Colloquium

Seminar information archive ~02/11Next seminarFuture seminars 02/12~

Organizer(s) ASUKE Taro, TERADA Itaru, HASEGAWA Ryu, MIYAMOTO Yasuhito (chair)
URL https://www.ms.u-tokyo.ac.jp/seminar/colloquium_e/index_e.html

Seminar information archive

2016/03/22

16:50-17:50   Room #大講義室 (Graduate School of Math. Sci. Bldg.)
Shihoko Ishii  (Graduate School of Mathematical Sciences, University of Tokyo)
Singularities and Jet schemes (JAPANESE)
[ Reference URL ]
http://faculty.ms.u-tokyo.ac.jp/~shihoko/

2016/01/08

16:50-17:50   Room #123 (Graduate School of Math. Sci. Bldg.)
Keiji Oguiso (Graduate School of Mathematical Sciences, University of Tokyo)
Birational geometry through complex dymanics (ENGLISH)
[ Abstract ]
Birational geometry and complex dymanics are rich subjects having
interactions with many branches of mathematics. On the other hand,
though these two subjects share many common interests hidden especially
when one considers group symmetry of manifolds, it seems rather recent
that their rich interations are really notified, perhaps after breaking
through works for surface automorphisms in the view of topological
entropy by Cantat and McMullen early in this century, by which I was so
mpressed.

The notion of entropy of automorphism is a fundamental invariant which
measures how fast two general points spread out fast under iteration. So,
the exisitence of surface automorphism of positive entropy with Siegel
disk due to McMullen was quite surprizing. The entropy also measures, by
the fundamenal theorem of Gromov-Yomdin, the
logarithmic growth of the degree of polarization under iteration. For
instance, the Mordell-Weil group of an elliptic fibration is a very
intersting rich subject in algebraic geometry and number theory, but the
group preserves the fibration so that it might not be so interesting
from dynamical view point. However, if the surface admits two different
elliptic fibrations, which often happens in K3 surfaces of higher Picard
number, then highly non-commutative dynamically rich phenomena can be
observed.

In this talk, I would like to explain the above mentioned phenomena with
a few unexpected applications that I noticed in these years:

(1) Kodaira problem on small deformation of compact Kaehler manifolds in
higher dimension via K3 surface automorphism with Siegel disk;

(2) Geometric liftability problem of automorphisms in positive
characteristic to chacateristic 0 via Mordell-Weil groups and number
theoretic aspect of entropy;

(3) Existence problem on primitive automorphisms of projective manifolds,
through (relative) dynamical degrees due to Dinh-Sibony, Dinh-Nguyen-
Troung, a powerful refinement of the notion of entropy, with by-product
for Ueno-Campana's problem on (uni)rationality of manifolds of torus
quotient.

2015/12/04

16:50-17:50   Room #123 (Graduate School of Math. Sci. Bldg.)
Makiko Sasada (Graduate School of Mathematical Sciences, University of Tokyo)
Exact forms and closed forms on some infinite product spaces appearing in the study of probability theory
(JAPANESE)
[ Reference URL ]
https://www.ms.u-tokyo.ac.jp/teacher/sasada.html

2015/11/27

16:50-17:50   Room #056 (Graduate School of Math. Sci. Bldg.)
Yoshikata Kida (Graduate School of Mathematical Sciences, University of Tokyo)
Recent development in amenable groups (JAPANESE)
[ Reference URL ]
https://www.ms.u-tokyo.ac.jp/~kida/

2015/09/25

16:50-17:50   Room #大講義室 (Graduate School of Math. Sci. Bldg.)
Gerhard Huisken (The Mathematisches Forschungsinstitut Oberwolfach )
Mean curvature flow with surgery
[ Abstract ]
We study the motion of hypersurfaces in a Riemannian manifold
with normal velocity equal to the mean curvature of the
evolving hypersurface. In general this quasilinear, parabolic
evolution system may have complicated singularities in finite time.
However, under natural assumptions such as embeddedness of the surface
and positivity of the mean curvature (case of 2-dimensional surfaces)
all singularities can be classified and developing "necks" can be
removed by a surgery procedure similar to techniques employed
by Hamilton and Perelman in the Ricci-flow of Riemannian metrics.
The lecture describes results and techniques for mean curvature flow
with surgery developed in joint work with C. Sinestrari and S. Brendle.
[ Reference URL ]
http://www.mfo.de/about-the-institute/staff/prof.-dr.-gerhard-huisken

