## Seminar information archive

Seminar information archive ～05/20｜Today's seminar 05/21 | Future seminars 05/22～

### 2014/02/10

#### thesis presentations

11:00-12:15 Room #118 (Graduate School of Math. Sci. Bldg.)

Liouville type theorems for the Navier-Stokes equations andapplications(ナヴィエ・ストークス方程式に対するリウヴィル型定理とその応用)

(JAPANESE)

**許 本源**(東京大学大学院数理科学研究科)Liouville type theorems for the Navier-Stokes equations andapplications(ナヴィエ・ストークス方程式に対するリウヴィル型定理とその応用)

(JAPANESE)

#### thesis presentations

13:00-14:15 Room #118 (Graduate School of Math. Sci. Bldg.)

Mathematical and numerical analysis for incompressible fluid equations under friction boundary conditions(摩擦型境界条件下での非圧縮流体の方程式に対する数学解析と数値解析) (JAPANESE)

**柏原 崇人**(東京大学大学院数理科学研究科)Mathematical and numerical analysis for incompressible fluid equations under friction boundary conditions(摩擦型境界条件下での非圧縮流体の方程式に対する数学解析と数値解析) (JAPANESE)

#### thesis presentations

08:00-09:15 Room #128 (Graduate School of Math. Sci. Bldg.)

A cellular approach to the Hecke-Clifford superalgebra(セルラー代数の手法によるHecke-Clifford スーパー代数の研究) (JAPANESE)

**森 真樹**(東京大学大学院数理科学研究科)A cellular approach to the Hecke-Clifford superalgebra(セルラー代数の手法によるHecke-Clifford スーパー代数の研究) (JAPANESE)

#### thesis presentations

09:30-10:45 Room #128 (Graduate School of Math. Sci. Bldg.)

Good reduction criterion for K3 surfaces(K3曲面の良い還元の判定法)

(JAPANESE)

**柗本 雄也**(東京大学大学院数理科学研究科)Good reduction criterion for K3 surfaces(K3曲面の良い還元の判定法)

(JAPANESE)

#### thesis presentations

13:00-14:15 Room #128 (Graduate School of Math. Sci. Bldg.)

Spaces of stability conditions on Calabi-Yau categories associated with quivers(箙に付随するCalabi-Yau圏の安定性条件の空間について)

(JAPANESE)

**池田 暁志**(東京大学大学院数理科学研究科)Spaces of stability conditions on Calabi-Yau categories associated with quivers(箙に付随するCalabi-Yau圏の安定性条件の空間について)

(JAPANESE)

### 2014/02/05

#### Number Theory Seminar

17:10-18:10 Room #002 (Graduate School of Math. Sci. Bldg.)

The Franke filtration of spaces of automorphic forms (ENGLISH)

**Neven Grbac**(University of Rijeka)The Franke filtration of spaces of automorphic forms (ENGLISH)

[ Abstract ]

The Franke filtration is a filtration of the space of all adelic automorphic forms on a reductive group defined over a number field. The filtration steps can be described as certain induced representations, which has applications to the study of Eisenstein cohomology. In this talk, we shall describe the Franke filtration in general, give several examples, and explain its connection to cohomology.

The Franke filtration is a filtration of the space of all adelic automorphic forms on a reductive group defined over a number field. The filtration steps can be described as certain induced representations, which has applications to the study of Eisenstein cohomology. In this talk, we shall describe the Franke filtration in general, give several examples, and explain its connection to cohomology.

### 2014/02/03

#### Algebraic Geometry Seminar

15:30-17:00 Room #122 (Graduate School of Math. Sci. Bldg.)

Classification of log del Pezzo surfaces of index three (JAPANESE)

**Kento Fujita**(RIMS)Classification of log del Pezzo surfaces of index three (JAPANESE)

[ Abstract ]

Log del Pezzo surfaces constitute an interesting class of rational surfaces and naturally appear in the minimal model program. I will describe an algorithm to classify all the log del Pezzo surfaces of fixed (Q-Gorenstein) index $a$. Especially, I will focus on the case that $a$ is equal to three. This is joint work with Kazunori Yasutake.

