## Seminar information archive

Seminar information archive ～04/19｜Today's seminar 04/20 | Future seminars 04/21～

#### Algebraic Geometry Seminar

15:30-17:00 Room #128 (Graduate School of Math. Sci. Bldg.)

Three Dimensional Birational Geoemtry--updates and problems (ENGLISH)

**Jungkai Alfred Chen**(National Taiwan University)Three Dimensional Birational Geoemtry--updates and problems (ENGLISH)

[ Abstract ]

In this talk I will talk about some recent results on

biratioanl classification and biratioanl geoemtry of threefolds.

Given a threefold of general type, we improved our previous result by

showing that $Vol \\ge 1/1680$ and $|mK_X|$ is biratioanl for $m \\ge

61$.

Compare with the worst known example that $X_{46} \\subset

\\mathbb{P}(4,5,6,7,23)$, one also knows that there are only finiteley

many singularities type

for threefolds of general type with $1/1680 \\le Vol \\le 1/420$. It is

then intereting to study threefolds of general type with given basket

of singularities and with given fiber structure.

Concerning threefolds with intermediate Kodaira dimension, we

considered the effective Iitaka fibration. For this purpose, it is

interesting to study threefolds with $\\kappa=1$ with given basket of

singularities and abelian fibration.

For explicit birational geoemtry, we will show our result that each

biratioanl map in minimal model program can be factored into a

sequence of following maps (or its inverse)

1. a divisorial contraction to a point of index r with discrepancy 1/r.

2. a blowup along a smooth curve

3. a flop

In this talk I will talk about some recent results on

biratioanl classification and biratioanl geoemtry of threefolds.

Given a threefold of general type, we improved our previous result by

showing that $Vol \\ge 1/1680$ and $|mK_X|$ is biratioanl for $m \\ge

61$.

Compare with the worst known example that $X_{46} \\subset

\\mathbb{P}(4,5,6,7,23)$, one also knows that there are only finiteley

many singularities type

for threefolds of general type with $1/1680 \\le Vol \\le 1/420$. It is

then intereting to study threefolds of general type with given basket

of singularities and with given fiber structure.

Concerning threefolds with intermediate Kodaira dimension, we

considered the effective Iitaka fibration. For this purpose, it is

interesting to study threefolds with $\\kappa=1$ with given basket of

singularities and abelian fibration.

For explicit birational geoemtry, we will show our result that each

biratioanl map in minimal model program can be factored into a

sequence of following maps (or its inverse)

1. a divisorial contraction to a point of index r with discrepancy 1/r.

2. a blowup along a smooth curve

3. a flop

### 2013/01/11

#### Lectures

10:00-11:00 Room #123 (Graduate School of Math. Sci. Bldg.)

A duality between easy quantum groups and reflection groups (ENGLISH)

**Sven Raum**(KU Leuven)A duality between easy quantum groups and reflection groups (ENGLISH)

#### Lectures

11:15-12:15 Room #123 (Graduate School of Math. Sci. Bldg.)

Some non-uniqueness results for Cartan subalgebras in II$_1$ factors (ENGLISH)

**An Speelman**(KU Leuven)Some non-uniqueness results for Cartan subalgebras in II$_1$ factors (ENGLISH)

#### Lectures

14:00-15:00 Room #123 (Graduate School of Math. Sci. Bldg.)

Structural results for II$_1$ factors of negatively curved groups (ENGLISH)

**Ionut Chifan**(University of Iowa)Structural results for II$_1$ factors of negatively curved groups (ENGLISH)

#### Lectures

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

UHF slicing and classification of nuclear $C^*$-algebras (ENGLISH)

**Karen Strung**(Universit\"at M\"unster)UHF slicing and classification of nuclear $C^*$-algebras (ENGLISH)

#### Lectures

16:30-17:30 Room #123 (Graduate School of Math. Sci. Bldg.)

The generator problem for $C^*$-algebras (ENGLISH)

**Hannes Thiel**(University of Copenhagen)The generator problem for $C^*$-algebras (ENGLISH)

#### GCOE Seminars

10:00-11:00 Room #123 (Graduate School of Math. Sci. Bldg.)

