observed that one is a good approximation of the other. In this talk, we would like to discuss some results on induction and restriction for reductive Lie groups from the viewpoint of orbit method.
[ Reference URL ]The orbit method aims to study unitary representations of Lie groups by relating them to coadjoint actions. It is known that for unipotent groups there exists a one-to-one correspondence between the unitary representations and the coadjoint orbits. For reductive groups it has been observed that one is a good approximation of the other. In this talk, we would like to discuss some results on induction and restriction for reductive Lie groups from the viewpoint of orbit method.
https://u-tokyo-ac-jp.zoom.us/meeting/register/tZIldu-vqD8tHtE0Vyl29MXHFfzp2NcC0MzR
2022/06/23
Information Mathematics Seminar
16:50-18:35 Room #123 (Graduate School of Math. Sci. Bldg.)
Yasunari Suzuki (NTT)
Design and control of quantum computersXI (Japanese)
Yasunari Suzuki (NTT)
Design and control of quantum computersXI (Japanese)
[ Abstract ]
On the error-correcting code of quantum computer.
On the error-correcting code of quantum computer.
2022/06/22
Number Theory Seminar
17:00-18:00 Hybrid
Yugo Takanashi (University of Tokyo)
Parity of conjugate self-dual representations of inner forms of $\mathrm{GL}_n$ over $p$-adic fields (JAPANESE)
Yugo Takanashi (University of Tokyo)
Parity of conjugate self-dual representations of inner forms of $\mathrm{GL}_n$ over $p$-adic fields (JAPANESE)
[ Abstract ]
There are two parametrizations of discrete series representations of $\mathrm{GL}_n$ over $p$-adic fields. One is the local Langlands correspondence, and the other is the local Jacquet-Langlands correspondence. The composite of these two maps the discrete series representations of an inner form of $\mathrm{GL}_n$ to Galois representations called discrete L-parameters. On the other hand, we can define the parity for each self-dual representation depending on whether the representation is orthogonal or symplectic. The composite preserves the notion of self-duality, and it transforms the parity in a nontrivial manner. Prasad and Ramakrishnan computed the transformation law, and Mieda proved its conjugate self-dual analog under some conditions on groups and representations. We will talk about the proof of the general case of this analog. We use the globalization method, as in the proof of Prasad and Ramakrishnan.
There are two parametrizations of discrete series representations of $\mathrm{GL}_n$ over $p$-adic fields. One is the local Langlands correspondence, and the other is the local Jacquet-Langlands correspondence. The composite of these two maps the discrete series representations of an inner form of $\mathrm{GL}_n$ to Galois representations called discrete L-parameters. On the other hand, we can define the parity for each self-dual representation depending on whether the representation is orthogonal or symplectic. The composite preserves the notion of self-duality, and it transforms the parity in a nontrivial manner. Prasad and Ramakrishnan computed the transformation law, and Mieda proved its conjugate self-dual analog under some conditions on groups and representations. We will talk about the proof of the general case of this analog. We use the globalization method, as in the proof of Prasad and Ramakrishnan.
Tokyo-Nagoya Algebra Seminar
17:00-18:30 Online
Please see the reference URL for details on the online seminar.
Martin Kalck (Freiburg University)
Update on singular equivalences between commutative rings (English)
https://www.math.nagoya-u.ac.jp/~aaron.chan/TNAseminar.html
Please see the reference URL for details on the online seminar.
Martin Kalck (Freiburg University)
Update on singular equivalences between commutative rings (English)
[ Abstract ]
We will start with an introduction to singularity categories, which were first studied by Buchweitz and later rediscovered by Orlov. Then we will explain what is known about triangle equivalences between singularity categories of commutative rings, recalling results of Knörrer, D. Yang (based on our joint works on relative singularity categories. This result also follows from work of Kawamata and was generalized in a joint work with Karmazyn) and a new equivalence obtained in arXiv:2103.06584.
In the remainder of the talk, we will focus on the case of Gorenstein isolated singularities and especially hypersurfaces, where we give a complete description of quasi-equivalence classes of dg enhancements of singularity categories, answering a question of Keller & Shinder. This is based on arXiv:2108.03292.
