Text only print
Full screen print
Seminar information archive
Seminar information archive ～04/22｜Today's seminar 04/23 | Future seminars 04/24～
2021/11/25
Applied Analysis
Information Mathematics Seminar
16:50-18:35 Online
Hiroshi Fujiwara (BroadBand Tower, Inc.)
Classification and Clustering in the Machine Learning (Japanese)
https://docs.google.com/forms/d/1I3XD63V937BT_IoqRWBVN67goQAtbkSoIKs-6hfLUAM
Hiroshi Fujiwara (BroadBand Tower, Inc.)
Classification and Clustering in the Machine Learning (Japanese)
[ Abstract ]
Explanation on classification and clustering in the Machine Learning
[ Reference URL ]Explanation on classification and clustering in the Machine Learning
https://docs.google.com/forms/d/1I3XD63V937BT_IoqRWBVN67goQAtbkSoIKs-6hfLUAM
2021/11/24
Number Theory Seminar
17:00-18:00 Online
Kazuma Ohara (University of Tokyo)
On the formal degree conjecture for non-singular supercuspidal representations (Japanese)
Kazuma Ohara (University of Tokyo)
On the formal degree conjecture for non-singular supercuspidal representations (Japanese)
[ Abstract ]
We prove the formal degree conjecture for non-singular supercuspidal representations based on Schwein's work proving the formal degree conjecture for regular supercuspidal representations. The main difference between our work and Schwein's work is that in non-singular case, the Deligne--Lusztig representations can be reducible, and the $S$-groups are not necessarily abelian. Therefore, we have to compare the dimensions of irreducible constituents of the Deligne--Lusztig representations and the dimensions of irreducible representations of $S$-groups.
We prove the formal degree conjecture for non-singular supercuspidal representations based on Schwein's work proving the formal degree conjecture for regular supercuspidal representations. The main difference between our work and Schwein's work is that in non-singular case, the Deligne--Lusztig representations can be reducible, and the $S$-groups are not necessarily abelian. Therefore, we have to compare the dimensions of irreducible constituents of the Deligne--Lusztig representations and the dimensions of irreducible representations of $S$-groups.
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.)
Yosuke Hasegawa (Institute of Industrial Science, the University of Tokyo)
乱流熱輸送現象の最適制御と複雑伝熱面の形状最適化 (日本語)
Yosuke Hasegawa (Institute of Industrial Science, the University of Tokyo)
乱流熱輸送現象の最適制御と複雑伝熱面の形状最適化 (日本語)
2021/11/23
Lie Groups and Representation Theory
17:00-18:00 Room #on line (Graduate School of Math. Sci. Bldg.)
Yuichiro Tanaka (The University of Tokyo)
A Cartan decomposition for a reductive real spherical subgroup
(Japanese)
Yuichiro Tanaka (The University of Tokyo)
A Cartan decomposition for a reductive real spherical subgroup
(Japanese)
[ Abstract ]
A closed subgroup H of a real reductive Lie group G is real spherical if a minimal parabolic subgroup of G has an open orbit on G/H.
In this talk I would like to show a proof of a Cartan decomposition G=KAH when H is reductive.
This is a conjecture of T. Kobayashi, introduced in the 3rd Number Theory Summer School in 1995.
A closed subgroup H of a real reductive Lie group G is real spherical if a minimal parabolic subgroup of G has an open orbit on G/H.
In this talk I would like to show a proof of a Cartan decomposition G=KAH when H is reductive.
This is a conjecture of T. Kobayashi, introduced in the 3rd Number Theory Summer School in 1995.
2021/11/19
Tokyo-Nagoya Algebra Seminar
17:00-18:30 Online
Please see the URL below for details on the online seminar.
Yuta Kozakai (Tokyo University of Science)
有限群のブロック上の$\tau$-傾理論 (Japanese) (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.
Yuta Kozakai (Tokyo University of Science)
有限群のブロック上の$\tau$-傾理論 (Japanese) (Japanese)
[ Reference URL ]
http://www.math.nagoya-u.ac.jp/~aaron.chan/TNAseminar.html
2021/11/18
Information Mathematics Seminar
16:50-18:35 Online
Hiroshi Fujiwara (BroadBand Tower, Inc.)