A duality between easy quantum groups and reflection groups (ENGLISH)

[ Reference URL ]

https://www.ms.u-tokyo.ac.jp/~yasuyuki/mini2013-1.htm

**Sven Raum**(KU Leuven)A duality between easy quantum groups and reflection groups (ENGLISH)

[ Reference URL ]

https://www.ms.u-tokyo.ac.jp/~yasuyuki/mini2013-1.htm

#### GCOE Seminars

11:15-12:15 Room #123 (Graduate School of Math. Sci. Bldg.)

Some non-uniqueness results for Cartan subalgebras in II$_1$ factors (ENGLISH)

[ Reference URL ]

https://www.ms.u-tokyo.ac.jp/~yasuyuki/mini2013-1.htm

**An Speelman**(KU Leuven)Some non-uniqueness results for Cartan subalgebras in II$_1$ factors (ENGLISH)

[ Reference URL ]

https://www.ms.u-tokyo.ac.jp/~yasuyuki/mini2013-1.htm

### 2013/01/08

#### Lie Groups and Representation Theory

16:30-18:00 Room #126 (Graduate School of Math. Sci. Bldg.)

On the group of holomorphic and anti-holomorphic transformations

of a compact Hermitian symmetric space and the $G$-structure (JAPANESE)

**Soji Kaneyuki**(Sophia University )On the group of holomorphic and anti-holomorphic transformations

of a compact Hermitian symmetric space and the $G$-structure (JAPANESE)

[ Abstract ]

Let $M$ be a compact irreducible Hermitian symmetric space. We determine the full group of holomorphic and anti-holomorphic transformations of $M$. Also we characterize that full group as the automorphism group of the $G$-structure on $M$, called a generalized conformal structure.

Let $M$ be a compact irreducible Hermitian symmetric space. We determine the full group of holomorphic and anti-holomorphic transformations of $M$. Also we characterize that full group as the automorphism group of the $G$-structure on $M$, called a generalized conformal structure.

#### GCOE lecture series

16:30-17:30 Room #118 (Graduate School of Math. Sci. Bldg.)

Probing factions and Direct sampling method (ENGLISH)

**Kazufumi Ito**(North Carolina State Univ.)Probing factions and Direct sampling method (ENGLISH)

[ Abstract ]

We develop probing functions for inverse medium problems arising in Helmholtz and conductivity and Schrodinger equations. direct sampling methods for determining inhomogeneous inclusions using a limited number of Cauchy data.

We develop probing functions for inverse medium problems arising in Helmholtz and conductivity and Schrodinger equations. direct sampling methods for determining inhomogeneous inclusions using a limited number of Cauchy data.

### 2013/01/07

#### GCOE lecture series

16:30-17:30 Room #118 (Graduate School of Math. Sci. Bldg.)

Traffic flow modeling and Hamilton Jacobi equation (ENGLISH)

**Kazufumi Ito**(North Carolina State Univ.)Traffic flow modeling and Hamilton Jacobi equation (ENGLISH)

[ Abstract ]

A traffic model based on Hamilton Jacobi equations are developed. The model incorporates the sag and source conditions of traffic flows and predict and classify the traffic congestion.

A traffic model based on Hamilton Jacobi equations are developed. The model incorporates the sag and source conditions of traffic flows and predict and classify the traffic congestion.

### 2012/12/26

#### Operator Algebra Seminars

15:45-18:00 Room #118 (Graduate School of Math. Sci. Bldg.)

Trouble in paradise (ENGLISH)

Algebraic K-theory of generalized schemes (ENGLISH)

**Henrik Densing Petersen**(Univ. Copenhagen) 15:45-16:45Trouble in paradise (ENGLISH)

**Stella Anevski**(Univ. Copenhagen) 17:00-18:00Algebraic K-theory of generalized schemes (ENGLISH)

### 2012/12/21

#### GCOE lecture series

15:00-16:00 Room #126 (Graduate School of Math. Sci. Bldg.)

Evolution equation approach to Fractional Differential Equations (ENGLISH)

**Kazufumi Ito**(North Carolina State Univ.)Evolution equation approach to Fractional Differential Equations (ENGLISH)

[ Abstract ]

A class of fractional differential equations is formulated as an evolution equation on the memory space with non-local boundary condition. Based on such a formulation the mathematical theory of evolution equations is applied to concrete examples of nonlinear fractional PDEs.

A class of fractional differential equations is formulated as an evolution equation on the memory space with non-local boundary condition. Based on such a formulation the mathematical theory of evolution equations is applied to concrete examples of nonlinear fractional PDEs.

