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Seminar information archive
Seminar information archive ～04/23｜Today's seminar 04/24 | Future seminars 04/25～
PDE Real Analysis Seminar
10:30-11:30 Room # Zoomによるオンライン開催 (Graduate School of Math. Sci. Bldg.)
Michał Łasica (Institute of Mathematics of the Polish Academy of Sciences / University of Tokyo)
Existence of the $1$-harmonic map flow (English)
Michał Łasica (Institute of Mathematics of the Polish Academy of Sciences / University of Tokyo)
Existence of the $1$-harmonic map flow (English)
[ Abstract ]
Similarly as in the real-valued case, the total variation of maps taking values in a Riemannian manifold extends to a lower semicontinuous functional on $L^2$. However, in general this functional is not geodesically semiconvex, so the existence of its gradient flow is not provided by general variational theory. Alternatively, one can try to apply the theory of parabolic PDE systems, mimicking the approach used for $p$-harmonic map flows, $p>1$. This poses some difficulties, because the PDE system corresponding to the flow is strongly nonlinear, singular and degenerate. However, in some cases, this approach was successful. In this talk, I will describe known results on the existence of the flow, focusing on my work with Lorenzo Giacomelli and Salvador Moll.
Similarly as in the real-valued case, the total variation of maps taking values in a Riemannian manifold extends to a lower semicontinuous functional on $L^2$. However, in general this functional is not geodesically semiconvex, so the existence of its gradient flow is not provided by general variational theory. Alternatively, one can try to apply the theory of parabolic PDE systems, mimicking the approach used for $p$-harmonic map flows, $p>1$. This poses some difficulties, because the PDE system corresponding to the flow is strongly nonlinear, singular and degenerate. However, in some cases, this approach was successful. In this talk, I will describe known results on the existence of the flow, focusing on my work with Lorenzo Giacomelli and Salvador Moll.
2020/11/30
Seminar on Geometric Complex Analysis
10:30-12:00 Online
IWAI Masataka (Osaka City Univ. and Kyoto Univ.)
On asymptotic base loci of relative anti-canonical divisors
[ Reference URL ]
https://zoom.us/meeting/register/tJ0vcu2rrDIqG9Rv5AT0Mpi37urIkJ1IRldB
IWAI Masataka (Osaka City Univ. and Kyoto Univ.)
On asymptotic base loci of relative anti-canonical divisors
[ Reference URL ]
https://zoom.us/meeting/register/tJ0vcu2rrDIqG9Rv5AT0Mpi37urIkJ1IRldB
2020/11/27
Seminar on Probability and Statistics
17:00-18:10 Room #on-line (Graduate School of Math. Sci. Bldg.)
Register at least 3 days before at the reference URL. The URL for participation sent before the seminar.
Yuliya Mishura (Taras Shevchenko National University of Kyiv)
Processes with small ball estimate: properties, examples, statistical inference (ENGLISH)
https://docs.google.com/forms/d/e/1FAIpQLSeYCDQS9c9i0gy-Y0YY-q5TPJlwGmWhCYnkKRE7udvMOoy0mw/viewform
Register at least 3 days before at the reference URL. The URL for participation sent before the seminar.
Yuliya Mishura (Taras Shevchenko National University of Kyiv)
Processes with small ball estimate: properties, examples, statistical inference (ENGLISH)
[ Abstract ]
The notion of a process with small ball estimate is introduced and studied. In particular, divergence of integral functional of such process is established and applied to statistical estimation. Several interesting examples are provided, and various modifications of the main group of properties are considered. The talk is based on the common research with Prof. Nakahiro Yoshida.
[ Reference URL ]The notion of a process with small ball estimate is introduced and studied. In particular, divergence of integral functional of such process is established and applied to statistical estimation. Several interesting examples are provided, and various modifications of the main group of properties are considered. The talk is based on the common research with Prof. Nakahiro Yoshida.
https://docs.google.com/forms/d/e/1FAIpQLSeYCDQS9c9i0gy-Y0YY-q5TPJlwGmWhCYnkKRE7udvMOoy0mw/viewform
2020/11/26
Information Mathematics Seminar
16:50-18:35 Online
Hiroshi Fujiwara (BroadBand Tower, Inc.)