2015/08/28

16:50-17:50   Room #002 (Graduate School of Math. Sci. Bldg.)
Athanase Papadopoulos (Institut de Recherche Mathématique Avancée, Université de Strasbourg et CNRS)
On the development of Riemann surfaces and moduli (ENGLISH)
[ Abstract ]
I will describe a selection of major fundamental ideas in the theory
of Riemann surfaces and moduli, starting from the work of Riemann, and
ending with recent works.

2015/06/26

16:50-17:50   Room #056 (Graduate School of Math. Sci. Bldg.)
Kazushi Ueda (Graduate School of Mathematical Sciences, University of Tokyo)
Dimer models and mirror symmetry (JAPANESE)

2015/04/24

16:50-17:50   Room #123 (Graduate School of Math. Sci. Bldg.)
Bent Oersted (Aarhus University and University of Tokyo)
Rigidity of conformal functionals on spheres (ENGLISH)
[ Abstract ]
On a compact smooth manifold one may construct a Riemannian metric in many different ways. Each metric gives rise to natural elliptic operators such as the Laplace-Beltrami operator and corresponding spectral invariants, e.g. the eigenvalues, the trace of the heat semigroup, and the zeta function. In
this lecture we shall consider such functionals on the space of metrics on the sphere, combining conformal differential geometry and representation theory of semisimple Lie groups to obtain results about local extremal properties of special functionals. This is based on joint work with Niels Martin Moeller.

2015/03/13

14:00-15:00   Room #大講義室 (Graduate School of Math. Sci. Bldg.)
Takayuki Oda (Graduate School of Mathematical Sciences, University of Tokyo)

[ Reference URL ]
https://www.ms.u-tokyo.ac.jp/~takayuki/index-j.html

2015/03/13

16:30-17:30   Room #大講義室 (Graduate School of Math. Sci. Bldg.)
Shigeo KUSUOKA (Graduate School of Mathematical Sciences, University of Tokyo)
(JAPANESE)
[ Reference URL ]
https://www.ms.u-tokyo.ac.jp/teacher/kusuoka.html

2015/03/13

15:10-16:10   Room #大講義室 (Graduate School of Math. Sci. Bldg.)
Yoichi Miyaoka (Graduate School of Mathematical Sciences, University of Tokyo)
(JAPANESE)
[ Reference URL ]
https://www.ms.u-tokyo.ac.jp/teacher/miyaoka.html

2015/01/23

16:30-17:30   Room #大講義室 (Graduate School of Math. Sci. Bldg.)
Luc Illusie (Université de Paris-Sud)
Grothendieck and algebraic geometry
[ Abstract ]
Between 1957 and 1970 Grothendieck deeply and durably transformed algebraic geometry. I will discuss some of his revolutionary contributions.

2014/11/28

16:30-17:30   Room #123 (Graduate School of Math. Sci. Bldg.)
Hiroshi Nishiura (Graduate School of Medicine, The University of Tokyo)
Estimating the reproduction numbers of emerging infectious diseases: Case studies of Ebola and dengue
(JAPANESE)
[ Abstract ]
The basic and effective reproduction numbers offer epidemiological
insights into the growth of generations of infectious disease cases,
informing the required control effort. Recently, the renewal process
model has appeared to be a usefu tool for quantifying the reproduction
numbers in real-time using only case data. Here I present methods,
results and pitfalls of the use of renewal process model, presenting
recent case studies of Ebola virus disease epidemic in West Africa and a
massive epidemic of dengue fever in the summer of Japan 2014.
[ Reference URL ]
http://www.ghp.m.u-tokyo.ac.jp/profile/staff/hnishiura/

