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Seminar information archive
Seminar information archive ～12/05｜Today's seminar 12/06 | Future seminars 12/07～
Tuesday Seminar on Topology
17:00-18:00 Online
Pre-registration required. See our seminar webpage.
Makoto Sakuma (Osaka City University Advanced Mathematical Institute)
Homotopy motions of surfaces in 3-manifolds (JAPANESE)
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
Pre-registration required. See our seminar webpage.
Makoto Sakuma (Osaka City University Advanced Mathematical Institute)
Homotopy motions of surfaces in 3-manifolds (JAPANESE)
[ Abstract ]
We introduce the concept of a homotopy motion of a subset in a manifold, and give a systematic study of homotopy motions of surfaces in closed orientable 3-manifolds. This notion arises from various natural problems in 3-manifold theory such as domination of manifold pairs, homotopical behaviour of simple loops on a Heegaard surface, and monodromies of virtual branched covering surface bundles associated to a Heegaard splitting. This is a joint work with Yuya Koda (arXiv:2011.05766).
[ Reference URL ]We introduce the concept of a homotopy motion of a subset in a manifold, and give a systematic study of homotopy motions of surfaces in closed orientable 3-manifolds. This notion arises from various natural problems in 3-manifold theory such as domination of manifold pairs, homotopical behaviour of simple loops on a Heegaard surface, and monodromies of virtual branched covering surface bundles associated to a Heegaard splitting. This is a joint work with Yuya Koda (arXiv:2011.05766).
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
Operator Algebra Seminars
16:45-18:15 Online
Makoto Yamashita (Univ. Oslo)
Quantization of locally compact groups from matched pairs
[ Reference URL ]
https://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm
Makoto Yamashita (Univ. Oslo)
Quantization of locally compact groups from matched pairs
[ Reference URL ]
https://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm
Lie Groups and Representation Theory
17:00-18:00 Room #Online (Graduate School of Math. Sci. Bldg.)
Yoshiki Oshima (Osaka University, Graduate School of Information Science and Technology)
Compactification of locally symmetric spaces and collapsing of canonical Kahler metrics (Japanese)
Yoshiki Oshima (Osaka University, Graduate School of Information Science and Technology)
Compactification of locally symmetric spaces and collapsing of canonical Kahler metrics (Japanese)
[ Abstract ]
The moduli spaces of Abelian varieties and K3 surfaces are known to have a structure of locally symmetric spaces. Around 1960, a finite number of compactifications of locally symmetric spaces are constructed by Ichiro Satake. In this talk, based on a joint work with Yuji Odaka (arXiv:1810:07685), we will see that one of Satake compactifications parametrizes limits of canonical (Ricci-flat) Kahler metrics on Abelian varieties and K3 surfaces.
The moduli spaces of Abelian varieties and K3 surfaces are known to have a structure of locally symmetric spaces. Around 1960, a finite number of compactifications of locally symmetric spaces are constructed by Ichiro Satake. In this talk, based on a joint work with Yuji Odaka (arXiv:1810:07685), we will see that one of Satake compactifications parametrizes limits of canonical (Ricci-flat) Kahler metrics on Abelian varieties and K3 surfaces.
2021/07/12
Seminar on Geometric Complex Analysis
10:30-12:00 Online
Katsuhiko Matsuzaki (Waseda University)
Parametrization of Weil-Petersson curves on the plane (Japanese)
https://u-tokyo-ac-jp.zoom.us/meeting/register/tJ0vcu2rrDIqG9Rv5AT0Mpi37urIkJ1IRldB
Katsuhiko Matsuzaki (Waseda University)
Parametrization of Weil-Petersson curves on the plane (Japanese)
[ Abstract ]
A Weil-Petersson curve is the image of the real line by a quasiconformal homeomorphism of the plane whose complex dilatation is square integrable with respect to the hyperbolic metrics on the upper and the lower half-planes. We consider two parameter spaces of all such curves and show that they are biholomorphically equivalent. As a consequence, we prove that the variant of the Beurling-Ahlfors quasiconformal extension defined by using the heat kernel for the convolution yields a global real-analytic section for the Teichmueller projection to the Weil-Petersson Teichmueller space. This is a joint work with Huaying Wei.
