## Seminar information archive

Seminar information archive ～05/28｜Today's seminar 05/29 | Future seminars 05/30～

#### Lie Groups and Representation Theory

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

Properly discontinuous isometric group actions on inhomogeneous Lorentzian manifolds (JAPANESE)

**Jun-ichi Mukuno**(Nagoya University)Properly discontinuous isometric group actions on inhomogeneous Lorentzian manifolds (JAPANESE)

[ Abstract ]

If a homogeneous space $G/H$ is acted properly discontinuously

upon by a subgroup $\\Gamma$ of $G$ via the left action, the quotient space $\\Gamma \\backslash G/H$ is called a

Clifford--Klein form. In 1962, E. Calabi and L. Markus proved that there is no infinite subgroup of the Lorentz group $O(n+1, 1)$ whose left action on the de Sitter space $O(n+1, 1)/O(n, 1)$ is properly discontinuous.

It follows that a compact Clifford--Klein form of the de Sitter space never exists.

In this talk, we present a new extension of the theorem of E. Calabi and L. Markus to a certain class of Lorentzian manifolds that are not necessarily homogeneous.

If a homogeneous space $G/H$ is acted properly discontinuously

upon by a subgroup $\\Gamma$ of $G$ via the left action, the quotient space $\\Gamma \\backslash G/H$ is called a

Clifford--Klein form. In 1962, E. Calabi and L. Markus proved that there is no infinite subgroup of the Lorentz group $O(n+1, 1)$ whose left action on the de Sitter space $O(n+1, 1)/O(n, 1)$ is properly discontinuous.

It follows that a compact Clifford--Klein form of the de Sitter space never exists.

In this talk, we present a new extension of the theorem of E. Calabi and L. Markus to a certain class of Lorentzian manifolds that are not necessarily homogeneous.

#### thesis presentations

13:15-14:30 Room #128 (Graduate School of Math. Sci. Bldg.)

Martingale theory (JAPANESE)

**Koichiro TAKAOKA**(Graduate School of Mathematical Sciences University of Tokyo)Martingale theory (JAPANESE)

### 2011/05/23

#### Algebraic Geometry Seminar

17:00-18:30 Room #126 (Graduate School of Math. Sci. Bldg.)

Alpha invariant and K-stability of Fano varieties (JAPANESE)

**Yuji Sano**(Kumamoto University)Alpha invariant and K-stability of Fano varieties (JAPANESE)

[ Abstract ]

From the results of Tian, it is proved that the lower bounds of alpha invariant implies K-stability of Fano manifolds via the existence of Kähler-Einstein metrics. In this talk, I will give a direct proof of this relation in algebro-geometric way without using Kähler-Einstein metrics. This is joint work with Yuji Odaka (RIMS).

From the results of Tian, it is proved that the lower bounds of alpha invariant implies K-stability of Fano manifolds via the existence of Kähler-Einstein metrics. In this talk, I will give a direct proof of this relation in algebro-geometric way without using Kähler-Einstein metrics. This is joint work with Yuji Odaka (RIMS).

### 2011/05/19

#### Applied Analysis

16:00-17:30 Room #128 (Graduate School of Math. Sci. Bldg.)

Wave front set defined by wave packet transform and its application (JAPANESE)

**Shingo Ito**(Tokyo University of Science)Wave front set defined by wave packet transform and its application (JAPANESE)

### 2011/05/18

#### Seminar on Mathematics for various disciplines

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

On the perturbation theory for many-electron systems at positive temperature (JAPANESE)

[ Reference URL ]

http://info.ms.u-tokyo.ac.jp/seminar/mathvar/future.html

**Yohei Kashima**(University of Tokyo)On the perturbation theory for many-electron systems at positive temperature (JAPANESE)

[ Reference URL ]

http://info.ms.u-tokyo.ac.jp/seminar/mathvar/future.html

#### Number Theory Seminar

16:30-17:30 Room #056 (Graduate School of Math. Sci. Bldg.)