Reinforcement learning and Regression algorithm to support AI (Japanese)
https://forms.gle/Uhy8uBujZatjNMsGA
Hiroshi Fujiwara (BroadBand Tower, Inc.)
Reinforcement learning and Regression algorithm to support AI (Japanese)
[ Abstract ]
Explanation on the reinforcement learning and regression algorithm to support AI
[ Reference URL ]Explanation on the reinforcement learning and regression algorithm to support AI
https://forms.gle/Uhy8uBujZatjNMsGA
Mathematical Biology Seminar
15:00-16:00 Room # (Graduate School of Math. Sci. Bldg.)
Yukihiko Nakata (Department of Physics and Mathematics, Aoyama Gakuin University)
Some reinfection models (Japanese)
Yukihiko Nakata (Department of Physics and Mathematics, Aoyama Gakuin University)
Some reinfection models (Japanese)
2020/11/24
Tuesday Seminar on Topology
17:30-18:30 Online
Pre-registration required. See our seminar webpage.
Shinpei Baba (Osaka University)
Intersection of Poincare holonomy varieties and Bers' simultaneous uniformization theorem (JAPANESE)
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
Pre-registration required. See our seminar webpage.
Shinpei Baba (Osaka University)
Intersection of Poincare holonomy varieties and Bers' simultaneous uniformization theorem (JAPANESE)
[ Abstract ]
Given a marked compact Riemann surface X, the vector space of holomorphic quadratic differentials on X is identified with the space of CP1-structures on X. Then, by the holonomy representations of CP1-structures, this vector space properly embeds into the PSL(2, C)-character variety, the space of representations of the fundamental group of X into PSL(2,C).
In this manner, different Riemann surfaces structures yield different half-dimensional smooth analytic subvarieties in the character variety. In this talk, we discuss some properties of their intersection. To do so, we utilize a cut-and-paste operation, called grafting, of CP1-structures.
[ Reference URL ]Given a marked compact Riemann surface X, the vector space of holomorphic quadratic differentials on X is identified with the space of CP1-structures on X. Then, by the holonomy representations of CP1-structures, this vector space properly embeds into the PSL(2, C)-character variety, the space of representations of the fundamental group of X into PSL(2,C).
In this manner, different Riemann surfaces structures yield different half-dimensional smooth analytic subvarieties in the character variety. In this talk, we discuss some properties of their intersection. To do so, we utilize a cut-and-paste operation, called grafting, of CP1-structures.
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
2020/11/20
Colloquium
15:30-16:30 Online
Please register at the link below to attend this online colloquium
Osamu Iyama (University of Tokyo)
Tilting theory and its companions (JAPANESE)
[ Reference URL ]
https://zoom.us/meeting/register/tJIrcu-prjoiGdNRSs0z3a5rl1SiuVgk0W8K
Please register at the link below to attend this online colloquium
Osamu Iyama (University of Tokyo)
Tilting theory and its companions (JAPANESE)
[ Reference URL ]
https://zoom.us/meeting/register/tJIrcu-prjoiGdNRSs0z3a5rl1SiuVgk0W8K
2020/11/19
Operator Algebra Seminars
16:45-18:15 Online
Vincenzo Morinelli (University of Rome, Tor Vergata)
Covariant homogeneous nets of standard subspaces (English)
[ Reference URL ]
https://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm
Vincenzo Morinelli (University of Rome, Tor Vergata)
Covariant homogeneous nets of standard subspaces (English)
[ Reference URL ]
https://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm
Information Mathematics Seminar
16:50-18:35 Online
Hiroshi Fujiwara (BroadBand Tower, Inc.)
The consideration of the account injustice access case and zero trust by Microsoft (Japanese)
https://forms.gle/Uhy8uBujZatjNMsGA
Hiroshi Fujiwara (BroadBand Tower, Inc.)
