Seminar information archive

Seminar information archive ~10/22Today's seminar 10/23 | Future seminars 10/24~

GCOE lecture series

16:30-18:00   Room #128 (Graduate School of Math. Sci. Bldg.)
Michael Eastwood (Australian National University)
Invariant differential operators on the sphere (ENGLISH)
[ Abstract ]
The circle is acted upon by the rotation group SO(2) and there are plenty of differential operators invariant under this action. But the circle is also acted upon by SL(2,R) and this larger symmetry group cuts down the list of invariant differential operators to something smaller but more interesting! I shall explain what happens and how this phenomenon generalises to spheres. These constructions are part of a general theory but have numerous unexpected applications, for example in suggesting a new stable finite-element scheme in linearised elasticity (due to Arnold, Falk, and Winther).
[ Reference URL ]
http://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar2010.html#20101102eastwood

2010/11/05

GCOE lecture series

16:30-18:00   Room #123 (Graduate School of Math. Sci. Bldg.)
Michael Eastwood (Australian National University)
How to recognise the geodesics of a metric connection (ENGLISH)
[ Abstract ]
The geodesics on a Riemannian manifold form a distinguished family of curves, one in every direction through every point. Sometimes two metrics can provide the same family of curves: the Euclidean metric and the round metric on the hemisphere have this property. It is also possible that a family of curves does not arise from a metric at all. Following a classical procedure due to Roger Liouville, I shall explain how to tell these cases apart on a surface. This is joint work with Robert Bryant and Maciej Dunajski.
[ Reference URL ]
http://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar2010.html#20101102eastwood

2010/11/04

Operator Algebra Seminars

16:30-18:00   Room #122 (Graduate School of Math. Sci. Bldg.)
Yoshiko Ogata (Univ.Tokyo)
Nonequilibrium Statistical Mechanics (JAPANESE)

Lectures

10:40-12:10   Room #123 (Graduate School of Math. Sci. Bldg.)
Jean Meyer, Yasuko HISAMATSU (Risk Capital Market Tokyo, BNP Paribas)
Market, Liquidity and Counterparty Risk (ENGLISH)
[ Abstract ]
1. Introduction to the market risk

- Introduction to the Risk Management
in the Financial institutions
- Overview of the main market risks

2. Market & Liquidity Risks –Basics

-Presentation of the main Greeks
-Focus on volatility risk
-Focus on correlation risk
-Conclusion (common features of the market risks)

3. Risk measure

- Stress test
- Value at risk
- Risks measure for counterparty risk

2010/11/02

Lectures

13:00-16:10   Room #122 (Graduate School of Math. Sci. Bldg.)
Vladimir Bogachev (Moscow)
The Malliavin calculus on configuration spaces and applications (ENGLISH)
[ Abstract ]
It is planned to discuss first a general scheme of the Malliavin
calculus on an abstract measurable
manifold with minimal assumptions about the manifold.
Then a practical realization of this scheme will be discussed in
several concrete examples with emphasis
on configuration spaces, i.e., spaces of locally finite configurations
in a given manifold (for example, just
a finite-dimensional Euclidean space), which can be alternatively
described as the spaces of integer-valued
discrete measures equipped with suitable differential structures.
No acquaintance with the Malliavin calculus and differential geometry
is assumed.

Tuesday Seminar on Topology

16:30-18:00   Room #056 (Graduate School of Math. Sci. Bldg.)
Daniel Ruberman (Brandeis University)
Periodic-end manifolds and SW theory (ENGLISH)
[ Abstract ]
We study an extension of Seiberg-Witten invariants to
4-manifolds with the homology of S^1 \\times S^3. This extension has
many potential applications in low-dimensional topology, including the
study of the homology cobordism group. Because b_2^+ =0, the usual
strategy for defining invariants does not work--one cannot disregard
reducible solutions. In fact, the count of solutions can jump in a
family of metrics or perturbations. To remedy this, we define an
index-theoretic counter-term that jumps by the same amount. The
counterterm is the index of the Dirac operator on a manifold with a
periodic end modeled at infinity by the infinite cyclic cover of the
manifold. This is joint work with Tomasz Mrowka and Nikolai Saveliev.