Reinforcement learning and Regression algorithm to support AI (Japanese)
https://docs.google.com/forms/d/1I3XD63V937BT_IoqRWBVN67goQAtbkSoIKs-6hfLUAM
Hiroshi Fujiwara (BroadBand Tower, Inc.)
Reinforcement learning and Regression algorithm to support AI (Japanese)
[ Abstract ]
Explanation on reinforcement learning and regression algorithm to support AI
[ Reference URL ]Explanation on reinforcement learning and regression algorithm to support AI
https://docs.google.com/forms/d/1I3XD63V937BT_IoqRWBVN67goQAtbkSoIKs-6hfLUAM
2021/11/17
Seminar on Probability and Statistics
15:30-17:00 Room # (Graduate School of Math. Sci. Bldg.)
Jean Bertoin (Institut of Mathematics, University of Zurich (UZH))
On the local times of noise reinforced Bessel processes
https://docs.google.com/forms/d/e/1FAIpQLSeuK9AOw6QUqvUge9ukw__v04j5jpfogzrGxlPLpEgNhW09kg/viewform
Jean Bertoin (Institut of Mathematics, University of Zurich (UZH))
On the local times of noise reinforced Bessel processes
[ Abstract ]
Asia-Pacific Seminar in Probability and Statistics (APSPS)
https://sites.google.com/view/apsps/home
Bessel processes form a one-parameter family of self-similar diffusion on $[0,\infty)$ with the same Hurst exponent 1/2 as Brownian motion. Loosely speaking, in this setting, linear noise reinforcement with reinforcement parameter $p$ consists of repeating (if $p>0$) or counterbalancing (if $p<0$)infinitesimal increments of the process, uniformly at random and at a fixed rate as time passes. In this talk, we will investigate the effect of noise reinforcement on the local time at level $0$, that is, informally, the time that the process spends at $0$. A connection with increasing self-similar Markov processes will play a key role.
[ Reference URL ]Asia-Pacific Seminar in Probability and Statistics (APSPS)
https://sites.google.com/view/apsps/home
Bessel processes form a one-parameter family of self-similar diffusion on $[0,\infty)$ with the same Hurst exponent 1/2 as Brownian motion. Loosely speaking, in this setting, linear noise reinforcement with reinforcement parameter $p$ consists of repeating (if $p>0$) or counterbalancing (if $p<0$)infinitesimal increments of the process, uniformly at random and at a fixed rate as time passes. In this talk, we will investigate the effect of noise reinforcement on the local time at level $0$, that is, informally, the time that the process spends at $0$. A connection with increasing self-similar Markov processes will play a key role.
https://docs.google.com/forms/d/e/1FAIpQLSeuK9AOw6QUqvUge9ukw__v04j5jpfogzrGxlPLpEgNhW09kg/viewform
2021/11/16
Tuesday Seminar of Analysis
16:00-17:30 Online
KUBO Hideo (Hokkaido University)
TBA (Japanese)
[ Reference URL ]
https://forms.gle/6ZCp8hQxKA3vq3DB9
KUBO Hideo (Hokkaido University)
TBA (Japanese)
[ Reference URL ]
https://forms.gle/6ZCp8hQxKA3vq3DB9
Tuesday Seminar on Topology
17:00-18:00 Online
Pre-registration required. See our seminar webpage.
Wataru Yuasa (RIMS, Kyoto University)
Skein and cluster algebras of marked surfaces without punctures for sl(3) (JAPANESE)
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
Pre-registration required. See our seminar webpage.
Wataru Yuasa (RIMS, Kyoto University)
Skein and cluster algebras of marked surfaces without punctures for sl(3) (JAPANESE)
[ Abstract ]
We consider a skein algebra consisting of sl(3)-webs with the boundary skein relations for a marked surface without punctures. We construct a quantum cluster algebra coming from the moduli space of decorated SL(3)-local systems of the surface inside the skew-field of fractions of the skein algebra. In this talk, we introduce the sticking trick and the cutting trick for sl(3)-webs. The sticking trick expands the boundary-localized skein algebra into the cluster algebra. The cutting trick gives Laurent expressions of "elevation-preserving" webs with positive coefficients in certain clusters. We can also apply these tricks in the case of sp(4). This talk is based on joint works with Tsukasa Ishibashi.