[ Reference URL ]A Weil-Petersson curve is the image of the real line by a quasiconformal homeomorphism of the plane whose complex dilatation is square integrable with respect to the hyperbolic metrics on the upper and the lower half-planes. We consider two parameter spaces of all such curves and show that they are biholomorphically equivalent. As a consequence, we prove that the variant of the Beurling-Ahlfors quasiconformal extension defined by using the heat kernel for the convolution yields a global real-analytic section for the Teichmueller projection to the Weil-Petersson Teichmueller space. This is a joint work with Huaying Wei.
https://u-tokyo-ac-jp.zoom.us/meeting/register/tJ0vcu2rrDIqG9Rv5AT0Mpi37urIkJ1IRldB
2021/07/08
Tokyo-Nagoya Algebra Seminar
16:00-17:30 Online
Please see the URL below for details on the online seminar.
Tsukasa Ishibashi (RIMS, Kyoto University)
Sign-stable mutation loops and pseudo-Anosov mapping classes (Japanese)
[ Reference URL ]
http://www.math.nagoya-u.ac.jp/~aaron.chan/TNAseminar.html
Please see the URL below for details on the online seminar.
Tsukasa Ishibashi (RIMS, Kyoto University)
Sign-stable mutation loops and pseudo-Anosov mapping classes (Japanese)
[ Reference URL ]
http://www.math.nagoya-u.ac.jp/~aaron.chan/TNAseminar.html
Information Mathematics Seminar
16:50-18:35 Online
Hiroshi Fujiwara (BroadBand Tower, Inc.)
Telework society and menace of the cyber attack (Japanese)
https://docs.google.com/forms/d/1zdmPdHWcVgH6Sn62nVHNp0ODVBJ7fyHKJHdABtDd_Tw
Hiroshi Fujiwara (BroadBand Tower, Inc.)
Telework society and menace of the cyber attack (Japanese)
[ Abstract ]
Explanation on the telework society and the menace of cyber attack.
[ Reference URL ]Explanation on the telework society and the menace of cyber attack.
https://docs.google.com/forms/d/1zdmPdHWcVgH6Sn62nVHNp0ODVBJ7fyHKJHdABtDd_Tw
2021/07/07
Discrete mathematical modelling seminar
17:15-19:00 Online
This seminar will be held using Zoom. If you wish to participate, please contact R. Willox by email.
Iwao Shinsuke (Tokai University)
Combinatorics of K-theoretic special polynomials -- free fermion representation and integrable systems (Japanese)
This seminar will be held using Zoom. If you wish to participate, please contact R. Willox by email.
Iwao Shinsuke (Tokai University)
Combinatorics of K-theoretic special polynomials -- free fermion representation and integrable systems (Japanese)
Number Theory Seminar
17:00-18:00 Online
Takumi Yoshida (Keio University)
On the BSD conjecture for the quadratic twists of the elliptic curve $X_0(49)$ (Japanese)
Takumi Yoshida (Keio University)
On the BSD conjecture for the quadratic twists of the elliptic curve $X_0(49)$ (Japanese)
[ Abstract ]
The full BSD conjecture (the full Birch-Swinnerton-Dyer conjecture) is the important conjecture, which connects the algebraic invariants and analytic invariants of elliptic curves. When the elliptic curve is defined over $\mathbb{Q}$, these invariants are known to be rational numbers. Now, even when the elliptic curve is defined over $\mathbb{Q}$ and the $L$-function is not $0$ at $s=1$, it is not shown that the $2$-orders of these invariants are equal. Coates, Kim, Liang and Zhao proved the full BSD conjecture for some quadratic twists of $X_0(49)$, by proving that these $2$-orders are same. We extends this result, and prove the full BSD conjecture for more twists.
The full BSD conjecture (the full Birch-Swinnerton-Dyer conjecture) is the important conjecture, which connects the algebraic invariants and analytic invariants of elliptic curves. When the elliptic curve is defined over $\mathbb{Q}$, these invariants are known to be rational numbers. Now, even when the elliptic curve is defined over $\mathbb{Q}$ and the $L$-function is not $0$ at $s=1$, it is not shown that the $2$-orders of these invariants are equal. Coates, Kim, Liang and Zhao proved the full BSD conjecture for some quadratic twists of $X_0(49)$, by proving that these $2$-orders are same. We extends this result, and prove the full BSD conjecture for more twists.