### 2012/12/19

#### Operator Algebra Seminars

15:45-18:00 Room #118 (Graduate School of Math. Sci. Bldg.)

$W^*$-superrigidity for left-right wreath products (ENGLISH)

A classification of approximate subhomogeneous $C^*$-algebras (ENGLISH)

**Mihaita Berbec**(KU Leuven) 15:45-16:45$W^*$-superrigidity for left-right wreath products (ENGLISH)

**Zhuang Niu**(Univ. Wyoming) 17:00-18:00A classification of approximate subhomogeneous $C^*$-algebras (ENGLISH)

#### Geometry Colloquium

10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)

Funk metric on Weil-Petersson spaces (JAPANESE)

**FUJIWARA, Koji**(Kyoto University)Funk metric on Weil-Petersson spaces (JAPANESE)

[ Abstract ]

We discuss the Funk function $F(x; y)$ on a Teichmuller space with the Weil-Petersson metric introduced by Yamada, $F(x; y)$ is an asymmetric distance and invariant by the action of the mapping class group. The Funk metric was originally studied for an open convex subset in a Euclidean space by Funk. Its symmetrization is the Hilbert metric.

We discuss the Funk function $F(x; y)$ on a Teichmuller space with the Weil-Petersson metric introduced by Yamada, $F(x; y)$ is an asymmetric distance and invariant by the action of the mapping class group. The Funk metric was originally studied for an open convex subset in a Euclidean space by Funk. Its symmetrization is the Hilbert metric.

#### Number Theory Seminar

16:40-17:40 Room #056 (Graduate School of Math. Sci. Bldg.)

A generalization of Kato's local epsilon conjecture for

(φ, Γ)-modules over the Robba ring (JAPANESE)

**Kentarou Nakamura**(Hokkaido University)A generalization of Kato's local epsilon conjecture for

(φ, Γ)-modules over the Robba ring (JAPANESE)

[ Abstract ]

In his preprint “Lectures on the approach to Iwasawa theory of Hasse-Weil L-functions via B_dR, Part II ", Kazuya Kato proposed a conjecture called local epsilon conjecture. This conjecture predicts that the determinant of the Galois cohomology of a family of p-adic Galois representations has a canonical base whose specializations at de Rham points can be characterized by using Bloch-Kato exponential, L-factors and Deligne-Langlands epsilon constants of the associated Weil-Deligne representations.

In my talk, I generalize his conjecture for families of (φ, Γ)-modules over the Robba ring, and prove a part of this conjecture in the trianguline case. The two key ingredients are the recent result of Kedlaya-Pottharst-Xiao on the ﬁniteness of cohomologies of (φ, Γ)-modules and my result on Bloch-Kato exponential map for (φ, Γ)-modules.

In his preprint “Lectures on the approach to Iwasawa theory of Hasse-Weil L-functions via B_dR, Part II ", Kazuya Kato proposed a conjecture called local epsilon conjecture. This conjecture predicts that the determinant of the Galois cohomology of a family of p-adic Galois representations has a canonical base whose specializations at de Rham points can be characterized by using Bloch-Kato exponential, L-factors and Deligne-Langlands epsilon constants of the associated Weil-Deligne representations.

In my talk, I generalize his conjecture for families of (φ, Γ)-modules over the Robba ring, and prove a part of this conjecture in the trianguline case. The two key ingredients are the recent result of Kedlaya-Pottharst-Xiao on the ﬁniteness of cohomologies of (φ, Γ)-modules and my result on Bloch-Kato exponential map for (φ, Γ)-modules.

#### GCOE Seminars

15:45-16:45 Room #118 (Graduate School of Math. Sci. Bldg.)

$W^*$-superrigidity for left-right wreath products (ENGLISH)

**Mihaita Berbec**(KU Leuven)$W^*$-superrigidity for left-right wreath products (ENGLISH)

### 2012/12/18

#### FMSP Lectures

10:30-11:30 Room #056 (Graduate School of Math. Sci. Bldg.)

On convergence to equilibrium with applications of Lojasiewicz-Simon

inequality (II) (ENGLISH)

**Jie Jiang**(Wuhan Institute of Physics and Mathematics, Chinese Academy of Sciences)On convergence to equilibrium with applications of Lojasiewicz-Simon

inequality (II) (ENGLISH)

### 2012/12/17

#### Seminar on Geometric Complex Analysis

10:30-12:00 Room #126 (Graduate School of Math. Sci. Bldg.)

