Seminar information archive
Seminar information archive ～02/01｜Today's seminar 02/02  Future seminars 02/03～
Number Theory Seminar
17:0018:00 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 BirchSwinnertonDyer 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 BirchSwinnertonDyer 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
16:3018:00 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
17:3018:30 Online
Preregistration required. See our seminar webpage.
Yosuke Kubota (Shinshu University)
Codimension 2 transfer map in higher index theory (JAPANESE)
https://park.itc.utokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
Preregistration 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 Kgroup 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 HankePapeSchick 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 Kgroups, which we call the codimension 2 transfer map, relating the Rosenberg index of M to that of N directly. This shows that HankePapeSchick'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 nullcobordant.
[ Reference URL ]The Rosenberg index is a topological invariant taking value in the Kgroup 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 HankePapeSchick 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 Kgroups, which we call the codimension 2 transfer map, relating the Rosenberg index of M to that of N directly. This shows that HankePapeSchick'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 nullcobordant.
https://park.itc.utokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
Lie Groups and Representation Theory
17:0018:00 Room #Online (Graduate School of Math. Sci. Bldg.)
Taito Tauchi (Kyushu University )
A counterexample to a Qseries analogue of Casselman's subrepresentation theorem (Japanese)
Taito Tauchi (Kyushu University )
A counterexample to a Qseries 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 Qseries if it occurs as a subquotient of some degenerate principal series representation induced from Q. Then, any irreducible admissible representation belongs to Pseries by HarishChandra’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 Pseries can be realized as a
subrepresentation of some principal series representation induced from P. In this talk, we discuss a counterexample to a Qseries analogue of this subrepresentation theorem. More precisely, we show that there exists an irreducible admissible representation belonging to Qseries, 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 Qseries if it occurs as a subquotient of some degenerate principal series representation induced from Q. Then, any irreducible admissible representation belongs to Pseries by HarishChandra’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 Pseries can be realized as a
subrepresentation of some principal series representation induced from P. In this talk, we discuss a counterexample to a Qseries analogue of this subrepresentation theorem. More precisely, we show that there exists an irreducible admissible representation belonging to Qseries, 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
10:3012:00 Online
Nitta Yasufumi (Tokyo University of Science)
Several stronger concepts of relative Kstability for polarized toric manifolds (Japanese)
https://utokyoacjp.zoom.us/meeting/register/tJ0vcu2rrDIqG9Rv5AT0Mpi37urIkJ1IRldB
Nitta Yasufumi (Tokyo University of Science)
Several stronger concepts of relative Kstability for polarized toric manifolds (Japanese)
[ Abstract ]
We study relations between algebrogeometric stabilities for polarized toric manifolds. In this talk, we introduce several strengthenings of relative Kstability such as uniform stability and Kstability 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 YauTianDonaldson 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 algebrogeometric stabilities for polarized toric manifolds. In this talk, we introduce several strengthenings of relative Kstability such as uniform stability and Kstability 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 YauTianDonaldson conjecture for Calabi's extremal Kähler metrics in the toric setting. This talk is based on a joint work with Shunsuke Saito.
https://utokyoacjp.zoom.us/meeting/register/tJ0vcu2rrDIqG9Rv5AT0Mpi37urIkJ1IRldB
Algebraic Geometry Seminar
16:0017:00 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
10:5517:10 Room # (Graduate School of Math. Sci. Bldg.)
 ()

[ Reference URL ]
http://www.sigmath.es.osakau.ac.jp/statmodel/?page_id=2028
 ()

[ Reference URL ]
http://www.sigmath.es.osakau.ac.jp/statmodel/?page_id=2028
2021/07/01
Algebraic Geometry Seminar
10:0011:00 Room # (Graduate School of Math. Sci. Bldg.)
Fumiaki Suzuki (UCLA)
An Oacyclic variety of even index
Fumiaki Suzuki (UCLA)
An Oacyclic variety of even index
[ Abstract ]
I will construct a family of Enriques surfaces parametrized by P^1 such that any multisection has even degree over the base P^1. Over the function field of a complex curve, this gives the first example of an Oacyclic variety (H^i(X,O)=0 for i>0) whose index is not equal to one, and an affirmative answer to a question of ColliotThélène and Voisin. I will also discuss applications to related problems, including the integral Hodge conjecture and Murre’s question on universality of the AbelJacobi maps. This is joint work with John Christian Ottem.
