Seminar information archive

Seminar information archive ~02/01Today's seminar 02/02 | Future seminars 02/03~

Number Theory Seminar

16:30-17:30   Room #117 (Graduate School of Math. Sci. Bldg.)
Antoine Chambert-Loir (Universite de Rennes 1)
Equidistribution theorems in Arakelov geometry
[ Abstract ]
The proof of Bogomolov's conjecture by Zhang made a crucial use
of an equidistribution property for the Galois orbits of points of small
heights in Abelian varieties defined over number fields.
Such an equidistribution property is proved using a method invented
by Szpiro, Ullmo and Zhang, and makes use of Arakelov theory.
This equidistribution theorem takes place in the complex torus
associated to the Abelian variety. I will show how a similar
equidistribution theorem can be proven for the p-adic topology ;
we have to use Berkovich space. Thanks to recent results of Yuan
about `big line bundles' in Arakelov geometry, the situation
is now very well understood.

Seminar on Probability and Statistics

14:50-16:00   Room #122 (Graduate School of Math. Sci. Bldg.)
Marc HOFFMANN (Universite Paris-est Marne la vallee)
Statistical analysis of fragmentation chains
[ Abstract ]
We address statistical inference in self-similar conservative fragmentation chains, when only observations on the size of the fragments below a given threshold are available. (Possibly, the measurement of the fragments themselves are subject to further systematic experimental noise.) This framework, introduced by Bertoin and Martinez is motivated by mineral crushing in mining industry. We compute upper and lower rates of estimation for several functionals of the dislocation measure, both in a semi-parametric and a non-parametric framework. The underlying estimated object is the step distribution of the random walk associated to a randomly tagged fragment that evolves along the genealogical tree representation of the fragmentation process. We establish a formal link with the statistical problem of estimating the overshoot of the distribution as the crossing level goes to infinity with the size of the dataset; in particular the difficulty of the estimation problem in the non-parametric case is comparable to ill-posed linear inverse problems of order 1 in signal denoising.
[ Reference URL ]


Tuesday Seminar on Topology

16:30-17:30   Room #056 (Graduate School of Math. Sci. Bldg.)
飯田 修一 (東京大学大学院数理科学研究科)
Adiabatic limits of eta-invariants and the Meyer functions
[ Abstract ]
The Meyer function is the function defined on the hyperelliptic
mapping class group, which gives a signature formula for surface
bundles over surfaces.
In this talk, we introduce certain generalizations of the Meyer
function by using eta-invariants and we discuss the uniqueness of this
function and compute the values for Dehn twists.

Lie Groups and Representation Theory

16:30-18:00   Room #126 (Graduate School of Math. Sci. Bldg.)
Fulton Gonzalez (Tufts University)
Group contractions, invariant differential operators and the matrix Radon transform

[ Abstract ]
Let $M_{n,k}$ denote the vector space of real $n\\times k$ matrices.
The matrix motion group is the semidirect product $(\\text O(n)\\times \\text O(k))\\ltimes M_{n,k}$, and is the Cartan motion group
associated with the real Grassmannian $G_{n,n+k}$.
The matrix Radon transform is an
integral transform associated with a double fibration involving
homogeneous spaces of this group. We provide a set of
algebraically independent generators of the subalgebra of its
universal enveloping algebra invariant under the Adjoint
representation. One of the elements of this set characterizes the range of the matrix Radon transform.
[ Reference URL ]

Algebraic Geometry Seminar

10:00-12:00   Room #128 (Graduate School of Math. Sci. Bldg.)
Dmitry KALEDIN (Steklov研究所, 東大数理)
Homological methods in non-commutative geometry, part 9
[ Reference URL ]


Seminar on Probability and Statistics

16:20-17:30   Room #122 (Graduate School of Math. Sci. Bldg.)
金川 秀也 (武蔵工業大学)
Parameter estimated standardized U-statistics with degenerate kernel for weakly dependent random variables
[ Abstract ]
In this paper, extending the results of Gombay and Horv'{a}th (1998), we prove limit theorems for the maximum of standardized degenerate U-statistics defined by some absolutely regular sequences or functionals of them.
[ Reference URL ]


Tuesday Seminar of Analysis

16:30-18:00   Room #128 (Graduate School of Math. Sci. Bldg.)
Nikolay Tzvetkov (Lille大学)
On the restrictions of Laplace-Beltrami eigenfunctions to curves

