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Seminar information archive
Seminar information archive ～04/18｜Today's seminar 04/19 | Future seminars 04/20～
2017/12/05
Tuesday Seminar on Topology
17:00-18:30 Room #056 (Graduate School of Math. Sci. Bldg.)
Kazuhiro Kawamura (University of Tsukuba)
Derivations and cohomologies of Lipschitz algebras (JAPANESE)
Kazuhiro Kawamura (University of Tsukuba)
Derivations and cohomologies of Lipschitz algebras (JAPANESE)
[ Abstract ]
For a compact metric space M, Lip(M) denotes the Banach algebra of all complex-valued Lipschitz functions on M. Motivated by a classical work of de Leeuw, we define a compact, not necessarily metrizable, Hausdorff space \hat{M} so that each point of \hat{M} induces a derivation on Lip(M). To some extent, \hat{M} may be regarded as "the space of directions." We study, by an elementary method, the space of derivations and continuous Hochschild cohomologies (in the sense of B.E. Johnson and A.Y. Helemskii) of Lip(M) with coefficients C(\hat{M}) and C(M). The results so obtained show that the behavior of Lip(M) is (naturally) rather different than that of the algebra of smooth/C^1 functions on M.
For a compact metric space M, Lip(M) denotes the Banach algebra of all complex-valued Lipschitz functions on M. Motivated by a classical work of de Leeuw, we define a compact, not necessarily metrizable, Hausdorff space \hat{M} so that each point of \hat{M} induces a derivation on Lip(M). To some extent, \hat{M} may be regarded as "the space of directions." We study, by an elementary method, the space of derivations and continuous Hochschild cohomologies (in the sense of B.E. Johnson and A.Y. Helemskii) of Lip(M) with coefficients C(\hat{M}) and C(M). The results so obtained show that the behavior of Lip(M) is (naturally) rather different than that of the algebra of smooth/C^1 functions on M.
Algebraic Geometry Seminar
15:30-17:00 Room #122 (Graduate School of Math. Sci. Bldg.)
Kenta Sato (The University of Tokyo)
Ascending chain condition for F-pure thresholds on a fixed strongly F-regular germ (English or Japanese)
Kenta Sato (The University of Tokyo)
Ascending chain condition for F-pure thresholds on a fixed strongly F-regular germ (English or Japanese)
[ Abstract ]
For a germ of a variety in positive characteristic and a non-zero ideal sheaf on the variety, we can define the F-pure threshold of the ideal by using Frobenius morphisms, which measures the singularities of the pair. In this talk, I will show that the set of all F-pure thresholds on a fixed strongly F-regular germ satisfies the ascending chain condition. This is a positive characteristic analogue of the "ascending chain condition for log canonical thresholds" in characteristic 0, which was recently proved by Hacon, McKernan, and Xu.
For a germ of a variety in positive characteristic and a non-zero ideal sheaf on the variety, we can define the F-pure threshold of the ideal by using Frobenius morphisms, which measures the singularities of the pair. In this talk, I will show that the set of all F-pure thresholds on a fixed strongly F-regular germ satisfies the ascending chain condition. This is a positive characteristic analogue of the "ascending chain condition for log canonical thresholds" in characteristic 0, which was recently proved by Hacon, McKernan, and Xu.
2017/12/04
Tokyo Probability Seminar
16:00-17:30 Room #128 (Graduate School of Math. Sci. Bldg.)
Kazuki Okamura (Research Institute for Mathematical Sciences, Kyoto University)
Some results for range of random walk on graph with spectral dimension two (JAPANESE)
Kazuki Okamura (Research Institute for Mathematical Sciences, Kyoto University)
Some results for range of random walk on graph with spectral dimension two (JAPANESE)
[ Abstract ]
We consider the range of random walk on graphs with spectral dimension two. We show that a certain weak law of large numbers hold if a recurrent graph satisfies a uniform condition. We construct a recurrent graph such that the uniform condition holds but appropriately scaled expectations fluctuate. Our result is applicable to showing LILs for lamplighter random walks in the case that the spectral dimension of the underlying graph is two.
We consider the range of random walk on graphs with spectral dimension two. We show that a certain weak law of large numbers hold if a recurrent graph satisfies a uniform condition. We construct a recurrent graph such that the uniform condition holds but appropriately scaled expectations fluctuate. Our result is applicable to showing LILs for lamplighter random walks in the case that the spectral dimension of the underlying graph is two.