2014/10/10

16:30-17:30   Room #002 (Graduate School of Math. Sci. Bldg.)
Yoichi Mieda (Graduate School of Mathematical Sciences, University of Tokyo)
Etale cohomology of local Shimura varieties and the local Langlands correspondence (JAPANESE)

2014/09/19

16:30-17:30   Room #大講義室 (Graduate School of Math. Sci. Bldg.)
Etienne Ghys (École normale supérieure de Lyon)
William Thurston and foliation theory (ENGLISH)
[ Abstract ]
Between 1972 and 1976, William Thurston revolutionized foliation theory. Twenty years later, he described this period of his mathematical life in a remarkable paper « On proofs and progress in mathematics ». In this talk, I will begin by a general overview of some of Thurston's contribution to this theory. I will then describe some of the current development.

2014/07/25

16:30-17:30   Room #123 (Graduate School of Math. Sci. Bldg.)
Yasuhiro Takeuchi (Aoyama Gakuin University)
Mathematical modelling of Tumor Immune System Interaction (JAPANESE)
[ Abstract ]
We study the dynamical behavior of a tumor-immune system (T-IS) interaction model with two discrete delays,
namely the immune activation delay for effector cells (ECs) and activation delay for Helper T cells (HTCs).
By analyzing the characteristic equations, we establish the stability of two equilibria (tumor-free equilibrium and immune-control equilibrium) and the existence of Hopf bifurcations when two delays are used as the bifurcation parameter.
Our results exhibit that both delays do not affect the stability of tumor-free equilibrium.
However, they are able to destabilize the immune-control equilibrium and cause periodic solutions.
We numerically illustrate how these two delays can change the stability region of the immune-control equilibrium and display the different impacts to the control of tumors.
The numerical simulation results show that the immune activation delay for HTCs can induce heteroclinic cycles to connect the tumor-free equilibrium and immune-control equilibrium.
Furthermore, we observe that the immune activation delay for HTCs can even stabilize the unstable immune-control equilibrium.

2014/07/11

16:30-17:30   Room #123 (Graduate School of Math. Sci. Bldg.)
Toshiyuki Kobayashi (Graduate School of Mathematical Sciences, University of Tokyo)
Global Geometry and Analysis on Locally Symmetric Spaces with
Indefinite-metric (JAPANESE)
[ Abstract ]
The local to global study of geometries was a major trend of 20th
century geometry,
with remarkable developments achieved particularly in Riemannian geometry.
In contrast, in areas such as pseudo-Riemannian geometry, familiar to us
as the space-time of relativity theory, and more generally in
pseudo-Riemannian geometry of general signature, surprising little is
known about global properties of the geometry even if we impose a
locally homogeneous structure.

I plan to explain two programs:

1. (global shape) Existence problem of compact locally homogeneous spaces,
and deformation theory.

2. (spectral analysis) Construction of the spectrum of the Laplacian,
and its stability under the deformation of the geometric structure.

by taking anti-de Sitter manifolds as a typical example.


2014/06/06

16:30-17:30   Room #056 (Graduate School of Math. Sci. Bldg.)
Mikhail Kapranov (Kavli IPMU)
Lie algebras from secondary polytopes (ENGLISH)
[ Abstract ]
The secondary polytope of a point configuration
in the Euclidean space was introduced by Gelfand, Zelevinsky
and the speaker long time ago in order to understand discriminants
of multi-variable polynomials. These polytopes have
a remarkable factorization (or operadic) property: each
face of any secondary polytope is isomorphic to the
product of several other secondary polytopes.

The talk, based on joint work in progress with M. Kontsevich
and Y. Soibelman, will explain how the factorization property
can be used to construct Lie algebra-type objects:
$L_¥infty$ and $A_¥infty$-algebras. These algebras
turn out to be related to the problem of deformation
of triangulated categories with semiorthogonal decompositions.