[ Reference URL ]We will start with an introduction to singularity categories, which were first studied by Buchweitz and later rediscovered by Orlov. Then we will explain what is known about triangle equivalences between singularity categories of commutative rings, recalling results of Knörrer, D. Yang (based on our joint works on relative singularity categories. This result also follows from work of Kawamata and was generalized in a joint work with Karmazyn) and a new equivalence obtained in arXiv:2103.06584.
In the remainder of the talk, we will focus on the case of Gorenstein isolated singularities and especially hypersurfaces, where we give a complete description of quasi-equivalence classes of dg enhancements of singularity categories, answering a question of Keller & Shinder. This is based on arXiv:2108.03292.
https://www.math.nagoya-u.ac.jp/~aaron.chan/TNAseminar.html
2022/06/21
Tuesday Seminar on Topology
17:00-18:00 Online
Pre-registration required. See our seminar webpage.
Kazuhiro Ichihara (Nihon University)
Cosmetic surgeries on knots in the 3-sphere (JAPANESE)
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
Pre-registration required. See our seminar webpage.
Kazuhiro Ichihara (Nihon University)
Cosmetic surgeries on knots in the 3-sphere (JAPANESE)
[ Abstract ]
A pair of Dehn surgeries on a knot is called purely (resp. chirally) cosmetic if the obtained manifolds are orientation-preservingly (resp. -reversingly) homeomorphic. It is conjectured that if a knot in the 3-sphere admits purely (resp. chirally) cosmetic surgeries, then the knot is a trivial knot (resp. a torus knot or an amphicheiral knot). In this talk, after giving a brief survey on the studies on these conjectures, I will explain recent progresses on the conjectures. This is based on joint works with Tetsuya Ito (Kyoto University), In Dae Jong (Kindai University), and Toshio Saito (Joetsu University of Education).
[ Reference URL ]A pair of Dehn surgeries on a knot is called purely (resp. chirally) cosmetic if the obtained manifolds are orientation-preservingly (resp. -reversingly) homeomorphic. It is conjectured that if a knot in the 3-sphere admits purely (resp. chirally) cosmetic surgeries, then the knot is a trivial knot (resp. a torus knot or an amphicheiral knot). In this talk, after giving a brief survey on the studies on these conjectures, I will explain recent progresses on the conjectures. This is based on joint works with Tetsuya Ito (Kyoto University), In Dae Jong (Kindai University), and Toshio Saito (Joetsu University of Education).
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
2022/06/20
Seminar on Geometric Complex Analysis
10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Taiji Marugame (The University of Electro-Communications)
Constructions of CR GJMS operators in dimension three (Japanese)
https://forms.gle/hYT2hVhDE3q1wDSh6
Taiji Marugame (The University of Electro-Communications)
Constructions of CR GJMS operators in dimension three (Japanese)
[ Abstract ]
CR GJMS operators are invariant differential operators on CR manifolds whose leading parts are powers of the sublaplacian. Such operators can be constructed by Fefferman's ambient metric or the Cheng-Yau metric, but the construction is obstructed at a finite order due to the ambiguity of these metrics. Gover-Graham constructed some higher order CR GJMS operators by using tractor calculus and BGG constructions. In particular, they showed that three dimensional CR manifolds admit CR GJMS operators of all orders. In this talk, we give proofs to this fact in two different ways. One is by the use of self-dual Einstein ACH metric and the other is by the Graham-Hirachi inhomogeneous ambient metric adapted to the Fefferman conformal structure. We also state a conjecture on the relationship between these two metrics.
[ Reference URL ]CR GJMS operators are invariant differential operators on CR manifolds whose leading parts are powers of the sublaplacian. Such operators can be constructed by Fefferman's ambient metric or the Cheng-Yau metric, but the construction is obstructed at a finite order due to the ambiguity of these metrics. Gover-Graham constructed some higher order CR GJMS operators by using tractor calculus and BGG constructions. In particular, they showed that three dimensional CR manifolds admit CR GJMS operators of all orders. In this talk, we give proofs to this fact in two different ways. One is by the use of self-dual Einstein ACH metric and the other is by the Graham-Hirachi inhomogeneous ambient metric adapted to the Fefferman conformal structure. We also state a conjecture on the relationship between these two metrics.
https://forms.gle/hYT2hVhDE3q1wDSh6
Number Theory Seminar
15:00-16:00 Hybrid
Hiroki Kato (Paris-Saclay University)
p-adic weight-monodromy conjecture for complete intersections (Japanese)
Hiroki Kato (Paris-Saclay University)
p-adic weight-monodromy conjecture for complete intersections (Japanese)
2022/06/16
Information Mathematics Seminar
16:50-18:35 Room #123 (Graduate School of Math. Sci. Bldg.)