Log del Pezzo surfaces constitute an interesting class of rational surfaces and naturally appear in the minimal model program. I will describe an algorithm to classify all the log del Pezzo surfaces of fixed (Q-Gorenstein) index $a$. Especially, I will focus on the case that $a$ is equal to three. This is joint work with Kazunori Yasutake.

#### GCOE Seminars

16:00-17:00 Room #118 (Graduate School of Math. Sci. Bldg.)

On the influence of the coupling on the dynamics of under-observed cascade systems of PDE’s (ENGLISH)

**Fatiha Alabau**(University of Lorraine)On the influence of the coupling on the dynamics of under-observed cascade systems of PDE’s (ENGLISH)

[ Abstract ]

We consider observability of coupled dynamical systems of hyperbolic and parabolic type when the number of observations is strictly less that the number of unknowns. A main issue is to understand how the lack of observations of certain components is compensated by the coupling information. This talk will present a mathematical approach based on energy methods and some recent positive and negative results on these questions.

We consider observability of coupled dynamical systems of hyperbolic and parabolic type when the number of observations is strictly less that the number of unknowns. A main issue is to understand how the lack of observations of certain components is compensated by the coupling information. This talk will present a mathematical approach based on energy methods and some recent positive and negative results on these questions.

#### GCOE Seminars

17:00-18:00 Room #118 (Graduate School of Math. Sci. Bldg.)

Compactness estimates for Hamilton-Jacobi equations (ENGLISH)

**Piermarco Cannarsa**(University of Rome Tor Vergata)Compactness estimates for Hamilton-Jacobi equations (ENGLISH)

[ Abstract ]

For scalar conservations laws in one space dimension, P. Lax was the first to obtain compactness properties of the solution semigroup. Such properties were subsequently analyzed by several authors in quantitative terms using Kolmogorov's entropy. In this talk, we shall explain how to adapt such approach to the Hopf-Lax semigroup of solutions to first order Hamilton-Jacobi equations in arbitrary space dimension, and discuss related controllability issues.

For scalar conservations laws in one space dimension, P. Lax was the first to obtain compactness properties of the solution semigroup. Such properties were subsequently analyzed by several authors in quantitative terms using Kolmogorov's entropy. In this talk, we shall explain how to adapt such approach to the Hopf-Lax semigroup of solutions to first order Hamilton-Jacobi equations in arbitrary space dimension, and discuss related controllability issues.

### 2014/02/01

#### Monthly Seminar on Arithmetic of Automorphic Forms

13:30-16:00 Room #123 (Graduate School of Math. Sci. Bldg.)

On the three dimensional Whittaker functions on SU(2,2) (ENGLISH)

Minimal submanifolds on type IV symmetric domains (ENGLISH)

**Bayarmagnai, G.**(National University of Mongolia) 13:30-14:30On the three dimensional Whittaker functions on SU(2,2) (ENGLISH)

[ Abstract ]

The speaker will discuss the technical aspect to have explicit Whittaker functions belonging to principal series representations of SU(2,2) with non-trivial minimal K-types.

The speaker will discuss the technical aspect to have explicit Whittaker functions belonging to principal series representations of SU(2,2) with non-trivial minimal K-types.

**Takayuki Oda**(Univ. of Tokyo) 15:00-16:00Minimal submanifolds on type IV symmetric domains (ENGLISH)

[ Abstract ]

In the explicit constructions of fundamental domains in some typical classical domains with respect standard arithmetic discrete subgroups, there appears real minimal hypersurfaces. But this was known only for real rank one cases. We try to find the situation for the cases of rank 2 by some exapmles.