On the linear independence of values of some Dirichlet series (JAPANESE)

**Masaki Nishimoto**(University of Tokyo)On the linear independence of values of some Dirichlet series (JAPANESE)

### 2011/05/17

#### Tuesday Seminar on Topology

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

Quandle colorings with non-commutative flows (JAPANESE)

**Atsushi Ishii**(University of Tsukuba)Quandle colorings with non-commutative flows (JAPANESE)

[ Abstract ]

This is a joint work with Masahide Iwakiri, Yeonhee Jang and Kanako Oshiro.

We introduce quandle coloring invariants and quandle cocycle invariants

with non-commutative flows for knots, spatial graphs, handlebody-knots,

where a handlebody-knot is a handlebody embedded in the $3$-sphere.

Two handlebody-knots are equivalent if one can be transformed into the

other by an isotopy of $S^3$.

The quandle coloring (resp. cocycle) invariant is a ``twisted'' quandle

coloring (resp. cocycle) invariant.

This is a joint work with Masahide Iwakiri, Yeonhee Jang and Kanako Oshiro.

We introduce quandle coloring invariants and quandle cocycle invariants

with non-commutative flows for knots, spatial graphs, handlebody-knots,

where a handlebody-knot is a handlebody embedded in the $3$-sphere.

Two handlebody-knots are equivalent if one can be transformed into the

other by an isotopy of $S^3$.

The quandle coloring (resp. cocycle) invariant is a ``twisted'' quandle

coloring (resp. cocycle) invariant.

### 2011/05/16

#### Seminar on Geometric Complex Analysis

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

Linearity of order isomorphisms of regular convex cones (JAPANESE)

**Chifune Kai**(Kanazawa Univeristy)Linearity of order isomorphisms of regular convex cones (JAPANESE)

#### Algebraic Geometry Seminar

17:00-18:30 Room #126 (Graduate School of Math. Sci. Bldg.)

On images of Mori dream spaces (JAPANESE)

**Shinnosuke Okawa**(University of Tokyo)On images of Mori dream spaces (JAPANESE)

[ Abstract ]

Mori dream space (MDS), introduced by Y. Hu and S. Keel, is a class of varieties whose geometry can be controlled via the VGIT of the Cox ring. It is a generalization of both toric varieties and log Fano varieties.

The purpose of this talk is to study the image of a morphism from a MDS.

Firstly I prove that such an image again is a MDS.

Secondly I introduce a fan structure on the effective cone of a MDS and show that the fan of the image coincides with the restriction of that of the source.

This fan encodes some information of the Zariski decompositions, which turns out to be equivalent to the information of the GIT equivalence. In toric case, this fan coincides with the so called GKZ decomposition.

The point is that these results can be clearly explained via the VGIT description for MDS.

If I have time, I touch on generalizations and an application to the Shokurov polytopes.

Mori dream space (MDS), introduced by Y. Hu and S. Keel, is a class of varieties whose geometry can be controlled via the VGIT of the Cox ring. It is a generalization of both toric varieties and log Fano varieties.

The purpose of this talk is to study the image of a morphism from a MDS.

Firstly I prove that such an image again is a MDS.

Secondly I introduce a fan structure on the effective cone of a MDS and show that the fan of the image coincides with the restriction of that of the source.

This fan encodes some information of the Zariski decompositions, which turns out to be equivalent to the information of the GIT equivalence. In toric case, this fan coincides with the so called GKZ decomposition.

The point is that these results can be clearly explained via the VGIT description for MDS.

If I have time, I touch on generalizations and an application to the Shokurov polytopes.

### 2011/05/11

#### Number Theory Seminar

17:30-18:30 Room #056 (Graduate School of Math. Sci. Bldg.)

Permanence following Temkin (ENGLISH)

**Michel Raynaud**(Universite Paris-Sud)Permanence following Temkin (ENGLISH)

[ Abstract ]

When one proceeds to a specialization, the good properties of algebraic equations may be destroyed. Starting with a bad specialization, one can try to improve it by performing modifications under control. If, at the end of the process, the initial good properties are preserved, one speaks of permanence. I shall give old and new examples of permanence. The new one concerns the relative semi-stable reduction of curves recently proved by Temkin.