Yasunari Suzuki (NTT)
Design and control of quantum computers X (Japanese)
Yasunari Suzuki (NTT)
Design and control of quantum computers X (Japanese)
[ Abstract ]
Error-correcting of quantum computer
Error-correcting of quantum computer
2022/06/15
Number Theory Seminar
17:00-18:00 Hybrid
Junnosuke Koizumi (University of Tokyo)
Steinberg symbols and reciprocity sheaves (JAPANESE)
Junnosuke Koizumi (University of Tokyo)
Steinberg symbols and reciprocity sheaves (JAPANESE)
[ Abstract ]
The norm residue symbol and the differential symbol are known to satisfy the common relation $(a,1-a)=0$ which is called the Steinberg relation. Hu-Kriz showed that the Steinberg relation can be understood as a relation between certain morphisms in the stable motivic homotopy category. On the other hand, there is also an “additive variant” of the Steinberg relation, namely $(a,a)+(1-a,1-a)=0$, for which the classical motivic theory is no longer applicable. In this talk we will explain how the theory of reciprocity sheaves due to Kahn-Saito-Yamazaki can be utilized to generalize the theory of Hu-Kriz to include the additive Steinberg relation.
The norm residue symbol and the differential symbol are known to satisfy the common relation $(a,1-a)=0$ which is called the Steinberg relation. Hu-Kriz showed that the Steinberg relation can be understood as a relation between certain morphisms in the stable motivic homotopy category. On the other hand, there is also an “additive variant” of the Steinberg relation, namely $(a,a)+(1-a,1-a)=0$, for which the classical motivic theory is no longer applicable. In this talk we will explain how the theory of reciprocity sheaves due to Kahn-Saito-Yamazaki can be utilized to generalize the theory of Hu-Kriz to include the additive Steinberg relation.
Seminar on Mathematics for various disciplines
10:30-11:30 Room # Zoomによるオンライン開催 (Graduate School of Math. Sci. Bldg.)
This seminar is held on Wednesday.
Kazuyasu Sugiyama (Graduate School of Engineering Science, Osaka University)
Voxel-based fluid-structure interaction methods (日本語)
[ Reference URL ]
https://u-tokyo-ac-jp.zoom.us/j/82678271212?pwd=S05lczNlK2ZHM1BwMk5RRnhQTjcrdz09
This seminar is held on Wednesday.
Kazuyasu Sugiyama (Graduate School of Engineering Science, Osaka University)
Voxel-based fluid-structure interaction methods (日本語)
[ Reference URL ]
https://u-tokyo-ac-jp.zoom.us/j/82678271212?pwd=S05lczNlK2ZHM1BwMk5RRnhQTjcrdz09
Tokyo-Nagoya Algebra Seminar
10:30-12:00 Online
Please see the reference URL for details on the online seminar.
Nicholas Williams (The University of Tokyo)
Cyclic polytopes and higher Auslander--Reiten theory 1 (English)
https://www.math.nagoya-u.ac.jp/~aaron.chan/TNAseminar.html
Please see the reference URL for details on the online seminar.
Nicholas Williams (The University of Tokyo)
Cyclic polytopes and higher Auslander--Reiten theory 1 (English)
[ Abstract ]
In this series of three talks, we expand upon the previous talk given at the seminar and study the relationship between cyclic polytopes and higher Auslander--Reiten theory in more detail.
http://www.math.nagoya-u.ac.jp/~aaron.chan/TNA/2021/Williams-Cyclic_polytopes_and_higher_AR.pdf
In the first talk, we focus on cyclic polytopes. We survey important properties of cyclic polytopes, such as different ways to construct them, the Upper Bound Theorem, and their Ramsey-theoretic properties. We then move on to triangulations of cyclic polytopes. We give efficient combinatorial descriptions of triangulations of even-dimensional and odd-dimensional cyclic polytopes, which we will use in subsequent talks. We finally define the higher Stasheff--Tamari orders on triangulations of cyclic polytopes. We give important results on the orders, including Rambau's Theorem, and the equality of the two orders.