Operator Algebra Seminars
16:45-18:15 Room #126 (Graduate School of Math. Sci. Bldg.)
Pieter Naaijkens (UC Davis)
Subfactors and wiretapping channels
(English)
Pieter Naaijkens (UC Davis)
Subfactors and wiretapping channels
(English)
2017/11/28
Tuesday Seminar on Topology
17:00-18:30 Room #056 (Graduate School of Math. Sci. Bldg.)
Sang-hyun Kim (Seoul National University)
Diffeomorphism Groups of One-Manifolds (ENGLISH)
Sang-hyun Kim (Seoul National University)
Diffeomorphism Groups of One-Manifolds (ENGLISH)
[ Abstract ]
Let a>=2 be a real number and k = [a]. We denote by Diff^a(S^1) the group of C^k diffeomorphisms such that the k--th derivatives are Hölder--continuous of exponent (a - k). For each real number a>=2, we prove that there exists a finitely generated group G < Diff^a(S^1) such that G admits no injective homomorphisms into Diff^b(S^1) for any b>a. This is joint work with Thomas Koberda.
Let a>=2 be a real number and k = [a]. We denote by Diff^a(S^1) the group of C^k diffeomorphisms such that the k--th derivatives are Hölder--continuous of exponent (a - k). For each real number a>=2, we prove that there exists a finitely generated group G < Diff^a(S^1) such that G admits no injective homomorphisms into Diff^b(S^1) for any b>a. This is joint work with Thomas Koberda.
Algebraic Geometry Seminar
15:30-17:00 Room #122 (Graduate School of Math. Sci. Bldg.)
Hiromu Tanaka (Tokyo)
Kodaira vanishing theorem for Witt canonical sheaves (English)
Hiromu Tanaka (Tokyo)
Kodaira vanishing theorem for Witt canonical sheaves (English)
[ Abstract ]
We establish an analogue of the Kodaira vanishing theorem in terms of de Rham-Witt complex. More specifically, given a smooth projective variety over a perfect field of positive characteristic, we prove that the higher cohomologies vanish for the tensor product of the Witt canonical sheaf and the Teichmuller lift of an ample invertible sheaf.
We establish an analogue of the Kodaira vanishing theorem in terms of de Rham-Witt complex. More specifically, given a smooth projective variety over a perfect field of positive characteristic, we prove that the higher cohomologies vanish for the tensor product of the Witt canonical sheaf and the Teichmuller lift of an ample invertible sheaf.
Numerical Analysis Seminar
16:50-18:20 Room #117 (Graduate School of Math. Sci. Bldg.)
Daisuke Koyama (The University of Electro-Communications)
Hybrid discontinuous Galerkin methods for nearly incompressible elasticity problems
(Japanese)
Daisuke Koyama (The University of Electro-Communications)
Hybrid discontinuous Galerkin methods for nearly incompressible elasticity problems
(Japanese)
[ Abstract ]
A Hybrid discontinuous Galerkin (HDG) method for linear elasticity problems has been introduced by Kikuchi et al. [Theor. Appl. Mech. Japan, vol.57, 395--404 (2009)], [RIMS Kokyuroku, vol.1971, 28--46 (2015)]. We consider to seek numerical solutions of the plane strain problem by the HDG method, especially in the case when materials are nearly incompressible, that is, when the first Lam\'e parameter $\lambda$ is large. In this talk, we consider two cases when the HDG method uses a lifting term and does not use it. When the lifting term is used, the method can be free of volumetric locking. On the other hand, when the lifting term is not used, we have to take an interior penalty parameter of order $\lambda$ as $\lambda$ tends to infinity, in order to guarantee the coercivity of the bilinear form. Taking such an interior penalty parameter causes volumetric locking phenomena. We thus conclude that the lifting term is essential for avoiding the volumetric locking in the HDG method.
A Hybrid discontinuous Galerkin (HDG) method for linear elasticity problems has been introduced by Kikuchi et al. [Theor. Appl. Mech. Japan, vol.57, 395--404 (2009)], [RIMS Kokyuroku, vol.1971, 28--46 (2015)]. We consider to seek numerical solutions of the plane strain problem by the HDG method, especially in the case when materials are nearly incompressible, that is, when the first Lam\'e parameter $\lambda$ is large. In this talk, we consider two cases when the HDG method uses a lifting term and does not use it. When the lifting term is used, the method can be free of volumetric locking. On the other hand, when the lifting term is not used, we have to take an interior penalty parameter of order $\lambda$ as $\lambda$ tends to infinity, in order to guarantee the coercivity of the bilinear form. Taking such an interior penalty parameter causes volumetric locking phenomena. We thus conclude that the lifting term is essential for avoiding the volumetric locking in the HDG method.