The consideration of the account injustice access case and zero trust by Microsoft (Japanese)
[ Abstract ]
We give a consideration of the account injustice access case and zero trust by Microsoft
[ Reference URL ]We give a consideration of the account injustice access case and zero trust by Microsoft
https://forms.gle/Uhy8uBujZatjNMsGA
2020/11/18
Discrete mathematical modelling seminar
17:00-18:00 Online
This seminar will be held using Zoom. If you wish to participate, please contact R. Willox by email.
Giorgio GUBBIOTTI (The University of Sydney, School of Mathematics and Statistics)
Recent developments on variational difference equations and their classification (English)
This seminar will be held using Zoom. If you wish to participate, please contact R. Willox by email.
Giorgio GUBBIOTTI (The University of Sydney, School of Mathematics and Statistics)
Recent developments on variational difference equations and their classification (English)
[ Abstract ]
We review some recent development in the theory of variational difference equations of order higher than two. In particular we present our recent solution of the inverse problem of calculus variations. Then, we present the application of such solution in the classification of variational fourth-order difference equations. To be more specific, we will present the most general form of variational additive and multiplicative fourth-order difference equations.
We review some recent development in the theory of variational difference equations of order higher than two. In particular we present our recent solution of the inverse problem of calculus variations. Then, we present the application of such solution in the classification of variational fourth-order difference equations. To be more specific, we will present the most general form of variational additive and multiplicative fourth-order difference equations.
Number Theory Seminar
17:00-18:00 Online
Daichi Takeuchi (University of Tokyo)
Symmetric bilinear forms and local epsilon factors of isolated singularities in positive characteristic (Japanese)
Daichi Takeuchi (University of Tokyo)
Symmetric bilinear forms and local epsilon factors of isolated singularities in positive characteristic (Japanese)
[ Abstract ]
For a function on a smooth variety with an isolated singular point, we have two invariants. One is a non-degenerate symmetric bilinear form (de Rham), and the other is the vanishing cycles complex (\'etale). The latter is a Galois representation of a local field measuring a complexity of the singularity.
In this talk, I will give a formula which expresses the local epsilon factor of the vanishing cycles complex in terms of the bilinear form. In particular, the sign of the local epsilon factor is determined by the discriminant of the bilinear form. This can be regarded as a refinement of Milnor formula in SGA 7, which compares the rank of the bilinear form and the total dimension of the vanishing cycles.
In characteristic 2, we find a generalization of Arf invariant, which can be regarded as an invariant for a non-degenerate quadratic singularity, to a general isolated singularity.
For a function on a smooth variety with an isolated singular point, we have two invariants. One is a non-degenerate symmetric bilinear form (de Rham), and the other is the vanishing cycles complex (\'etale). The latter is a Galois representation of a local field measuring a complexity of the singularity.
In this talk, I will give a formula which expresses the local epsilon factor of the vanishing cycles complex in terms of the bilinear form. In particular, the sign of the local epsilon factor is determined by the discriminant of the bilinear form. This can be regarded as a refinement of Milnor formula in SGA 7, which compares the rank of the bilinear form and the total dimension of the vanishing cycles.
In characteristic 2, we find a generalization of Arf invariant, which can be regarded as an invariant for a non-degenerate quadratic singularity, to a general isolated singularity.
Seminar on Probability and Statistics
14:30-16:00 Room #Zoom (Graduate School of Math. Sci. Bldg.)
Please register at least 3 days before at the reference URL. The URL for participation will be sent before the seminar.
Sanjay Chaudhuri (National University of Singapore)
Hamiltonian Monte Carlo In Bayesian Empirical Likelihood Computation (English)
https://docs.google.com/forms/d/e/1FAIpQLSfbk6GTAzQuj0__YUtUMiAgbPWabT-M1vmbgldohiwPxPltuw/viewform
Please register at least 3 days before at the reference URL. The URL for participation will be sent before the seminar.
