## Colloquium

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

Seminar information archive

### 2018/03/10

14:30-15:30   Room #大講義室 (Graduate School of Math. Sci. Bldg.)
Yujiro KAWAMATA (Univ. Tokyo)
(JAPANESE)

### 2018/03/10

16:00-17:00   Room #大講義室 (Graduate School of Math. Sci. Bldg.)
Hiroshi MATANO (Univ. Tokyo)
(JAPANESE)

### 2018/02/23

15:30-16:30   Room #002 (Graduate School of Math. Sci. Bldg.)
Hiromu Tanaka (Univ. Tokyo)
(JAPANESE)

### 2018/01/26

15:30-16:30   Room #002 (Graduate School of Math. Sci. Bldg.)
Yuta Koike (Univ. Tokyo)
(JAPANESE)

### 2017/11/24

15:30-16:30   Room #002 (Graduate School of Math. Sci. Bldg.)
Yukari Ito (IPMU, Nagoya University)
(JAPANESE)

### 2017/10/06

15:30-16:30   Room #002 (Graduate School of Math. Sci. Bldg.)
Akihiko Miyachi (Tokyo Woman's Christian University)
Singular Integrals and Real Variable Methods in Harmonic Analysis (JAPANESE)
[ Reference URL ]
http://lab.twcu.ac.jp/miyachi/English.html

### 2017/07/07

15:30-16:30   Room #002 (Graduate School of Math. Sci. Bldg.)
Richard Stanley (MIT)
Smith Normal Form and Combinatorics (English)
[ Abstract ]
Let R be a commutative ring (with identity) and A an n x n matrix over R. Suppose there exist n x n matrices P,Q invertible over $R$ for which PAQ is a diagonal matrix
diag(e_1,...,e_r,0,...,0), where e_i divides e_{i+1} in R. We then call PAQ a Smith normal form (SNF) of $A$. If R is a PID then an SNF always exists and is unique up to multiplication by units. Moreover if A is invertible then det A=ua_1\cdots a_n, where u is a unit, so SNF gives a
canonical factorization of det A.

We will survey some connections between SNF and combinatorics. Topics will include (1) the general theory of SNF, (2) a close connection between SNF and chip firing in graphs, (3) the SNF of a random matrix of integers (joint work with Yinghui Wang), (4) SNF of special classes of matrices, including some arising in the theory of symmetric functions, hyperplane arrangements, and lattice paths.
[ Reference URL ]
http://www-math.mit.edu/~rstan/

### 2017/06/20

15:30-16:30   Room #002 (Graduate School of Math. Sci. Bldg.)
Nicolas Bacaër (Institute de Resherrche pour le Developpement, the University of Tokyo)
Some stochastic population models in a random environment (English)
[ Abstract ]
Two population models will be considered: an epidemic model [1] and a linear birth-and-death process [2]. The goal is to study the first non-zero eigenvalue, which is related to the speed of convergence towards extinction, using either WKB approximations or probabilistic arguments.
[1] "Le modèle stochastique SIS pour une épidémie dans un environnement aléatoire". Journal of Mathematical Biology (2016)
[2] "Sur les processus linéaires de naissance et de mort sous-critiques dans un environnement aléatoire". Journal of Mathematical Biology (2017)
[ Reference URL ]
http://www.ummisco.ird.fr/perso/bacaer/

### 2017/05/26

15:30-16:30   Room #002 (Graduate School of Math. Sci. Bldg.)
Shigeki Aida (Graduate School of Mathematical Sciences, The University of Tokyo)
ループ空間上のスペクトルギャップの漸近挙動について (JAPANESE)

### 2017/04/28

15:30-16:30   Room #002 (Graduate School of Math. Sci. Bldg.)
Chihiro Matsui (Graduate School of Mathematical Sciences, the University of Tokyo)

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

### 2017/03/21

14:40-15:40   Room #大講義室 (Graduate School of Math. Sci. Bldg.)
Kiyoomi Kataoka (Graduate School of Mathematical Sciences, The University of Tokyo)
A tour around microlocal analysis and algebraic analysis (JAPANESE)
[ Reference URL ]
https://www.ms.u-tokyo.ac.jp/~kiyoomi/index.html