2017/11/27
Tokyo Probability Seminar
16:00-17:30 Room #128 (Graduate School of Math. Sci. Bldg.)
Antar Bandyopadhyay (Indian Statistical Institute)
Random Recursive Tree, Branching Markov Chains and Urn Models (ENGLISH)
Antar Bandyopadhyay (Indian Statistical Institute)
Random Recursive Tree, Branching Markov Chains and Urn Models (ENGLISH)
[ Abstract ]
In this talk, we will establish a connection between random recursive tree, branching Markov chain and urn model. Exploring the connection further we will derive fairly general scaling limits for urn models with colors indexed by a Polish Space and show that several exiting results on classical/non-classical urn schemes can be easily derived out of such general asymptotic. We will further show that the connection can be used to derive exact asymptotic for the sizes of the connected components of a "random recursive forest", obtained by removing the root of a random recursive tree.
[This is a joint work with Debleena Thacker]
In this talk, we will establish a connection between random recursive tree, branching Markov chain and urn model. Exploring the connection further we will derive fairly general scaling limits for urn models with colors indexed by a Polish Space and show that several exiting results on classical/non-classical urn schemes can be easily derived out of such general asymptotic. We will further show that the connection can be used to derive exact asymptotic for the sizes of the connected components of a "random recursive forest", obtained by removing the root of a random recursive tree.
[This is a joint work with Debleena Thacker]
Seminar on Geometric Complex Analysis
10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Genki Hosono (The University of Tokyo)
On the proof of the optimal $L^2$ extension theorem by Berndtsson-Lempert and related results
Genki Hosono (The University of Tokyo)
On the proof of the optimal $L^2$ extension theorem by Berndtsson-Lempert and related results
[ Abstract ]
We will present the recent progress on the Ohsawa-Takegoshi $L^2$ extension theorem. A version of the Ohsawa-Takegoshi $L^2$ extension with a optimal estimate has been proved by Blocki and Guan-Zhou. After that, by Berndtsson-Lempert, a new proof of the optimal $L^2$ extension theorem was given. In this talk, we will show an optimal $L^2$ extension theorem for jets of holomorphic functions by the Berndtsson-Lempert method. We will also explain the recent result about jet extensions by McNeal-Varolin. Their proof is also based on Berndtsson-Lempert, but there are some differences.
We will present the recent progress on the Ohsawa-Takegoshi $L^2$ extension theorem. A version of the Ohsawa-Takegoshi $L^2$ extension with a optimal estimate has been proved by Blocki and Guan-Zhou. After that, by Berndtsson-Lempert, a new proof of the optimal $L^2$ extension theorem was given. In this talk, we will show an optimal $L^2$ extension theorem for jets of holomorphic functions by the Berndtsson-Lempert method. We will also explain the recent result about jet extensions by McNeal-Varolin. Their proof is also based on Berndtsson-Lempert, but there are some differences.
2017/11/24
Colloquium
15:30-16:30 Room #002 (Graduate School of Math. Sci. Bldg.)
Yukari Ito (IPMU, Nagoya University)
(JAPANESE)
Yukari Ito (IPMU, Nagoya University)
(JAPANESE)
2017/11/21
Tuesday Seminar on Topology
17:00-18:30 Room #056 (Graduate School of Math. Sci. Bldg.)
Keiichi Sakai (Shinshu University)
The space of short ropes and the classifying space of the space of long knots (JAPANESE)
Keiichi Sakai (Shinshu University)
The space of short ropes and the classifying space of the space of long knots (JAPANESE)
[ Abstract ]
We prove affirmatively the conjecture raised by J. Mostovoy; the space of short ropes is weakly homotopy equivalent to the classifying space of the topological monoid (or category) of long knots in R^3. We make use of techniques developed by S. Galatius and O. Randal-Williams to construct a manifold space model of the classifying space of the space of long knots, and we give an explicit map from the space of short ropes to the model in a geometric way. This is joint work with Syunji Moriya (Osaka Prefecture University).
