Text only print
Full screen print
Seminar information archive
Seminar information archive ～12/05｜Today's seminar 12/06 | Future seminars 12/07～
2018/06/12
Algebraic Geometry Seminar
15:30-17:00 Room #122 (Graduate School of Math. Sci. Bldg.)
Takahiro Shibata (Kyoto)
Ample canonical heights for endomorphisms on projective varieties (English or Japanese)
Takahiro Shibata (Kyoto)
Ample canonical heights for endomorphisms on projective varieties (English or Japanese)
[ Abstract ]
Given a smooth projective variety on a number field and an
endomorphism on it, we would like to know how the height of a point
grows by iteration of the action of the endomorphism. When the
endomorphism is polarized, Call and Silverman construct the canonical
height, which is an important tool for the calculation of growth of
heights. In this talk, we will give a generalization of the Call-
Silverman canonical heights for not necessarily polarized endomorphisms,
ample canonical heights, and propose an analogue of the Northcott
finiteness theorem as a conjecture. We will see that the conjecture
holds when the variety is an abelian variety or a surface.
Given a smooth projective variety on a number field and an
endomorphism on it, we would like to know how the height of a point
grows by iteration of the action of the endomorphism. When the
endomorphism is polarized, Call and Silverman construct the canonical
height, which is an important tool for the calculation of growth of
heights. In this talk, we will give a generalization of the Call-
Silverman canonical heights for not necessarily polarized endomorphisms,
ample canonical heights, and propose an analogue of the Northcott
finiteness theorem as a conjecture. We will see that the conjecture
holds when the variety is an abelian variety or a surface.
Tuesday Seminar on Topology
17:00-18:30 Room #056 (Graduate School of Math. Sci. Bldg.)
Yoshihiko Mitsumatsu (Chuo University)
Turbulization of 2-dimensional foliations on 4-manifolds (JAPANESE)
Yoshihiko Mitsumatsu (Chuo University)
Turbulization of 2-dimensional foliations on 4-manifolds (JAPANESE)
[ Abstract ]
This is a report on a joint work with Elmar VOGT(Freie Universität Berlin). For codimension 1 foliations, the process of turbulization, i.e., inserting a Reeb component along a closed transversal, is well-known, while for higher codimensional foliation, similar processes were not understood until around 2006.
In this talk, first we formulate the turbulization along a closed transversal. Then in our dimension setting, namely 2-dimensional foliations on 4-manifolds ((4,2)-foliations), a cohomological criterion is given for a given transversal to a foliation, which tells the turbulization is possible or not, relying on the Thurston's h-principle. Also we give cocrete geometric constructions of turbulizations.
The cohomological criterion for turbulization is deduced from a more general criterion for a given embedded surface to be a compact leaf or a closed transversal of some foliation, which is stated in terms of the euler classes of tangent and normal bndle of the foliation to look for. The anormalous cohomological solutions for certain cases suggested the geometric realization of turbulization, while the cohomological criterion is obtained by the h-principle.
Some other modifications are also formulated for (4,2)-foliations and their possibility are assured by the anormalous solutions mentioned above. For some of them, good geometric realizations are not yet known. So far the difficulty lies on the problem of the connected components of the space of representations of the surface groups to Diff S^1.
If the time permits, some special features on the h-principle for 2-dimensional foliations are also explained.
This is a report on a joint work with Elmar VOGT(Freie Universität Berlin). For codimension 1 foliations, the process of turbulization, i.e., inserting a Reeb component along a closed transversal, is well-known, while for higher codimensional foliation, similar processes were not understood until around 2006.
In this talk, first we formulate the turbulization along a closed transversal. Then in our dimension setting, namely 2-dimensional foliations on 4-manifolds ((4,2)-foliations), a cohomological criterion is given for a given transversal to a foliation, which tells the turbulization is possible or not, relying on the Thurston's h-principle. Also we give cocrete geometric constructions of turbulizations.
The cohomological criterion for turbulization is deduced from a more general criterion for a given embedded surface to be a compact leaf or a closed transversal of some foliation, which is stated in terms of the euler classes of tangent and normal bndle of the foliation to look for. The anormalous cohomological solutions for certain cases suggested the geometric realization of turbulization, while the cohomological criterion is obtained by the h-principle.