Sanjay Chaudhuri (National University of Singapore)
Hamiltonian Monte Carlo In Bayesian Empirical Likelihood Computation (English)
[ Abstract ]
Asia-Pacific Seminar in Probability and Statistics https://sites.google.com/view/apsps/home
Abstract: We consider Bayesian empirical likelihood estimation and develop an efficient Hamiltonian Monte Carlo method for sampling from the posterior distribution of the parameters of interest. The proposed method uses hitherto unknown properties of the gradient of the underlying log-empirical likelihood function. It is seen that these properties hold under minimal assumptions on the parameter space, prior density and the functions used in the estimating equations determining the empirical likelihood. We overcome major challenges posed by complex, non-convex boundaries of the support routinely observed for empirical likelihood which prevents efficient implementation of traditional Markov chain Monte Carlo methods like random walk Metropolis-Hastings etc. with or without parallel tempering. Our method employs finite number of estimating equations and observations but produces valid semi-parametric inference for a large class of statistical models including mixed effects models, generalised linear models, hierarchical Bayes models etc. A simulation study confirms that our proposed method converges quickly and draws samples from the posterior support efficiently. We further illustrate its utility through an analysis of a discrete data-set in small area estimation.
Keywords: Constrained convex optimisation; Empirical likelihood; Generalised linear models; Hamiltonian Monte Carlo; Mixed effect models; Score equations; Small area estimation; Unbiased estimating equations.
This is a joint work with Debashis Mondal, Oregon State University and Yin Teng, E&Y, Singapore.
[ Reference URL ]Asia-Pacific Seminar in Probability and Statistics https://sites.google.com/view/apsps/home
Abstract: We consider Bayesian empirical likelihood estimation and develop an efficient Hamiltonian Monte Carlo method for sampling from the posterior distribution of the parameters of interest. The proposed method uses hitherto unknown properties of the gradient of the underlying log-empirical likelihood function. It is seen that these properties hold under minimal assumptions on the parameter space, prior density and the functions used in the estimating equations determining the empirical likelihood. We overcome major challenges posed by complex, non-convex boundaries of the support routinely observed for empirical likelihood which prevents efficient implementation of traditional Markov chain Monte Carlo methods like random walk Metropolis-Hastings etc. with or without parallel tempering. Our method employs finite number of estimating equations and observations but produces valid semi-parametric inference for a large class of statistical models including mixed effects models, generalised linear models, hierarchical Bayes models etc. A simulation study confirms that our proposed method converges quickly and draws samples from the posterior support efficiently. We further illustrate its utility through an analysis of a discrete data-set in small area estimation.
Keywords: Constrained convex optimisation; Empirical likelihood; Generalised linear models; Hamiltonian Monte Carlo; Mixed effect models; Score equations; Small area estimation; Unbiased estimating equations.
This is a joint work with Debashis Mondal, Oregon State University and Yin Teng, E&Y, Singapore.
https://docs.google.com/forms/d/e/1FAIpQLSfbk6GTAzQuj0__YUtUMiAgbPWabT-M1vmbgldohiwPxPltuw/viewform
2020/11/17
Tuesday Seminar on Topology
17:00-18:00 Online
Pre-registration required. See our seminar webpage.
Yoshihiko Mitsumatsu (Chuo University)
Lefschetz fibration on the Milnor fibers of simple elliptic and cusp singularities (JAPANESE)
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
Pre-registration required. See our seminar webpage.
Yoshihiko Mitsumatsu (Chuo University)
Lefschetz fibration on the Milnor fibers of simple elliptic and cusp singularities (JAPANESE)
[ Abstract ]
In this talk a joint work with Naohiko Kasuya(Kyoto Sangyo U.), Hiroki Kodama(Tohoku U.), and Atsuhide Mori(Osaka Dental U.) is reported. The main result is the following.
There exist a Lefschetz fibration of the Milnor fiber of T_{pqr}-singularity (1/p + 1/q + 1/r ≦ 1) to the unit disk with regular fiber diffeomorphic to T^2.