[ Reference URL ]In this series of three talks, we expand upon the previous talk given at the seminar and study the relationship between cyclic polytopes and higher Auslander--Reiten theory in more detail.
http://www.math.nagoya-u.ac.jp/~aaron.chan/TNA/2021/Williams-Cyclic_polytopes_and_higher_AR.pdf
In the first talk, we focus on cyclic polytopes. We survey important properties of cyclic polytopes, such as different ways to construct them, the Upper Bound Theorem, and their Ramsey-theoretic properties. We then move on to triangulations of cyclic polytopes. We give efficient combinatorial descriptions of triangulations of even-dimensional and odd-dimensional cyclic polytopes, which we will use in subsequent talks. We finally define the higher Stasheff--Tamari orders on triangulations of cyclic polytopes. We give important results on the orders, including Rambau's Theorem, and the equality of the two orders.
https://www.math.nagoya-u.ac.jp/~aaron.chan/TNAseminar.html
2022/06/14
Tuesday Seminar on Topology
17:30-18:30 Online
Pre-registration required. See our seminar webpage.
Katsuhiko Kuribayashi (Shinshu University)
Cartan calculi on the free loop spaces (JAPANESE)
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
Pre-registration required. See our seminar webpage.
Katsuhiko Kuribayashi (Shinshu University)
Cartan calculi on the free loop spaces (JAPANESE)
[ Abstract ]
A typical example of a Cartan calculus is the Lie algebra representation of vector fields of a manifold on the derivation ring of the de Rham complex. In this talk, a `second stage' of the Cartan calculus is investigated. In a more general setting, the stage is formulated with a Lie algebra representation of the Andre-Quillen cohomology of a commutative differential graded algebra A on the endomorphism ring of the Hochschild homology of A in terms of the homotopy Cartan calculi in the sense of Fiorenza and Kowalzig. Moreover, the Lie algebra representation in the Cartan calculus is interpreted geometrically as a map from the rational homotopy group of the monoid of self-homotopy equivalences on a simply-connected space M to the derivation ring on the loop cohomology of M. An extension of the representation to the string cohomology and its geometric counterpart are also discussed together with the BV exactness which is a new rational homotopy invariant introduced in our work. This talk is based on joint work in progress with T. Naito, S. Wakatsuki and T. Yamaguchi.
[ Reference URL ]A typical example of a Cartan calculus is the Lie algebra representation of vector fields of a manifold on the derivation ring of the de Rham complex. In this talk, a `second stage' of the Cartan calculus is investigated. In a more general setting, the stage is formulated with a Lie algebra representation of the Andre-Quillen cohomology of a commutative differential graded algebra A on the endomorphism ring of the Hochschild homology of A in terms of the homotopy Cartan calculi in the sense of Fiorenza and Kowalzig. Moreover, the Lie algebra representation in the Cartan calculus is interpreted geometrically as a map from the rational homotopy group of the monoid of self-homotopy equivalences on a simply-connected space M to the derivation ring on the loop cohomology of M. An extension of the representation to the string cohomology and its geometric counterpart are also discussed together with the BV exactness which is a new rational homotopy invariant introduced in our work. This talk is based on joint work in progress with T. Naito, S. Wakatsuki and T. Yamaguchi.
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
2022/06/09
Information Mathematics Seminar
16:50-18:35 Room #123 (Graduate School of Math. Sci. Bldg.)
Yasunari Suzuki (NTT)
Design and control of quantum computers IX (Japanese)
Yasunari Suzuki (NTT)
Design and control of quantum computers IX (Japanese)
[ Abstract ]
On stabilizer codes and toric codes
On stabilizer codes and toric codes
2022/06/08
Tokyo-Nagoya Algebra Seminar
10:30-12:00 Online
Please see the reference URL for details on the online seminar.
