Seminar information archive

2012/04/17

Tuesday Seminar on Topology

16:30-18:00   Room #056 (Graduate School of Math. Sci. Bldg.)
Eriko Hironaka (Florida State University)
Pseudo-Anosov mapping classes with small dilatation (ENGLISH)
[ Abstract ]
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.

2012/04/16

Algebraic Geometry Seminar

15:30-17:00   Room #122 (Graduate School of Math. Sci. Bldg.)
Makoto Miura (University of Tokyo)
Toric degenerations of minuscule Schubert varieties and mirror symmetry (JAPANESE)
[ Abstract ]
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.

Seminar on Geometric Complex Analysis

10:30-12:00   Room #126 (Graduate School of Math. Sci. Bldg.)
Yusuke Okuyama (Kyoto Institute of Technology)
Fekete configuration, quantitative equidistribution and wanderting critical orbits in non-archimedean dynamics
(JAPANESE)

2012/04/14

Monthly Seminar on Arithmetic of Automorphic Forms

13:30-16:00   Room #123 (Graduate School of Math. Sci. Bldg.)
Kazutoshi Kariyama (Onomichi city university) 13:30-14:30
Explicit formula for the formal degree of the discrete series representations of GL_m(D). (JAPANESE)
Keijyu Souno (Math.-Sci., Tokyo Univ.) 15:00-16:00
Moments of the derivatives of the Riemann zeta function (JAPANESE)
[ Abstract ]
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.

2012/04/13

Seminar on Probability and Statistics

14:50-16:00   Room #006 (Graduate School of Math. Sci. Bldg.)
KAMATANI, Kengo (Graduate School of Engineering Science, Osaka University)
Asymptotic properties of MCMC for cumulative link model (JAPANESE)
[ Reference URL ]
https://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2012/00.html

2012/04/11

Operator Algebra Seminars

16:30-18:00   Room #128 (Graduate School of Math. Sci. Bldg.)
Shweta Sharma (Univ. Paris Sud)
Mathematical Aspects of Fractional Quantum Hall Effect (ENGLISH)

Number Theory Seminar

17:30-18:30   Room #056 (Graduate School of Math. Sci. Bldg.)
Damian Rossler (CNRS, Universite de Toulouse)
Around the Mordell-Lang conjecture in positive characteristic (ENGLISH)
[ Abstract ]
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).

2012/04/10

Tuesday Seminar on Topology

16:30-18:00   Room #056 (Graduate School of Math. Sci. Bldg.)
Takuya Sakasai (The University of Tokyo)
On homology of symplectic derivation Lie algebras of
the free associative algebra and the free Lie algebra (JAPANESE)
[ Abstract ]
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.

2012/04/09

Algebraic Geometry Seminar

15:30-17:00   Room #122 (Graduate School of Math. Sci. Bldg.)
Kazushi Ueda (Osaka University)
On mirror symmetry for weighted Calabi-Yau hypersurfaces (JAPANESE)
[ Abstract ]
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.

Seminar on Geometric Complex Analysis

10:30-12:00   Room #126 (Graduate School of Math. Sci. Bldg.)
Shigeharu TAKAYAMA (University of Tokyo)
Effective estimate on the number of deformation types of families of canonically polarized manifolds over curves
(JAPANESE)

2012/04/04

PDE Real Analysis Seminar

10:30-11:30   Room #056 (Graduate School of Math. Sci. Bldg.)
Jens Hoppe (Sogang University / KTH Royal Institute of Technology)
Multi linear formulation of differential geometry and matrix regularizations (ENGLISH)
[ Abstract ]
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.

2012/04/03

Monthly Seminar on Arithmetic of Automorphic Forms

13:30-16:00   Room #123 (Graduate School of Math. Sci. Bldg.)
Kazutoshi Kariyama (Onomichi city university) 13:30-14:30
Explicit formula for the formal degree of the discrete series representations of GL_m(D). (JAPANESE)
Keijyu Souno (Math.-Sci., Tokyo Univ.) 15:00-16:00
Moments of the derivatives of the Riemann zeta function (JAPANESE)
[ Abstract ]
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.

2012/03/23

Operator Algebra Seminars

16:30-18:00   Room #117 (Graduate School of Math. Sci. Bldg.)
Alex Kumjian (University of Nevada, Reno)
Higher Rank Graph $C^*$-algebras (ENGLISH)

Lectures

10:30-11:30   Room #117 (Graduate School of Math. Sci. Bldg.)
R. Penner (Aarhus/Caltech)
Cell decomposition of homotopy Deligne-Mumford. (ENGLISH)
[ Abstract ]
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.

2012/03/21

Lectures

10:15-12:00   Room #123 (Graduate School of Math. Sci. Bldg.)
R. Penner (Aarhus/Caltech)
Geochemical structure of biological macromolecules (ENGLISH)
[ Abstract ]
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.

