## 過去の記録

### 2012年04月18日(水)

#### 代数学コロキウム

16:40-17:40   数理科学研究科棟(駒場) 056号室
Alan Lauder 氏 (University of Oxford)
Explicit constructions of rational points on elliptic curves (ENGLISH)
[ 講演概要 ]
I will present an algorithm for computing certain special
values of p-adic L-functions, and discuss an application to
the efficient construction of rational points on elliptic curves.

#### 作用素環セミナー

16:30-18:00   数理科学研究科棟(駒場) 128号室

Classification of Group Actions on Factors (after Masuda) (JAPANESE)

### 2012年04月17日(火)

#### トポロジー火曜セミナー

16:30-18:00   数理科学研究科棟(駒場) 056号室
Tea: 16:00 - 16:30 コモンルーム
Eriko Hironaka 氏 (Florida State University)
Pseudo-Anosov mapping classes with small dilatation (ENGLISH)
[ 講演概要 ]
A mapping class is a homeomorphism of an oriented surface
to itself modulo isotopy. It is pseudo-Anosov if the lengths of essential
simple closed curves under iterations of the map have exponential growth
rate. The growth rate, an algebraic integer of degree bounded with
respect to the topology of the surface, is called the dilatation of the
mapping class. In this talk we will discuss the minimization problem
for dilatations of pseudo-Anosov mapping classes, and give two general
constructions of pseudo-Anosov mapping classes with small dilatation.

### 2012年04月16日(月)

#### 代数幾何学セミナー

15:30-17:00   数理科学研究科棟(駒場) 122号室

Toric degenerations of minuscule Schubert varieties and mirror symmetry (JAPANESE)
[ 講演概要 ]
Minuscule Schubert varieties admit the flat degenerations to projective
Hibi toric varieties, whose combinatorial structure is explicitly
described by finite posets. In this talk, I will explain these toric
degenerations and discuss the mirror symmetry for complete intersection
Calabi-Yau varieties in Gorenstein minuscule Schubert varieties.

#### 複素解析幾何セミナー

10:30-12:00   数理科学研究科棟(駒場) 126号室

Fekete configuration, quantitative equidistribution and wanderting critical orbits in non-archimedean dynamics
(JAPANESE)

### 2012年04月14日(土)

#### 保型形式の整数論月例セミナー

13:30-16:00   数理科学研究科棟(駒場) 123号室

) 13:30-14:30
GL_m(D)の離散系列表現の形式次数に関する明示公式 (JAPANESE)

Moments of the derivatives of the Riemann zeta function (JAPANESE)
[ 講演概要 ]
In my talk, we consider the integral moments of the derivatives of the Riemann zeta function on the critical line. We give certain lower bounds for these moments under the assumption of the Riemann hypothesis.

### 2012年04月13日(金)

#### 統計数学セミナー

14:50-16:00   数理科学研究科棟(駒場) 006号室

Asymptotic properties of MCMC for cumulative link model (JAPANESE)
[ 講演概要 ]
ベイズ統計学におけるCumulative link modelに対するマルコフ連鎖モンテカルロ法の 振る舞いを解析する. 前半では,一般的に使われている Albert and Chib (JASA 1993)による手法は局所退化性を持ち, 極めて悪い収束レートを持つことを示す.また改善手法と一般に みなされている手法(Marginal augmentation; MA, Liu and Wu 1999, Meng and Dyk 1999)も, ある射影を施すことでやはり局所退化していることを示す. 後半は,MAを若干変更することで,カテゴリの数があまり多くなければ, 殆ど計算負荷を変えること無く局所一致性を持つ手法を構成できる(MA2)事を示す. またカテゴリの数によらず常に局所一致性を持つ手法(MMA)も紹介する. 数値実験を通してこれらの振る舞いを比較する. 前半部分は一部,昨年の駒場のSART2011での講演と同じである.
[ 参考URL ]
https://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2012/00.html

### 2012年04月11日(水)

#### 作用素環セミナー

16:30-18:00   数理科学研究科棟(駒場) 128号室
Shweta Sharma 氏 (Univ. Paris Sud)
Mathematical Aspects of Fractional Quantum Hall Effect (ENGLISH)

#### 代数学コロキウム

17:30-18:30   数理科学研究科棟(駒場) 056号室
Damian Rossler 氏 (CNRS, Universite de Toulouse)
Around the Mordell-Lang conjecture in positive characteristic (ENGLISH)
[ 講演概要 ]
Let V be a subvariety of an abelian variety A over C and let G\\subseteq A(C) be a subgroup. The classical Mordell-Lang conjecture predicts that if V is of general type and G\\otimesQ is finite dimensional, then V\\cap G is not Zariski dense in V. This statement contains the Mordell conjecture as well as the Manin-Mumford conjecture (for curves). The positive characteristic analog of the Mordell-Lang conjecture makes sense, when A is supposed to have no subquotient, which is defined over a finite field. This positive characteristic analog was proven in 1996 by E. Hrushovski using model-theoretic methods. We shall discuss the prehistory and context of this proof. We shall also discuss the proof (due to the speaker) of the fact that in positive characteristic, the Manin-Mumford conjecture implies the Mordell-Lang conjecture (whereas this seems far from true in characteristic 0).

