## Colloquium

Seminar information archive ～05/28｜Next seminar｜Future seminars 05/29～

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**

### 2018/03/10

14:30-15:30 Room #大講義室 (Graduate School of Math. Sci. Bldg.)

(JAPANESE)

**Yujiro KAWAMATA**(Univ. Tokyo)(JAPANESE)

### 2018/03/10

16:00-17:00 Room #大講義室 (Graduate School of Math. Sci. Bldg.)

(JAPANESE)

**Hiroshi MATANO**(Univ. Tokyo)(JAPANESE)

### 2018/02/23

15:30-16:30 Room #002 (Graduate School of Math. Sci. Bldg.)

(JAPANESE)

**Hiromu Tanaka**(Univ. Tokyo)(JAPANESE)

### 2018/01/26

15:30-16:30 Room #002 (Graduate School of Math. Sci. Bldg.)

(JAPANESE)

**Yuta Koike**(Univ. Tokyo)(JAPANESE)

### 2017/11/24

15:30-16:30 Room #002 (Graduate School of Math. Sci. Bldg.)

(JAPANESE)

**Yukari Ito**(IPMU, Nagoya University)(JAPANESE)

### 2017/10/06

15:30-16:30 Room #002 (Graduate School of Math. Sci. Bldg.)

Singular Integrals and Real Variable Methods in Harmonic Analysis (JAPANESE)

[ Reference URL ]

http://lab.twcu.ac.jp/miyachi/English.html

**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.)

Smith Normal Form and Combinatorics (English)

http://www-math.mit.edu/~rstan/

**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 ]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.

http://www-math.mit.edu/~rstan/

### 2017/06/20

15:30-16:30 Room #002 (Graduate School of Math. Sci. Bldg.)

Some stochastic population models in a random environment (English)

http://www.ummisco.ird.fr/perso/bacaer/

**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 ]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)

http://www.ummisco.ird.fr/perso/bacaer/

### 2017/05/26

15:30-16:30 Room #002 (Graduate School of Math. Sci. Bldg.)

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)

**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.)

可積分量子スピン鎖における隠れた超対称性 (JAPANESE)

[ Reference URL ]

https://www.ms.u-tokyo.ac.jp/~matsui/index.html

**Chihiro Matsui**(Graduate School of Mathematical Sciences, the University of Tokyo)可積分量子スピン鎖における隠れた超対称性 (JAPANESE)

[ 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.)

A tour around microlocal analysis and algebraic analysis (JAPANESE)

[ Reference URL ]

https://www.ms.u-tokyo.ac.jp/~kiyoomi/index.html

**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.)

40 years along with stochastic analysis --- Motivated by statistical physics problems --- (JAPANESE)

[ Reference URL ]

https://www.ms.u-tokyo.ac.jp/~funaki/

**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.)

On a conjecture of Bloch and Kato, and a local analogue.

**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.

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.)

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

**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.)

Waning and boosting : on the dynamics of immune status (ENGLISH)

http://www.uu.nl/staff/ODiekmann

**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 ]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

http://www.uu.nl/staff/ODiekmann

### 2016/06/24

15:30-16:30 Room #123 (Graduate School of Math. Sci. Bldg.)

Recent developments of MMP and around (JAPANESE)

[ Reference URL ]

https://www.ms.u-tokyo.ac.jp/teacher/gongyo.html

**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.)

Moduli spaces of linear representations and splittings of 3-manifolds

**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.)

Using mathematical objects (ENGLISH)

**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.

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.)

Singularities and Jet schemes (JAPANESE)

[ Reference URL ]

http://faculty.ms.u-tokyo.ac.jp/~shihoko/

**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.)

Birational geometry through complex dymanics (ENGLISH)

**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.

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.)

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

**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.)

Recent development in amenable groups (JAPANESE)

[ Reference URL ]

https://www.ms.u-tokyo.ac.jp/~kida/

**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.)

Mean curvature flow with surgery

http://www.mfo.de/about-the-institute/staff/prof.-dr.-gerhard-huisken

**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 ]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.

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.)

On the development of Riemann surfaces and moduli (ENGLISH)

**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.

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.)

Dimer models and mirror symmetry (JAPANESE)

**Kazushi Ueda**(Graduate School of Mathematical Sciences, University of Tokyo)Dimer models and mirror symmetry (JAPANESE)