2021/07/06
Numerical Analysis Seminar
16:30-18:00 Online
Ken Hayami (National Institute of Informatics (Professor Emeritus))
Iterative solution methods for least squares problems and their applications
(Japanese)
[ Reference URL ]
https://forms.gle/B5Hwxa7o8F36hZKr7
Ken Hayami (National Institute of Informatics (Professor Emeritus))
Iterative solution methods for least squares problems and their applications
(Japanese)
[ Reference URL ]
https://forms.gle/B5Hwxa7o8F36hZKr7
Tuesday Seminar on Topology
17:30-18:30 Online
Pre-registration required. See our seminar webpage.
Yosuke Kubota (Shinshu University)
Codimension 2 transfer map in higher index theory (JAPANESE)
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
Pre-registration required. See our seminar webpage.
Yosuke Kubota (Shinshu University)
Codimension 2 transfer map in higher index theory (JAPANESE)
[ Abstract ]
The Rosenberg index is a topological invariant taking value in the K-group of the C*-algebra of the fundamental group, which is a strong obstruction for a closed spin manifold to admit a positive scalar curvature (psc) metric. In 2015 Hanke-Pape-Schick proves that, for a nice codimension 2 submanifold N of M, the Rosenberg index of N obstructs to a psc metric on M. This is a far reaching generalization of a classical result of Gromov and Lawson. In this talk I introduce a joint work with T. Schick and its continuation concerned with this `codimension 2 index' obstruction. We construct a map between C*-algebra K-groups, which we call the codimension 2 transfer map, relating the Rosenberg index of M to that of N directly. This shows that Hanke-Pape-Schick's obstruction is dominated by a standard one, the Rosenberg index of M. We also extend our codimension 2 transfer map to secondary index invariants called the higher rho invariant. As a consequence, we obtain some example of psc manifolds are not psc null-cobordant.
[ Reference URL ]The Rosenberg index is a topological invariant taking value in the K-group of the C*-algebra of the fundamental group, which is a strong obstruction for a closed spin manifold to admit a positive scalar curvature (psc) metric. In 2015 Hanke-Pape-Schick proves that, for a nice codimension 2 submanifold N of M, the Rosenberg index of N obstructs to a psc metric on M. This is a far reaching generalization of a classical result of Gromov and Lawson. In this talk I introduce a joint work with T. Schick and its continuation concerned with this `codimension 2 index' obstruction. We construct a map between C*-algebra K-groups, which we call the codimension 2 transfer map, relating the Rosenberg index of M to that of N directly. This shows that Hanke-Pape-Schick's obstruction is dominated by a standard one, the Rosenberg index of M. We also extend our codimension 2 transfer map to secondary index invariants called the higher rho invariant. As a consequence, we obtain some example of psc manifolds are not psc null-cobordant.
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
Lie Groups and Representation Theory
17:00-18:00 Room #Online (Graduate School of Math. Sci. Bldg.)
Taito Tauchi (Kyushu University )
A counterexample to a Q-series analogue of Casselman's subrepresentation theorem (Japanese)
Taito Tauchi (Kyushu University )
A counterexample to a Q-series analogue of Casselman's subrepresentation theorem (Japanese)
[ Abstract ]
Let G be a real reductive Lie group, Q a parabolic subgroup of G, and π an irreducible admissible representation of G. We say that π belongs to Q-series if it occurs as a subquotient of some degenerate principal series representation induced from Q. Then, any irreducible admissible representation belongs to P-series by Harish-Chandra’s subquotient theorem, where P is a minimal parabolic subgroup of G. On the other hand, Casselman’s subrepresentation theorem implies any representation belonging to P-series can be realized as a
subrepresentation of some principal series representation induced from P. In this talk, we discuss a counterexample to a Q-series analogue of this subrepresentation theorem. More precisely, we show that there exists an irreducible admissible representation belonging to Q-series, which can not be realized as a subrepresentation of any degenerate
principal series representation induced from Q.
Let G be a real reductive Lie group, Q a parabolic subgroup of G, and π an irreducible admissible representation of G. We say that π belongs to Q-series if it occurs as a subquotient of some degenerate principal series representation induced from Q. Then, any irreducible admissible representation belongs to P-series by Harish-Chandra’s subquotient theorem, where P is a minimal parabolic subgroup of G. On the other hand, Casselman’s subrepresentation theorem implies any representation belonging to P-series can be realized as a
subrepresentation of some principal series representation induced from P. In this talk, we discuss a counterexample to a Q-series analogue of this subrepresentation theorem. More precisely, we show that there exists an irreducible admissible representation belonging to Q-series, which can not be realized as a subrepresentation of any degenerate
principal series representation induced from Q.