Some other modifications are also formulated for (4,2)-foliations and their possibility are assured by the anormalous solutions mentioned above. For some of them, good geometric realizations are not yet known. So far the difficulty lies on the problem of the connected components of the space of representations of the surface groups to Diff S^1.
If the time permits, some special features on the h-principle for 2-dimensional foliations are also explained.
Lectures
15:00-16:00 Room #056 (Graduate School of Math. Sci. Bldg.)
Alexander Kupers (Harvard University)
Cellular E_2-algebras and the unstable homology of mapping class groups
Alexander Kupers (Harvard University)
Cellular E_2-algebras and the unstable homology of mapping class groups
[ Abstract ]
We discuss joint work with Soren Galatius and Oscar Randal-Williams on the application of higher-algebraic techniques to classical questions about the homology of mapping class groups. This uses a new "multiplicative" approach to homological stability -- in contrast to the "additive" one due to Quillen -- which has the advantage of providing information outside of the stable range.
We discuss joint work with Soren Galatius and Oscar Randal-Williams on the application of higher-algebraic techniques to classical questions about the homology of mapping class groups. This uses a new "multiplicative" approach to homological stability -- in contrast to the "additive" one due to Quillen -- which has the advantage of providing information outside of the stable range.
2018/06/11
Seminar on Geometric Complex Analysis
10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Yusaku Tiba (Ochanomizu University)
Cohomology of non-pluriharmonic loci (JAPANESE)
Yusaku Tiba (Ochanomizu University)
Cohomology of non-pluriharmonic loci (JAPANESE)
[ Abstract ]
In this talk, we study a pseudoconvex counterpart of the Lefschetz hyperplane theorem.
We show a relation between the cohomology of a pseudoconvex domain and the cohomology of the non-pluriharmonic locus of an exhaustive plurisubharmonic function.
In this talk, we study a pseudoconvex counterpart of the Lefschetz hyperplane theorem.
We show a relation between the cohomology of a pseudoconvex domain and the cohomology of the non-pluriharmonic locus of an exhaustive plurisubharmonic function.
2018/06/06
Number Theory Seminar
17:30-18:30 Room #056 (Graduate School of Math. Sci. Bldg.)
Nicolas Templier (Cornell University)
On the Ramanujan conjecture for automorphic forms over function fields
Nicolas Templier (Cornell University)
On the Ramanujan conjecture for automorphic forms over function fields
[ Abstract ]
Let G be a reductive group over a function field of large enough characteristic. We prove the temperedness at unramified places of automorphic representations of G, subject to a local assumption at one place, stronger than supercuspidality. Such an assumption is necessary, as was first shown by Saito-Kurokawa and Howe-Piatetskii-Shapiro in the 70's. Our method relies on the l-adic geometry of Bun_G, and on trace formulas. Work with Will Sawin.
Let G be a reductive group over a function field of large enough characteristic. We prove the temperedness at unramified places of automorphic representations of G, subject to a local assumption at one place, stronger than supercuspidality. Such an assumption is necessary, as was first shown by Saito-Kurokawa and Howe-Piatetskii-Shapiro in the 70's. Our method relies on the l-adic geometry of Bun_G, and on trace formulas. Work with Will Sawin.
2018/06/05
Tuesday Seminar on Topology
17:00-18:30 Room #056 (Graduate School of Math. Sci. Bldg.)
Hiroki Matui (Chiba University)
Topological full groups and generalizations of the Higman-Thompson groups (JAPANESE)
Hiroki Matui (Chiba University)
Topological full groups and generalizations of the Higman-Thompson groups (JAPANESE)
[ Abstract ]
For a topological dynamical system on the Cantor set, one can introduce its topological full group, which is a countable subgroup of the homeomorphism group of the Cantor set. The Higman-Thompson group V_n is regarded as the topological full group of the one-sided full shift over n symbols. Replacing the one-sided full shift with other dynamical systems, we obtain variants of the Higman-Thompson group. It is then natural to ask whether those generalized Higman-Thompson groups possess similar (or different) features. I would like to discuss isomorphism classes of these groups, finiteness properties, abelianizations, connections to C*-algebras and their K-theory, and so on.