On the existence of strictly effective basis on an arithmetic variety (JAPANESE)

**Hideaki Ikoma**(Kyoto University)On the existence of strictly effective basis on an arithmetic variety (JAPANESE)

[ Abstract ]

I would like to talk about some recent work of mine on the asymptotic behavior of the successive minima associated to a graded arithmetic linear series. A complete arithmetic linear series belonging to a hermitian line bundle on an arithmetic variety is defined as the Z-module of the global sections endowed with the supremum-norm, and the successive minima are invariants that measure the size of the sections with small norms.

If time permits, I would like to also explain some close relationship between the results and the general equi-distribution theory of rational points on an arithmetic variety.

I would like to talk about some recent work of mine on the asymptotic behavior of the successive minima associated to a graded arithmetic linear series. A complete arithmetic linear series belonging to a hermitian line bundle on an arithmetic variety is defined as the Z-module of the global sections endowed with the supremum-norm, and the successive minima are invariants that measure the size of the sections with small norms.

If time permits, I would like to also explain some close relationship between the results and the general equi-distribution theory of rational points on an arithmetic variety.

### 2012/12/15

#### Infinite Analysis Seminar Tokyo

13:30-15:00 Room #117 (Graduate School of Math. Sci. Bldg.)

current and integrability (ENGLISH)

**Vincent Pasquier**(CEA, Saclay, France)current and integrability (ENGLISH)

[ Abstract ]

I will describe some problems related to currents in XXZ chains:

Drude conductivity, Linbladt equation, tasep, matrix ansatz,

in particular the relation of permanent currents with integrability.

If time permits I will also discuss a nonrelated subject:

deformation of fusion rules in minimal models and Macdonald polynomials.

I will describe some problems related to currents in XXZ chains:

Drude conductivity, Linbladt equation, tasep, matrix ansatz,

in particular the relation of permanent currents with integrability.

If time permits I will also discuss a nonrelated subject:

deformation of fusion rules in minimal models and Macdonald polynomials.

### 2012/12/13

#### Algebraic Geometry Seminar

10:40-12:10 Room #118 (Graduate School of Math. Sci. Bldg.)

The asymptotic variety of polynomial maps (ENGLISH)

**Jean-Paul Brasselet**(CNRS (Luminy))The asymptotic variety of polynomial maps (ENGLISH)

[ Abstract ]

The asymptotic variety, or set of non-properness has been intensively studied by Zbigniew Jelonek. In a recent paper, Anna and Guillaume Valette associate to a polynomial map $F: {\\mathbb C}^n \\to {\\mathbb C}^n$ a singular variety $N_F$ and relate properness property of $F$ to the vanishing of some intersection homology groups of $N_F$. I will explain how stratifications of the asymptotic variety of $F$ play an important role in the story and how recently, one of my students, Nguyen Thi Bich Thuy, found a nice way to exhibit such a suitable stratification.

The asymptotic variety, or set of non-properness has been intensively studied by Zbigniew Jelonek. In a recent paper, Anna and Guillaume Valette associate to a polynomial map $F: {\\mathbb C}^n \\to {\\mathbb C}^n$ a singular variety $N_F$ and relate properness property of $F$ to the vanishing of some intersection homology groups of $N_F$. I will explain how stratifications of the asymptotic variety of $F$ play an important role in the story and how recently, one of my students, Nguyen Thi Bich Thuy, found a nice way to exhibit such a suitable stratification.

### 2012/12/12

#### Number Theory Seminar

18:00-19:00 Room #002 (Graduate School of Math. Sci. Bldg.)

The Tate conjecture for K3 surfaces and holomorphic symplectic varieties over finite fields (ENGLISH)

**François Charles**(CNRS & Université de Rennes 1)The Tate conjecture for K3 surfaces and holomorphic symplectic varieties over finite fields (ENGLISH)

[ Abstract ]

We prove the Tate conjecture for divisors on reductions of holomorphic symplectic varieties over finite fields -- with some restrictions on the characteristic of the base field. We will be concerned mostly with the supersingular case. As a special case, we prove the Tate conjecture, also known as Artin's conjecture in our case, for K3 surfaces over finite fields of characteristic at least 5 and for codimension 2 cycles on cubic fourfolds.

