## Seminar information archive

#### Seminar on Geometric Complex Analysis

10:30-12:00   Room #128 (Graduate School of Math. Sci. Bldg.)
Colin Guillarmou (Ecole Normale Superieure)
Eta invariant and Selberg Zeta function of odd type over convex co-compact hyperbolic manifolds

#### Algebraic Geometry Seminar

16:40-18:10   Room #126 (Graduate School of Math. Sci. Bldg.)

On weak Fano varieties with log canonical singularities
[ Abstract ]
We prove that the anti-canonical divisors of weak Fano
3-folds with log canonical singularities are semiample. Moreover, we consider
semiampleness of the anti-log canonical divisor of any weak log Fano pair
with log canonical singularities. We show semiampleness dose not hold in
general by constructing several examples. Based on those examples, we propose
sufficient conditions which seem to be the best possible and we prove
semiampleness under such conditions. In particular we derive semiampleness of the
anti-canonical divisors of log canonical weak Fano 4-folds whose lc centers
are at most 1-dimensional. We also investigate the Kleiman-Mori cones of
weak log Fano pairs with log canonical singularities.

### 2010/01/22

#### Lecture Series on Mathematical Sciences in Soceity

16:20-17:50   Room #117 (Graduate School of Math. Sci. Bldg.)

#### Lectures

16:30-18:00   Room #118 (Graduate School of Math. Sci. Bldg.)

Fractional Evolution Equations and Applications 3
[ Abstract ]
In recent years increasing interests and considerable
researches have been given to the fractional differential equations both
in time and space variables.
These are due to the applications of the fractional calculus
to problems in a wide areas of physics and engineering science and a rapid
development of the corresponding theory. A motivating example includes
the so-called continuous time random walk process
and the Levy process model for the mathematical finance.
In this lecture we develop solution techniques based on the linear and
nonlinear semigroup theory and apply it to solve the associated inverse
and optimal control problems. The property and stability of the solutions
as well as numerical integration methods
are discussed. The lecture also covers the basis and application of the
so-called Crandall-Ligget theory and the locally quasi-dissipative
operator method developed by Kobayashi-Kobayashi-Oharu.

Nonlinear evolution equations, Crandall-Ligget theory,
Locally quasi-dissipative operators approach

### 2010/01/21

#### Operator Algebra Seminars

16:30-18:00   Room #128 (Graduate School of Math. Sci. Bldg.)

On Subfactors Arising from Asymptotic Representations of Symmetric Groups

#### Applied Analysis

16:00-17:30   Room #122 (Graduate School of Math. Sci. Bldg.)
Danielle Hilhorst (パリ南大学 / CNRS)
A finite volume method on general meshes for a degenerate parabolic convection-reaction-diffusion equation
[ Abstract ]
We propose a finite volume method on general meshes for degenerate parabolic convection-reaction-diffusion equations. Such equations arise for instance in the modeling of contaminant transport in groundwater. After giving a convergence proof, we present the results of numerical tests.

### 2010/01/20

#### Geometry Seminar

17:00-18:30   Room #122 (Graduate School of Math. Sci. Bldg.)
Craig Van Coevering (MIT)
Asymptotically conical manifolds and the Monge-Ampere equation
[ Abstract ]
Some analysis is considered on manifolds with a conical end. Then we show that in the Kahler case the complex Monge-Ampere equation can be solved with the same regularity as is known in the ALE case. By considering resolutions of toric singularities and hypersurface singularities this can easily be used to produce many Calabi-Yau manifolds with a conical end.

#### Lectures

16:30-18:00   Room #118 (Graduate School of Math. Sci. Bldg.)

Fractional Evolution Equations and Applications 2
[ Abstract ]
In recent years increasing interests and considerable
researches have been given to the fractional differential equations both
in time and space variables.
These are due to the applications of the fractional calculus
to problems in a wide areas of physics and engineering science and a rapid
development of the corresponding theory. A motivating example includes
the so-called continuous time random walk process
and the Levy process model for the mathematical finance.
In this lecture we develop solution techniques based on the linear and
nonlinear semigroup theory and apply it to solve the associated inverse
and optimal control problems. The property and stability of the solutions
as well as numerical integration methods
are discussed. The lecture also covers the basis and application of the
so-called Crandall-Ligget theory and the locally quasi-dissipative
operator method developed by Kobayashi-Kobayashi-Oharu.

Existence and Uniqueness by C_0 semigroup theory, dissipative linear
operator
and Hille-Yoshida, Trotter-Kato theory.

#### Mathematical Biology Seminar

14:40-16:10   Room #052 (Graduate School of Math. Sci. Bldg.)