[ Reference URL ]We consider a skein algebra consisting of sl(3)-webs with the boundary skein relations for a marked surface without punctures. We construct a quantum cluster algebra coming from the moduli space of decorated SL(3)-local systems of the surface inside the skew-field of fractions of the skein algebra. In this talk, we introduce the sticking trick and the cutting trick for sl(3)-webs. The sticking trick expands the boundary-localized skein algebra into the cluster algebra. The cutting trick gives Laurent expressions of "elevation-preserving" webs with positive coefficients in certain clusters. We can also apply these tricks in the case of sp(4). This talk is based on joint works with Tsukasa Ishibashi.
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
Operator Algebra Seminars
16:45-18:15 Online
Michiya Mori (RIKEN)
On regular $*$-algebras of bounded linear operators: A new approach towards a theory of noncommutative Boolean algebras
[ Reference URL ]
https://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm
Michiya Mori (RIKEN)
On regular $*$-algebras of bounded linear operators: A new approach towards a theory of noncommutative Boolean algebras
[ Reference URL ]
https://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm
Lie Groups and Representation Theory
17:00-18:00 Room #on line (Graduate School of Math. Sci. Bldg.)
Ryosuke Nakahama (Kyushu University)
Computation of weighted Bergman norms on block diagonal matrices in bounded symmetric domains (Japanese)
Ryosuke Nakahama (Kyushu University)
Computation of weighted Bergman norms on block diagonal matrices in bounded symmetric domains (Japanese)
[ Abstract ]
Let $G/K\simeq D\subset\mathfrak{p}^+$ be a Hermitian symmetric space realized as a bounded symmetric domain, and we consider the weighted Bergman space $\mathcal{H}_\lambda(D)$ on $D$.
Then the norm on each $K$-type in $\mathcal{H}_\lambda(D)$ is explicitly computed by Faraut--Kor\'anyi (1990).
In this talk, we consider the cases $\mathfrak{p}^+=\operatorname{Sym}(r,\mathbb{C})$, $M(r,\mathbb{C})$, $\operatorname{Alt}(2r,\mathbb{C})$, fix $r=r'+r''$, and decompose $\mathfrak{p}^+$ into $2\times 2$ block matrices.
Then the speaker presents the results on explicit computation of the norm of $\mathcal{H}_\lambda(D)$ on each $K'$-type in the space of polynomials on the block diagonal matrices $\mathfrak{p}^+_{11}\oplus\mathfrak{p}^+_{22}$.
Also, as an application, the speaker presents the results on Plancherel-type formulas on the branching laws for symmetric pairs $(Sp(r,\mathbb{R}),U(r',r''))$, $(U(r,r),U(r',r'')\times U(r'',r'))$, $(SO^*(4r),U(2r',2r''))$.
Let $G/K\simeq D\subset\mathfrak{p}^+$ be a Hermitian symmetric space realized as a bounded symmetric domain, and we consider the weighted Bergman space $\mathcal{H}_\lambda(D)$ on $D$.
Then the norm on each $K$-type in $\mathcal{H}_\lambda(D)$ is explicitly computed by Faraut--Kor\'anyi (1990).
In this talk, we consider the cases $\mathfrak{p}^+=\operatorname{Sym}(r,\mathbb{C})$, $M(r,\mathbb{C})$, $\operatorname{Alt}(2r,\mathbb{C})$, fix $r=r'+r''$, and decompose $\mathfrak{p}^+$ into $2\times 2$ block matrices.
Then the speaker presents the results on explicit computation of the norm of $\mathcal{H}_\lambda(D)$ on each $K'$-type in the space of polynomials on the block diagonal matrices $\mathfrak{p}^+_{11}\oplus\mathfrak{p}^+_{22}$.
Also, as an application, the speaker presents the results on Plancherel-type formulas on the branching laws for symmetric pairs $(Sp(r,\mathbb{R}),U(r',r''))$, $(U(r,r),U(r',r'')\times U(r'',r'))$, $(SO^*(4r),U(2r',2r''))$.