2014/05/02

16:30-17:30   Room #123 (Graduate School of Math. Sci. Bldg.)
A.P. Veselov (Loughborough, UK and Tokyo, Japan)
From hyperplane arrangements to Deligne-Mumford moduli spaces: Kohno-Drinfeld way (ENGLISH)
[ Abstract ]
Gaudin subalgebras are abelian Lie subalgebras of maximal
dimension spanned by generators of the Kohno-Drinfeld Lie algebra t_n,
associated to A-type hyperplane arrangement.
It turns out that Gaudin subalgebras form a smooth algebraic variety
isomorphic to the Deligne-Mumford moduli space \\bar M_{0,n+1} of
stable genus zero curves with n+1 marked points.
A real version of this result allows to describe the
moduli space of integrable n-dimensional tops and
separation coordinates on the unit sphere
in terms of the geometry of Stasheff polytope.

The talk is based on joint works with L. Aguirre and G. Felder and with K.
Schoebel.

2014/01/31

16:30-17:30   Room #122 (Graduate School of Math. Sci. Bldg.)
Jean-Pierre Puel (Université de Versailles Saint-Quentin-en-Yvelines)
Controllability of fluid flows (ENGLISH)
[ Abstract ]
First of all we will describe in an abstract situation the various concepts
of controllability for evolution equations.
We will then present some problems and results concerning the
controllability of systems modeling fluid flows.
First of all we will consider the Euler equation describing the motion of an
incompressible inviscid fluid.
Then we will give some results concerning the Navier-Stokes equations,
modeling an incompressible viscous fluid, and some related systems.
Finally we will give a first result of controllability for the case of a
compressible fluid (in dimension 1) and some important open problems.

2014/01/24

16:30-17:30   Room #002 (Graduate School of Math. Sci. Bldg.)
Bo Berndtsson (Chalmers University of Technology)
Complex Brunn-Minkowski theory (ENGLISH)
[ Abstract ]
The classical Brunn-Minkowski theory deals with the volume of convex sets.
It can be formulated as a statement about how the volume of slices of a convex set varies when the slice changes. Its complex counterpart deals with slices of pseudo convex sets, or more generally fibers of a complex fibration. It describes how $L^2$-norms of holomorphic functions, or sections of a line bundle, vary when the fibers change, and says essentially that a certain associated vector bundle has positive curvature. In the presence of enough symmetry this implies convexity properties of volumes; the real Brunn-Minkowski theorem corresponding to maximal symmetry. There are also applications and relations in other directions, like variations of Kahler metrics, variations of complex structures and the study of plurisubharmonic functions.

2013/12/06

16:30-17:30   Room #002 (Graduate School of Math. Sci. Bldg.)
Naoki Imai (Graduate School of Mathematical Scinences, The University of Tokyo)
Local Langlands correspondence and Lubin-Tate perfectoid spaces (JAPANESE)

2013/12/06

16:30-17:30   Room #002 (Graduate School of Math. Sci. Bldg.)
Naoki Imai (Graduate School of Mathematical Sciences, The University of Tokyo)
Local Langlands correspondence and Lubin-Tate perfectoid spaces (JAPANESE)

2013/11/08

16:30-17:30   Room #123 (Graduate School of Math. Sci. Bldg.)
Dipendra Prasad (Tata Institute of Fundamental Research)
Ext Analogues of Branching laws (ENGLISH)
[ Abstract ]
The decomposition of a representation of a group when restricted to a
subgroup is an important problem well-studied for finite and compact Lie
groups, and continues to be of much contemporary interest in the context
of real and $p$-adic groups. We will survey some of the questions that have
recently been considered, and look at a variation of these questions involving concepts in homological algebra which gives rise to interesting newer questions.

2013/07/26

16:30-17:30   Room #123 (Graduate School of Math. Sci. Bldg.)
Matthias Hieber (TU Darmstadt, Germany)
Analysis of the Navier-Stokes and Complex Fluids Flow (ENGLISH)
[ Abstract ]
In this talk, we discuss the dynamics of fluid flow generated by the Navier-Stokes equations or, more generally, by models describing complex fluid flows. Besides classical questions concerning well-posedness of the underlying equations, we investigate analytically models arising in the theory of free boundary value problems, viscoelastic fluids and liquid crystals.

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