Lie Groups and Representation Theory

16:30-18:00   Room #126 (Graduate School of Math. Sci. Bldg.)
Michael Eastwood (University of Adelaide)
Twistor theory and the harmonic hull (ENGLISH)
[ Abstract ]
Harmonic functions are real-analytic and so automatically extend from being functions of real variables to being functions of complex variables. But how far do they extend? This question may be answered by twistor theory, the Penrose transform, and associated geometry. I shall base the constructions on a formula of Bateman from 1904. This is joint work with Feng Xu.

2010/11/01

Algebraic Geometry Seminar

16:40-18:10   Room #126 (Graduate School of Math. Sci. Bldg.)
Atsushi Ito (Univ. of Tokyo)
How to estimate Seshadri constants (JAPANESE)
[ Abstract ]
Seshadri constant is an invariant which measures the positivities of ample line bundles. This relates with adjoint bundles, Nagata conjecture, slope stabilities, Gromov width (an invariant of symplectic manifolds) and so on. But it is very diffiult to compute or estimate Seshadri constants in general, especially in higher dimension.
In this talk, we first study Seshadri constants of toric varieties, and next consider about non-toric cases using toric degenerations. For example, good estimations are obtained for complete intersections in projective spaces.

Lectures

16:00-18:15   Room #270 (Graduate School of Math. Sci. Bldg.)
Michel Cristofol (マルセイユ大学) 16:00-17:00
Inverse problems in non linear parabolic equations : Two differents approaches (ENGLISH)
[ Reference URL ]
http://www.ms.u-tokyo.ac.jp/~kengok/abstractTokyo.pdf
Patricia Gaitan (マルセイユ大学) 17:15-18:15
Inverse Problems for parabolic System
(ENGLISH)
[ Abstract ]
I will present a review of stability and controllability results for linear parabolic coupled systems with coupling of first and zeroth-order terms by data of reduced number of components. The key ingredients are global Carleman estimates.

2010/10/29

Colloquium

16:30-17:30   Room #002 (Graduate School of Math. Sci. Bldg.)
Robin Graham (University of Washington)
Ambient metrics and exceptional holonomy (ENGLISH)
[ Abstract ]
The holonomy of a pseudo-Riemannian metric is a subgroup of the orthogonal group which measures the structure preserved by parallel translation. Construction of pseudo-Riemannian metrics whose holonomy is an exceptional Lie group has been of great interest in recent years. This talk will outline a construction of metrics in dimension 7 whose holonomy is contained in the split real form of the exceptional group $G_2$. The datum for the construction is a generic real-analytic 2-plane field on a manifold of dimension 5; the metric in dimension 7 arises as the ambient metric of a conformal structure on the 5-manifold defined by Nurowski in terms of the 2-plane field.

2010/10/28

Operator Algebra Seminars

16:30-18:00   Room #122 (Graduate School of Math. Sci. Bldg.)
Makoto Yamashita (Univ. Tokyo)
Type III representations of the infinite symmetric group (ENGLISH)
[ Abstract ]
Based on earlier results about the structure of the II$_1$ representations of the infinite symmetric group, we investigate its type III representations and the related inclusion of von Neumann algebras of type III.

Lectures

10:40-12:10   Room #123 (Graduate School of Math. Sci. Bldg.)
Jean Meyer, Yasuko HISAMATSU (Risk Capital Market Tokyo, BNP Paribas)
Market, Liquidity and Counterparty Risk (ENGLISH)
[ Abstract ]
1. Introduction to the market risk

- Introduction to the Risk Management
in the Financial institutions
- Overview of the main market risks

2. Market & Liquidity Risks –Basics

-Presentation of the main Greeks
-Focus on volatility risk
-Focus on correlation risk
-Conclusion (common features of the market risks)

3. Risk measure

- Stress test
- Value at risk
- Risks measure for counterparty risk

2010/10/26

Seminar on Geometric Complex Analysis

13:00-14:30   Room #123 (Graduate School of Math. Sci. Bldg.)
Dan Popovici (Toulouse)
Limits of Moishezon Manifolds under Holomorphic Deformations (ENGLISH)
[ Abstract ]
We prove that if all the fibres, except one, of a holomorphic family of compact complex manifolds are supposed to be Moishezon (i.e. bimeromorphic to projective manifolds), then the remaining (limit) fibre is again Moishezon. The two ingredients of the proof are the relative Barlet space of divisors contained in the fibres for which we show properness over the base of the family and the "strongly Gauduchon" (sG) metrics that we have introduced for the purpose of controlling volumes of cycles. These new metrics enjoy stability properties under both deformations and modifications and play a crucial role in obtaining a uniform control on volumes of relative divisors that prove the above-mentioned properness.