2021/11/15
Seminar on Geometric Complex Analysis
10:30-12:00 Online
Katsusuke Nabeshima (Tokyo University of Science)
Computing logarithmic vector fields along an isolated singularity and Bruce-Roberts Milnor ideals (Japanese)
https://u-tokyo-ac-jp.zoom.us/meeting/register/tJ0vcu2rrDIqG9Rv5AT0Mpi37urIkJ1IRldB
Katsusuke Nabeshima (Tokyo University of Science)
Computing logarithmic vector fields along an isolated singularity and Bruce-Roberts Milnor ideals (Japanese)
[ Abstract ]
The concept of logarithmic vector fields along a hypersurface, introduced by K. Saito (1980), is of considerable importance in singularity theory.
Logarithmic vector fields have been extensively studied and utilized by several researchers. A. G. Aleksandrov (1986) and J. Wahl (1983) considered quasihomogeneous complete intersection cases and gave independently, among other things, a closed formula of generators of logarithmic vector fields. However, there is no closed formula for generators of logarithmic vector fields, even for semi-quasihomogeneous hypersurface isolated singularity cases. Many problems related with logarithmic vector fields remain still unsolved, especially for non-quasihomogeneous cases.
Bruce-Roberts Milnor number was introduced in 1988 by J. W. Bruce and R. M. Roberts as a generalization of the Milnor number, a multiplicity of an isolated critical point of a holomorphic function germ. This number is defined for a critical point of a holomorphic function on a singular variety in terms of logarithmic vector fields. Recently, Bruce-Robert Milnor numbers are investigated by several researchers. However, many problems related with Bruce-Roberts Milnor numbers remain unsolved.
In this talk, we consider logarithmic vector fields along a hypersurface with an isolated singularity. We present methods to study complex analytic properties of logarithmic vector fields and illustrate an algorithm for computing logarithmic vector fields. As an application of logarithmic vector fields, we consider Bruce-Roberts Milnor numbers in the context of symbolic computation.
[ Reference URL ]The concept of logarithmic vector fields along a hypersurface, introduced by K. Saito (1980), is of considerable importance in singularity theory.
Logarithmic vector fields have been extensively studied and utilized by several researchers. A. G. Aleksandrov (1986) and J. Wahl (1983) considered quasihomogeneous complete intersection cases and gave independently, among other things, a closed formula of generators of logarithmic vector fields. However, there is no closed formula for generators of logarithmic vector fields, even for semi-quasihomogeneous hypersurface isolated singularity cases. Many problems related with logarithmic vector fields remain still unsolved, especially for non-quasihomogeneous cases.
Bruce-Roberts Milnor number was introduced in 1988 by J. W. Bruce and R. M. Roberts as a generalization of the Milnor number, a multiplicity of an isolated critical point of a holomorphic function germ. This number is defined for a critical point of a holomorphic function on a singular variety in terms of logarithmic vector fields. Recently, Bruce-Robert Milnor numbers are investigated by several researchers. However, many problems related with Bruce-Roberts Milnor numbers remain unsolved.
In this talk, we consider logarithmic vector fields along a hypersurface with an isolated singularity. We present methods to study complex analytic properties of logarithmic vector fields and illustrate an algorithm for computing logarithmic vector fields. As an application of logarithmic vector fields, we consider Bruce-Roberts Milnor numbers in the context of symbolic computation.
https://u-tokyo-ac-jp.zoom.us/meeting/register/tJ0vcu2rrDIqG9Rv5AT0Mpi37urIkJ1IRldB
2021/11/11
Information Mathematics Seminar
16:50-18:35 Online
Hiroshi Fujiwara (BroadBand Tower, Inc.)
Supervised/Unsupervised Learning and Reinforcement learning for Deep Learning (Japanese)
https://docs.google.com/forms/d/1I3XD63V937BT_IoqRWBVN67goQAtbkSoIKs-6hfLUAM
Hiroshi Fujiwara (BroadBand Tower, Inc.)