We prove the Tate conjecture for divisors on reductions of holomorphic symplectic varieties over finite fields -- with some restrictions on the characteristic of the base field. We will be concerned mostly with the supersingular case. As a special case, we prove the Tate conjecture, also known as Artin's conjecture in our case, for K3 surfaces over finite fields of characteristic at least 5 and for codimension 2 cycles on cubic fourfolds.

#### Operator Algebra Seminars

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

Large subalgebras of crossed product $C^*$-algebras (ENGLISH)

**N. Christopher Phillips**(Univ. Oregon)Large subalgebras of crossed product $C^*$-algebras (ENGLISH)

#### FMSP Lectures

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

Large subalgebras of crossed product C*-algebras (ENGLISH)

**N. Christopher Phillips**(Univ. Oregon)Large subalgebras of crossed product C*-algebras (ENGLISH)

[ Abstract ]

This is work in progress; not everything has been checked.

We define a "large subalgebra" and a "centrally large subalgebra" of a C*-algebra. The motivating example is what we now call the "orbit breaking subalgebra" of the crossed product by a minimal homeomorphism h of a compact metric space X. Let v be the standard unitary in the crossed product C* (Z, X, h). For a closed subset Y of X, we form the subalgebra of C* (Z, X, h) generated by C (X) and all elements f v for f in C (X) such that f vanishes on Y. When each orbit meets Y at most once, this subalgebra is centrally large in the crossed product. Crossed products by smooth free minimal actions of Zd also contain centrally large subalgebras which are simple direct limits, with no dimension growth, of recursive subhomogeneous algebras.

If B is a large subalgebra of A, then the Cuntz semigroups of A and B are the almost the same: if one deletes the classes of nonzero projections, then the inclusion is a bijection on what is left. Also (joint work with Dawn Archey), if B is a centrally large subalgebra of A, and B has stable rank one, then so does A. Moreover, if B is a centrally large subalgebra of A, if B is Z-stable, and if A is nuclear, then A is Z-stable.

This is work in progress; not everything has been checked.

We define a "large subalgebra" and a "centrally large subalgebra" of a C*-algebra. The motivating example is what we now call the "orbit breaking subalgebra" of the crossed product by a minimal homeomorphism h of a compact metric space X. Let v be the standard unitary in the crossed product C* (Z, X, h). For a closed subset Y of X, we form the subalgebra of C* (Z, X, h) generated by C (X) and all elements f v for f in C (X) such that f vanishes on Y. When each orbit meets Y at most once, this subalgebra is centrally large in the crossed product. Crossed products by smooth free minimal actions of Zd also contain centrally large subalgebras which are simple direct limits, with no dimension growth, of recursive subhomogeneous algebras.

If B is a large subalgebra of A, then the Cuntz semigroups of A and B are the almost the same: if one deletes the classes of nonzero projections, then the inclusion is a bijection on what is left. Also (joint work with Dawn Archey), if B is a centrally large subalgebra of A, and B has stable rank one, then so does A. Moreover, if B is a centrally large subalgebra of A, if B is Z-stable, and if A is nuclear, then A is Z-stable.

### 2012/12/11

#### Tuesday Seminar on Topology

16:30-18:00 Room #056 (Graduate School of Math. Sci. Bldg.)

Homotopy-theoretic methods in the study of spaces of knots and links (ENGLISH)

**Ismar Volic**(Wellesley College)Homotopy-theoretic methods in the study of spaces of knots and links (ENGLISH)

[ Abstract ]

I will survey the ways in which some homotopy-theoretic

methods, manifold calculus of functors main among them, have in recent

years been used for extracting information about the topology of

spaces of knots and links. Cosimplicial spaces and operads will also

be featured. I will end with some recent results about spaces of

homotopy string links and in particular about how one can use functor

calculus in combination with configuration space integrals to extract

information about Milnor invariants.

I will survey the ways in which some homotopy-theoretic

methods, manifold calculus of functors main among them, have in recent

years been used for extracting information about the topology of

spaces of knots and links. Cosimplicial spaces and operads will also

be featured. I will end with some recent results about spaces of

homotopy string links and in particular about how one can use functor

calculus in combination with configuration space integrals to extract

information about Milnor invariants.

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