In the explicit constructions of fundamental domains in some typical classical domains with respect standard arithmetic discrete subgroups, there appears real minimal hypersurfaces. But this was known only for real rank one cases. We try to find the situation for the cases of rank 2 by some exapmles.

#### Monthly Seminar on Arithmetic of Automorphic Forms

13:30-16:00 Room #123 (Graduate School of Math. Sci. Bldg.)

On the three dimensional Whittaker functions on SU(2,2) (ENGLISH)

Minimal submanifolds on type IV symmetric domains (ENGLISH)

**Bayarmagnai, G.**(National University of Mongolia) 13:30-14:30On the three dimensional Whittaker functions on SU(2,2) (ENGLISH)

[ Abstract ]

The speaker will discuss the technical aspect to have explicit Whittaker functions belonging to principal series representations of SU(2,2) with non-trivial minimal K-types.

The speaker will discuss the technical aspect to have explicit Whittaker functions belonging to principal series representations of SU(2,2) with non-trivial minimal K-types.

**Takayuki Oda**(Univ. of Tokyo) 15:00-16:00Minimal submanifolds on type IV symmetric domains (ENGLISH)

[ Abstract ]

In the explicit constructions of fundamental domains in some typical classical domains with respect standard arithmetic discrete subgroups, there appears real minimal hypersurfaces. But this was known only for real rank one cases. We try to find the situation for the cases of rank 2 by some exapmles.

In the explicit constructions of fundamental domains in some typical classical domains with respect standard arithmetic discrete subgroups, there appears real minimal hypersurfaces. But this was known only for real rank one cases. We try to find the situation for the cases of rank 2 by some exapmles.

#### Monthly Seminar on Arithmetic of Automorphic Forms

13:30-16:00 Room #123 (Graduate School of Math. Sci. Bldg.)

On the three dimensional Whittaker functions on SU(2,2) (ENGLISH)

Minimal submanifolds on type IV symmetric domains (ENGLISH)

**Bayarmagnai, G.**(National University of Mongolia) 13:30-14:30On the three dimensional Whittaker functions on SU(2,2) (ENGLISH)

[ Abstract ]

The speaker will discuss the technical aspect to have explicit Whittaker functions belonging to principal series representations of SU(2,2) with non-trivial minimal K-types.

The speaker will discuss the technical aspect to have explicit Whittaker functions belonging to principal series representations of SU(2,2) with non-trivial minimal K-types.

**Takayuki Oda**(Univ. of Tokyo) 15:00-16:00Minimal submanifolds on type IV symmetric domains (ENGLISH)

[ Abstract ]

In the explicit constructions of fundamental domains in some typical classical domains with respect standard arithmetic discrete subgroups, there appears real minimal hypersurfaces. But this was known only for real rank one cases. We try to find the situation for the cases of rank 2 by some exapmles.

In the explicit constructions of fundamental domains in some typical classical domains with respect standard arithmetic discrete subgroups, there appears real minimal hypersurfaces. But this was known only for real rank one cases. We try to find the situation for the cases of rank 2 by some exapmles.

#### Monthly Seminar on Arithmetic of Automorphic Forms

**Bayarmagnai, G.**(National University of Mongolia) 13:30-14:30

On the three dimensional Whittaker functions on SU(2,2) (ENGLISH)

The speaker will discuss the technical aspect to have explicit Whittaker functions belonging to principal series representations of SU(2,2) with non-trivial minimal K-types.

**Takayuki Oda**(Univ. of Tokyo) 15:00-16:00

Minimal submanifolds on type IV symmetric domains (ENGLISH)

In the explicit constructions of fundamental domains in some typical classical domains with respect standard arithmetic discrete subgroups, there appears real minimal hypersurfaces. But this was known only for real rank one cases. We try to find the situation for the cases of rank 2 by some exapmles.

