Seminar information archive
Seminar information archive ~12/05|Today's seminar 12/06 | Future seminars 12/07~
2020/11/18
Discrete mathematical modelling seminar
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)
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
Daichi Takeuchi (University of Tokyo)
Symmetric bilinear forms and local epsilon factors of isolated singularities in positive characteristic (Japanese)
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
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)
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
Pre-registration required. See our seminar webpage.
Yoshihiko Mitsumatsu (Chuo University)
Lefschetz fibration on the Milnor fibers of simple elliptic and cusp singularities (JAPANESE)
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
Sutanu Roy (NISER)
Contraction and bosonisation (English)
[ Reference URL ]
https://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm
Tokyo-Nagoya Algebra Seminar
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
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
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
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
( )
Hölder gradient estimates on L^p-viscosity solutions of fully nonlinear parabolic equations with VMO coefficients (Japanese)
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
Hiroshi Fujiwara (BroadBand Tower, Inc.)
History of PC rise and fall /What is a parallel processing? What is a
quantum gate? (Japanese)
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
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
Hiroshi Fujiwara (BroadBand Tower, Inc.)
Supervised/Unsupervised Learning and Reinforcement Learning for Deep
Learning (Japanese)
Explanation on supervised/unsupervised learning and reinforcement learning for deep
learning
https://forms.gle/Uhy8uBujZatjNMsGA
2020/10/27
Numerical Analysis Seminar
Buyang Li (The Hong Kong Polytechnic University)
Convergent evolving finite element algorithms for mean curvature flow and Willmore flow of closed surfaces (English)
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
Son Tu (University of Wisconsin Madison)
Vanishing discount problems for Hamilton-Jacobi equations on changing domains (English)
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
Pre-registration required. See our seminar webpage.
Jun Yoshida (The University of Tokyo)
Vassiliev derivatives of Khovanov homology and its application (JAPANESE)
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
Tokyo-Nagoya Algebra Seminar
Please see the URL below for details on the online seminar.
Yasuaki Gyoda (Nagoya University)
Positive cluster complex and $\tau$-tilting complex (Japanese)
In cluster algebra theory, cluster complexes are actively studied as simplicial complexes, which represent the structure of a seed and its mutations. In this talk, I will discuss a certain subcomplex, called positive cluster complex, of a cluster complex. This is a subcomplex whose vertex set consists of all cluster variables except for those in the initial seed. I will also introduce another simplicial complex in this talk - the tau-tilting complex, which has vertices given by all indecomposable tau-rigid modules, and simplices given by basic tau-rigid modules. In the case of a cluster-tilted algebra, it turns out that a tau-tilting complex corresponds to some positive cluster complex. Due to this fact, we can investigate the structure of a tau-tilting complex of tau-tilting finite type by using the tools of cluster algebra theory. This is joint work with Haruhisa Enomoto.
2020/10/26
Seminar on Geometric Complex Analysis
HATTORI Kota (Keio University)
Spectral convergence in geometric quantization
[ Reference URL ]
https://zoom.us/meeting/register/tJ0vcu2rrDIqG9Rv5AT0Mpi37urIkJ1IRldB
2020/10/22
Operator Algebra Seminars
Hiroyasu Hamada (National Institute of Technology, Sasebo College)
$C^*$-algebras generated by multiplication operators and composition operators by functions with self-similar branches
[ Reference URL ]
https://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm
Information Mathematics Seminar
Hiroshi Fujiwara (BroadBand Tower, Inc.)
Think about a zero trust from information security 10 size menace 2020 (Japanese)
In this talk, we think about a zero trust from information security 10 size menace 2020.
https://forms.gle/Uhy8uBujZatjNMsGA
2020/10/20
Tuesday Seminar on Topology
Pre-registration required. See our seminar webpage.
Alexandru Oancea (Sorbonne Université)
Poincaré duality for free loop spaces (ENGLISH)
A certain number of dualities between homological and cohomological invariants of free loop spaces have been observed over the years, having the flavour of Poincaré duality but nevertheless holding in an infinite dimensional setting. The goal of the talk will be to explain these through a new duality theorem, whose proof uses symplectic methods. The talk will report on joint work with Kai Cieliebak and Nancy Hingston.
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
2020/10/19
Seminar on Geometric Complex Analysis
MATSUMURA, Shin-ichi (Tohoku University)
On projective manifolds with pseudo-effective tangent bundle
In this talk, I would like to discuss projective manifolds whose tangent bundle is pseudo-effective or admits a positively curved singular metric. I will explain a structure theorem for such manifolds and the classification in the two-dimensional case, comparing our theory with classical results for nef tangent bundle or non-negative bisectional curvature. Related open problems will be discussed if time permits.
This is joint work with Genki Hosono (Tohoku University) and Masataka Iwai (Osaka City University).
https://zoom.us/meeting/register/tJ0vcu2rrDIqG9Rv5AT0Mpi37urIkJ1IRldB
Seminar on Probability and Statistics
Yuta Koike (University of Tokyo)
Development of high-dimensional CLTs arising from high-frequency data analysis (日本語)
[ Reference URL ]
https://docs.google.com/forms/d/e/1FAIpQLSfDhlzlC6haR8dsDn9_mCxi1s9RtXZxTi_U7Nb_Xl6q7Gw1dA/viewform
2020/10/15
Operator Algebra Seminars
Sven Raum (Stockholm Univ.)
Structure of Hecke von Neumann algebras and applications to representation theory
[ Reference URL ]
https://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm
Information Mathematics Seminar
Hiroshi Fujiwara (BroadBand Tower, Inc.)
Basics of the speedup technique of the classic computing and Innovation of Causality in the root of the quantum computing (Japanese)
Explanation on the speedup technique of the classic computing and Innovation of causality in the root of the quantum computing
https://forms.gle/Uhy8uBujZatjNMsGA
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