When one proceeds to a specialization, the good properties of algebraic equations may be destroyed. Starting with a bad specialization, one can try to improve it by performing modifications under control. If, at the end of the process, the initial good properties are preserved, one speaks of permanence. I shall give old and new examples of permanence. The new one concerns the relative semi-stable reduction of curves recently proved by Temkin.

### 2011/05/10

#### Numerical Analysis Seminar

16:30-18:00 Room #002 (Graduate School of Math. Sci. Bldg.)

Conservative finite difference method for the three body problem (JAPANESE)

[ Reference URL ]

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

**Yukitaka Minesaki**(Tokushima Bunri University)Conservative finite difference method for the three body problem (JAPANESE)

[ Reference URL ]

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

#### Tuesday Seminar on Topology

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

Isotated points in the space of group left orderings (JAPANESE)

**Tetsuya Ito**(The University of Tokyo)Isotated points in the space of group left orderings (JAPANESE)

[ Abstract ]

The set of all left orderings of a group G admits a natural

topology. In general the space of left orderings is homeomorphic to the

union of Cantor set and finitely many isolated points. In this talk I

will give a new method to construct left orderings corresponding to

isolated points, and will explain how such isolated orderings reflect

the structures of groups.

The set of all left orderings of a group G admits a natural

topology. In general the space of left orderings is homeomorphic to the

union of Cantor set and finitely many isolated points. In this talk I

will give a new method to construct left orderings corresponding to

isolated points, and will explain how such isolated orderings reflect

the structures of groups.

### 2011/05/09

#### Algebraic Geometry Seminar

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

Fourier--Mukai partners of elliptic ruled surfaces (JAPANESE)

**Hokuto Uehara**(Tokyo Metropolitan University)Fourier--Mukai partners of elliptic ruled surfaces (JAPANESE)

[ Abstract ]

Atiyah classifies vector bundles on elliptic curves E over an algebraically closed field of any characteristic. On the other hand, a rank 2 vector bundle on E defines a surface S with P^1-bundle structure on E.

We study when S has an elliptic fibration according to the Atiyah's classification. As its application, we determines the set of Fourier--Mukai partners of elliptic ruled surfaces over the complex number field.

Atiyah classifies vector bundles on elliptic curves E over an algebraically closed field of any characteristic. On the other hand, a rank 2 vector bundle on E defines a surface S with P^1-bundle structure on E.

We study when S has an elliptic fibration according to the Atiyah's classification. As its application, we determines the set of Fourier--Mukai partners of elliptic ruled surfaces over the complex number field.

#### Seminar on Geometric Complex Analysis

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

Order of meromorphic maps and rationality of the image space (JAPANESE)

**Junjiro Noguchi**(University of Tokyo)Order of meromorphic maps and rationality of the image space (JAPANESE)

### 2011/05/02

#### Algebraic Geometry Seminar

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

Projective varieties admitting an embedding with Gauss map of rank zero (JAPANESE)

**Katsuhisa Furukawa**(Waseda University)Projective varieties admitting an embedding with Gauss map of rank zero (JAPANESE)

[ Abstract ]

I will talk about the study of Gauss map in positivity characteristic which is a joint work with S. Fukasawa and H. Kaji. I will also talk about my resent research of this topic.

We call that a projective variety $X$ satisfies (GMRZ) if there exists an embedding $¥iota: X ¥hookrightarrow ¥mathbb{P}^M$ whose Gauss map $X ¥dashrightarrow G(¥dim(X), ¥mathbb{P}^M)$ is of rank zero at a general point.

We study the case where $X$ has a rational curve $C$. Then, as a fundamental theorem, it follows that the property (GMRZ) makes the splitting type of the normal bundle $N_{C/X}$ very special. We also have a characterization of the Fermat cubic hypersurface in characteristic two in terms of (GMRZ). In this talk, I will also explain the relation of blow-ups and the property (GMRZ).