We prove affirmatively the conjecture raised by J. Mostovoy; the space of short ropes is weakly homotopy equivalent to the classifying space of the topological monoid (or category) of long knots in R^3. We make use of techniques developed by S. Galatius and O. Randal-Williams to construct a manifold space model of the classifying space of the space of long knots, and we give an explicit map from the space of short ropes to the model in a geometric way. This is joint work with Syunji Moriya (Osaka Prefecture University).
PDE Real Analysis Seminar
10:30-11:30 Room #056 (Graduate School of Math. Sci. Bldg.)
Felix Schulze (University College London)
Optimal isoperimetric inequalities for surfaces in any codimension
in Cartan-Hadamard manifolds (English)
Felix Schulze (University College London)
Optimal isoperimetric inequalities for surfaces in any codimension
in Cartan-Hadamard manifolds (English)
[ Abstract ]
Let $(M^n,g)$ be simply connected, complete, with non-positive sectional
curvatures, and $\Sigma$ a 2-dimensional surface in $M^n$. Let $S$ be an area
minimising 3-current such that $\partial S = \Sigma$. We use a weak mean
curvature flow, obtained via elliptic regularisation, starting from
$\Sigma$, to show that $S$ satisfies the optimal Euclidean isoperimetric
inequality: $|S| \leq 1/(6\sqrt{\pi}) |\Sigma|^{3/2}$. We also obtain the
optimal estimate in case the sectional curvatures of $M$ are bounded from
above by $\kappa < 0$ and characterise the case of equality. The proof
follows from an almost monotonicity of a suitable isoperimetric
difference along the approximating flows in one dimension higher.
Let $(M^n,g)$ be simply connected, complete, with non-positive sectional
curvatures, and $\Sigma$ a 2-dimensional surface in $M^n$. Let $S$ be an area
minimising 3-current such that $\partial S = \Sigma$. We use a weak mean
curvature flow, obtained via elliptic regularisation, starting from
$\Sigma$, to show that $S$ satisfies the optimal Euclidean isoperimetric
inequality: $|S| \leq 1/(6\sqrt{\pi}) |\Sigma|^{3/2}$. We also obtain the
optimal estimate in case the sectional curvatures of $M$ are bounded from
above by $\kappa < 0$ and characterise the case of equality. The proof
follows from an almost monotonicity of a suitable isoperimetric
difference along the approximating flows in one dimension higher.
Algebraic Geometry Seminar
15:30-17:00 Room #122 (Graduate School of Math. Sci. Bldg.)
Frédéric Campana (Université de Lorraine/KIAS)
Orbifold rational connectedness (English)
Frédéric Campana (Université de Lorraine/KIAS)
Orbifold rational connectedness (English)
[ Abstract ]
The first step in the decomposition by canonical fibrations with fibres of `signed' canonical bundle of an arbitrary complex projective manifolds $X$ is its `rational quotient' (also called `MRC' fibration): it has rationally connected fibres and non-uniruled base. In general, the further steps (such as the Moishezon-Iitaka fibration) of this decomposition will require the consideration of 'orbifold base' of fibrations in order to deal with the multiple fibres (as seen already for elliptic surfaces). One thus needs to work in the larger category of (smooth) `orbifold pairs' $(X,D)$ to achieve this decomposition. The aim of the talk is thus to introduce the notions of Rational Connectedness and 'rational quotient' in this context, by means of suitable equivalent notions of negativity for the orbifold cotangent bundle (suitably defined. When $D$ is reduced, this is just the usual Log-version). The expected equivalence with connecting families of `orbifold rational curves' remains however presently open.
The first step in the decomposition by canonical fibrations with fibres of `signed' canonical bundle of an arbitrary complex projective manifolds $X$ is its `rational quotient' (also called `MRC' fibration): it has rationally connected fibres and non-uniruled base. In general, the further steps (such as the Moishezon-Iitaka fibration) of this decomposition will require the consideration of 'orbifold base' of fibrations in order to deal with the multiple fibres (as seen already for elliptic surfaces). One thus needs to work in the larger category of (smooth) `orbifold pairs' $(X,D)$ to achieve this decomposition. The aim of the talk is thus to introduce the notions of Rational Connectedness and 'rational quotient' in this context, by means of suitable equivalent notions of negativity for the orbifold cotangent bundle (suitably defined. When $D$ is reduced, this is just the usual Log-version). The expected equivalence with connecting families of `orbifold rational curves' remains however presently open.