Tuesday Seminar on Topology

17:00-18:00   Room #056 (Graduate School of Math. Sci. Bldg.)
Kazuo Habiro (RIMS, Kyoto University)
Quantum fundamental groups and quantum representation varieties for 3-manifolds (JAPANESE)
[ Abstract ]
We define a refinement of the fundamental groups of 3-manifolds and
a generalization of representation variety of the fundamental group
of 3-manifolds. We consider the category $H$ whose morphisms are
nonnegative integers, where $n$ corresponds to a genus $n$ handlebody
equipped with an embedding of a disc into the boundary, and whose
morphisms are the isotopy classes of embeddings of handlebodies
compatible with the embeddings of the disc into the boundaries. For
each 3-manifold $M$ with an embedding of a disc into the boundary, we
can construct a contravariant functor from $H$ to the category of
sets, where the object $n$ of $H$ is mapped to the set of isotopy
classes of embedding of the genus $n$ handlebody into $M$, compatible
with the embeddings of the disc into the boundaries. This functor can
be regarded as a refinement of the fundamental group of $M$, and we
call it the quantum fundamental group of $M$. Using this invariant, we
can construct for each co-ribbon Hopf algebra $A$ an invariant of
3-manifolds which may be regarded as (the space of regular functions
on) the representation variety of $M$ with respect to $A$.

Numerical Analysis Seminar

16:30-18:00   Room #128 (Graduate School of Math. Sci. Bldg.)
Tomoaki Okayama (Hitotsubashi University)
Theoretical analysis of Sinc schemes for integral equations of the second kind (JAPANESE)
[ Reference URL ]
http://www.infsup.jp/utnas/

Lie Groups and Representation Theory

16:30-18:00   Room #126 (Graduate School of Math. Sci. Bldg.)
Daniel Sternheimer (Keio University and Institut de Mathematiques de Bourgogne)
Some instances of the reasonable effectiveness (and limitations) of symmetries and deformations in fundamental physics (ENGLISH)
[ Abstract ]
In this talk we survey some applications of group theory and deformation theory (including quantization) in mathematical physics. We start with sketching applications of rotation and discrete groups representations in molecular physics (``dynamical" symmetry breaking in crystals, Racah-Flato-Kibler; chains of groups and symmetry breaking). These methods led to the use of ``classification Lie groups" (``internal symmetries") in particle physics. Their relation with space-time symmetries will be discussed. Symmetries are naturally deformed, which eventually brought to Flato's deformation philosophy and the realization that quantization can be viewed as a deformation, including the many avatars of deformation quantization (such as quantum groups and quantized spaces). Nonlinear representations of Lie groups can be viewed as deformations (of their linear part), with applications to covariant nonlinear evolution equations. Combining all these suggests an Ansatz based on Anti de Sitter space-time and group, a deformation of the Poincare group of Minkowski space-time, which could eventually be quantized, with possible implications in particle physics and cosmology. Prospects for future developments between mathematics and physics will be indicated.
[ Reference URL ]
http://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar2010.html

2010/10/21

Operator Algebra Seminars

16:30-18:00   Room #122 (Graduate School of Math. Sci. Bldg.)
Benoit Collins (Univ. Ottawa)
Free probability and entropy additivity problems for Quantum information theory (ENGLISH)

2010/10/20

Seminar on Mathematics for various disciplines

10:30-11:30   Room #056 (Graduate School of Math. Sci. Bldg.)
Naohisa Ogawa (Hokkaido Institute of Technology)
Curvature Dependent Diffusion Flow on Surface with Thickness (JAPANESE)
[ Abstract ]
Particle diffusion in a two dimensional curved surface with thickness

embedded in $R_3$ is considered.

In addition to the usual diffusion flow, we find a new flow with an explicit

curvature dependence in $\\epsilon$ (thickness of surface) expansion.

As an example, the surface of elliptic cylinder is considered, and curvature

dependent diffusion coefficient is calculated. In addition, we consider the

1 dimensional object in $R_3$ (Tube),

and check the physical meaning of curvature effect.

2010/10/19

Tuesday Seminar on Topology

16:30-18:00   Room #002 (Graduate School of Math. Sci. Bldg.)
Jinseok Cho (Waseda University)
Optimistic limits of colored Jones invariants (ENGLISH)
[ Abstract ]
Yokota made a wonderful theory on the optimistic limit of Kashaev
invariant of a hyperbolic knot
that the limit determines the hyperbolic volume and the Chern-Simons
invariant of the knot.
Especially, his theory enables us to calculate the volume of a knot
combinatorially from its diagram for many cases.