For a topological dynamical system on the Cantor set, one can introduce its topological full group, which is a countable subgroup of the homeomorphism group of the Cantor set. The Higman-Thompson group V_n is regarded as the topological full group of the one-sided full shift over n symbols. Replacing the one-sided full shift with other dynamical systems, we obtain variants of the Higman-Thompson group. It is then natural to ask whether those generalized Higman-Thompson groups possess similar (or different) features. I would like to discuss isomorphism classes of these groups, finiteness properties, abelianizations, connections to C*-algebras and their K-theory, and so on.
2018/06/04
Tokyo Probability Seminar
16:00-17:30 Room #126 (Graduate School of Math. Sci. Bldg.)
Hiroyoshi MITAKE (Graduate School of Mathematical Sciences, The University of Tokyo)
Uniqueness set for degenerate Hamilton-Jacobi equations (JAPANESE)
Hiroyoshi MITAKE (Graduate School of Mathematical Sciences, The University of Tokyo)
Uniqueness set for degenerate Hamilton-Jacobi equations (JAPANESE)
Seminar on Geometric Complex Analysis
10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Junjiro Noguchi (The University of Tokyo)
(JAPANESE)
Junjiro Noguchi (The University of Tokyo)
(JAPANESE)
2018/05/31
Numerical Analysis Seminar
16:30-18:00 Room #056 (Graduate School of Math. Sci. Bldg.)
Olivier Pironneau (Sorbonne University and Academy of Sciences)
Parallel Computing Methods for Quantitative Finance: the Parareal Algorithm for American Options (English)
Olivier Pironneau (Sorbonne University and Academy of Sciences)
Parallel Computing Methods for Quantitative Finance: the Parareal Algorithm for American Options (English)
[ Abstract ]
With parallelism in mind we investigate the parareal method for American contracts both theoretically and numerically. Least-Square Monte-Carlo (LSMC) and parareal time decomposition with two or more levels are used, leading to an efficient parallel implementation which scales linearly with the number of processors and is appropriate to any multiprocessor-memory architecture in its multilevel version. We prove $L^2$ superlinear convergence for an LSMC backward in time computation of American contracts, when the conditional expectations are known, i.e. before Monte-Carlo discretization. In all cases the computing time is increased only by a constant factor, compared to the sequential algorithm on the finest grid, and speed-up is guaranteed when the number of processors is larger than that constant. A numerical implementation will be shown to confirm the theoretical error estimates.
With parallelism in mind we investigate the parareal method for American contracts both theoretically and numerically. Least-Square Monte-Carlo (LSMC) and parareal time decomposition with two or more levels are used, leading to an efficient parallel implementation which scales linearly with the number of processors and is appropriate to any multiprocessor-memory architecture in its multilevel version. We prove $L^2$ superlinear convergence for an LSMC backward in time computation of American contracts, when the conditional expectations are known, i.e. before Monte-Carlo discretization. In all cases the computing time is increased only by a constant factor, compared to the sequential algorithm on the finest grid, and speed-up is guaranteed when the number of processors is larger than that constant. A numerical implementation will be shown to confirm the theoretical error estimates.
2018/05/30
Number Theory Seminar
17:00-18:00 Room #056 (Graduate School of Math. Sci. Bldg.)
Daichi Takeuchi (University of Tokyo)
Blow-ups and the class field theory for curves (JAPANESE)
Daichi Takeuchi (University of Tokyo)
Blow-ups and the class field theory for curves (JAPANESE)
2018/05/29
Tuesday Seminar on Topology
17:00-18:30 Room #056 (Graduate School of Math. Sci. Bldg.)
Kouki Sato (The university of Tokyo)
A partial order on nu+ equivalence classes (JAPANESE)
Kouki Sato (The university of Tokyo)
A partial order on nu+ equivalence classes (JAPANESE)
[ Abstract ]
The nu+ equivalence is an equivalence relation on the knot concordance group. Hom proves that many concordance invariants derived from Heegaard Floer homology are invariant under nu+ equivalence. In this work, we introduce a partial order on nu+ equivalence classes, and study its algebraic and geometrical properties. As an application, we prove that any genus one knot is nu+ equivalent to one of the unknot, the trefoil and its mirror.
The nu+ equivalence is an equivalence relation on the knot concordance group. Hom proves that many concordance invariants derived from Heegaard Floer homology are invariant under nu+ equivalence. In this work, we introduce a partial order on nu+ equivalence classes, and study its algebraic and geometrical properties. As an application, we prove that any genus one knot is nu+ equivalent to one of the unknot, the trefoil and its mirror.