2021/07/05
Seminar on Geometric Complex Analysis
10:30-12:00 Online
Nitta Yasufumi (Tokyo University of Science)
Several stronger concepts of relative K-stability for polarized toric manifolds (Japanese)
https://u-tokyo-ac-jp.zoom.us/meeting/register/tJ0vcu2rrDIqG9Rv5AT0Mpi37urIkJ1IRldB
Nitta Yasufumi (Tokyo University of Science)
Several stronger concepts of relative K-stability for polarized toric manifolds (Japanese)
[ Abstract ]
We study relations between algebro-geometric stabilities for polarized toric manifolds. In this talk, we introduce several strengthenings of relative K-stability such as uniform stability and K-stability tested by more objects than test configurations, and show that these approaches are all equivalent. As a consequence, we solve a uniform version of the Yau-Tian-Donaldson conjecture for Calabi's extremal Kähler metrics in the toric setting. This talk is based on a joint work with Shunsuke Saito.
[ Reference URL ]We study relations between algebro-geometric stabilities for polarized toric manifolds. In this talk, we introduce several strengthenings of relative K-stability such as uniform stability and K-stability tested by more objects than test configurations, and show that these approaches are all equivalent. As a consequence, we solve a uniform version of the Yau-Tian-Donaldson conjecture for Calabi's extremal Kähler metrics in the toric setting. This talk is based on a joint work with Shunsuke Saito.
https://u-tokyo-ac-jp.zoom.us/meeting/register/tJ0vcu2rrDIqG9Rv5AT0Mpi37urIkJ1IRldB
Algebraic Geometry Seminar
16:00-17:00 Room #zoom (Graduate School of Math. Sci. Bldg.)
Paolo Cascini (Imperial College London)
Birational geometry of foliations (English)
Paolo Cascini (Imperial College London)
Birational geometry of foliations (English)
[ Abstract ]
I will survey about some recent progress towards the Minimal Model Program for foliations on complex varieties, focusing mainly on the case of threefolds and the case of algebraically integrable foliations.
I will survey about some recent progress towards the Minimal Model Program for foliations on complex varieties, focusing mainly on the case of threefolds and the case of algebraically integrable foliations.
2021/07/03
Seminar on Probability and Statistics
10:55-17:10 Room # (Graduate School of Math. Sci. Bldg.)
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[ Reference URL ]
http://www.sigmath.es.osaka-u.ac.jp/statmodel/?page_id=2028
- (-)
-
[ Reference URL ]
http://www.sigmath.es.osaka-u.ac.jp/statmodel/?page_id=2028
2021/07/01
Algebraic Geometry Seminar
10:00-11:00 Room # (Graduate School of Math. Sci. Bldg.)
Fumiaki Suzuki (UCLA)
An O-acyclic variety of even index
Fumiaki Suzuki (UCLA)
An O-acyclic variety of even index
[ Abstract ]
I will construct a family of Enriques surfaces parametrized by P^1 such that any multi-section has even degree over the base P^1. Over the function field of a complex curve, this gives the first example of an O-acyclic variety (H^i(X,O)=0 for i>0) whose index is not equal to one, and an affirmative answer to a question of Colliot-Thélène and Voisin. I will also discuss applications to related problems, including the integral Hodge conjecture and Murre’s question on universality of the Abel-Jacobi maps. This is joint work with John Christian Ottem.
I will construct a family of Enriques surfaces parametrized by P^1 such that any multi-section has even degree over the base P^1. Over the function field of a complex curve, this gives the first example of an O-acyclic variety (H^i(X,O)=0 for i>0) whose index is not equal to one, and an affirmative answer to a question of Colliot-Thélène and Voisin. I will also discuss applications to related problems, including the integral Hodge conjecture and Murre’s question on universality of the Abel-Jacobi maps. This is joint work with John Christian Ottem.
Information Mathematics Seminar
16:50-18:35 Online
Hiroshi Fujiwara (BroadBand Tower, Inc.)
Telework society and importance of the cyber security to increase (Japanese)
https://docs.google.com/forms/d/1zdmPdHWcVgH6Sn62nVHNp0ODVBJ7fyHKJHdABtDd_Tw
Hiroshi Fujiwara (BroadBand Tower, Inc.)
Telework society and importance of the cyber security to increase (Japanese)
[ Abstract ]
Explanation of the importance of cyber security in the telework society.