Masahiko Yoshinaga (Osaka University)
超平面配置の特性準多項式 II (Japanese)
[ Reference URL ]
http://www.math.nagoya-u.ac.jp/~aaron.chan/TNAseminar.html
Please see the reference URL for details on the online seminar.
Masahiko Yoshinaga (Osaka University)
超平面配置の特性準多項式 II (Japanese)
[ Reference URL ]
http://www.math.nagoya-u.ac.jp/~aaron.chan/TNAseminar.html
2022/06/07
Operator Algebra Seminars
16:45-18:15 Room #128 (Graduate School of Math. Sci. Bldg.)
Taro Sogabe (Univ. Tokyo)
Kirchberg algebras sharing the same homotopy groups of their automorphism groups
[ Reference URL ]
https://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm
Taro Sogabe (Univ. Tokyo)
Kirchberg algebras sharing the same homotopy groups of their automorphism groups
[ Reference URL ]
https://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm
Tuesday Seminar on Topology
17:00-18:00 Online
Pre-registration required. See our seminar webpage.
早稲田大学 (Waseda University)
Dynamical zeta functions for geodesic flows and the higher-dimensional Reidemeister torsion for Fuchsian groups (JAPANESE)
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
Pre-registration required. See our seminar webpage.
早稲田大学 (Waseda University)
Dynamical zeta functions for geodesic flows and the higher-dimensional Reidemeister torsion for Fuchsian groups (JAPANESE)
[ Abstract ]
We discuss a relation between a dynamical zeta function defined by the geodesic flow on a 2-dimensional hyperbolic orbifold and the asymptotic behavior of the Reidemeister torsion for the unit tangent bundle over the orbifold. The unit tangent bundle over a hyperbolic orbifold is a Seifert fibered space with a geometric structure given by the universal cover of PSL(2, R). This geometric structure induces an SL(2, R)-representation of the fundamental group. Here the asymptotic behavior of the Reidemeister torsion means the limit of the leading coefficient in the Reidemeister torsion for the unit tangent bundle over a hyperbolic orbifold and the SL(n, R)-representations induced by the SL(2, R)-one of its fundamental group. For a hyperbolic 3-manifold, we can derive the hyperbolic volume from the limit of the leading coefficient in the Reidemeister torsion with a dynamical zeta function according to previous works. For the unit tangent bundle over a 2-dimensional hyperbolic orbifold, which is not a hyperbolic 3-manifold, we can find the orbifold Euler characteristic of the orbifold in the limit of the leading coefficient in the Reidemeister torsion for the unit tangent bundle from the relation with the dynamical zeta function defined by the geodesic flow on the orbifold.
[ Reference URL ]We discuss a relation between a dynamical zeta function defined by the geodesic flow on a 2-dimensional hyperbolic orbifold and the asymptotic behavior of the Reidemeister torsion for the unit tangent bundle over the orbifold. The unit tangent bundle over a hyperbolic orbifold is a Seifert fibered space with a geometric structure given by the universal cover of PSL(2, R). This geometric structure induces an SL(2, R)-representation of the fundamental group. Here the asymptotic behavior of the Reidemeister torsion means the limit of the leading coefficient in the Reidemeister torsion for the unit tangent bundle over a hyperbolic orbifold and the SL(n, R)-representations induced by the SL(2, R)-one of its fundamental group. For a hyperbolic 3-manifold, we can derive the hyperbolic volume from the limit of the leading coefficient in the Reidemeister torsion with a dynamical zeta function according to previous works. For the unit tangent bundle over a 2-dimensional hyperbolic orbifold, which is not a hyperbolic 3-manifold, we can find the orbifold Euler characteristic of the orbifold in the limit of the leading coefficient in the Reidemeister torsion for the unit tangent bundle from the relation with the dynamical zeta function defined by the geodesic flow on the orbifold.
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
2022/06/02
Information Mathematics Seminar
16:50-18:35 Room #123 (Graduate School of Math. Sci. Bldg.)
Yasunari Suzuki (NTT)
Design and control of quantum computers VIII (Japanese)
Yasunari Suzuki (NTT)
Design and control of quantum computers VIII (Japanese)
[ Abstract ]
Explanation of error correcting code of quantum computer
------stabilizer method
Explanation of error correcting code of quantum computer
------stabilizer method
2022/06/01
Tokyo-Nagoya Algebra Seminar
10:30-12:00 Online
Please see the reference URL for details on the online seminar.