2017/11/20
Seminar on Geometric Complex Analysis
10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Yasufumi Nitta (Tokyo Institute of Technology)
Relative GIT stabilities of toric Fano manifolds in low dimensions
Yasufumi Nitta (Tokyo Institute of Technology)
Relative GIT stabilities of toric Fano manifolds in low dimensions
[ Abstract ]
In 2000, Mabuchi extended the notion of Kaehler-Einstein metrics to Fano manifolds with non-vanishing Futaki invariant. Such a metric is called generalized Kaehler-Einstein metric or Mabuchi metric in the literature. Recently this metrics were rediscovered by Yao in the story of Donaldson's infinite dimensional moment map picture. Moreover, he introduced (uniform) relative Ding stability for toric Fano manifolds and showed that the existence of generalized Kaehler-Einstein metrics is equivalent to its uniform relative Ding stability. This equivalence is in the context of the Yau-Tian-Donaldson conjecture. In this talk, we focus on uniform relative Ding stability of toric Fano manifolds. More precisely, we determine all the uniformly relatively Ding stable toric Fano 3- and 4-folds as well as unstable ones. This talk is based on a joint work with Shunsuke Saito and Naoto Yotsutani.
In 2000, Mabuchi extended the notion of Kaehler-Einstein metrics to Fano manifolds with non-vanishing Futaki invariant. Such a metric is called generalized Kaehler-Einstein metric or Mabuchi metric in the literature. Recently this metrics were rediscovered by Yao in the story of Donaldson's infinite dimensional moment map picture. Moreover, he introduced (uniform) relative Ding stability for toric Fano manifolds and showed that the existence of generalized Kaehler-Einstein metrics is equivalent to its uniform relative Ding stability. This equivalence is in the context of the Yau-Tian-Donaldson conjecture. In this talk, we focus on uniform relative Ding stability of toric Fano manifolds. More precisely, we determine all the uniformly relatively Ding stable toric Fano 3- and 4-folds as well as unstable ones. This talk is based on a joint work with Shunsuke Saito and Naoto Yotsutani.
2017/11/16
Mathematical Biology Seminar
16:30-18:00 Room #123 (Graduate School of Math. Sci. Bldg.)
Jun Nakabayashi (Yokohama City University)
(JAPANESE)
Jun Nakabayashi (Yokohama City University)
(JAPANESE)
Seminar on Probability and Statistics
13：00-16：00 Room #123 (Graduate School of Math. Sci. Bldg.)
2017/11/15
PDE Real Analysis Seminar
10:30-11:30 Room #056 (Graduate School of Math. Sci. Bldg.)
Kaj Nyström (Uppsala University)
Boundary value problems for parabolic equations with measurable coefficients (English)
Kaj Nyström (Uppsala University)
Boundary value problems for parabolic equations with measurable coefficients (English)
[ Abstract ]
In recent joint works with P. Auscher and M. Egert we establish new results concerning boundary value problems in the upper half-space for second order parabolic equations (and systems) assuming only measurability and some transversal regularity in the coefficients of the elliptic part. To establish our results we introduce and develop a first order strategy by means of a parabolic Dirac operator at the boundary to obtain, in particular, Green's representation for solutions in natural classes involving square functions and non-tangential maximal functions, well-posedness results with data in $L^2$-Sobolev spaces together with invertibility of layer potentials, and perturbation results. In addition we solve the Kato square root problem for parabolic operators with coefficients of the elliptic part depending measurably on all variables. Using these results we are also able to solve the $L^p$-Dirichlet problem for parabolic equations with real, time-dependent, elliptic but non-symmetric coefficients. In this talk I will briefly describe some of these developments.
In recent joint works with P. Auscher and M. Egert we establish new results concerning boundary value problems in the upper half-space for second order parabolic equations (and systems) assuming only measurability and some transversal regularity in the coefficients of the elliptic part. To establish our results we introduce and develop a first order strategy by means of a parabolic Dirac operator at the boundary to obtain, in particular, Green's representation for solutions in natural classes involving square functions and non-tangential maximal functions, well-posedness results with data in $L^2$-Sobolev spaces together with invertibility of layer potentials, and perturbation results. In addition we solve the Kato square root problem for parabolic operators with coefficients of the elliptic part depending measurably on all variables. Using these results we are also able to solve the $L^p$-Dirichlet problem for parabolic equations with real, time-dependent, elliptic but non-symmetric coefficients. In this talk I will briefly describe some of these developments.