Supervised/Unsupervised Learning and Reinforcement learning for Deep Learning (Japanese)
[ Abstract ]
Explanation on supervised/unsupervised learning and reinforcement learning for deep learning
[ Reference URL ]Explanation on supervised/unsupervised learning and reinforcement learning for deep learning
https://docs.google.com/forms/d/1I3XD63V937BT_IoqRWBVN67goQAtbkSoIKs-6hfLUAM
2021/11/09
Tuesday Seminar on Topology
17:00-18:00 Online
Pre-registration required. See our seminar webpage.
Shuhei Maruyama (Nagoya University)
The spaces of non-descendible quasimorphisms and bounded characteristic classes (JAPANESE)
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
Pre-registration required. See our seminar webpage.
Shuhei Maruyama (Nagoya University)
The spaces of non-descendible quasimorphisms and bounded characteristic classes (JAPANESE)
[ Abstract ]
A quasimorphism is a real-valued function on a group which is a homomorphism up to bounded error. In this talk, we discuss the (non-)descendibility of quasimorphisms. In particular, we consider the space of non-descendible quasimorphisms on universal covering groups and explain its relation to the space of bounded characteristic classes of foliated bundles. This talk is based on a joint work with Morimichi Kawasaki.
[ Reference URL ]A quasimorphism is a real-valued function on a group which is a homomorphism up to bounded error. In this talk, we discuss the (non-)descendibility of quasimorphisms. In particular, we consider the space of non-descendible quasimorphisms on universal covering groups and explain its relation to the space of bounded characteristic classes of foliated bundles. This talk is based on a joint work with Morimichi Kawasaki.
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
Operator Algebra Seminars
16:45-18:15 Online
Yoh Tanimoto (University of Rome, Tor Vergata)
Construction of Haag-Kastler nets for factorizing S-matrices with bound states
[ Reference URL ]
https://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm
Yoh Tanimoto (University of Rome, Tor Vergata)
Construction of Haag-Kastler nets for factorizing S-matrices with bound states
[ Reference URL ]
https://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm
Lie Groups and Representation Theory
17:00-18:00 Room #on line (Graduate School of Math. Sci. Bldg.)
Yoshiki Oshima (Osaka University)
On the support of Plancherel measures and the image of moment map
(Japanese)
Yoshiki Oshima (Osaka University)
On the support of Plancherel measures and the image of moment map
(Japanese)
[ Abstract ]
We see a relationship between the support of Plancherel measures for homogeneous spaces and the image of moment maps from cotangent bundles based on a joint work with Benjamin Harris.
Moreover, we discuss related problems and conjectures about inductions and restrictions for representations of Lie groups in general settings.
We see a relationship between the support of Plancherel measures for homogeneous spaces and the image of moment maps from cotangent bundles based on a joint work with Benjamin Harris.
Moreover, we discuss related problems and conjectures about inductions and restrictions for representations of Lie groups in general settings.
2021/11/04
Information Mathematics Seminar
16:50-18:35 Online
Hiroshi Fujiwara (BroadBand Tower, Inc.)
Internet business establishment/GPU application/Quantum computer design (Japanese)
https://docs.google.com/forms/d/1I3XD63V937BT_IoqRWBVN67goQAtbkSoIKs-6hfLUAM
Hiroshi Fujiwara (BroadBand Tower, Inc.)
Internet business establishment/GPU application/Quantum computer design (Japanese)
[ Abstract ]
Explanation on Internet business establishment, GPU application and quantum computer design
[ Reference URL ]Explanation on Internet business establishment, GPU application and quantum computer design
https://docs.google.com/forms/d/1I3XD63V937BT_IoqRWBVN67goQAtbkSoIKs-6hfLUAM
2021/11/02
Operator Algebra Seminars
16:45-18:15 Online
Tarahiro Miyao (Hokkaido Univ.)
Magnetic properties of ground states in many-electron systems
[ Reference URL ]
https://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm
Tarahiro Miyao (Hokkaido Univ.)
Magnetic properties of ground states in many-electron systems
[ 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.
Takefumi Nosaka (Tokyo Institute of Technolog)
Meta-nilpotent knot invariants and symplectic automorphism groups of free nilpotent groups (JAPANESE)
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
Pre-registration required. See our seminar webpage.