#### Monthly Seminar on Arithmetic of Automorphic Forms

**Bayarmagnai, G.**(National University of Mongolia) 13:30-14:30

On the three dimensional Whittaker functions on SU(2,2) (ENGLISH)

The speaker will discuss the technical aspect to have explicit Whittaker functions belonging to principal series representations of SU(2,2) with non-trivial minimal K-types.

**Takayuki Oda**(Univ. of Tokyo) 15:00-16:00

Minimal submanifolds on type IV symmetric domains (ENGLISH)

In the explicit constructions of fundamental domains in some typical classical domains with respect standard arithmetic discrete subgroups, there appears real minimal hypersurfaces. But this was known only for real rank one cases. We try to find the situation for the cases of rank 2 by some exapmles.

#### Monthly Seminar on Arithmetic of Automorphic Forms

**Bayarmagnai, G.**(National University of Mongolia) 13:30-14:30

On the three dimensional Whittaker functions on SU(2,2) (ENGLISH)

The speaker will discuss the technical aspect to have explicit Whittaker functions belonging to principal series representations of SU(2,2) with non-trivial minimal K-types.

**Takayuki Oda**(Univ. of Tokyo) 15:00-16:00

Minimal submanifolds on type IV symmetric domains (ENGLISH)

In the explicit constructions of fundamental domains in some typical classical domains with respect standard arithmetic discrete subgroups, there appears real minimal hypersurfaces. But this was known only for real rank one cases. We try to find the situation for the cases of rank 2 by some exapmles.

#### Monthly Seminar on Arithmetic of Automorphic Forms

**Bayarmagnai, G.**(National University of Mongolia) 13:30-14:30

On the three dimensional Whittaker functions on SU(2,2) (ENGLISH)

The speaker will discuss the technical aspect to have explicit Whittaker functions belonging to principal series representations of SU(2,2) with non-trivial minimal K-types.

**Takayuki Oda**(Univ. of Tokyo) 15:00-16:00

Minimal submanifolds on type IV symmetric domains (ENGLISH)

In the explicit constructions of fundamental domains in some typical classical domains with respect standard arithmetic discrete subgroups, there appears real minimal hypersurfaces. But this was known only for real rank one cases. We try to find the situation for the cases of rank 2 by some exapmles.

#### Monthly Seminar on Arithmetic of Automorphic Forms

**Bayarmagnai, G.**(National University of Mongolia) 13:30-14:30

On the three dimensional Whittaker functions on SU(2,2) (ENGLISH)

The speaker will discuss the technical aspect to have explicit Whittaker functions belonging to principal series representations of SU(2,2) with non-trivial minimal K-types.

**Takayuki Oda**(Univ. of Tokyo) 15:00-16:00

Minimal submanifolds on type IV symmetric domains (ENGLISH)

In the explicit constructions of fundamental domains in some typical classical domains with respect standard arithmetic discrete subgroups, there appears real minimal hypersurfaces. But this was known only for real rank one cases. We try to find the situation for the cases of rank 2 by some exapmles.

### 2014/01/31

#### Colloquium

16:30-17:30 Room #122 (Graduate School of Math. Sci. Bldg.)

Controllability of fluid flows (ENGLISH)

**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.

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.

### 2014/01/30

#### Kavli IPMU Komaba Seminar

17:00-18:30 Room #128 (Graduate School of Math. Sci. Bldg.)

Characteristic classes from 2d renormalized sigma-models (ENGLISH)

**Hans Jockers**(The University of Bonn)Characteristic classes from 2d renormalized sigma-models (ENGLISH)

[ Abstract ]

The Hirzebruch-Riemann-Roch formula relates the holomorphic Euler characteristic

of holomorphic vector bundles to topological invariants of compact complex manifold.

I will explain a generalization of the Mukai's modified first Chern character map, which

introduces certain characteristic classes that have not been considered in this form by

Hirzebruch. This naturally leads to the characteristic Gamma class based on the Gamma

function. The characteristic Gamma class has a surprising relation to the quantum theory

of certain 2d sigma-models with compact complex manifolds as their target spaces. I will

argue that the Gamma class describes perturbative quantum corrections to the classical

theory of those sigma models.