We will briefly discuss Yokota theory, and then move to the optimistic
limit of colored Jones invariant.
We will explain a parallel version of Yokota theory based on the
optimistic limit of colored Jones invariant.
Especially, we will show the optimistic limit of colored Jones
invariant coincides with that of Kashaev invariant modulo 2\\pi^2.
This implies the optimistic limit of colored Jones invariant also
determines the volume and Chern-Simons invariant of the knot, and
probably more information.

This is a joint-work with Jun Murakami of Waseda University.

2010/10/18

Seminar on Geometric Complex Analysis

10:30-11:30   Room #128 (Graduate School of Math. Sci. Bldg.)
Sergey Ivashkovitch (Univ. de Lille)
Limiting behavior of minimal trajectories of parabolic vector fields on the complex projective plane. (ENGLISH)
[ Abstract ]
The classical Poincare-Bendixson theory describes the way a trajectory of a vector field on the real plane behaves when accumulating to the singular locus of the vector field. We shall describe, in the first approximation, the way a minimal trajectory of a parabolic complex polynomial vector field (or, a holomorphic foliation) on the complex projective plane approaches the singular locus. In particular we shall prove that if a holomorphic foliation has an exceptional minimal set then its nef model is necessarily hyperbolic.

Seminar on Geometric Complex Analysis

13:00-14:00   Room #128 (Graduate School of Math. Sci. Bldg.)
Philippe Eyssidieux (Institut Fourier, Grenoble)
Degenerate complex Monge-Ampere equations (ENGLISH)

Kavli IPMU Komaba Seminar

16:30-18:00   Room #002 (Graduate School of Math. Sci. Bldg.)
Todor Milanov (IPMU)
Quasi-modular forms and Gromov--Witten theory of elliptic orbifold $\\mathbb{P}^1$ (ENGLISH)
[ Abstract ]
This talk is based on my current work with Y. Ruan. Our project is part of the so called Landau--Ginzburg/Calabi-Yau correspondence. The latter is a conjecture, due to Ruan, that describes the relation between the $W$-spin invariants of a Landau-Ginzburg potential $W$ and the Gromov--Witten invariants of a certain Calabi--Yau orbifold. I am planning first to explain the higher-genus reconstruction formalism of Givental. This formalism together with the work of M. Krawitz and Y. Shen allows us to express the Gromov--Witten invariants of the orbifold $\\mathbb{P}^1$'s with weights $(3,3,3)$, $(2,4,4)$, and $(2,3,6)$ in terms of Saito's Frobenius structure associated with the simple elliptic singularities $P_8$, $X_9$, and $J_{10}$ respectively. After explaining Givental's formalism, my goal would be to discuss the Saito's flat structure, and to explain how its modular behavior fits in the Givental's formalism. This allows us to prove that the Gromov--Witten invariants are quasi-modular forms on an appropriate modular group.

Algebraic Geometry Seminar

16:40-18:10   Room #126 (Graduate School of Math. Sci. Bldg.)
Akiyoshi Sannai (Univ. of Tokyo)
Galois extensions and maps on local cohomology (JAPANESE)

2010/10/14

Operator Algebra Seminars

16:30-18:00   Room #122 (Graduate School of Math. Sci. Bldg.)
Yasuyuki Kawahigashi (Univ. Tokyo)
Nonstandard analysis for operator algebraists (JAPANESE)

2010/10/12

Tuesday Seminar on Topology

16:30-18:00   Room #056 (Graduate School of Math. Sci. Bldg.)
Andrei Pajitnov (Univ. de Nantes, The University of Tokyo)
Asymptotics of Morse numbers of finite coverings of manifolds (ENGLISH)
[ Abstract ]
Let X be a closed manifold;
denote by m(X) the Morse number of X
(that is, the minimal number of critical
points of a Morse function on X).
Let Y be a finite covering of X of degree d.

In this survey talk we will address the following question
posed by M. Gromov: What are the asymptotic properties
of m(N) as d goes to infinity?

It turns out that for high-dimensional manifolds with
free abelian fundamental group the asymptotics of
the number m(N)/d is directly related to the Novikov homology
of N. We prove this theorem and discuss related results.

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