I will talk about the study of Gauss map in positivity characteristic which is a joint work with S. Fukasawa and H. Kaji. I will also talk about my resent research of this topic.

We call that a projective variety $X$ satisfies (GMRZ) if there exists an embedding $¥iota: X ¥hookrightarrow ¥mathbb{P}^M$ whose Gauss map $X ¥dashrightarrow G(¥dim(X), ¥mathbb{P}^M)$ is of rank zero at a general point.

We study the case where $X$ has a rational curve $C$. Then, as a fundamental theorem, it follows that the property (GMRZ) makes the splitting type of the normal bundle $N_{C/X}$ very special. We also have a characterization of the Fermat cubic hypersurface in characteristic two in terms of (GMRZ). In this talk, I will also explain the relation of blow-ups and the property (GMRZ).

### 2011/04/27

#### Number Theory Seminar

16:30-17:30 Room #056 (Graduate School of Math. Sci. Bldg.)

An analogue of Sturm's theorem for Hilbert modular forms (JAPANESE)

**Yuuki Takai**(University of Tokyo)An analogue of Sturm's theorem for Hilbert modular forms (JAPANESE)

### 2011/04/26

#### Numerical Analysis Seminar

16:30-18:00 Room #002 (Graduate School of Math. Sci. Bldg.)

Remarks on the discontinuous Galerkin finite element method (JAPANESE)

[ Reference URL ]

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

**Fumio Kikuchi**(Hitotsubashi University)Remarks on the discontinuous Galerkin finite element method (JAPANESE)

[ Reference URL ]

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

#### Lie Groups and Representation Theory

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

Topological Blow-up (JAPANESE)

**Taro YOSHINO**(the University of Tokyo)Topological Blow-up (JAPANESE)

[ Abstract ]

Suppose that a Lie group $G$ acts on a manifold

$M$. The quotient space $X:=G\\backslash M$ is locally compact,

but not Hausdorff in general. Our aim is to understand

such a non-Hausdorff space $X$.

The space $X$ has the crack $S$. Rougly speaking, $S$ is

the causal subset of non-Hausdorffness of $X$, and especially

$X\\setminus S$ is Hausdorff.

We introduce the concept of `topological blow-up' as a `repair'

of the crack. The `repaired' space $\\tilde{X}$ is

locally compact and Hausdorff space containing $X\\setminus S$

as its open subset. Moreover, the original space $X$ can be

recovered from the pair of $(\\tilde{X}, S)$.

Suppose that a Lie group $G$ acts on a manifold

$M$. The quotient space $X:=G\\backslash M$ is locally compact,

but not Hausdorff in general. Our aim is to understand

such a non-Hausdorff space $X$.

The space $X$ has the crack $S$. Rougly speaking, $S$ is

the causal subset of non-Hausdorffness of $X$, and especially

$X\\setminus S$ is Hausdorff.

We introduce the concept of `topological blow-up' as a `repair'

of the crack. The `repaired' space $\\tilde{X}$ is

locally compact and Hausdorff space containing $X\\setminus S$

as its open subset. Moreover, the original space $X$ can be

recovered from the pair of $(\\tilde{X}, S)$.

#### Tuesday Seminar on Topology

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

Topological Blow-up (JAPANESE)

**Taro Yoshino**(The University of Tokyo)Topological Blow-up (JAPANESE)

[ Abstract ]

Suppose that a Lie group $G$ acts on a manifold

$M$. The quotient space $X:=G\\backslash M$ is locally compact,

but not Hausdorff in general. Our aim is to understand

such a non-Hausdorff space $X$.

The space $X$ has the crack $S$. Roughly speaking, $S$ is

the causal subset of non-Hausdorffness of $X$, and especially

$X\\setminus S$ is Hausdorff.

We introduce the concept of `topological blow-up' as a `repair'

of the crack. The `repaired' space $\\tilde{X}$ is

locally compact and Hausdorff space containing $X\\setminus S$

as its open subset. Moreover, the original space $X$ can be

recovered from the pair of $(\\tilde{X}, S)$.