Takefumi Nosaka (Tokyo Institute of Technolog)
Meta-nilpotent knot invariants and symplectic automorphism groups of free nilpotent groups (JAPANESE)
[ Abstract ]
There are many developments of fibered knots and homology cylinders from topological and algebraic viewpoints. In a converse sense, we discuss meta-nilpotent localization of knot groups,
which can deal with any knot like fibered knots. The monodoromy can be regarded as a symplectic automorphism of free nilpotent group, and the conjugacy classes in the outer automorphism groups produce knot invariants in terms of Johnson homomorphisms. In this talk, I show the construction of the monodoromies, and some results on the knot invariants. I also talk approaches from Fox pairings.
[ Reference URL ]There are many developments of fibered knots and homology cylinders from topological and algebraic viewpoints. In a converse sense, we discuss meta-nilpotent localization of knot groups,
which can deal with any knot like fibered knots. The monodoromy can be regarded as a symplectic automorphism of free nilpotent group, and the conjugacy classes in the outer automorphism groups produce knot invariants in terms of Johnson homomorphisms. In this talk, I show the construction of the monodoromies, and some results on the knot invariants. I also talk approaches from Fox pairings.
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)
Difference between the distribution and hyperfunction solution spaces of an irregular holonomic D-module (Japanese)
Taito TAUCHI (Kyushu University)
Difference between the distribution and hyperfunction solution spaces of an irregular holonomic D-module (Japanese)
[ Abstract ]
Let M be a holonomic D-module. Then the distribution and hyperfunction solution spaces of M coincide if M is regular. However, there is a difference between them in general if M is irregular. In this talk, we explain this phenomena taking a Whittaker functional of the principal series representation of SL(2, R) as a concrete example.
Let M be a holonomic D-module. Then the distribution and hyperfunction solution spaces of M coincide if M is regular. However, there is a difference between them in general if M is irregular. In this talk, we explain this phenomena taking a Whittaker functional of the principal series representation of SL(2, R) as a concrete example.
2021/10/29
Colloquium
15:30-16:30 Online
Registration was closed
Takahito Kashiwabara (Graduate School of Mathematical Sciences, University of Tokyo)
Well-posedness of friction- or Signorini-type boundary value problems in the non-stationary case (JAPANESE)
Registration was closed
Takahito Kashiwabara (Graduate School of Mathematical Sciences, University of Tokyo)
Well-posedness of friction- or Signorini-type boundary value problems in the non-stationary case (JAPANESE)
2021/10/28
Applied Analysis
16:00-17:00 Online
Xiaodan Zhou (OIST)
Quasiconformal and Sobolev mappings on metric measure
https://forms.gle/QATECqmwmWGvXoU56
Xiaodan Zhou (OIST)
Quasiconformal and Sobolev mappings on metric measure
[ Abstract ]
The study of quasiconformal mappings has been an important and active topic since its introduction in the 1930s and the theory has been widely applied to different fields including differential geometry, harmonic analysis, PDEs, etc. In the Euclidean space, it is a fundamental result that three definitions (metric, geometric and analytic) of quasiconformality are equivalent. The theory of quasiconformal mappings has been extended to metric measure spaces by Heinonen and Koskela in the 1990s and their work laid the foundation of analysis on metric spaces. In general, the equivalence of the three characterizations will no longer hold without appropriate assumptions on the spaces and mappings. It is a question of general interest to find minimal assumptions on the metric spaces and on the mapping to guarantee the metric definition implies the analytic characterization or geometric characterization. In this talk, we will give an brief review of the above mentioned classical theory and present some recent results we achieved in obtaining the analytic property, in particular, the Sobolev regularity of a metric quasiconformal mapping with relaxed spaces and mapping conditions. Unexpectedly, we can apply this to prove results that are new even in the classical Euclidean setting. This is joint work with Panu Lahti (Chinese Academy of Sciences).