Algebraic Geometry Seminar

10:00-12:00   Room #128 (Graduate School of Math. Sci. Bldg.)
Dmitry KALEDIN (Steklov研究所, 東大数理)
Homological methods in non-commutative geometry, part 8


Seminar on Mathematics for various disciplines

13:30-14:30   Room #056 (Graduate School of Math. Sci. Bldg.)
伊藤一文 (North Carolina State University)
An Optimal Feedback Solution to Quantum Control Problems.
[ Abstract ]
Control of quantum systems described by Schrodinger equation is considered. Feedback control laws are developed for the orbit tracking via a controled Hamiltonian. Asymptotic tracking properties of the feedback laws are analyzed. Numerical integrations via time-splitting are also analyzed and used to demonstrate the feasibility of the proposed feedback laws.
[ Reference URL ]


Tuesday Seminar of Analysis

16:30-18:00   Room #128 (Graduate School of Math. Sci. Bldg.)
青木 貴史 (近畿大理工)
[ Abstract ]


Operator Algebra Seminars

16:30-18:00   Room #056 (Graduate School of Math. Sci. Bldg.)
Pinhas Grossman (Vanderbilt University)
Pairs of intermediate subfactors


Tuesday Seminar of Analysis

16:30-18:00   Room #128 (Graduate School of Math. Sci. Bldg.)
Gregory Eskin (UCLA)
Inverse boundary value problems for the Schrodinger equation with time-dependent electromagnetic potentials and the Aharonov-Bohm effect
[ Abstract ]
We consider the determination of the time-dependent magnetic and electric potentials (modulo gauge transforamtions) by the boundary measurements in domains with obstacles. We use the geometric optics and the tomography of broken rays. The presence of the obstacles leads to the Aharonov-Bohm effect caused by the magnetic and electric fluxes.


Infinite Analysis Seminar Tokyo

13:00-16:30   Room #117 (Graduate School of Math. Sci. Bldg.)
池田岳 (岡山理大理) 13:00-14:30
Double Schubert polynomials for the classical Lie groups
[ Abstract ]
For each infinite series of the classical Lie groups of type $B$,
$C$ or $D$, we introduce a family of polynomials parametrized by the
elements of the corresponding Weyl group of infinite rank. These
represent the Schubert classes in the equivariant cohomology of the
flag variety. When indexed by maximal Grassmannian elements of the Weyl
these polynomials are equal to the factorial analogues of Schur $Q$- or
$P$-functions defined earlier by Ivanov. This talk is based on joint work
with L. Mihalcea and H. Naruse.
前野 俊昭 (京大工) 15:00-16:30
Nichols-Woronowicz model of the K-ring of flag vaieties G/B
[ Abstract ]
We give a model of the equivariant $K$-ring $K_T(G/B)$ for
generalized flag varieties $G/B$ in the braided Hopf algebra
called Nichols-Woronowicz algebra. Our model is based on
the Chevalley-type formula for $K_T(G/B)$ due to Lenart
and Postnikov, which is described in terms of alcove paths.
We also discuss a conjecture on the model of the quantum
$K$-ring $QK(G/B)$.



17:00-18:00   Room #123 (Graduate School of Math. Sci. Bldg.)
D. Eisenbud (Univ. of California, Berkeley)
Plato's Cave: what we still don't know about generic projections
[ Abstract ]
Riemann Surfaces were first studied algebraically by first projecting them into the complex projective plan; later the same idea was applied to surfaces and higher dimensional varieties, projecting them to hypersurfaces. How much damage is done in this process? For example, what can the fibers of a generic linear projection look like? This is pretty easy for smooth curves and surfaces (though there are still open questions), not so easy in the higher-dimensional case. I'll explain some of what's known, including recent work of mine with Roya Beheshti, Joe Harris, and Craig Huneke.