Algebraic Geometry Seminar
15:30-17:00 Room #122 (Graduate School of Math. Sci. Bldg.)
Alessandra Sarti (Universit\'e de Poitiers)
Nikulin configurations on Kummer surfaces (English)
Alessandra Sarti (Universit\'e de Poitiers)
Nikulin configurations on Kummer surfaces (English)
[ Abstract ]
A Nikulin configuration is the data of
16 disjoint smooth rational curves on a K3 surface.
According to results of Nikulin this means that the K3 surface
is a Kummer surface and the abelian surface in the Kummer structure
is determined by the 16 curves. An old question of Shioda is about the
existence of non isomorphic Kummer structures on the same Kummer K3
surface.
The question was positively answered and studied by several authors, and
it was shown that the number of non-isomorphic Kummer structures is
finite,
but no explicit geometric construction of such structures was given.
In the talk I will show how to construct explicitely non isomorphic
Kummer structures on generic Kummer K3 surfaces.
This is a joint work with X. Roulleau.
A Nikulin configuration is the data of
16 disjoint smooth rational curves on a K3 surface.
According to results of Nikulin this means that the K3 surface
is a Kummer surface and the abelian surface in the Kummer structure
is determined by the 16 curves. An old question of Shioda is about the
existence of non isomorphic Kummer structures on the same Kummer K3
surface.
The question was positively answered and studied by several authors, and
it was shown that the number of non-isomorphic Kummer structures is
finite,
but no explicit geometric construction of such structures was given.
In the talk I will show how to construct explicitely non isomorphic
Kummer structures on generic Kummer K3 surfaces.
This is a joint work with X. Roulleau.
2018/05/28
Seminar on Geometric Complex Analysis
10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Satoshi Nakamura (Tohoku University)
A generalization of Kähler Einstein metrics for Fano manifolds with non-vanishing Futaki invariant (JAPANESE)
Satoshi Nakamura (Tohoku University)
A generalization of Kähler Einstein metrics for Fano manifolds with non-vanishing Futaki invariant (JAPANESE)
[ Abstract ]
The existence problem of Kähler Einstein metrics for Fano manifolds was one of the central problems in Kähler Geometry. The vanishing of the Futaki invariant is known as an obstruction to the existence of Kähler Einstein metrics. Generalized Kähler Einstein metrics (GKE for short), introduced by Mabuchi in 2000, is a generalization of Kähler Einstein metrics for Fano manifolds with non-vanishing Futaki invariant. In this talk, we give the followings:
(i) The positivity for the Hessian of the Ricci Calabi functional which characterizes GKE as its critical points, and its application.
(ii) A criterion for the existence of GKE on toric Fano manifolds from view points of an algebraic stability and an analytic stability.
The existence problem of Kähler Einstein metrics for Fano manifolds was one of the central problems in Kähler Geometry. The vanishing of the Futaki invariant is known as an obstruction to the existence of Kähler Einstein metrics. Generalized Kähler Einstein metrics (GKE for short), introduced by Mabuchi in 2000, is a generalization of Kähler Einstein metrics for Fano manifolds with non-vanishing Futaki invariant. In this talk, we give the followings:
(i) The positivity for the Hessian of the Ricci Calabi functional which characterizes GKE as its critical points, and its application.
(ii) A criterion for the existence of GKE on toric Fano manifolds from view points of an algebraic stability and an analytic stability.
Mathematical Biology Seminar
15:30-16:30 Room #122 (Graduate School of Math. Sci. Bldg.)