An outline of the construction will be explained, through which, the space of 2-jets of (R^4, 0) to (R^2, 0) is analysed. This is motivated by F. Presas' suggestion that the speaker's construction of regular Poisson structures(=leafwise symplectic foliations) on S^5 might be interpreted by ``leafwise Lefschetz fibration''. These Lefschetz fibrations give a way to look at K3 surfaces through an extended class of Arnol'd's strange duality. These applications are introduced as well.
[ Reference URL ]In this talk a joint work with Naohiko Kasuya(Kyoto Sangyo U.), Hiroki Kodama(Tohoku U.), and Atsuhide Mori(Osaka Dental U.) is reported. The main result is the following.
There exist a Lefschetz fibration of the Milnor fiber of T_{pqr}-singularity (1/p + 1/q + 1/r ≦ 1) to the unit disk with regular fiber diffeomorphic to T^2.
An outline of the construction will be explained, through which, the space of 2-jets of (R^4, 0) to (R^2, 0) is analysed. This is motivated by F. Presas' suggestion that the speaker's construction of regular Poisson structures(=leafwise symplectic foliations) on S^5 might be interpreted by ``leafwise Lefschetz fibration''. These Lefschetz fibrations give a way to look at K3 surfaces through an extended class of Arnol'd's strange duality. These applications are introduced as well.
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
2020/11/12
Operator Algebra Seminars
16:45-18:15 Online
Sutanu Roy (NISER)
Contraction and bosonisation (English)
[ Reference URL ]
https://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm
Sutanu Roy (NISER)
Contraction and bosonisation (English)
[ Reference URL ]
https://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm
Tokyo-Nagoya Algebra Seminar
16:00-17:30 Online
Please see the URL below for details on the online seminar.
Arashi Sakai (Nagoya University)
ICE-closed subcategories and wide tau-tilting modules (Japanese)
Please see the URL below for details on the online seminar.
Arashi Sakai (Nagoya University)
ICE-closed subcategories and wide tau-tilting modules (Japanese)
2020/11/11
Discrete mathematical modelling seminar
17:00-18:00 Online
The seminar will be held using Zoom. If you wish to participate, please contact R. Willox by email.
Atsushi NAGAI (Tsuda University, Department of Computer Science)
Discrete Sobolev inequalities and their applications -- from periodic lattices to 1812 C60 fullerene isomers (Japanese)
The seminar will be held using Zoom. If you wish to participate, please contact R. Willox by email.
Atsushi NAGAI (Tsuda University, Department of Computer Science)
Discrete Sobolev inequalities and their applications -- from periodic lattices to 1812 C60 fullerene isomers (Japanese)
2020/11/09
Seminar on Geometric Complex Analysis
10:30-12:00 Online
NOSE Toshihiro (Fukuoka Institute of Technology)
Meromorphic continuation of local zeta functions and nonpolar singularities
[ Reference URL ]
https://zoom.us/meeting/register/tJ0vcu2rrDIqG9Rv5AT0Mpi37urIkJ1IRldB
NOSE Toshihiro (Fukuoka Institute of Technology)
Meromorphic continuation of local zeta functions and nonpolar singularities
[ Reference URL ]
https://zoom.us/meeting/register/tJ0vcu2rrDIqG9Rv5AT0Mpi37urIkJ1IRldB
2020/11/05
Operator Algebra Seminars
16:45-18:15 Online
Zhengwei Liu (Tsinghua University)
Subfactors and Quantum Fourier Analysis (English)
[ Reference URL ]
https://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm
Zhengwei Liu (Tsinghua University)
Subfactors and Quantum Fourier Analysis (English)
[ Reference URL ]
https://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm
Applied Analysis
16:00-17:30 Room #オンライン開催 (Graduate School of Math. Sci. Bldg.)