Operator Algebra Seminars

16:30-18:00   Room #056 (Graduate School of Math. Sci. Bldg.)
崎山理史 (東大数理)
Gauge-invariant ideal structure of ultragraph $C^*$-algebras


10:40-12:10   Room #128 (Graduate School of Math. Sci. Bldg.)
Mikael Pichot (東大数理)
Topics in ergodic theory, von Neumann algebras, and rigidity
[ Reference URL ]


Seminar on Probability and Statistics

16:20-17:30   Room #122 (Graduate School of Math. Sci. Bldg.)
永井 圭二 (横浜国立大学)
Sequential Tests for Criticality of Branching Processes.
[ Abstract ]
We consider sequential testing procedures for detection of
criticality of Galton-Watson branching process with or without
immigration. We develop a t-test from fixed accuracy estimation
theory and a sequential probability ratio test (SPRT). We provide
local asymptotic normality (LAN) of the t-test and some asymptotic
optimality of the SPRT. We consider a general framework of
diffusion approximations from discrete-time processes and develop
sequential tests for one-dimensional diffusion processes to
investigate the operating characteristics of sequential tests
of the discrete-time processes. Especially the Bessel process with
constant drift plays a important role for the sequential test
of criticality of branching process with immigration.

(Joint work with K. Hitomi (Kyoto Institute of Technology)
and Y. Nishiyama (Kyoto Univ.))
[ Reference URL ]


Tuesday Seminar on Topology

16:30-18:00   Room #056 (Graduate School of Math. Sci. Bldg.)
R.C. Penner (USC and Aarhus University)
Groupoid lifts of representations of mapping classes
[ Abstract ]
The "Ptolemy groupoid" is the fundamental path groupoid of the dual to the ideal cell decomposition of the decorated Teichmueller space of a punctured or bordered surface, and the "Torelli groupoid" is thesimilar discretization of the fundamental path groupoid of the quotient
by the Torelli subgroup of mapping classes that acts identically on the first integral homology of the surface. Mapping classes can be represented as appropriate elements of the Ptolemy groupoid and likewise for elements of the Torelli group in the Torelli groupoid.

A natural series of questions is to wonder which representations of mapping class groups, Torelli groups, and their subgroups can be lifted to the groupoid level. In a series of joint works with J. Andersen, A. Bene, N. Kawazumi, and S. Morita, we have given explicit lifts of a number of classical representations: The Johnson representations of the classical and higher Torelli groups
and the symplectic representation of the mapping class group all lift to the Torelli groupoid. Furthermore, the Nielsen representation of the mapping class group as automorphisms of a
free group lifts to the Ptolemy groupoid, and hence so too does any representation
of the mapping class group that factors through its action on the fundamental group of
the surface such as the Magnus representation. We shall survey these various groupoid lifts and discuss current and potential future applications.

Lie Groups and Representation Theory

16:30-18:00   Room #126 (Graduate School of Math. Sci. Bldg.)
阿部 紀行 (東京大学)
On the existence of homomorphisms between principal series of complex
semisimple Lie groups
[ Abstract ]
The principal series representations of a semisimple Lie group play an important role in the representation theory. We study the principal series representation of a complex semisimple Lie group and determine when there exists a nonzero homomorphism between the representations.
[ Reference URL ]


Seminar on Geometric Complex Analysis

10:30-12:00   Room #128 (Graduate School of Math. Sci. Bldg.)
寺杣友秀 (東京大学)
種数3の曲線とあるCalabi-Yau threefoldの代数的対応(松本圭司氏との共同研究)

Kavli IPMU Komaba Seminar

17:00-18:30   Room #002 (Graduate School of Math. Sci. Bldg.)
Ken-Ichi Yoshikawa (The University of Tokyo)
Analytic torsion for Calabi-Yau threefolds
[ Abstract ]
In 1994, Bershadky-Cecotti-Ooguri-Vafa conjectured that analytic torsion
gives rise to a function on the moduli space of Calabi-Yau threefolds and
that it coincides with the quantity $F_{1}$ in string theory.
Since the holomorphic part of $F_{1}$ is conjecturally the generating function
of the counting problem of elliptic curves in the mirror Calabi-Yau threefold,
this implies the conjectural equivalence of analytic torsion and the counting
problem of elliptic curves for Calabi-Yau threefolds through mirror symmetry.

After Bershadsky-Cecotti-Ooguri-Vafa, we introduced an invariant of
Calabi-Yau threefolds, which we obtained using analytic torsion and
a Bott-Chern secondary class. In this talk, we will talk about the construction
and some explicit formulae of this analytic torsion invariant.
Some part of this talk is based on the joint work with H. Fang and Z. Lu.