The Hirzebruch-Riemann-Roch formula relates the holomorphic Euler characteristic

of holomorphic vector bundles to topological invariants of compact complex manifold.

I will explain a generalization of the Mukai's modified first Chern character map, which

introduces certain characteristic classes that have not been considered in this form by

Hirzebruch. This naturally leads to the characteristic Gamma class based on the Gamma

function. The characteristic Gamma class has a surprising relation to the quantum theory

of certain 2d sigma-models with compact complex manifolds as their target spaces. I will

argue that the Gamma class describes perturbative quantum corrections to the classical

theory of those sigma models.

### 2014/01/28

#### Numerical Analysis Seminar

16:30-18:00 Room #118 (Graduate School of Math. Sci. Bldg.)

Mathematical models of cell-cell adhesion (JAPANESE)

[ Reference URL ]

http://www.infsup.jp/utnas/

**Hideki Murakawa**(Kyushu University)Mathematical models of cell-cell adhesion (JAPANESE)

[ Reference URL ]

http://www.infsup.jp/utnas/

#### Tuesday Seminar of Analysis

16:30-18:00 Room #128 (Graduate School of Math. Sci. Bldg.)

Asymptotic behaviour of a non-local diffusive logistic equation (ENGLISH)

**Arnaud Ducrot**(University of Bordeaux)Asymptotic behaviour of a non-local diffusive logistic equation (ENGLISH)

[ Abstract ]

In this talk we investigate the long time behaviour of a logistic type equation modelling the motion of cells. The equation we consider takes into account birth and death process using a simple logistic effect as well as a non-local motion of cells using non-local Darcy’s law with regular kernel. Using the periodic framework we first investigate the well-posedness of the problem before deriving some information about its long time behaviour. The lack of asymptotic compactness of the system is overcome by making use of Young measure theory. This allows us to conclude that the semiflow converges for the Young measure topology.

In this talk we investigate the long time behaviour of a logistic type equation modelling the motion of cells. The equation we consider takes into account birth and death process using a simple logistic effect as well as a non-local motion of cells using non-local Darcy’s law with regular kernel. Using the periodic framework we first investigate the well-posedness of the problem before deriving some information about its long time behaviour. The lack of asymptotic compactness of the system is overcome by making use of Young measure theory. This allows us to conclude that the semiflow converges for the Young measure topology.

#### GCOE Seminars

16:30-18:00 Room #128 (Graduate School of Math. Sci. Bldg.)

Asymptotic behaviour of a non-local diffusive logistic equation (ENGLISH)

http://agusta.ms.u-tokyo.ac.jp/analysis.html

**Arnaud Ducrot**(University of Bordeaux)Asymptotic behaviour of a non-local diffusive logistic equation (ENGLISH)

[ Abstract ]

In this talk we investigate the long time behaviour of a logistic type equation modelling the motion of cells. The equation we consider takes into account birth and death process using a simple logistic effect as well as a non-local motion of cells using non-local Darcy’s law with regular kernel. Using the periodic framework we first investigate the well-posedness of the problem before deriving some information about its long time behaviour. The lack of asymptotic compactness of the system is overcome by making use of Young measure theory. This allows us to conclude that the semiflow converges for the Young measure topology.

[ Reference URL ]In this talk we investigate the long time behaviour of a logistic type equation modelling the motion of cells. The equation we consider takes into account birth and death process using a simple logistic effect as well as a non-local motion of cells using non-local Darcy’s law with regular kernel. Using the periodic framework we first investigate the well-posedness of the problem before deriving some information about its long time behaviour. The lack of asymptotic compactness of the system is overcome by making use of Young measure theory. This allows us to conclude that the semiflow converges for the Young measure topology.

http://agusta.ms.u-tokyo.ac.jp/analysis.html

### 2014/01/27

#### Seminar on Geometric Complex Analysis

11:00-12:00 Room #126 (Graduate School of Math. Sci. Bldg.)