2017/11/14
Algebraic Geometry Seminar
15:30-17:00 Room #122 (Graduate School of Math. Sci. Bldg.)
Meng Chen (Fudan)
A characterization of the birationality of 4-canonical maps of minimal 3-folds (English)
Meng Chen (Fudan)
A characterization of the birationality of 4-canonical maps of minimal 3-folds (English)
[ Abstract ]
We explain the following theorem: For any minimal 3-fold X of general type with p_g>4, the 4-canonical map is non-birational if and only if X is birationally fibred by a pencil of (1,2) surfaces. The statement fails in the case of p_g=4.
We explain the following theorem: For any minimal 3-fold X of general type with p_g>4, the 4-canonical map is non-birational if and only if X is birationally fibred by a pencil of (1,2) surfaces. The statement fails in the case of p_g=4.
Numerical Analysis Seminar
16:50-18:20 Room #002 (Graduate School of Math. Sci. Bldg.)
Ai Ishikawa (Kobe University)
Energy-preserving numerical method based on the variational principle and application to unconstrained optimization problems (Japanese)
Ai Ishikawa (Kobe University)
Energy-preserving numerical method based on the variational principle and application to unconstrained optimization problems (Japanese)
2017/11/13
Tokyo Probability Seminar
16:00-17:30 Room #128 (Graduate School of Math. Sci. Bldg.)
Masaki Wada (Faculty of Human Development and Culture, Fukushima University)
(JAPANESE)
Masaki Wada (Faculty of Human Development and Culture, Fukushima University)
(JAPANESE)
Seminar on Geometric Complex Analysis
10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Georg Schumacher (Philipps-Universität Marburg)
Relative Canonical Bundles for Families of Calabi-Yau Manifolds
Georg Schumacher (Philipps-Universität Marburg)
Relative Canonical Bundles for Families of Calabi-Yau Manifolds
[ Abstract ]
We consider holomorphic families of Calabi-Yau manifolds (here being defined by the vanishing of the first real Chern class). We study induced hermitian metrics on the relative canonical bundle, which are related to the Weil-Petersson form on the base. Under a certain condition the total space possesses a Kähler form, whose restriction to fibers are equal to the Ricci flat metrics. Furthermore we prove an extension theorem for the Weil-Petersson form and give applications.
We consider holomorphic families of Calabi-Yau manifolds (here being defined by the vanishing of the first real Chern class). We study induced hermitian metrics on the relative canonical bundle, which are related to the Weil-Petersson form on the base. Under a certain condition the total space possesses a Kähler form, whose restriction to fibers are equal to the Ricci flat metrics. Furthermore we prove an extension theorem for the Weil-Petersson form and give applications.
Operator Algebra Seminars
16:45-18:15 Room #126 (Graduate School of Math. Sci. Bldg.)
Juan Orendain (UNAM)
Globularily generated double categories: On the problem of existence of internalizations for decorated bicategories (English)
Juan Orendain (UNAM)
Globularily generated double categories: On the problem of existence of internalizations for decorated bicategories (English)
2017/11/10
Infinite Analysis Seminar Tokyo
17:00-18:30 Room #122 (Graduate School of Math. Sci. Bldg.)
Fabio Novaes (International Institute of Physics (UFRN))
Chern-Simons, gravity and integrable systems. (ENGLISH)
http://www.iip.ufrn.br/eventslecturer?inf==0EVRpXTR1TP
Fabio Novaes (International Institute of Physics (UFRN))
Chern-Simons, gravity and integrable systems. (ENGLISH)
[ Abstract ]
It is known since the 80's that pure three-dimensional gravity is classically equivalent to a Chern-Simons theory with gauge group SL(2,R) x SL(2,R). For a given set of boundary conditions, the asymptotic classical phase space has a central extension in terms of two copies of Virasoro algebra. In particular, this gives a conformal field theory representation of black hole solutions in 3d gravity, also known as BTZ black holes. The BTZ black hole entropy can then be recovered using CFT. In this talk, we review this story and discuss recent results on how to relax the BTZ boundary conditions to obtain the KdV hierarchy at the boundary. More generally, this shows that Chern-Simons theory can represent virtually any integrable system at the boundary, given some consistency conditions. We also briefly discuss how this formulation can be useful to describe non-relativistic systems.