10:40-12:10   Room #128 (Graduate School of Math. Sci. Bldg.)
Mikael Pichot (東大数理)
Topics in ergodic theory, von Neumann algebras, and rigidity
[ Reference URL ]

Applied Analysis

16:00-17:30   Room #126 (Graduate School of Math. Sci. Bldg.)
Danielle Hilhorst (CNRS / パリ第11大学)
Singular limit of a competition-diffusion system
[ Abstract ]
We revisit a competition-diffusion system for the densities of biological populations, and (i) prove the strong convergence in L^2 of the densities of the biological species (joint work with Iida, Mimura and Ninomiya); (ii) derive the singular limit of some reaction terms as the reaction coefficient tends to infinity (joint work with Martin and Mimura).


Seminar on Probability and Statistics

15:20-16:30   Room #122 (Graduate School of Math. Sci. Bldg.)
Stefano IACUS (Department of Economics, Business and Statistics, University of Milan)
Inference problems for the telegraph process observed at discrete times
[ Abstract ]
The telegraph process {X(t), t>0}, has been introduced (see
Goldstein, 1951) as an alternative model to the Brownian motion B(t).
This process describes a motion of a particle on the real line which
alternates its velocity, at Poissonian times, from +v to -v. The
density of the distribution of the position of the particle at time t
solves the hyperbolic differential equation called telegraph equation
and hence the name of the process.
Contrary to B(t) the process X(t) has finite variation and
continuous and differentiable paths. At the same time it is
mathematically challenging to handle. Several variation of this
process have been recently introduced in the context of Finance.

In this talk we will discuss pseudo-likelihood and moment type
estimators of the intensity of the Poisson process, from discrete
time observations of standard telegraph process X(t). We also
discuss the problem of change point estimation for the intensity of
the underlying Poisson process and show the performance of this
estimator on real data.
[ Reference URL ]


Tuesday Seminar on Topology

16:30-18:40   Room #056 (Graduate School of Math. Sci. Bldg.)
Xavier G\'omez-Mont (CIMAT, Mexico) 16:30-17:30
A Singular Version of The Poincar\\'e-Hopf Theorem
[ Abstract ]
The Poincar\\'e-Hopf Theorem asserts that the Euler Characteristic of a compact manifold is the sum of the indices of any vector field on it with isolated singularities.

A hypersurface in real or complex number space may be considered as the limit of the smooth hypersurfaces obtained from nearby regular values. The singularity contains “hidden” topology, which is unfolded by a smooth regeneration. At the singularity one has an algebraic invariant, the Jacobi Algebra, which is obtained by considering analytic functions modulo the partial derivatives. It contains topological information of the singularity.

One may consider vector fields tangent to a hypersurface with isolated singularities, and define topologically an index, which coincides with the sum of the Poincar\\'e-Hopf indices of a regeneration of it tangent to a nearby smooth hypersurface.

I will explain how to compute the index of a vector field X tangent to an isolated hypersurface singularity V using Homological Algebra, as the Euler Characteristic of the homology of the complex obtained by contracting differential forms on V with the vector field X. The formula contains several terms, but the higher order terms may be translated from the invariants of the singular point to invariants in the Jacobi Algebra, making this translation a local version of the Poincar\\'e-Hopf Theorem.

I will also explain how some of these ideas can be extended to complete intersections.
Miguel A. Xicotencatl (CINVESTAV, Mexico) 17:40-18:40
Chen Ruan cohomology of cotangent orbifolds and Chas-Sullivan string topology
[ Abstract ]
(Joint with: A. Gonzalez, E. Lupercio, C. Segovia, and B. Uribe)

At the end of 90's, two theories of topology were invented roughly at the same time and attracted considerable interest in the mathematical community. One is the Chas-Sullivan's loop product on the homology of loop space and the second one is Chen-Ruan's stringy cohomology of orbifold. It was an observation of Chen that inertia orbifold (which carries Chen-Ruan cohomology) is the space of constant loops of an orbifold. Therefore, two theories should interact. In this work we show that for an interesting family of orbifolds, the virtual orbifold cohomology, turns out to be a subalgebra of the homology of the loop orbifold, and is isomorphic, as algebras, to the Chen-Ruan orbifold cohomology of its cotangent orbifold.

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