Logarithmic 1-forms and distributions of entire curves and integral points (JAPANESE)

**Junjiro Noguchi**(The University of Tokyo)Logarithmic 1-forms and distributions of entire curves and integral points (JAPANESE)

[ Abstract ]

The Log-Bloch-Ochiai Theorem says, in the most general form so far, that every entire curve in a Zariski open $X$ of a compact Kahler manifold $\bar{X}$ must be degenerate, if $\bar{q}(X)> \dim X$ ([NW02] Noguchi-Winkelmann, Math.\ Z. 239, 2002). If $X$ is defined a quasi-projective algebraic variety defined over a number field, then there is no Zariski dense $(S, D)$-integral subset in $X$ ($D=\partial X=\bar{X}\subset X$). We discuss this kind of properties more.

In the talk we will fix an error in an application in [NW02], and we will show

Theorem 1. (i) Let $M$ be a complex projective algebraic manifold, and let $D=\sum_{j=1}^l D_j$ be a sum of divisors on $M$ which are independent in supports. If $l> \dim M+r(\{D_j\})-q(M)$, then every entire curve $f:\mathbf{C} \to M\setminus D$ must be degenerate.

(ii) Let $M$ and $D_j$ be defined over a number field. If $l> \dim M+r(\{D_j\})-q(M)$, then there is no Zariski-dense $(S,D)$-integral subset of $M\setminus D$.

For the finiteness we obtain

Theorem 2. Let the notation be as above.

(i) If $l \geq 2 \dim M+r(\{D_j\})$, then $M\setminus D$ is completehyperbolic and hyperbolically embedded into $M$.

(ii) Let $M$ and $D_j$ be defined over a number field. If $l> 2\dim M+r(\{D_j\})$, then every $(S,D)$-integral subset of $M\setminus D$ is finite.

Precise definitions will be given in the talk. We will also discuss an application of Theorem 1 (ii) to generalize Siegel's Theorem on integral points on affine curves,

recent due to A. Levin.

The Log-Bloch-Ochiai Theorem says, in the most general form so far, that every entire curve in a Zariski open $X$ of a compact Kahler manifold $\bar{X}$ must be degenerate, if $\bar{q}(X)> \dim X$ ([NW02] Noguchi-Winkelmann, Math.\ Z. 239, 2002). If $X$ is defined a quasi-projective algebraic variety defined over a number field, then there is no Zariski dense $(S, D)$-integral subset in $X$ ($D=\partial X=\bar{X}\subset X$). We discuss this kind of properties more.

In the talk we will fix an error in an application in [NW02], and we will show

Theorem 1. (i) Let $M$ be a complex projective algebraic manifold, and let $D=\sum_{j=1}^l D_j$ be a sum of divisors on $M$ which are independent in supports. If $l> \dim M+r(\{D_j\})-q(M)$, then every entire curve $f:\mathbf{C} \to M\setminus D$ must be degenerate.

(ii) Let $M$ and $D_j$ be defined over a number field. If $l> \dim M+r(\{D_j\})-q(M)$, then there is no Zariski-dense $(S,D)$-integral subset of $M\setminus D$.

For the finiteness we obtain

Theorem 2. Let the notation be as above.

(i) If $l \geq 2 \dim M+r(\{D_j\})$, then $M\setminus D$ is completehyperbolic and hyperbolically embedded into $M$.

(ii) Let $M$ and $D_j$ be defined over a number field. If $l> 2\dim M+r(\{D_j\})$, then every $(S,D)$-integral subset of $M\setminus D$ is finite.

Precise definitions will be given in the talk. We will also discuss an application of Theorem 1 (ii) to generalize Siegel's Theorem on integral points on affine curves,

recent due to A. Levin.