I will construct a family of Enriques surfaces parametrized by P^1 such that any multisection has even degree over the base P^1. Over the function field of a complex curve, this gives the first example of an Oacyclic variety (H^i(X,O)=0 for i>0) whose index is not equal to one, and an affirmative answer to a question of ColliotThélène and Voisin. I will also discuss applications to related problems, including the integral Hodge conjecture and Murre’s question on universality of the AbelJacobi maps. This is joint work with John Christian Ottem.
Information Mathematics Seminar
16:5018:35 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
17:0018:00 Online
Kimihiko Li (University of Tokyo)
Prismatic and qcrystalline sites of higher level (Japanese)
Kimihiko Li (University of Tokyo)
Prismatic and qcrystalline sites of higher level (Japanese)
[ Abstract ]
Two new padic cohomology theories, called prismatic cohomology and qcrystalline cohomology, were defined for generalizing crystalline cohomology and they recover most known integral padic cohomology theories. On the other hand, higher level crystalline cohomology was defined for constructing padic 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 qcrystalline sites and prove a certain equivalence between the category of crystals on the mprismatic site or the mqcrystalline site and that on the usual prismatic site or the usual qcrystalline 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 mprismatic site and that on the (m1)qcrystalline site.
Two new padic cohomology theories, called prismatic cohomology and qcrystalline cohomology, were defined for generalizing crystalline cohomology and they recover most known integral padic cohomology theories. On the other hand, higher level crystalline cohomology was defined for constructing padic 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 qcrystalline sites and prove a certain equivalence between the category of crystals on the mprismatic site or the mqcrystalline site and that on the usual prismatic site or the usual qcrystalline 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 mprismatic site and that on the (m1)qcrystalline site.
Discrete mathematical modelling seminar
17:1518:45 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
17:0018:00 Online
Preregistration required. See our seminar webpage.
Kenta Hayano (Keio University)
Stability of nonproper functions (JAPANESE)
https://park.itc.utokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
Preregistration required. See our seminar webpage.
Kenta Hayano (Keio University)
Stability of nonproper functions (JAPANESE)
[ Abstract ]
In this talk, we will give a sufficient condition for (strong) stability of nonproper 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 nonproper 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.utokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
Operator Algebra Seminars
16:4518:15 Online
Rui Okayasu (Osaka Kyoiku University)
Injective factors with trivial bicentralizer
[ Reference URL ]
https://www.ms.utokyo.ac.jp/~yasuyuki/tokyoseminar.htm
Rui Okayasu (Osaka Kyoiku University)
Injective factors with trivial bicentralizer
[ Reference URL ]
https://www.ms.utokyo.ac.jp/~yasuyuki/tokyoseminar.htm
Lie Groups and Representation Theory
17:0018:00 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 Ginvariant 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 CorwinGreenleaf 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 Hinvariant 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 Kinvariant 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 Kinvariant 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 Ginvariant 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 CorwinGreenleaf 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 Hinvariant 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 Kinvariant 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 Kinvariant 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
10:3012:00 Online
Yûsuke Okuyama (Kyoto Institute of Technology)
Orevkov's theorem, Bézout's theorem, and the converse of Brolin's theorem (Japanese)
https://utokyoacjp.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://utokyoacjp.zoom.us/meeting/register/tJ0vcu2rrDIqG9Rv5AT0Mpi37urIkJ1IRldB
2021/06/25
Colloquium
15:3016:30 Online
Registration is closed (12:00, June 25).
Hisashi Okamoto (Gakushuin University)
The PrandtlBatchelor theory and its applications to Kolmogorov's problem (JAPANESE)
Registration is closed (12:00, June 25).
Hisashi Okamoto (Gakushuin University)
The PrandtlBatchelor theory and its applications to Kolmogorov's problem (JAPANESE)
2021/06/24
TokyoNagoya Algebra Seminar
16:0017:30 Online
Please see the URL below for details on the online seminar.