( )
Hölder gradient estimates on L^p-viscosity solutions of fully nonlinear parabolic equations with VMO coefficients (Japanese)
https://docs.google.com/forms/d/e/1FAIpQLSf4Rmd6B0m9_t_-xdy2hT1ZC1Ziz2qEc3yLRCQNZBilAOB1Ag/viewform?usp=sf_link
( )
Hölder gradient estimates on L^p-viscosity solutions of fully nonlinear parabolic equations with VMO coefficients (Japanese)
[ Abstract ]
We discuss fully nonlinear second-order uniformly parabolic equations, including parabolic Isaacs equations. Isaacs equations arise in the theory of stochastic differential games. In 2014, N.V. Krylov proved the existence of L^p-viscosity solutions of boundary value problems for equations with VMO (vanishing mean oscillation) “coefficients” when p>n+2. Furthermore, the solutions were in the parabolic Hölder space C^{1,α} for 0<α<1. Our purpose is to show C^{1,α} estimates on L^p-viscosity solutions of fully nonlinear parabolic equations under the same conditions as in Krylov’s result.
[ Reference URL ]We discuss fully nonlinear second-order uniformly parabolic equations, including parabolic Isaacs equations. Isaacs equations arise in the theory of stochastic differential games. In 2014, N.V. Krylov proved the existence of L^p-viscosity solutions of boundary value problems for equations with VMO (vanishing mean oscillation) “coefficients” when p>n+2. Furthermore, the solutions were in the parabolic Hölder space C^{1,α} for 0<α<1. Our purpose is to show C^{1,α} estimates on L^p-viscosity solutions of fully nonlinear parabolic equations under the same conditions as in Krylov’s result.
https://docs.google.com/forms/d/e/1FAIpQLSf4Rmd6B0m9_t_-xdy2hT1ZC1Ziz2qEc3yLRCQNZBilAOB1Ag/viewform?usp=sf_link
Information Mathematics Seminar
16:50-18:35 Online
Hiroshi Fujiwara (BroadBand Tower, Inc.)
History of PC rise and fall /What is a parallel processing? What is a
quantum gate? (Japanese)
https://forms.gle/Uhy8uBujZatjNMsGA
Hiroshi Fujiwara (BroadBand Tower, Inc.)
History of PC rise and fall /What is a parallel processing? What is a
quantum gate? (Japanese)
[ Abstract ]
Explanation of the history of PC rise and fall, and also of a parallel processing and a quantum gate.
[ Reference URL ]Explanation of the history of PC rise and fall, and also of a parallel processing and a quantum gate.
https://forms.gle/Uhy8uBujZatjNMsGA
2020/10/29
Operator Algebra Seminars
15:30-17:00 Online
Yoh Tanimoto (University of Rome, Tor Vergata)
Continuum (free) fields from lattice wavelet renormalization
[ Reference URL ]
https://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm
Yoh Tanimoto (University of Rome, Tor Vergata)
Continuum (free) fields from lattice wavelet renormalization
[ Reference URL ]
https://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm
Information Mathematics Seminar
16:50-18:35 Online
Hiroshi Fujiwara (BroadBand Tower, Inc.)
Supervised/Unsupervised Learning and Reinforcement Learning for Deep
Learning (Japanese)
https://forms.gle/Uhy8uBujZatjNMsGA
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://forms.gle/Uhy8uBujZatjNMsGA
2020/10/27
Numerical Analysis Seminar
16:30-18:00 Online
Buyang Li (The Hong Kong Polytechnic University)
Convergent evolving finite element algorithms for mean curvature flow and Willmore flow of closed surfaces (English)
https://forms.gle/HeuUxWLGa696KPvz8
Buyang Li (The Hong Kong Polytechnic University)
Convergent evolving finite element algorithms for mean curvature flow and Willmore flow of closed surfaces (English)
[ Abstract ]
We construct evolving surface finite element methods for the mean curvature and Willmore flow through equivalently reformulating the original equations into coupled systems governing the evolution of surface position, velocity, normal vector and mean curvature. Then we prove $H^1$-norm convergence of the proposed evolving surface finite element methods for the reformulated systems, by combining stability estimates and consistency estimates. The stability analysis is based on the matrix–vector formulation of the finite element method and does not use geometric arguments. The geometry enters only into the consistency estimates. Numerical experiments illustrate and complement the theoretical results.