### 2017/03/21

16:00-17:00   Room #大講義室 (Graduate School of Math. Sci. Bldg.)
Tadahisa Funaki (Graduate School of Mathematical Sciences, The University of Tokyo)
40 years along with stochastic analysis --- Motivated by statistical physics problems --- (JAPANESE)
[ Reference URL ]
https://www.ms.u-tokyo.ac.jp/~funaki/

### 2016/12/07

15:30-16:30   Room #056 (Graduate School of Math. Sci. Bldg.)
Uwe Jannsen
On a conjecture of Bloch and Kato, and a local analogue.
[ Abstract ]
In their seminal paper on Tamagawa Numbers of motives,
Bloch and Kato introduced a notion of motivic pairs, without
loss of generality over the rational numbers, which should
satisfy certain properties (P1) to (P4). The last property
postulates the existence of a Galois stable lattice T in the
associated adelic Galois representation V such that for each
prime p the fixed module of the inertia group of Q_p of
V/T is l-divisible for almost all primes l different from p.

I postulate an analogous local conjecture and show that it
implies the global conjecture.

### 2016/11/25

15:30-16:30   Room #056 (Graduate School of Math. Sci. Bldg.)
Tsuyoshi Yoneda (Graduate School of Mathematical Sciences, The University of Tokyo)
An instability mechanism of pulsatile flow along particle trajectories for the axisymmetric Euler equations
[ Reference URL ]
https://www.ms.u-tokyo.ac.jp/~yoneda/index.html

### 2016/10/04

15:30-16:30   Room #002 (Graduate School of Math. Sci. Bldg.)
Odo Diekmann (Utrecht University)
Waning and boosting : on the dynamics of immune status (ENGLISH)
[ Abstract ]
A first aim is to briefly review various mathematical models of infectious disease dynamics that incorporate waning and boosting of immunity. The focus will be on models that are described by delay equations, in particular renewal equations [1]. Concerning within-host dynamics, we limit ourselves to the rather caricatural models of Aron [2] and de Graaf e.a. [3].From a biomedical point of view the main conclusion is that a higher force of infection may lead to less disease,see [4] and the references given there.

[1] O.Diekmann, M.Gyllenberg, J.A.J.Metz, H.R.Thieme, On the formulation and analysis
of general deterministic structured population models. I. Linear theory, J. Math. Biol. (1998) 36 : 349 - 388
[2] J.L. Aron, Dynamics of acquired immunity boosted by exposure to infection, Math. Biosc. (1983) 64 : 249-259
[3] W.F. de Graaf, M.E.E. Kretzschmar, P.M.F. Teunis, O. Diekmann, A two-phase within host model for immune response and its application to seriological profiles of pertussis, Epidemics (2014) 9 : 1-7
[4] A.N. Swart, M. Tomasi, M. Kretzschmar, A.H. Havelaar, O. Diekmann, The protective effect of temporary immunity under imposed infection pressure, Epidemics (2012) 4 : 43-47
[ Reference URL ]
http://www.uu.nl/staff/ODiekmann

### 2016/06/24

15:30-16:30   Room #123 (Graduate School of Math. Sci. Bldg.)
GONGYO Yoshinori (Graduate School of Mathematical Sciences, The University of Tokyo)
Recent developments of MMP and around (JAPANESE)
[ Reference URL ]
https://www.ms.u-tokyo.ac.jp/teacher/gongyo.html

### 2016/05/27

15:30-16:30   Room #123 (Graduate School of Math. Sci. Bldg.)
Takahiro Kitayama (Graduate School of Mathematical Sciences, University of Tokyo)
Moduli spaces of linear representations and splittings of 3-manifolds

### 2016/04/08

15:30-16:30   Room #123 (Graduate School of Math. Sci. Bldg.)
François Apery (l'IRMA à Strasbourg)
Using mathematical objects (ENGLISH)
[ Abstract ]
Mathematical models are not only teaching tools or pieces of museum but can also have inspiring influence to discovering new truths in mathematics. Through some examples including the Boy surface we will show how models have played a major role in the emergence of new results.

### 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)