Sourav Kumar Sasmal (Department of Physics and Mathematics, Aoyama Gakuin University)
T-cell mediated adaptive immunity in primary dengue infections
https://www.sciencedirect.com/science/article/pii/S0022519317303211
Sourav Kumar Sasmal (Department of Physics and Mathematics, Aoyama Gakuin University)
T-cell mediated adaptive immunity in primary dengue infections
[ Abstract ]
Currently, dengue virus (DENV) is the most common mosquito-borne viral disease in the world, which is endemic across tropical Asia, Latin America, and Africa. The global DENV incidence is increasing day by day due to climate changing. According to a report, DENV cases increase almost five times since 1980, than the previous 30 years. Mathematical modeling is a common tool for understanding, studying and analyzing the mechanisms that govern the dynamics of infectious disease. In addition, models can be used to study different mitigation measures to control outbreaks. Here, we present a mathematical model of DENV dynamics in micro-environment (cellular level) consisting of healthy cells, infected cells, virus particles and T -cell mediated adaptive immunity. We have considered the explicit role of cytokines and antibody in our model. We find that the virus load goes down to zero within 6 days as it is common for DENV infection. We have shown that the cytokine mediated virus clearance plays a very important role in dengue dynamics. It can change the dynamical behavior of the system and causes essential extinction of the virus. Finally, we have incorporated the antiviral treatment effect for DENV in our model and shown that the basic reproduction number is directly proportional to the antiviral treatment effects.
[ Reference URL ]Currently, dengue virus (DENV) is the most common mosquito-borne viral disease in the world, which is endemic across tropical Asia, Latin America, and Africa. The global DENV incidence is increasing day by day due to climate changing. According to a report, DENV cases increase almost five times since 1980, than the previous 30 years. Mathematical modeling is a common tool for understanding, studying and analyzing the mechanisms that govern the dynamics of infectious disease. In addition, models can be used to study different mitigation measures to control outbreaks. Here, we present a mathematical model of DENV dynamics in micro-environment (cellular level) consisting of healthy cells, infected cells, virus particles and T -cell mediated adaptive immunity. We have considered the explicit role of cytokines and antibody in our model. We find that the virus load goes down to zero within 6 days as it is common for DENV infection. We have shown that the cytokine mediated virus clearance plays a very important role in dengue dynamics. It can change the dynamical behavior of the system and causes essential extinction of the virus. Finally, we have incorporated the antiviral treatment effect for DENV in our model and shown that the basic reproduction number is directly proportional to the antiviral treatment effects.
https://www.sciencedirect.com/science/article/pii/S0022519317303211
2018/05/25
Colloquium
15:30-16:30 Room #056 (Graduate School of Math. Sci. Bldg.)
Noriyuki ABE (The University of Tokyo)
Mod p representation theory of p-adic reductive groups
(日本語)
Noriyuki ABE (The University of Tokyo)
Mod p representation theory of p-adic reductive groups
(日本語)
Algebraic Geometry Seminar
15:30-17:00 Room #122 (Graduate School of Math. Sci. Bldg.)
De Qi Zhang (Singapore)
Endomorphisms of normal projective variety and equivariant-MMP (English)
De Qi Zhang (Singapore)
Endomorphisms of normal projective variety and equivariant-MMP (English)
[ Abstract ]
We report some recent joint works on polarized or int-amplified endomorphisms f on a normal projective variety X with mild singularities, and prove the pseudo-effectivity of the anti-canonical divisor of X, and the f-equivariance, after replacing f by its power, for every minimal model program starting from X. Fano varieties and Q-abelian varieties turn out to be building blocks having such symmetries. The ground field is closed and of characteristic 0 or at least 7.
We report some recent joint works on polarized or int-amplified endomorphisms f on a normal projective variety X with mild singularities, and prove the pseudo-effectivity of the anti-canonical divisor of X, and the f-equivariance, after replacing f by its power, for every minimal model program starting from X. Fano varieties and Q-abelian varieties turn out to be building blocks having such symmetries. The ground field is closed and of characteristic 0 or at least 7.
2018/05/24
Applied Analysis
16:00-17:30 Room #128 (Graduate School of Math. Sci. Bldg.)
Eiji Yanagida (Tokyo Institute of Technology)
Sign-changing solutions for a one-dimensional semilinear parabolic problem (Japanese)
Eiji Yanagida (Tokyo Institute of Technology)
Sign-changing solutions for a one-dimensional semilinear parabolic problem (Japanese)
[ Abstract ]
This talk is concerned with a nonlinear parabolic equation on a bounded interval with the homogeneous Dirichlet or Neumann boundary condition. Under rather general conditions on the nonlinearity, we consider the blow-up and global existence of sign-changing solutions. It is shown that there exists a nonnegative integer $k$ such that the solution blows up in finite time if the initial value changes its sign at most $k$ times, whereas there exists a stationary solution with more than $k$ zeros. The proof is based on an intersection number argument combined with a topological method.