[ Reference URL ]It is known since the 80's that pure three-dimensional gravity is classically equivalent to a Chern-Simons theory with gauge group SL(2,R) x SL(2,R). For a given set of boundary conditions, the asymptotic classical phase space has a central extension in terms of two copies of Virasoro algebra. In particular, this gives a conformal field theory representation of black hole solutions in 3d gravity, also known as BTZ black holes. The BTZ black hole entropy can then be recovered using CFT. In this talk, we review this story and discuss recent results on how to relax the BTZ boundary conditions to obtain the KdV hierarchy at the boundary. More generally, this shows that Chern-Simons theory can represent virtually any integrable system at the boundary, given some consistency conditions. We also briefly discuss how this formulation can be useful to describe non-relativistic systems.
http://www.iip.ufrn.br/eventslecturer?inf==0EVRpXTR1TP
2017/11/09
Kavli IPMU Komaba Seminar
13:30-14:30 Room #056 (Graduate School of Math. Sci. Bldg.)
Edouard Brezin (lpt ens, Paris)
Various applications of supersymmetry in statistical physics (English)
Edouard Brezin (lpt ens, Paris)
Various applications of supersymmetry in statistical physics (English)
[ Abstract ]
Supersymmetry is a fundamental concept in particle physics (although it has not been seen experimentally so far). But it is although a powerful tool in a number of problems arising in quantum mechanics and statistical physics. It has been widely used in the theory of disordered systems (Efetov et al.), it led to dimensional reduction for branched polymers (Parisi-Sourlas), for the susy classical gas (Brydges and Imbrie), for Landau levels with impurities. If has also many powerful applications in the theory of random matrices. I will briefly review some of these topics.
Supersymmetry is a fundamental concept in particle physics (although it has not been seen experimentally so far). But it is although a powerful tool in a number of problems arising in quantum mechanics and statistical physics. It has been widely used in the theory of disordered systems (Efetov et al.), it led to dimensional reduction for branched polymers (Parisi-Sourlas), for the susy classical gas (Brydges and Imbrie), for Landau levels with impurities. If has also many powerful applications in the theory of random matrices. I will briefly review some of these topics.
2017/11/08
Number Theory Seminar
18:00-19:00 Room #056 (Graduate School of Math. Sci. Bldg.)
Xin Wan (Morningside Center for Mathematics)
Iwasawa theory and Bloch-Kato conjecture for modular forms (ENGLISH)
Xin Wan (Morningside Center for Mathematics)
Iwasawa theory and Bloch-Kato conjecture for modular forms (ENGLISH)
[ Abstract ]
Bloch and Kato formulated conjectures relating sizes of p-adic Selmer groups with special values of L-functions. Iwasawa theory is a useful tool for studying these conjectures and BSD conjecture for elliptic curves. For example the Iwasawa main conjecture for modular forms formulated by Kato implies the Tamagawa number formula for modular forms of analytic rank 0.
In this talk I'll first briefly review the above theory. Then we will focus on a different Iwasawa theory approach for this problem. The starting point is a recent joint work with Jetchev and Skinner proving the BSD formula for elliptic curves of analytic rank 1. We will discuss how such results are generalized to modular forms. If time allowed we may also explain the possibility to use it to deduce Bloch-Kato conjectures in both analytic rank 0 and 1 cases. In certain aspects such approach should be more powerful than classical Iwasawa theory, and has some potential to attack cases with bad ramification at p.
Bloch and Kato formulated conjectures relating sizes of p-adic Selmer groups with special values of L-functions. Iwasawa theory is a useful tool for studying these conjectures and BSD conjecture for elliptic curves. For example the Iwasawa main conjecture for modular forms formulated by Kato implies the Tamagawa number formula for modular forms of analytic rank 0.
In this talk I'll first briefly review the above theory. Then we will focus on a different Iwasawa theory approach for this problem. The starting point is a recent joint work with Jetchev and Skinner proving the BSD formula for elliptic curves of analytic rank 1. We will discuss how such results are generalized to modular forms. If time allowed we may also explain the possibility to use it to deduce Bloch-Kato conjectures in both analytic rank 0 and 1 cases. In certain aspects such approach should be more powerful than classical Iwasawa theory, and has some potential to attack cases with bad ramification at p.
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