[ Reference URL ]Explanation of the importance of cyber security in the telework society.
https://docs.google.com/forms/d/1zdmPdHWcVgH6Sn62nVHNp0ODVBJ7fyHKJHdABtDd_Tw
2021/06/30
Number Theory Seminar
17:00-18:00 Online
Kimihiko Li (University of Tokyo)
Prismatic and q-crystalline sites of higher level (Japanese)
Kimihiko Li (University of Tokyo)
Prismatic and q-crystalline sites of higher level (Japanese)
[ Abstract ]
Two new p-adic cohomology theories, called prismatic cohomology and q-crystalline cohomology, were defined for generalizing crystalline cohomology and they recover most known integral p-adic cohomology theories. On the other hand, higher level crystalline cohomology was defined for constructing p-adic cohomology theory over a ramified base. In this talk, for a positive integer m, we will give a construction of the level m primastic and q-crystalline sites and prove a certain equivalence between the category of crystals on the m-prismatic site or the m-q-crystalline site and that on the usual prismatic site or the usual q-crystalline site, which can be regarded as the prismatic analogue of the Frobenius descent. We will also prove the equivalence between the category of crystals on the m-prismatic site and that on the (m-1)-q-crystalline site.
Two new p-adic cohomology theories, called prismatic cohomology and q-crystalline cohomology, were defined for generalizing crystalline cohomology and they recover most known integral p-adic cohomology theories. On the other hand, higher level crystalline cohomology was defined for constructing p-adic cohomology theory over a ramified base. In this talk, for a positive integer m, we will give a construction of the level m primastic and q-crystalline sites and prove a certain equivalence between the category of crystals on the m-prismatic site or the m-q-crystalline site and that on the usual prismatic site or the usual q-crystalline site, which can be regarded as the prismatic analogue of the Frobenius descent. We will also prove the equivalence between the category of crystals on the m-prismatic site and that on the (m-1)-q-crystalline site.
Discrete mathematical modelling seminar
17:15-18:45 Online
This seminar will be held using Zoom. If you wish to participate, please contact R. Willox by email.
Joe PALLISTER (Chiba University)
Affine A and D cluster algebras: Dynamical systems, triangulated surfaces and friezes (English)
This seminar will be held using Zoom. If you wish to participate, please contact R. Willox by email.
Joe PALLISTER (Chiba University)
Affine A and D cluster algebras: Dynamical systems, triangulated surfaces and friezes (English)
[ Abstract ]
We first review the dynamical systems previously obtained for affine A and D type cluster algebras, given by the "cluster map", and the periodic quantities found for these systems. Then, by viewing the clusters as triangulations of appropriate surfaces, we show that all cluster variables either:
(i) Appear after applying the cluster map
(ii) Can be written as a determinant function of the periodic quantities.
Finally we show that the sets of cluster variables (i) and (ii) both form friezes.
We first review the dynamical systems previously obtained for affine A and D type cluster algebras, given by the "cluster map", and the periodic quantities found for these systems. Then, by viewing the clusters as triangulations of appropriate surfaces, we show that all cluster variables either:
(i) Appear after applying the cluster map
(ii) Can be written as a determinant function of the periodic quantities.
Finally we show that the sets of cluster variables (i) and (ii) both form friezes.
2021/06/29
Tuesday Seminar on Topology
17:00-18:00 Online
Pre-registration required. See our seminar webpage.
Kenta Hayano (Keio University)
Stability of non-proper functions (JAPANESE)
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
Pre-registration required. See our seminar webpage.
Kenta Hayano (Keio University)
Stability of non-proper functions (JAPANESE)
[ Abstract ]
In this talk, we will give a sufficient condition for (strong) stability of non-proper functions (with respect to the Whitney topology). As an application, we will give a strongly stable but not infinitesimally stable function. We will further show that any Nash function on the Euclidean space becomes stable after a generic linear perturbation.
[ Reference URL ]In this talk, we will give a sufficient condition for (strong) stability of non-proper functions (with respect to the Whitney topology). As an application, we will give a strongly stable but not infinitesimally stable function. We will further show that any Nash function on the Euclidean space becomes stable after a generic linear perturbation.
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
Operator Algebra Seminars
16:45-18:15 Online
Rui Okayasu (Osaka Kyoiku University)
Injective factors with trivial bicentralizer
[ Reference URL ]
https://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm
Rui Okayasu (Osaka Kyoiku University)
Injective factors with trivial bicentralizer
[ Reference URL ]
https://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm
Lie Groups and Representation Theory
17:00-18:00 Room #Online (Graduate School of Math. Sci. Bldg.)