Suppose that a Lie group $G$ acts on a manifold

$M$. The quotient space $X:=G\\backslash M$ is locally compact,

but not Hausdorff in general. Our aim is to understand

such a non-Hausdorff space $X$.

The space $X$ has the crack $S$. Roughly speaking, $S$ is

the causal subset of non-Hausdorffness of $X$, and especially

$X\\setminus S$ is Hausdorff.

We introduce the concept of `topological blow-up' as a `repair'

of the crack. The `repaired' space $\\tilde{X}$ is

locally compact and Hausdorff space containing $X\\setminus S$

as its open subset. Moreover, the original space $X$ can be

recovered from the pair of $(\\tilde{X}, S)$.

#### Tuesday Seminar of Analysis

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

On the system of fifth-order differential equations which describes surfaces containing six continuous families of circles (JAPANESE)

**Kiyoomi KATAOKA**(Graduate School of Mathematical Sciences, the University of Tokyo)On the system of fifth-order differential equations which describes surfaces containing six continuous families of circles (JAPANESE)

### 2011/04/25

#### Algebraic Geometry Seminar

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

Mirror symmetry and projective geometry of Reye congruences (JAPANESE)

**Hiromichi Takagi**(University of Tokyo)Mirror symmetry and projective geometry of Reye congruences (JAPANESE)

[ Abstract ]

This is a joint work with Shinobu Hosono.

It is well-known that the projective dual of the second Veronese variety v_2(P^n) is the symmetric determinantal hypersurface H. However, in the context of homological projective duality after Kuznetsov, it is natural to consider that the Chow^2 P^n and H are dual (note that Chow^2 P^n is the secant variety of v_2(P^n)).

Though we did not yet formulate what this duality exactly means in full generality, we show some results in this context for the values n¥leq 4.

For example, let n=4. We consider Chow^2 P^4 in P(S^2 V) and H in P(S^2 V^*), where V is the vector space such that P^4 =P(V). Take a general 4-plane P in

P(S^2 V^*) and let P' be the orthogonal space to P in P(S^2 V). Then X:=Chow^2 P^4 ¥cap P' is a smooth Calabi-Yau 3-fold, and there exists a natural double cover Y -> H¥cap P with a smooth Calabi-Yau 3-fold Y. It is easy to check

that X and Y are not birational each other.

Our main result asserts the derived equivalence of X and Y. This derived equivalence is given by the Fourier Mukai functor D(X)-> D(Y) whose kernel is the ideal sheaf in X×Y of a flat family of curves on Y parameterized by X.

Curves on Y in this family have degree 5 and arithmetic genus 3, and these have a nice interpretation by a BPS number of Y. The proof of the derived equivalence is slightly involved so I explain a similar result in the case where n=3. In this case, we obtain a fully faithful functor from D(X)-> D(Y), where X is a so called the Reye congruence Enriques surface and Y is the 'big resolution' of the Artin-Mumford quartic double solid.

This is a joint work with Shinobu Hosono.

It is well-known that the projective dual of the second Veronese variety v_2(P^n) is the symmetric determinantal hypersurface H. However, in the context of homological projective duality after Kuznetsov, it is natural to consider that the Chow^2 P^n and H are dual (note that Chow^2 P^n is the secant variety of v_2(P^n)).

Though we did not yet formulate what this duality exactly means in full generality, we show some results in this context for the values n¥leq 4.

For example, let n=4. We consider Chow^2 P^4 in P(S^2 V) and H in P(S^2 V^*), where V is the vector space such that P^4 =P(V). Take a general 4-plane P in

P(S^2 V^*) and let P' be the orthogonal space to P in P(S^2 V). Then X:=Chow^2 P^4 ¥cap P' is a smooth Calabi-Yau 3-fold, and there exists a natural double cover Y -> H¥cap P with a smooth Calabi-Yau 3-fold Y. It is easy to check

that X and Y are not birational each other.