[ Abstract ]

はない.そこで本研究では,individual based modelに東京都市圏パーソント
リップ調査を組み合わせることにより感染拡大モデルを構築し,数値シミュレー
ションによって外出規制および施設閉鎖の効果を検討した.外出規制に関して
は,規制日数が12日以上と長い場合には効果が大きいことがわかった.また,施

わらないものの,累積罹患率は低下することがわかった.

### 2010/01/19

#### Tuesday Seminar of Analysis

16:30-18:00   Room #128 (Graduate School of Math. Sci. Bldg.)

#### Operator Algebra Seminars

16:30-18:00   Room #126 (Graduate School of Math. Sci. Bldg.)

Entire Cyclic Cohomology of Noncommutative Spheres

#### Tuesday Seminar on Topology

17:00-18:00   Room #056 (Graduate School of Math. Sci. Bldg.)

Localization via group action and its application to
the period condition of algebraic minimal surfaces
[ Abstract ]
The optimal estimate for the number of exceptional
values of the Gauss map of algebraic minimal surfaces is a long
standing problem. In this lecture, I will introduce new ideas
toward the solution of this problem. The collective Cohn-Vossen
inequality" is the key idea. From this we have effective
Nevanlinna's lemma on logarithmic derivative for a certain class
of meromorphic functions on the disk. On the other hand, we can
construct a family holomorphic functions on the disk from the
Weierstrass data of the algebraic minimal surface under
consideration, which encodes the period condition.
Applying effective Lemma on logarithmic derivative to these
functions, we can extract an intriguing inequality.

#### Lectures

16:30-18:00   Room #118 (Graduate School of Math. Sci. Bldg.)

Fractional Evolution Equations and Applications 1
[ Abstract ]
In recent years increasing interests and considerable
researches have been given to the fractional differential equations both
in time and space variables.
These are due to the applications of the fractional calculus
to problems in a wide areas of physics and engineering science and a rapid
development of the corresponding theory. A motivating example includes
the so-called continuous time random walk process
and the Levy process model for the mathematical finance.
In this lecture we develop solution techniques based on the linear and
nonlinear semigroup theory and apply it to solve the associated inverse
and optimal control problems. The property and stability of the solutions
as well as numerical integration methods
are discussed. The lecture also covers the basis and application of the
so-called Crandall-Ligget theory and the locally quasi-dissipative
operator method developed by Kobayashi-Kobayashi-Oharu.

Motivation: Continuous time random walk (CTRW) process
Fractional differential equations in time and Mittag-Leffler functions

### 2010/01/18

#### Seminar on Geometric Complex Analysis

10:30-12:00   Room #128 (Graduate School of Math. Sci. Bldg.)

スプライス商特異点について

#### Algebraic Geometry Seminar

16:40-18:10   Room #126 (Graduate School of Math. Sci. Bldg.)
Anne-Sophie Kaloghiros (RIMS)
The divisor class group of terminal Gorenstein Fano 3-folds and rationality questions
[ Abstract ]
Let Y be a quartic hypersurface in CP^4 with mild singularities, e.g. no worse than ordinary double points.
If Y contains a surface that is not a hyperplane section, Y is not Q-factorial and the divisor class group of Y, Cl Y, contains divisors that are not Cartier. However, the rank of Cl Y is bounded.

In this talk, I will show that in most cases, it is possible to describe explicitly the divisor class group Cl Y by running a Minimal Model Program (MMP) on X, a small Q-factorialisation of Y. In this case, the generators of Cl Y/ Pic Y are topological traces " of K-negative extremal contractions on X.
This has surprising consequences: it is possible to conclude that a number of families of non-factorial quartic 3-folds are rational.
In particular, I give some examples of rational quartic hypersurfaces Y_4\\subset CP^4 with rk Cl Y=2 and show that when the divisor class group of Y has sufficiently high rank, Y is always rational.

### 2010/01/15

#### Lecture Series on Mathematical Sciences in Soceity

16:20-17:50   Room #117 (Graduate School of Math. Sci. Bldg.)

### 2010/01/14

#### Operator Algebra Seminars

16:30-18:00   Room #128 (Graduate School of Math. Sci. Bldg.)
Marius Junge (Univ. Illinois, Urbana-Champaign)
Applications of operator algebras in Quantum information theory

### 2010/01/13

#### Lectures

16:45-17:45   Room #128 (Graduate School of Math. Sci. Bldg.)
Felix Rubin (Zurich 大学)
Scaled limit for the largest eigenvalue from the generalized Cauchy ensemble

#### Lectures

15:30-16:30   Room #128 (Graduate School of Math. Sci. Bldg.)
Michael Allman (Warwick 大学)
Breaking the chain: slow versus fast pulling

### 2010/01/12

#### Lie Groups and Representation Theory

16:30-18:00   Room #126 (Graduate School of Math. Sci. Bldg.)