Lectures

15:15-17:00   Room #123 (Graduate School of Math. Sci. Bldg.)
R. Penner (Aarhus/Caltech)
Moduli space techniques in computational biology
(ENGLISH)
[ Abstract ]
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 Real Analysis Seminar

10:00-11:00   Room #056 (Graduate School of Math. Sci. Bldg.)
Chiun-Chang Lee (National Taiwan University)
The asymptotic behaviors of the solutions of Poisson-Boltzmann type of equations (ENGLISH)
[ Abstract ]
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.

2012/03/16

Colloquium

16:30-17:30   Room #123 (Graduate School of Math. Sci. Bldg.)
Chun LIU (University of Tokyo / Penn State University)
On Complex Fluids (ENGLISH)
[ Abstract ]
The talk is on the mathematical theories, in particular the energetic variational approaches, of anisotropic complex fluids, such as viscoelastic materials, liquid crystals and ionic fluids in proteins and bio-solutions.

Complex fluids, including mixtures and solutions, are abundant in our daily life. The complicated phenomena and properties exhibited by these materials reflects the coupling and competition between the microscopic interactions and the macroscopic dynamics. We study the underlying energetic variational structures that is common among all these multiscale-multiphysics systems.

In this talk, I will demonstrate the modeling as well as analysis and numerical issues arising from various complex fluids.

2012/03/14

PDE Real Analysis Seminar

10:30-11:30   Room #056 (Graduate School of Math. Sci. Bldg.)
Exponential convergence to equilibria for a general model in hydrodynamics (ENGLISH)
[ Abstract ]
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.

2012/03/13

Colloquium

15:00-16:00   Room #050 (Graduate School of Math. Sci. Bldg.)
Aleksandar Ivic (University of Belgrade, the Serbian Academy of Science and Arts)
Problems and results on Hardy's Z-function (JAPANESE)
[ Abstract ]
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.

Mathematical Biology Seminar

14:00-15:00   Room #154 (Graduate School of Math. Sci. Bldg.)
Tsuyoshi Kajiwara (Okayama University)
On construction of Lyapunov functions and functionals (JAPANESE)

2012/03/09

Infinite Analysis Seminar Tokyo

13:30-14:30   Room #002 (Graduate School of Math. Sci. Bldg.)
Shintarou Yanagida (Kobe Univ.)
On Hall algebra of complexes (JAPANESE)
[ Abstract ]
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.

2012/03/07

GCOE Seminars

17:00-18:00   Room #370 (Graduate School of Math. Sci. Bldg.)
Kazufumi Ito (North Carolina State Univ.)
Nonsmooth Optimization, Theory and Applications. (ENGLISH)
[ Abstract ]
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.

2012/03/06

GCOE Seminars

16:00-17:00   Room #370 (Graduate School of Math. Sci. Bldg.)
Dietmar Hoemberg (Weierstrass Institute, Berlin)
On the phase field approach to shape and topology optimization (ENGLISH)
[ Abstract ]
Owing to different densities of the respective phases, solid-solid phase transitions often are accompanied by (often undesired) changes in workpiece size and shape. In my talk I will address the reverse question of finding an optimal phase mixture in order to accomplish a desired workpiece shape.
From mathematical point of view this corresponds to an optimal shape design problem subject to a static mechanical equilibrium problem with phase dependent stiffness tensor, in which the two phases exhibit different densities leading to different internal stresses. Our goal is to tackle this problem using a phasefield relaxation.
To this end we first briefly recall previous works regarding phasefield approaches to topology optimization (e.g. by Bourdin ¥& Chambolle, Burger ¥& Stainko and Blank, Garcke et al.).
We add a Ginzburg-Landau term to our cost functional, derive an adjoint equation for the displacement and choose a gradient flow dynamics with an articial time variable for our phasefield variable. We discuss well-posedness results for the resulting system and conclude with some numerical results.

GCOE Seminars

17:00-18:00   Room #370 (Graduate School of Math. Sci. Bldg.)
Thomas Petzold (Weierstrass Institute, Berlin)
Finite element simulations of induction hardening of steel parts (ENGLISH)
[ Abstract ]
Induction hardening is a modern method for the heat treatment of steel parts.
A well directed heating by electromagnetic waves and subsequent quenching of the workpiece increases the hardness of the surface layer.
The process is very fast and energy efficient and plays a big role in modern manufacturing facilities in many industrial application areas.
In this talk a model for induction hardening of steel parts is presented. It consist of a system of partial differential equations including Maxwell's equations and the heat equation.
The finite element method is used to perform numerical simulations in 3D.
This requires a suitable discretization of Maxwell's equations leading to so called edge-finite-elements.
We will give a short overview of edge elements and present numerical simulations of induction hardening.
We will address some of the difficulties arising when solving the large system of non-linear coupled PDEs in three space dimensions.