[ Reference URL ]The study of quasiconformal mappings has been an important and active topic since its introduction in the 1930s and the theory has been widely applied to different fields including differential geometry, harmonic analysis, PDEs, etc. In the Euclidean space, it is a fundamental result that three definitions (metric, geometric and analytic) of quasiconformality are equivalent. The theory of quasiconformal mappings has been extended to metric measure spaces by Heinonen and Koskela in the 1990s and their work laid the foundation of analysis on metric spaces. In general, the equivalence of the three characterizations will no longer hold without appropriate assumptions on the spaces and mappings. It is a question of general interest to find minimal assumptions on the metric spaces and on the mapping to guarantee the metric definition implies the analytic characterization or geometric characterization. In this talk, we will give an brief review of the above mentioned classical theory and present some recent results we achieved in obtaining the analytic property, in particular, the Sobolev regularity of a metric quasiconformal mapping with relaxed spaces and mapping conditions. Unexpectedly, we can apply this to prove results that are new even in the classical Euclidean setting. This is joint work with Panu Lahti (Chinese Academy of Sciences).
https://forms.gle/QATECqmwmWGvXoU56
Discrete mathematical modelling seminar
19:00-20:00 Online
This seminar will be held using Zoom. If you wish to participate, please contact R. Willox by email.
Andrew Hone (University of Kent)
Deformations of cluster mutations and invariant presymplectic forms
This seminar will be held using Zoom. If you wish to participate, please contact R. Willox by email.
Andrew Hone (University of Kent)
Deformations of cluster mutations and invariant presymplectic forms
[ Abstract ]
We consider deformations of sequences of cluster mutations in finite type cluster algebras, which destroy the Laurent property but preserve the presymplectic structure defined by the exchange matrix. The simplest example is the Lyness 5-cycle, arising from the cluster algebra of type A_2: this deforms to the Lyness family of integrable symplectic maps in the plane. For types A_3 and A_4 we find suitable conditions such that the deformation produces a two-parameter family of Liouville integrable maps (in dimensions two and four, respectively). We also perform Laurentification for these maps, by lifting them to a higher-dimensional space of tau functions with a cluster algebra structure, where the Laurent property is restored. More general types of deformed mutations associated with affine Dynkin quivers are shown to correspond to four-dimensional symplectic maps arising as reductions of the discrete sine-Gordon equation.
We consider deformations of sequences of cluster mutations in finite type cluster algebras, which destroy the Laurent property but preserve the presymplectic structure defined by the exchange matrix. The simplest example is the Lyness 5-cycle, arising from the cluster algebra of type A_2: this deforms to the Lyness family of integrable symplectic maps in the plane. For types A_3 and A_4 we find suitable conditions such that the deformation produces a two-parameter family of Liouville integrable maps (in dimensions two and four, respectively). We also perform Laurentification for these maps, by lifting them to a higher-dimensional space of tau functions with a cluster algebra structure, where the Laurent property is restored. More general types of deformed mutations associated with affine Dynkin quivers are shown to correspond to four-dimensional symplectic maps arising as reductions of the discrete sine-Gordon equation.
Information Mathematics Seminar
16:50-18:35 Online
Hiroshi Fujiwara (BroadBand Tower, Inc.)
Internet Business Appearance/The basics of GPU/2Iinput Quantum Gates (Japanese)
https://docs.google.com/forms/d/1I3XD63V937BT_IoqRWBVN67goQAtbkSoIKs-6hfLUAM
Hiroshi Fujiwara (BroadBand Tower, Inc.)
Internet Business Appearance/The basics of GPU/2Iinput Quantum Gates (Japanese)
[ Abstract ]
Explanation on internet business appearance, the basics of GPU and 2Iinput quantum gates.
[ Reference URL ]Explanation on internet business appearance, the basics of GPU and 2Iinput quantum gates.
https://docs.google.com/forms/d/1I3XD63V937BT_IoqRWBVN67goQAtbkSoIKs-6hfLUAM
< Previous 123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960616263646566676869707172737475767778798081828384858687888990919293949596979899100101102103104105106107108109110111112113114115116117118119120121122123124125126127128129130131132133134135136137138139140141142143144145146147148149150151152153154155156157158159160161162163164165166167168169170171172173174175176177178179180181182183184185 Next >