[ Abstract ]

[ Reference URL ]
http://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar2010.html#20100112nishioka

#### Tuesday Seminar on Topology

16:30-18:30   Room #056 (Graduate School of Math. Sci. Bldg.)

Index problem for generically-wild homoclinic classes in dimension three
[ Abstract ]
In the sphere of non-hyperbolic differentiable dynamical systems, one can construct an example of a homolinic class which does not admit any kind of dominated splittings (a weak form of hyperbolicity) in a robust way. In this talk, we discuss the index (dimension of the unstable manifold) of the periodic points inside such homoclinic classes from a $C^1$-generic viewpoint.

On a generalized suspension theorem for directed Fukaya categories
[ Abstract ]
The directed Fukaya category $\\mathrm{Fuk} W$ of exact Lefschetz
fibration $W : X \\to \\mathbb{C}$ proposed by Kontsevich is a
categorification of the Milnor lattice of $W$. This is defined as the
directed $A_\\infty$-category $\\mathrm{Fuk} W = \\mathrm{Fuk}^\\to \\mathbb{V}$ generated by a distinguished basis $\\mathbb{V}$ of
vanishing cycles.

Recently Seidel has proved that this is stable under the suspension $W + u^2$ as a consequence of his foundational work on the directed
Fukaya category. We generalize his suspension theorem to the $W + u^d$
case by considering partial tensor product $\\mathrm{Fuk} W \\otimes' \\mathcal{A}_{d-1}$, where $\\mathcal{A}_{d-1}$ is the category
corresponding to the $A_n$-type quiver. This also generalizes a recent
work by the author with Kazushi Ueda.

### 2010/01/08

#### Colloquium

16:30-17:30   Room #123 (Graduate School of Math. Sci. Bldg.)

[ Abstract ]

### 2010/01/07

#### Operator Algebra Seminars

16:30-18:00   Room #128 (Graduate School of Math. Sci. Bldg.)
Luc Rey-Bellet (Univ. Massachusetts)
Large deviations, Billiards, and Non-equilibrium Statistical Mechanics

#### GCOE Seminars

16:30-18:00   Room #128 (Graduate School of Math. Sci. Bldg.)
LucRey-Bellet (Univ. Massachusetts)
Large deviations, Billiards, and Non-equilibrium Statistical Mechanics
[ Abstract ]
Large deviations have applications in many aspects of statistical mechanics. New applications for the steady states of non-equilibrium statistical mechanics have emerged during the past ten years and these applications deal with the fluctuations of the entropy production. After discussing some general aspects of entropy production we turn to concrete examples, in particular billiards with and without external forces and discuss large deviations theorems for such systems.

### 2010/01/05

#### Tuesday Seminar on Topology

16:30-18:30   Room #056 (Graduate School of Math. Sci. Bldg.)

The volume growth of hyperkaehler manifolds of type $A_{\\infty}$
[ Abstract ]
Hyperkaehler manifolds of type $A_{\\infty}$ were constructed due to Anderson-Kronheimer-LeBrun and Goto. These manifolds are 4-demensional, noncompact and their homology groups are infinitely generated. We focus on the volume growth of these hyperkaehler metrics. Here, the volume growth is asymptotic behavior of the volume of a ball of radius $r0$ with the center fixed. There are known examples of hyperkaehler manifolds whose volume growth is $r^4$ (ALE space) or $r^3$ (Taub-NUT space). In this talk we show that there exists a hyperkaehler manifold of type $A_{\\infty}$ whose volume growth is $r^c$ for a given \$3 松尾 信一郎 (東京大学大学院数理科学研究科) 17:30-18:30
On the Runge theorem for instantons
[ Abstract ]
A classical theorem of Runge in complex analysis asserts that a
meromorphic function on a domain in the Riemann sphere can be
approximated, over compact subsets, by rational functions, that is,
meromorphic functions on the Riemann sphere.
This theorem can be paraphrased by saying that any solution of the
Cauchy-Riemann equations on a domain in the Riemann sphere can be
approximated, over compact subsets, by global solutions.
In this talk we will present an analogous result in which the
Cauchy-Riemann equations on Riemann surfaces are replaced by the
Yang-Mills instanton equations on oriented 4-manifolds.
We will also mention that the Runge theorem for instantons can be
applied to develop Yang-Mills gauge theory on open 4-manifolds.