Our main result asserts the derived equivalence of X and Y. This derived equivalence is given by the Fourier Mukai functor D(X)-> D(Y) whose kernel is the ideal sheaf in X×Y of a flat family of curves on Y parameterized by X.

Curves on Y in this family have degree 5 and arithmetic genus 3, and these have a nice interpretation by a BPS number of Y. The proof of the derived equivalence is slightly involved so I explain a similar result in the case where n=3. In this case, we obtain a fully faithful functor from D(X)-> D(Y), where X is a so called the Reye congruence Enriques surface and Y is the 'big resolution' of the Artin-Mumford quartic double solid.

#### Seminar on Geometric Complex Analysis

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

On the classification of CR mappings between generalized pseudoellipsoids (JAPANESE)

**Atsushi Hayashimoto**(Nagano National College of Technology)On the classification of CR mappings between generalized pseudoellipsoids (JAPANESE)

### 2011/04/20

#### PDE Real Analysis Seminar

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

Stochastic power law fluids (JAPANESE)

http://www.math.kyoto-u.ac.jp/~nobuo/

**Yoshida, Nobuo**(Department of Mathematics, Kyoto University)Stochastic power law fluids (JAPANESE)

[ Abstract ]

This talk is based in part on a joint work with Yutaka Terasawa.

We consider a SPDE (stochastic partial differential equation) which describes the velocity field of a viscous, incompressible non-Newtonian fluid subject to a random force.

Here, the extra stress tensor of the fluid is given by a polynomial of degree $p-1$ of the rate of strain tensor, while the colored noise is considered as a random force.

We first investigate the existence and the uniqueness of weak solutions to this SPDE.

We next turn to the special case: $p \\in [1 + {d \\over 2},{2d\\overd-2})$,

where $d$ is the dimension of the space. We prove there that the Galerkin scheme approximates the velocity field in a strong sense. As a consequence, we establish the energy equality for the velocity field.

[ Reference URL ]This talk is based in part on a joint work with Yutaka Terasawa.

We consider a SPDE (stochastic partial differential equation) which describes the velocity field of a viscous, incompressible non-Newtonian fluid subject to a random force.

Here, the extra stress tensor of the fluid is given by a polynomial of degree $p-1$ of the rate of strain tensor, while the colored noise is considered as a random force.

We first investigate the existence and the uniqueness of weak solutions to this SPDE.

We next turn to the special case: $p \\in [1 + {d \\over 2},{2d\\overd-2})$,

where $d$ is the dimension of the space. We prove there that the Galerkin scheme approximates the velocity field in a strong sense. As a consequence, we establish the energy equality for the velocity field.

http://www.math.kyoto-u.ac.jp/~nobuo/

### 2011/04/18

#### Algebraic Geometry Seminar

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

Ideal-adic semi-continuity problem for minimal log discrepancies (JAPANESE)

**Masayuki Kawakita**(Research Institute for Mathematical Sciences, Kyoto University)Ideal-adic semi-continuity problem for minimal log discrepancies (JAPANESE)

[ Abstract ]

De Fernex, Ein and Mustaţă, after Kollár, proved the ideal-adic semi-continuity of log canonicity to obtain Shokurov's ACC conjecture for log canonical thresholds on l.c.i. varieties. I discuss its generalisation to minimal log discrepancies, proposed by Mustaţă.

De Fernex, Ein and Mustaţă, after Kollár, proved the ideal-adic semi-continuity of log canonicity to obtain Shokurov's ACC conjecture for log canonical thresholds on l.c.i. varieties. I discuss its generalisation to minimal log discrepancies, proposed by Mustaţă.

#### Seminar on Geometric Complex Analysis

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

Asymptotic cohomology vanishing and a converse of the Andreotti-Grauert theorem on surface (JAPANESE)

**Shinichi Matsumura**(University of Tokyo)Asymptotic cohomology vanishing and a converse of the Andreotti-Grauert theorem on surface (JAPANESE)

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