This talk is concerned with a nonlinear parabolic equation on a bounded interval with the homogeneous Dirichlet or Neumann boundary condition. Under rather general conditions on the nonlinearity, we consider the blow-up and global existence of sign-changing solutions. It is shown that there exists a nonnegative integer $k$ such that the solution blows up in finite time if the initial value changes its sign at most $k$ times, whereas there exists a stationary solution with more than $k$ zeros. The proof is based on an intersection number argument combined with a topological method.
2018/05/23
Seminar on Probability and Statistics
14:00-15:10 Room #052 (Graduate School of Math. Sci. Bldg.)
Lorenzo Mercuri (University of Milan)
"yuima.law": From mathematical representation of general Lévy processes to a numerical implementation
Lorenzo Mercuri (University of Milan)
"yuima.law": From mathematical representation of general Lévy processes to a numerical implementation
[ Abstract ]
We present a new class called yuima.law that refers to the mathematical description of a general Lévy process used in the formal definition of a general Stochastic Differential Equation. The final aim is to have an object, defined by the user, that contains all possible information about the Lévy process considered. This class creates a link between YUIMA and other R packages available on CRAN that manage specific Lévy processes.
An example of yuima.law is shown based the Mixed Tempered Stable(MixedTS) Lévy processes. A review of the univariate MixedTS is given and some new results on the asymptotic tail behaviour are derived. The multivariate version of the Mixed Tempered Stable, which is a generalisation of the Normal Variance Mean Mixtures, is discussed. Characteristics of this distribution, its capacity in fitting tails and in capturing dependence structure between components are investigated.
We present a new class called yuima.law that refers to the mathematical description of a general Lévy process used in the formal definition of a general Stochastic Differential Equation. The final aim is to have an object, defined by the user, that contains all possible information about the Lévy process considered. This class creates a link between YUIMA and other R packages available on CRAN that manage specific Lévy processes.
An example of yuima.law is shown based the Mixed Tempered Stable(MixedTS) Lévy processes. A review of the univariate MixedTS is given and some new results on the asymptotic tail behaviour are derived. The multivariate version of the Mixed Tempered Stable, which is a generalisation of the Normal Variance Mean Mixtures, is discussed. Characteristics of this distribution, its capacity in fitting tails and in capturing dependence structure between components are investigated.
Seminar on Probability and Statistics
15:30-16:40 Room #052 (Graduate School of Math. Sci. Bldg.)
Emanuele Guidotti (University of Milan)
Latest Development in yuimaGUI - Interactive Platform for Computational Statistics and Finance
Emanuele Guidotti (University of Milan)
Latest Development in yuimaGUI - Interactive Platform for Computational Statistics and Finance
[ Abstract ]
The yuimaGUI package provides a user-friendly interface for the yuima package, including additional tools related to Quantitative Finance. It greatly simplifies tasks such as estimation and simulation of stochastic processes, data retrieval, time series clustering, change point and lead-lag analysis. Today we are going to discuss the latest development in yuimaGUI, extending the Platform with multivariate modeling and simulation, Levy processes, Point processes, broader model selection tools and more general distributions thanks to the new yuima-Law object.
The yuimaGUI package provides a user-friendly interface for the yuima package, including additional tools related to Quantitative Finance. It greatly simplifies tasks such as estimation and simulation of stochastic processes, data retrieval, time series clustering, change point and lead-lag analysis. Today we are going to discuss the latest development in yuimaGUI, extending the Platform with multivariate modeling and simulation, Levy processes, Point processes, broader model selection tools and more general distributions thanks to the new yuima-Law object.
2018/05/22
PDE Real Analysis Seminar
10:30-11:30 Room #056 (Graduate School of Math. Sci. Bldg.)
Qing Liu (Fukuoka University)
A discrete game interpretation for curvature flow equations with dynamic boundary conditions (日本語)
Qing Liu (Fukuoka University)
A discrete game interpretation for curvature flow equations with dynamic boundary conditions (日本語)
[ Abstract ]
A game-theoretic approach to motion by curvature was proposed by Kohn and Serfaty in 2006. They constructed a family of deterministic discrete games, whose value functions converge to the unique solution of the curvature flow equation. In this talk, we develop this method to provide an interpretation for the associated dynamic boundary value problems by including in the game setting a kind of nonlinear reflection near the boundary. We also discuss its applications to the fattening phenomenon. This talk is based on joint work with N. Hamamuki at Hokkaido University.