Kohei Kikuta (Chuo University)
Rank 2 free subgroups in autoequivalence groups of CalabiYau categories
http://www.math.nagoyau.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 CalabiYau categories
[ Abstract ]
Via homological mirror symmetry, there is a relation between autoequivalence groups of derived categories of coherent sheaves on CalabiYau 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 CalabiYau triangulated categories. In particular, we consider embeddings of rank 2 (noncommutative) 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 CalabiYau 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 CalabiYau triangulated categories. In particular, we consider embeddings of rank 2 (noncommutative) 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.nagoyau.ac.jp/~aaron.chan/TNAseminar.html
Information Mathematics Seminar
16:5018:35 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
2021/06/23
Number Theory Seminar
17:0018:00 Online
Koto Imai (University of Tokyo)
Ramification groups of some finite Galois extensions of maximal nilpotency class over local fields of positive characteristic (Japanese)
Koto Imai (University of Tokyo)
Ramification groups of some finite Galois extensions of maximal nilpotency class over local fields of positive characteristic (Japanese)
[ Abstract ]
Galois extensions of local fields is one of the most important subjects in the field of number theory. A ramification filtration is a filtration of a Galois group used to investigate the ramification of the extension. It is particularly useful when the extension is wildly ramified. In this talk, we examine the ramification groups of finite Galois extensions over complete discrete valuation fields of characteristic $p>0$. Brylinski calculated the ramification groups in the case where the Galois groups are abelian. We extend the results of Brylinski to some nonabelian cases where the Galois groups are of order $\leq p^{p+1}$ and of maximal nilpotency class.
Galois extensions of local fields is one of the most important subjects in the field of number theory. A ramification filtration is a filtration of a Galois group used to investigate the ramification of the extension. It is particularly useful when the extension is wildly ramified. In this talk, we examine the ramification groups of finite Galois extensions over complete discrete valuation fields of characteristic $p>0$. Brylinski calculated the ramification groups in the case where the Galois groups are abelian. We extend the results of Brylinski to some nonabelian cases where the Galois groups are of order $\leq p^{p+1}$ and of maximal nilpotency class.
Discrete mathematical modelling seminar
18:0019:30 Online
This seminar will be held using Zoom. If you wish to participate, please contact R. Willox by email.
Alexander STOKES (University College London)
Singularity confinement in delaydifferential Painlevé equations (English)
This seminar will be held using Zoom. If you wish to participate, please contact R. Willox by email.
Alexander STOKES (University College London)
Singularity confinement in delaydifferential Painlevé equations (English)
[ Abstract ]
Singularity confinement is a phenomenon first proposed as an integrability criterion for discrete systems, and has been used to great effect to obtain discrete analogues of the Painlevé differential equations. Its geometric interpretation has played a role in novel connections between discrete integrable systems and birational algebraic geometry, including Sakai's geometric framework and classification scheme for discrete Painlevé equations.
Examples of delaydifferential equations, which involve shifts and derivatives with respect to a single independent variable, have been proposed as analogues of the Painlevé equations according to a number of viewpoints. Among these are observations of a kind of singularity confinement and it is natural to ask whether this could lead to the development of a geometric theory of delaydifferential Painlevé equations.
In this talk we review previously proposed examples of delaydifferential Painlevé equations and what is known about their singularity confinement behaviour, including some recent results establishing the existence of infinite families of confined singularities. We also propose a geometric interpretation of these results in terms of mappings between jet spaces, defining certain singularities analogous to those of interest in the singularity analysis of discrete systems, and what it means for them to be confined.
Singularity confinement is a phenomenon first proposed as an integrability criterion for discrete systems, and has been used to great effect to obtain discrete analogues of the Painlevé differential equations. Its geometric interpretation has played a role in novel connections between discrete integrable systems and birational algebraic geometry, including Sakai's geometric framework and classification scheme for discrete Painlevé equations.
Examples of delaydifferential equations, which involve shifts and derivatives with respect to a single independent variable, have been proposed as analogues of the Painlevé equations according to a number of viewpoints. Among these are observations of a kind of singularity confinement and it is natural to ask whether this could lead to the development of a geometric theory of delaydifferential Painlevé equations.
In this talk we review previously proposed examples of delaydifferential Painlevé equations and what is known about their singularity confinement behaviour, including some recent results establishing the existence of infinite families of confined singularities. We also propose a geometric interpretation of these results in terms of mappings between jet spaces, defining certain singularities analogous to those of interest in the singularity analysis of discrete systems, and what it means for them to be confined.