Hidenori Fujiwara (Kindai University)
Polynomial conjectures for nilpotent Lie groups
(Japanese)
Hidenori Fujiwara (Kindai University)
Polynomial conjectures for nilpotent Lie groups
(Japanese)
[ Abstract ]
Let G = exp g be a connected and simply connected nilpotent Lie group with Lie algebra g. Let H = exp h be an analytic subgroup of G with Lie algebra h and χ a unitary character of H. We consider the monomial representation τ = ind^G_H χ of G. It is well known that the multiplicities in the irreducible disintegration of τ are either uniformly bounded or uniformly equal to ∞. In the former case, we say that τ has finite multiplicities.
Now let D_τ (G/H) be the algebra of the G-invariant differential operators on the fiber bundle over G/H associated to the data (H,χ). This algebra is commutative if and only if τ has finite multiplicities. In
1992 Corwin-Greenleaf presented the following polynomial conjecture :
when τ has finite multiplicities, the algebra D_τ (G/H) is isomorphic to the algebra C[Γ_τ]^H of the H-invariant polynomial functions on the affine subspace Γ_τ = {l ∈ g^* ; l |_h = - √ -1 dχ} of g^* .
It is well known in the representation theory of groups that between the two operations of induction and restriction there is a kind of duality. So, we think about a polynomial conjecture for restrictions. Let G be as above a connected and simply connected nilpotent Lie group and π an irreducible unitary representation of G. Let K be an analytic subgroup of G, and we consider the restriction π|_K of π to K. This time also it is known that the multiplicities in the irreducible disintegration of π|_K are either uniformly bounded or uniformly equal to ∞. In the former case, we say that π|_K has finite multiplicities and we assume
this eventuality. Let U(g) be the enveloping algebra of g_C, and we consider the algebra (U(g)/kerπ)_K of invariant differential operators. This means the set of the K-invariant elements. This algebra is commutative if and only if π|_K has finite multiplicities. In this case, is the algebra (U(g)/kerπ)^K isomorphic to the algebra C[Ω(π)]^K of the K-invariant polynomial functions on Ω(π)? Here, Ω(π) denotes the coadjoint orbit of G corresponding to π.
We would like to prove these two polynomial conjectures.
Let G = exp g be a connected and simply connected nilpotent Lie group with Lie algebra g. Let H = exp h be an analytic subgroup of G with Lie algebra h and χ a unitary character of H. We consider the monomial representation τ = ind^G_H χ of G. It is well known that the multiplicities in the irreducible disintegration of τ are either uniformly bounded or uniformly equal to ∞. In the former case, we say that τ has finite multiplicities.
Now let D_τ (G/H) be the algebra of the G-invariant differential operators on the fiber bundle over G/H associated to the data (H,χ). This algebra is commutative if and only if τ has finite multiplicities. In
1992 Corwin-Greenleaf presented the following polynomial conjecture :
when τ has finite multiplicities, the algebra D_τ (G/H) is isomorphic to the algebra C[Γ_τ]^H of the H-invariant polynomial functions on the affine subspace Γ_τ = {l ∈ g^* ; l |_h = - √ -1 dχ} of g^* .
It is well known in the representation theory of groups that between the two operations of induction and restriction there is a kind of duality. So, we think about a polynomial conjecture for restrictions. Let G be as above a connected and simply connected nilpotent Lie group and π an irreducible unitary representation of G. Let K be an analytic subgroup of G, and we consider the restriction π|_K of π to K. This time also it is known that the multiplicities in the irreducible disintegration of π|_K are either uniformly bounded or uniformly equal to ∞. In the former case, we say that π|_K has finite multiplicities and we assume
this eventuality. Let U(g) be the enveloping algebra of g_C, and we consider the algebra (U(g)/kerπ)_K of invariant differential operators. This means the set of the K-invariant elements. This algebra is commutative if and only if π|_K has finite multiplicities. In this case, is the algebra (U(g)/kerπ)^K isomorphic to the algebra C[Ω(π)]^K of the K-invariant polynomial functions on Ω(π)? Here, Ω(π) denotes the coadjoint orbit of G corresponding to π.
We would like to prove these two polynomial conjectures.