A game-theoretic approach to motion by curvature was proposed by Kohn and Serfaty in 2006. They constructed a family of deterministic discrete games, whose value functions converge to the unique solution of the curvature flow equation. In this talk, we develop this method to provide an interpretation for the associated dynamic boundary value problems by including in the game setting a kind of nonlinear reflection near the boundary. We also discuss its applications to the fattening phenomenon. This talk is based on joint work with N. Hamamuki at Hokkaido University.
Tuesday Seminar on Topology
17:00-18:30 Room #056 (Graduate School of Math. Sci. Bldg.)
Doman Takata (The university of Tokyo)
An analytic index theory for infinite-dimensional manifolds and KK-theory (JAPANESE)
Doman Takata (The university of Tokyo)
An analytic index theory for infinite-dimensional manifolds and KK-theory (JAPANESE)
[ Abstract ]
The Atiyah-Singer index theorem is one of the monumental works in geometry and topology, which states the coincidence between analytic index and topological index on closed manifolds. The overall goal of my research is to formulate and prove an infinite dimensional version of this theorem. For this purpose, it is natural to begin with simple cases, and my current problem is the following: For infinite-dimensional manifolds equipped with a "proper and cocompact" action of the loop group of the circle, construct a loop group equivariant index theory, from the viewpoint of KK-theory. Although this project has not been completed, I have constructed several core objects for the analytic side of this problem, including a Hilbert space regarded as an "$L^2$-space", in arXiv:1701.06055 and arXiv:1709.06205. In this talk, I am going to report the progress so far.
The Atiyah-Singer index theorem is one of the monumental works in geometry and topology, which states the coincidence between analytic index and topological index on closed manifolds. The overall goal of my research is to formulate and prove an infinite dimensional version of this theorem. For this purpose, it is natural to begin with simple cases, and my current problem is the following: For infinite-dimensional manifolds equipped with a "proper and cocompact" action of the loop group of the circle, construct a loop group equivariant index theory, from the viewpoint of KK-theory. Although this project has not been completed, I have constructed several core objects for the analytic side of this problem, including a Hilbert space regarded as an "$L^2$-space", in arXiv:1701.06055 and arXiv:1709.06205. In this talk, I am going to report the progress so far.
2018/05/21
Algebraic Geometry Seminar
15:30-17:00 Room #122 (Graduate School of Math. Sci. Bldg.)
Christopher Hacon (Utah/Kyoto)
Towards the termination of flips. (English)
https://www.math.utah.edu/~hacon/
Christopher Hacon (Utah/Kyoto)
Towards the termination of flips. (English)
[ Abstract ]
The minimal model program (MMP) predicts that if $X$ is a smooth complex projective variety which is not uniruled, then there is a finite sequence of "elementary" birational maps
$X=X_0-->X_1-->X_2-->...-->X_n$ known as divisorial contractions and flips whose output $\bar X=X_n$ is a minimal model so that $K_{\bar X}$ is a nef $Q$-divisor i.e it intersects all curves $C\subset \bar X$ non-negatively: $K_{\bar X}\cdot C\geq 0$.
The existence of these birational maps has been established, but in order to complete the MMP, it is necessary to show that flips terminate i.e. there are no infinite sequences of flips. In this talk we will discuss recent results towards the termination of flips.
[ Reference URL ]The minimal model program (MMP) predicts that if $X$ is a smooth complex projective variety which is not uniruled, then there is a finite sequence of "elementary" birational maps
$X=X_0-->X_1-->X_2-->...-->X_n$ known as divisorial contractions and flips whose output $\bar X=X_n$ is a minimal model so that $K_{\bar X}$ is a nef $Q$-divisor i.e it intersects all curves $C\subset \bar X$ non-negatively: $K_{\bar X}\cdot C\geq 0$.
The existence of these birational maps has been established, but in order to complete the MMP, it is necessary to show that flips terminate i.e. there are no infinite sequences of flips. In this talk we will discuss recent results towards the termination of flips.
https://www.math.utah.edu/~hacon/
Algebraic Geometry Seminar
13:30-15:00 Room #122 (Graduate School of Math. Sci. Bldg.)