(本講演は「東京パリ数論幾何セミナー」として、インターネットによる東大数理とIHESとの双方向同時中継で行います。)

### 2012年04月10日(火)

#### トポロジー火曜セミナー

16:30-18:00   数理科学研究科棟(駒場) 056号室
Tea: 16:00 - 16:30 コモンルーム

On homology of symplectic derivation Lie algebras of
the free associative algebra and the free Lie algebra (JAPANESE)
[ 講演概要 ]
We discuss homology of symplectic derivation Lie algebras of
the free associative algebra and the free Lie algebra
with particular stress on their abelianizations (degree 1 part).
Then, by using a theorem of Kontsevich,
we give some applications to rational cohomology of the moduli spaces of
Riemann surfaces and metric graphs.
This is a joint work with Shigeyuki Morita and Masaaki Suzuki.

### 2012年04月09日(月)

#### 代数幾何学セミナー

15:30-17:00   数理科学研究科棟(駒場) 122号室

On mirror symmetry for weighted Calabi-Yau hypersurfaces (JAPANESE)
[ 講演概要 ]
In the talk, I will discuss relation between homological mirror symmetry for weighted projective spaces, their Calabi-Yau hypersurfaces, and weighted homogeneous singularities.
If the time permits, I will also discuss an application to monodromy of hypergeometric functions.

#### 複素解析幾何セミナー

10:30-12:00   数理科学研究科棟(駒場) 126号室

Effective estimate on the number of deformation types of families of canonically polarized manifolds over curves
(JAPANESE)

### 2012年04月04日(水)

#### PDE実解析研究会

10:30-11:30   数理科学研究科棟(駒場) 056号室

Jens Hoppe 氏 (Sogang University / KTH Royal Institute of Technology)
Multi linear formulation of differential geometry and matrix regularizations (ENGLISH)
[ 講演概要 ]
We prove that many aspects of the differential geometry of embedded Riemannian manifolds can be formulated in terms of multi linear algebraic structures on the space of smooth functions. In particular, we find algebraic expressions for Weingarten's formula, the Ricci curvature and the Codazzi-Mainardi equations.
For matrix analogues of embedded surfaces we define discrete curvatures and Euler characteristics, and a non-commutative Gauss–Bonnet theorem is shown to follow. We derive simple expressions for the discrete Gauss curvature in terms of matrices representing the embedding coordinates, and a large class of explicit examples is provided.

### 2012年04月03日(火)

#### 保型形式の整数論月例セミナー

13:30-16:00   数理科学研究科棟(駒場) 123号室

) 13:30-14:30
GL_m(D)の離散系列表現の形式次数に関する明示公式 (JAPANESE)

Moments of the derivatives of the Riemann zeta function (JAPANESE)
[ 講演概要 ]
In my talk, we consider the integral moments of the derivatives of the Riemann zeta function on the critical line. We give certain lower bounds for these moments under the assumption of the Riemann hypothesis.

### 2012年03月23日(金)

#### 作用素環セミナー

16:30-18:00   数理科学研究科棟(駒場) 117号室
Alex Kumjian 氏 (University of Nevada, Reno)
Higher Rank Graph $C^*$-algebras (ENGLISH)

#### 講演会

10:30-11:30   数理科学研究科棟(駒場) 117号室
R. Penner 氏 (Aarhus/Caltech)
Cell decomposition of homotopy Deligne-Mumford. (ENGLISH)
[ 講演概要 ]
A long-standing problem has been to extend the ideal cell decomposition of Riemann's moduli space to its compactification by stable curves. In joint work with Doug LaFountain, we have solved this problem with an explicit generalization of fatgraphs. The solution immediately provides a construction of odd-degree cycles, which are conjectured to be non-trivial, thus addressing yet another long-standing issue.

### 2012年03月21日(水)

#### 講演会

10:15-12:00   数理科学研究科棟(駒場) 123号室
R. Penner 氏 (Aarhus/Caltech)
Geochemical structure of biological macromolecules (ENGLISH)
[ 講演概要 ]
This first of two lectures will explain the basic combinatorial and geometrical structures of both protein and RNA. It is intended to set the stage of subsequent discussions for an audience with mathematical background.

#### 講演会

15:15-17:00   数理科学研究科棟(駒場) 123号室
R. Penner 氏 (Aarhus/Caltech)
Moduli space techniques in computational biology
(ENGLISH)
[ 講演概要 ]
Basic fatgraph models of RNA and protein will be discussed, where edges are associated with base pairs in the former case and with hydrogen bonds between backbone atoms in the latter. For RNA, this leads to new methods described by context-free grammars of RNA folding prediction including certain classes of pseudo-knots. For protein, beyond these discrete invariants lie continuous ones which associate a rotation of
3-dimensional space to each hydrogen bond linking a pair of peptide units. Histograms of these rotations over the entire database of proteins exhibit a small number of "peptide unit legos" which can be used to advantage for the protein folding problem.