2021/06/22
Numerical Analysis Seminar
17:0018:30 Online
Taiji Suzuki (The University of Tokyo)
On approximation ability and adaptivity of deep neural network (Japanese)
[ Reference URL ]
https://forms.gle/HwetNGXCzbCyMC7B7
Taiji Suzuki (The University of Tokyo)
On approximation ability and adaptivity of deep neural network (Japanese)
[ Reference URL ]
https://forms.gle/HwetNGXCzbCyMC7B7
Operator Algebra Seminars
16:4518:15 Online
Johannes Christensen (KU Leuven)
KMS spectra for group actions on compact spaces (English)
[ Reference URL ]
https://www.ms.utokyo.ac.jp/~yasuyuki/tokyoseminar.htm
Johannes Christensen (KU Leuven)
KMS spectra for group actions on compact spaces (English)
[ Reference URL ]
https://www.ms.utokyo.ac.jp/~yasuyuki/tokyoseminar.htm
Tuesday Seminar on Topology
17:0018:30 Online
Preregistration required. See our seminar webpage.
Ryoma Kobayashi (National Institute of Technology, Ishikawa College)
On infinite presentations for the mapping class group of a compact non orientable surface and its twist subgroup (JAPANESE)
https://park.itc.utokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
Preregistration required. See our seminar webpage.
Ryoma Kobayashi (National Institute of Technology, Ishikawa College)
On infinite presentations for the mapping class group of a compact non orientable surface and its twist subgroup (JAPANESE)
[ Abstract ]
An infinite presentation for the mapping class group of any compact orientable surface was given by Gervais, and then a simpler one by Luo. Using these results, an infinite presentation for the mapping class group of any compact non orientable surfaces with boundary less than or equal to one was given by Omori (Tokyo University of Science), and then one with boundary more than or equal to two by Omori and the speaker. In this talk, we first introduce an infinite presentation for the twisted subgroup of the mapping class group of any compact non orientable surface. I will also present four simple infinite presentations for the mapping group of any compact non orientable surface, which are an improvement of the one given by Omori and the speaker. This work includes a joint work with Omori.
[ Reference URL ]An infinite presentation for the mapping class group of any compact orientable surface was given by Gervais, and then a simpler one by Luo. Using these results, an infinite presentation for the mapping class group of any compact non orientable surfaces with boundary less than or equal to one was given by Omori (Tokyo University of Science), and then one with boundary more than or equal to two by Omori and the speaker. In this talk, we first introduce an infinite presentation for the twisted subgroup of the mapping class group of any compact non orientable surface. I will also present four simple infinite presentations for the mapping group of any compact non orientable surface, which are an improvement of the one given by Omori and the speaker. This work includes a joint work with Omori.
https://park.itc.utokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
Lie Groups and Representation Theory
17:0018:00 Room #Online (Graduate School of Math. Sci. Bldg.)
Yosuke MORITA (Kyoto University)
Cartan projections of some nonreductive subgroups and the existence problem of compact CliffordKlein forms (Japanese)
Yosuke MORITA (Kyoto University)
Cartan projections of some nonreductive subgroups and the existence problem of compact CliffordKlein forms (Japanese)
[ Abstract ]
Let G be a reductive Lie group, H a closed subgroup of G, and Γ a discrete subgroup of G.
According to the KobayashiBenoist criterion, the properness of the Γaction on G/H is determined by the Cartan projections of H and Γ.
Although the Cartan projections of nonreductive subgroups are usually difficult to compute, there are some exceptions. Using them, we give some examples of homogeneous spaces of reductive type that do not admit compact CliffordKlein forms.
Let G be a reductive Lie group, H a closed subgroup of G, and Γ a discrete subgroup of G.
According to the KobayashiBenoist criterion, the properness of the Γaction on G/H is determined by the Cartan projections of H and Γ.
Although the Cartan projections of nonreductive subgroups are usually difficult to compute, there are some exceptions. Using them, we give some examples of homogeneous spaces of reductive type that do not admit compact CliffordKlein forms.
2021/06/17
Applied Analysis
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