Will Donovan (IPMU)
Perverse sheaves of categories and birational geometry (English)
Will Donovan (IPMU)
Perverse sheaves of categories and birational geometry (English)
[ Abstract ]
Kapranov and Schechtman have initiated a program to study perverse sheaves of categories, or perverse schobers. It is expected that examples arise from birational geometry, in particular from webs of flops. I explain progress towards constructing these objects for Grothendieck resolutions (work of the above authors with Bondal), and for 3-folds (joint work of myself and Wemyss).
Kapranov and Schechtman have initiated a program to study perverse sheaves of categories, or perverse schobers. It is expected that examples arise from birational geometry, in particular from webs of flops. I explain progress towards constructing these objects for Grothendieck resolutions (work of the above authors with Bondal), and for 3-folds (joint work of myself and Wemyss).
Seminar on Geometric Complex Analysis
10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Eiji Inoue (The University of Tokyo)
Kähler-Ricci soliton, K-stability and moduli space of Fano
manifolds (JAPANESE)
Eiji Inoue (The University of Tokyo)
Kähler-Ricci soliton, K-stability and moduli space of Fano
manifolds (JAPANESE)
[ Abstract ]
Kähler-Ricci soliton is a kind of canonical metrics on Fano manifolds and is a natural generalization of Kähler-Einstein metric in
view of Kähler-Ricci flow.
In this talk, I will explain the following good geometric features of Fano manifolds admitting Kähler-Ricci solitons:
1. Volume minimization, reductivity and uniqueness results established by Tian&Zhu.
2. Relation to algebraic (modified) K-stability estabilished by Berman&Witt-Niström and Datar&Székelyhidi.
3. Moment map picture for Kähler-Ricci soliton (‘real side’)
4. Moduli stack (‘virtual side’) and moduli space of them
A result in 1 is indispensable for the formulation in 3 and 4, and explains why we should consider solitons, beyond Einstein metrics. I also show an essential idea in the construction of the moduli space of Fano manifolds admitting Kähler-Ricci solitons and give some remarks on technical key point.
Kähler-Ricci soliton is a kind of canonical metrics on Fano manifolds and is a natural generalization of Kähler-Einstein metric in
view of Kähler-Ricci flow.
In this talk, I will explain the following good geometric features of Fano manifolds admitting Kähler-Ricci solitons:
1. Volume minimization, reductivity and uniqueness results established by Tian&Zhu.
2. Relation to algebraic (modified) K-stability estabilished by Berman&Witt-Niström and Datar&Székelyhidi.
3. Moment map picture for Kähler-Ricci soliton (‘real side’)
4. Moduli stack (‘virtual side’) and moduli space of them
A result in 1 is indispensable for the formulation in 3 and 4, and explains why we should consider solitons, beyond Einstein metrics. I also show an essential idea in the construction of the moduli space of Fano manifolds admitting Kähler-Ricci solitons and give some remarks on technical key point.
2018/05/16
FMSP Lectures
14:45-15:45 Room #122 (Graduate School of Math. Sci. Bldg.)
M.M. Lavrentʼev, Jr. (Novosibirsk State University)
Some strongly degenerate parabolic equations (joint with Prof. A. Tani) (ENGLISH)
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_MMLavrentev.pdf
M.M. Lavrentʼev, Jr. (Novosibirsk State University)
Some strongly degenerate parabolic equations (joint with Prof. A. Tani) (ENGLISH)
[ Abstract ]
We consider some nonlinear 1D parabolic equations with the positive leading coefficient which is not away from zero. "Hyperbolic phenomena" (gradient blowing up phenomena) were reported in literature for such models. We describe special cases of regular solvability for degenerate equations under study.
[ Reference URL ]We consider some nonlinear 1D parabolic equations with the positive leading coefficient which is not away from zero. "Hyperbolic phenomena" (gradient blowing up phenomena) were reported in literature for such models. We describe special cases of regular solvability for degenerate equations under study.
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_MMLavrentev.pdf
< Previous 123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960616263646566676869707172737475767778798081828384858687888990919293949596979899100101102103104105106107108109110111112113114115116117118119120121122123124125126127128129130131132133134135136137138139140141142143144145146147148149150151152153154155156157158159160161162163164165166167168169170171172173174175176177178179180181182183184185186187188189190191 Next >