#### PDE実解析研究会

10:00-11:00   数理科学研究科棟(駒場) 056号室

Chiun-Chang Lee 氏 (National Taiwan University)
The asymptotic behaviors of the solutions of Poisson-Boltzmann type of equations (ENGLISH)
[ 講演概要 ]
Understanding the existence of electrical double layers around particles in the colloidal dispersion (system) is a crucial phenomenon of the colloid science. The Poisson-Boltzmann (PB) equation is one of the most widely used models to describe the equilibrium phenomenon of an electrical double layer in colloidal systems. This motivates us to study the asymptotic behavior for the boundary layer of the solutions of the PB equation. In this talk, we introduce the precise asymptotic formulas for the slope of the boundary layers with the exact leading order term and the second-order term. In particular, these formulas show that the mean curvature of the boundary exactly appears in the second-order term. This part is my personal work.
On the other hand, to study how the ionic concentrations and ionic valences affect the difference between the boundary and interior potentials in an electrolyte solution, we also introduce a modified PB equation - New Poisson-Boltzmann (PB_n) equation - joint works with Prof. Tai-Chia Lin and Chun Liu and YunKyong Hyon. We give a specific formula showing the influence of these crucial physical quantities on the potential difference in an electrolyte solution. This cannot be found in the PB equation.

### 2012年03月16日(金)

#### 談話会・数理科学講演会

16:30-17:30   数理科学研究科棟(駒場) 123号室

お茶&Coffee&お菓子: 16:00～16:30 (コモンルーム)。

[ 講演概要 ]
この講演では、タンパク質と生体液における粘弾性材料、液晶、イオン流体といった異方的複雑流体のエネルギー的な変分法手法の数学理論について取 り上げる。

この講演では、さまざまな複雑流体についてのモデリングに加えて、数学解析や数値計算まで触れたい。

### 2012年03月14日(水)

#### PDE実解析研究会

10:30-11:30   数理科学研究科棟(駒場) 056号室

Jürgen Saal 氏 (Technische Universität Darmstadt)
Exponential convergence to equilibria for a general model in hydrodynamics (ENGLISH)
[ 講演概要 ]
We present a thorough analysis of the Navier-Stokes-Nernst-Planck-Poisson equations. This system describes the dynamics of charged particles dispersed in an incompressible fluid.
In contrast to existing literature and in view of its physical relevance, we also allow for different diffusion coefficients of the charged species.
In addition, the commonly assumed electro-neutrality condition is not required by our approach.
Our aim is to present results on local and global well-posedness as well as exponential stability of equilibria. The results are obtained jointly with Dieter Bothe and Andre Fischer at the Center of Smart Interfaces at TU Darmstadt.

### 2012年03月13日(火)

#### 談話会・数理科学講演会

15:00-16:00   数理科学研究科棟(駒場) 050号室

お茶&Coffee&お菓子: 14:30～15:00 (コモンルーム)。

Aleksandar Ivic 氏 (University of Belgrade, the Serbian Academy of Science and Arts)
Problems and results on Hardy's Z-function (JAPANESE)
[ 講演概要 ]
The title is self-explanatory: G.H. Hardy first used the function
$Z(t)$ to show that there are infinitely many zeta-zeros on the
critical line $\\Re s = 1/2$. In recent years there is a revived
interest in this function, with many results and open problems.

#### 数理人口学・数理生物学セミナー

14:00-15:00   数理科学研究科棟(駒場) 154号室

リアプノフ関数および汎関数の構成について (JAPANESE)
[ 講演概要 ]

### 2012年03月09日(金)

#### 東京無限可積分系セミナー

13:30-14:30   数理科学研究科棟(駒場) 002号室

On Hall algebra of complexes (JAPANESE)
[ 講演概要 ]
The topic of my talk is the Hall algebra of complexes,
which is recently introduced by T. Bridgeland.
I will discuss its properties and relation to
auto-equivalences of derived category.
If I have enough time,
I will also discuss the relation
of this Hall algebra to the so-called Ding-Iohara algebra.

### 2012年03月07日(水)

#### GCOEセミナー

17:00-18:00   数理科学研究科棟(駒場) 370号室
Kazufumi Ito 氏 (North Carolina State Univ.)
Nonsmooth Optimization, Theory and Applications. (ENGLISH)
[ 講演概要 ]
We develop a Lagrange multiplier theory for Nonsmooth optimization, including $L^¥infty$ and $L^1$ optimizations, $¥ell^0$ (counting meric) and $L^0$ (Ekeland mertic), Binary and Mixed integer optimizations and Data mining. A multitude of important problems can be treated by our approach and numerical algorithms are developed based on the Lagrange multiplier theory.