[1] https://doi.org/10.1007/s00211-019-01074-2
[2] https://arxiv.org/abs/2007.15257
[ Reference URL ]We construct evolving surface finite element methods for the mean curvature and Willmore flow through equivalently reformulating the original equations into coupled systems governing the evolution of surface position, velocity, normal vector and mean curvature. Then we prove $H^1$-norm convergence of the proposed evolving surface finite element methods for the reformulated systems, by combining stability estimates and consistency estimates. The stability analysis is based on the matrix–vector formulation of the finite element method and does not use geometric arguments. The geometry enters only into the consistency estimates. Numerical experiments illustrate and complement the theoretical results.
[1] https://doi.org/10.1007/s00211-019-01074-2
[2] https://arxiv.org/abs/2007.15257
https://forms.gle/HeuUxWLGa696KPvz8
PDE Real Analysis Seminar
10:30-11:30 Room # Zoomによるオンライン開催 (Graduate School of Math. Sci. Bldg.)
Son Tu (University of Wisconsin Madison)
Vanishing discount problems for Hamilton-Jacobi equations on changing domains (English)
Son Tu (University of Wisconsin Madison)
Vanishing discount problems for Hamilton-Jacobi equations on changing domains (English)
[ Abstract ]
We study the asymptotic behavior, as the discount factor vanishes, of the Hamilton-Jacobi equation with state-constraint on changing domains. Surprisingly, we can obtain both convergence results and non-convergence results in this convex setting. Moreover, we provide a very first result on the asymptotic expansion of the additive eigenvalue of the Hamiltonian with respect to the changing domains. The main tool we use is a duality representation of solution with viscosity Mather measures.
We study the asymptotic behavior, as the discount factor vanishes, of the Hamilton-Jacobi equation with state-constraint on changing domains. Surprisingly, we can obtain both convergence results and non-convergence results in this convex setting. Moreover, we provide a very first result on the asymptotic expansion of the additive eigenvalue of the Hamiltonian with respect to the changing domains. The main tool we use is a duality representation of solution with viscosity Mather measures.
Tuesday Seminar on Topology
17:00-18:00 Online
Pre-registration required. See our seminar webpage.
Jun Yoshida (The University of Tokyo)
Vassiliev derivatives of Khovanov homology and its application (JAPANESE)
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
Pre-registration required. See our seminar webpage.
Jun Yoshida (The University of Tokyo)
Vassiliev derivatives of Khovanov homology and its application (JAPANESE)
[ Abstract ]
Khovanov homology is a categorification of the Jones polynomial. It is known that Khovanov homology also arises from a categorical representation of braid groups, so we can regard it as a kind of quantum knot invariant. However, in contrast to the case of classical quantum invariants, its relation to Vassiliev invariants remains unclear. In this talk, aiming at the problem, we discuss a categorified version of Vassiliev skein relation on Khovanov homology. Namely, we extend Khovanov homology to singular links so that extended ones can be seen as "derivatives" in view of Vassiliev theory. As an application, we compute first derivatives to determine Khovanov homologies of twist knots. This talk is based on papers arXiv:2005.12664 (joint work with N.Ito) and arXiv:2007.15867.
[ Reference URL ]Khovanov homology is a categorification of the Jones polynomial. It is known that Khovanov homology also arises from a categorical representation of braid groups, so we can regard it as a kind of quantum knot invariant. However, in contrast to the case of classical quantum invariants, its relation to Vassiliev invariants remains unclear. In this talk, aiming at the problem, we discuss a categorified version of Vassiliev skein relation on Khovanov homology. Namely, we extend Khovanov homology to singular links so that extended ones can be seen as "derivatives" in view of Vassiliev theory. As an application, we compute first derivatives to determine Khovanov homologies of twist knots. This talk is based on papers arXiv:2005.12664 (joint work with N.Ito) and arXiv:2007.15867.
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
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