Masahiko Yoshinaga (Osaka University)
超平面配置の特性準多項式 I (Japanese)
[ Reference URL ]
http://www.math.nagoya-u.ac.jp/~aaron.chan/TNAseminar.html
Please see the reference URL for details on the online seminar.
Masahiko Yoshinaga (Osaka University)
超平面配置の特性準多項式 I (Japanese)
[ Reference URL ]
http://www.math.nagoya-u.ac.jp/~aaron.chan/TNAseminar.html
2022/05/31
Operator Algebra Seminars
16:45-18:15 Room #128 (Graduate School of Math. Sci. Bldg.)
Yusuke Isono (RIMS, Kyoto University)
Pointwise inner automorphisms of almost periodic factors
[ Reference URL ]
https://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm
Yusuke Isono (RIMS, Kyoto University)
Pointwise inner automorphisms of almost periodic factors
[ Reference URL ]
https://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm
Tuesday Seminar on Topology
17:00-18:00 Online
Pre-registration required. See our seminar webpage.
Kazushi Ueda (The Univesity of Tokyo)
Stable Fukaya categories of Milnor fibers (JAPANESE)
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
Pre-registration required. See our seminar webpage.
Kazushi Ueda (The Univesity of Tokyo)
Stable Fukaya categories of Milnor fibers (JAPANESE)
[ Abstract ]
We define the stable Fukaya category of a Liouville domain as the quotient of the wrapped Fukaya category by the full subcategory consisting of compact Lagrangians, and discuss the relation between the stable Fukaya categories of affine Fermat hypersurfaces and the Fukaya categories of projective hypersurfaces. We also discuss homological mirror symmetry for Milnor fibers of Brieskorn-Pham singularities along the way. This is a joint work in progress with Yanki Lekili.
[ Reference URL ]We define the stable Fukaya category of a Liouville domain as the quotient of the wrapped Fukaya category by the full subcategory consisting of compact Lagrangians, and discuss the relation between the stable Fukaya categories of affine Fermat hypersurfaces and the Fukaya categories of projective hypersurfaces. We also discuss homological mirror symmetry for Milnor fibers of Brieskorn-Pham singularities along the way. This is a joint work in progress with Yanki Lekili.
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
Tuesday Seminar of Analysis
16:00-17:30 Room #126 (Graduate School of Math. Sci. Bldg.)
OKABE Shinya (Tohoku University)
Convergence of Sobolev gradient trajectories to elastica (Japanese)
https://forms.gle/wkCbqdmNuz9zr3vA8
OKABE Shinya (Tohoku University)
Convergence of Sobolev gradient trajectories to elastica (Japanese)
[ Abstract ]
In this talk we consider a higher order Sobolev gradient flow for the modified elastic energy defined on closed space curves. The $L^2$-gradient flow for the modified elastic energy has been well studied, and standard results are solvability of the flow for smooth initial curve and subconvergence of solutions to elastica. Moreover, stronger convergence results, so called full limit convergence, are generally up to reparametrisation and sometimes translation. In this talk, we consider $H^2$-gradient flow for the modified elastic energy and prove (i) the solvability of the flow for initial curve in the energy class, (ii) full limit convergence to elastica by way of a Lojasiewicz—Simon gradient inequality. This talk is based on a joint work with Philip Schrader (Murdoch University).
[ Reference URL ]In this talk we consider a higher order Sobolev gradient flow for the modified elastic energy defined on closed space curves. The $L^2$-gradient flow for the modified elastic energy has been well studied, and standard results are solvability of the flow for smooth initial curve and subconvergence of solutions to elastica. Moreover, stronger convergence results, so called full limit convergence, are generally up to reparametrisation and sometimes translation. In this talk, we consider $H^2$-gradient flow for the modified elastic energy and prove (i) the solvability of the flow for initial curve in the energy class, (ii) full limit convergence to elastica by way of a Lojasiewicz—Simon gradient inequality. This talk is based on a joint work with Philip Schrader (Murdoch University).
https://forms.gle/wkCbqdmNuz9zr3vA8
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