2021/06/28
Seminar on Geometric Complex Analysis
10:30-12:00 Online
Yûsuke Okuyama (Kyoto Institute of Technology)
Orevkov's theorem, Bézout's theorem, and the converse of Brolin's theorem (Japanese)
https://u-tokyo-ac-jp.zoom.us/meeting/register/tJ0vcu2rrDIqG9Rv5AT0Mpi37urIkJ1IRldB
Yûsuke Okuyama (Kyoto Institute of Technology)
Orevkov's theorem, Bézout's theorem, and the converse of Brolin's theorem (Japanese)
[ Abstract ]
The converse of Brolin's theorem was a problem on characterizing polynomials among rational functions (on the complex projective line) in terms of the equilibrium measures canonically associated to rational functions. We would talk about a history on the studies of this problem, its optimal solution, and a proof outline. The proof is reduced to Bézout's theorem from algebraic geometry, thanks to Orevkov's irreducibility theorem on polynomial lemniscates. This talk is based on joint works with Małgorzata Stawiska (Mathematical Reviews).
[ Reference URL ]The converse of Brolin's theorem was a problem on characterizing polynomials among rational functions (on the complex projective line) in terms of the equilibrium measures canonically associated to rational functions. We would talk about a history on the studies of this problem, its optimal solution, and a proof outline. The proof is reduced to Bézout's theorem from algebraic geometry, thanks to Orevkov's irreducibility theorem on polynomial lemniscates. This talk is based on joint works with Małgorzata Stawiska (Mathematical Reviews).
https://u-tokyo-ac-jp.zoom.us/meeting/register/tJ0vcu2rrDIqG9Rv5AT0Mpi37urIkJ1IRldB
2021/06/25
Colloquium
15:30-16:30 Online
Registration is closed (12:00, June 25).
Hisashi Okamoto (Gakushuin University)
The Prandtl-Batchelor theory and its applications to Kolmogorov's problem (JAPANESE)
Registration is closed (12:00, June 25).
Hisashi Okamoto (Gakushuin University)
The Prandtl-Batchelor theory and its applications to Kolmogorov's problem (JAPANESE)
2021/06/24
Tokyo-Nagoya Algebra Seminar
16:00-17:30 Online
Please see the URL below for details on the online seminar.
Kohei Kikuta (Chuo University)
Rank 2 free subgroups in autoequivalence groups of Calabi-Yau categories
http://www.math.nagoya-u.ac.jp/~aaron.chan/TNAseminar.html
Please see the URL below for details on the online seminar.
Kohei Kikuta (Chuo University)
Rank 2 free subgroups in autoequivalence groups of Calabi-Yau categories
[ Abstract ]
Via homological mirror symmetry, there is a relation between autoequivalence groups of derived categories of coherent sheaves on Calabi-Yau varieties, and the symplectic mapping class groups of symplectic manifolds.
In this talk, as an analogue of mapping class groups of closed oriented surfaces, we study autoequivalence groups of Calabi-Yau triangulated categories. In particular, we consider embeddings of rank 2 (non-commutative) free groups generated by spherical twists. It is interesting that the proof of main results is almost similar to that of corresponding results in the theory of mapping class groups.
[ Reference URL ]Via homological mirror symmetry, there is a relation between autoequivalence groups of derived categories of coherent sheaves on Calabi-Yau varieties, and the symplectic mapping class groups of symplectic manifolds.
In this talk, as an analogue of mapping class groups of closed oriented surfaces, we study autoequivalence groups of Calabi-Yau triangulated categories. In particular, we consider embeddings of rank 2 (non-commutative) free groups generated by spherical twists. It is interesting that the proof of main results is almost similar to that of corresponding results in the theory of mapping class groups.
http://www.math.nagoya-u.ac.jp/~aaron.chan/TNAseminar.html
Information Mathematics Seminar
16:50-18:35 Online
Hiroshi Fujiwara (BroadBand Tower, Inc.)
From a neural network to deep learning (Japanese)
https://docs.google.com/forms/d/1zdmPdHWcVgH6Sn62nVHNp0ODVBJ7fyHKJHdABtDd_Tw
Hiroshi Fujiwara (BroadBand Tower, Inc.)
From a neural network to deep learning (Japanese)
[ Abstract ]
Explanation on the neural network and the deep learning
[ Reference URL ]Explanation on the neural network and the deep learning
https://docs.google.com/forms/d/1zdmPdHWcVgH6Sn62nVHNp0ODVBJ7fyHKJHdABtDd_Tw
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