### 2014/01/25

#### Harmonic Analysis Komaba Seminar

13:00-18:00 Room #128 (Graduate School of Math. Sci. Bldg.)

Unimodular Fourier multipliers on Wiener Amalgam Spaces (JAPANESE)

Analysis of mass-subcritical nonlinear Schrödinger equation (JAPANESE)

**Jayson Cunanan**(Nagoya University) 13:30-15:00Unimodular Fourier multipliers on Wiener Amalgam Spaces (JAPANESE)

**Satoshi Masaki**(Hiroshima University) 15:30-17:00Analysis of mass-subcritical nonlinear Schrödinger equation (JAPANESE)

### 2014/01/24

#### Number Theory Seminar

16:40-18:50 Room #056 (Graduate School of Math. Sci. Bldg.)

An approach to p-adic Hodge theory over number fields (ENGLISH)

Canonical lifts of norm fields and applications (ENGLISH)

**Christopher Davis**(University of Copenhagen) 16:40-17:40An approach to p-adic Hodge theory over number fields (ENGLISH)

[ Abstract ]

As motivation from classical Hodge theory, we will first compare singular cohomology and (algebraic) de Rham cohomology for a complex analytic variety. We will also describe a sense in which this comparison does not have a natural analogue over the real numbers. We think of the complex numbers as a "big" ring which is necessary for the comparison isomorphism to work. In the p-adic setting, the analogous study is known as p-adic Hodge theory, and the "big" rings there are even bigger. There are many approaches to p-adic Hodge theory, and we will introduce one tool in particular: (phi, Gamma)-modules. The goal of this talk is to describe a preliminary attempt to find an analogue of this theory (and analogues of its "big" rings) which makes sense over number fields (rather than p-adic fields). This is joint work with Kiran Kedlaya.

As motivation from classical Hodge theory, we will first compare singular cohomology and (algebraic) de Rham cohomology for a complex analytic variety. We will also describe a sense in which this comparison does not have a natural analogue over the real numbers. We think of the complex numbers as a "big" ring which is necessary for the comparison isomorphism to work. In the p-adic setting, the analogous study is known as p-adic Hodge theory, and the "big" rings there are even bigger. There are many approaches to p-adic Hodge theory, and we will introduce one tool in particular: (phi, Gamma)-modules. The goal of this talk is to describe a preliminary attempt to find an analogue of this theory (and analogues of its "big" rings) which makes sense over number fields (rather than p-adic fields). This is joint work with Kiran Kedlaya.

**Bryden Cais**(University of Arizona) 17:50-18:50Canonical lifts of norm fields and applications (ENGLISH)

[ Abstract ]

In this talk, we begin by outlining the Fontaine-Wintenberger theory of norm fields and explain its application to the classification of p-adic Galois representations on F_p-vector spaces. In order to lift this to a classification of p-adic representations on Z_p-modules, it is necessary to lift the characteristic p norm field constructions of Fontaine-Wintenberger to characteristic zero. We will explain how to canonically perform such lifting in many interesting cases, as well as applications to generalizing a theorem of Kisin on the restriction of crystalline p-adic Galois representations. This is joint work with Christopher Davis.

In this talk, we begin by outlining the Fontaine-Wintenberger theory of norm fields and explain its application to the classification of p-adic Galois representations on F_p-vector spaces. In order to lift this to a classification of p-adic representations on Z_p-modules, it is necessary to lift the characteristic p norm field constructions of Fontaine-Wintenberger to characteristic zero. We will explain how to canonically perform such lifting in many interesting cases, as well as applications to generalizing a theorem of Kisin on the restriction of crystalline p-adic Galois representations. This is joint work with Christopher Davis.

< Previous 123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960616263646566676869707172737475767778798081828384858687888990919293949596979899100101102103104105106107108109110111112113114115116117118119120121122123124125126127128129130131132133134135 Next >