## Seminar information archive

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

### 2015/06/03

#### Operator Algebra Seminars

16:45-18:15 Room #122 (Graduate School of Math. Sci. Bldg.)

The Furstenberg boundary and $C^*$-simplicity

**Narutaka Ozawa**(RIMS, Kyoto Univ.)The Furstenberg boundary and $C^*$-simplicity

#### Mathematical Biology Seminar

14:55-16:40 Room #128演習室 (Graduate School of Math. Sci. Bldg.)

Population dynamics of fish stock with migration and its management strategy

**Shigehide Iwata**(The graduate school of marine science and technology, Tokyo University of Marine Science and Technology)Population dynamics of fish stock with migration and its management strategy

### 2015/06/01

#### Algebraic Geometry Seminar

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

Rank 2 weak Fano bundles on cubic 3-folds (日本語)

**Daizo Ishikawa**(Waseda University)Rank 2 weak Fano bundles on cubic 3-folds (日本語)

[ Abstract ]

A vector bundle on a projective variety is called weak Fano if its

projectivization is a weak Fano manifold. This is a generalization of

Fano bundles.

In this talk, we will obtain a classification of rank 2 weak Fano

bundles on a nonsingular cubic hypersurface in a projective 4-space.

Specifically, we will show that there exist rank 2 indecomposable weak

Fano bundles on it.

A vector bundle on a projective variety is called weak Fano if its

projectivization is a weak Fano manifold. This is a generalization of

Fano bundles.

In this talk, we will obtain a classification of rank 2 weak Fano

bundles on a nonsingular cubic hypersurface in a projective 4-space.

Specifically, we will show that there exist rank 2 indecomposable weak

Fano bundles on it.

#### Tokyo Probability Seminar

16:50-18:20 Room #128 (Graduate School of Math. Sci. Bldg.)

**Masato Hoshino**(Graduate School of Mathematical Sciences, The University of Tokyo)### 2015/05/28

#### Infinite Analysis Seminar Tokyo

17:00-18:30 Room #002 (Graduate School of Math. Sci. Bldg.)

Unitary spherical representations of Drinfeld doubles (JAPANESE)

**Yuki Arano**(Graduate School of Mathematical Sciences, the University of Tokyo)Unitary spherical representations of Drinfeld doubles (JAPANESE)

[ Abstract ]

It is known that the Drinfeld double of the quantized

enveloping algebra of a semisimple Lie algebra looks similar to the

quantized enveloping algebra of the complexification of the Lie algebra.

In this talk, we investigate the unitary representation theory of such

Drinfeld double via its analogy to that of the complex Lie group.

We also talk on an application to operator algebras.

It is known that the Drinfeld double of the quantized

enveloping algebra of a semisimple Lie algebra looks similar to the

quantized enveloping algebra of the complexification of the Lie algebra.

In this talk, we investigate the unitary representation theory of such

Drinfeld double via its analogy to that of the complex Lie group.

We also talk on an application to operator algebras.

### 2015/05/27

#### Operator Algebra Seminars

16:45-18:15 Room #122 (Graduate School of Math. Sci. Bldg.)

Vertex operator algebras in umbral Moonshine

**John F. R. Duncan**(Case Western Reserve Univ.)Vertex operator algebras in umbral Moonshine

#### Number Theory Seminar

17:00-18:00 Room #056 (Graduate School of Math. Sci. Bldg.)

On a good reduction criterion for polycurves with sections (Japanese)

**Ippei Nagamachi**(University of Tokyo)On a good reduction criterion for polycurves with sections (Japanese)

### 2015/05/26

#### Lie Groups and Representation Theory

17:00-18:30 Room #122 (Graduate School of Math. Sci. Bldg.)

Local functional equations of Clifford quartic forms and homaloidal EKP-polynomials

**Takeyoshi Kogiso**(Josai University)Local functional equations of Clifford quartic forms and homaloidal EKP-polynomials

[ Abstract ]

It is known that one can associate local functional equation to the irreducible relative invariant of an irreducible regular prehomogeneous vector spaces. We construct Clifford quartic forms that cannot obtained from prehomogeneous vector spaces, but, for which one can associate local functional equations. The characterization of polynomials which satisfy local functional equations is an interesting problem. In relation to this characterization problem (in a more general form), Etingof, Kazhdan and Polishchuk raised a conjecture. We make a counter example of this conjecture from Clifford quartic forms. (This is based on the joint work with F.Sato)

It is known that one can associate local functional equation to the irreducible relative invariant of an irreducible regular prehomogeneous vector spaces. We construct Clifford quartic forms that cannot obtained from prehomogeneous vector spaces, but, for which one can associate local functional equations. The characterization of polynomials which satisfy local functional equations is an interesting problem. In relation to this characterization problem (in a more general form), Etingof, Kazhdan and Polishchuk raised a conjecture. We make a counter example of this conjecture from Clifford quartic forms. (This is based on the joint work with F.Sato)

#### Tuesday Seminar on Topology

17:00-18:30 Room #056 (Graduate School of Math. Sci. Bldg.)

Introduction to formalization of topology using a proof assistant. (JAPANESE)

**Ken'ichi Kuga**(Chiba University)Introduction to formalization of topology using a proof assistant. (JAPANESE)

[ Abstract ]

Although the program of formalization goes back to David

Hilbert, it is only recently that we can actually formalize

substantial theorems in modern mathematics. It is made possible by the

development of certain type theory and a computer software called a

proof assistant. We begin this talk by showing our formalization of

some basic geometric topology using a proof assistant COQ. Then we

introduce homotopy type theory (HoTT) of Voevodsky et al., which

interprets type theory from abstract homotopy theoretic perspective.

HoTT proposes "univalent" foundation of mathematics which is

particularly suited for computer formalization.

Although the program of formalization goes back to David

Hilbert, it is only recently that we can actually formalize

substantial theorems in modern mathematics. It is made possible by the

development of certain type theory and a computer software called a

proof assistant. We begin this talk by showing our formalization of

some basic geometric topology using a proof assistant COQ. Then we

introduce homotopy type theory (HoTT) of Voevodsky et al., which

interprets type theory from abstract homotopy theoretic perspective.

HoTT proposes "univalent" foundation of mathematics which is

particularly suited for computer formalization.

### 2015/05/25

#### Seminar on Geometric Complex Analysis

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

On uniform K-stability (Japanese)

**Tomoyuki Hisamoto**(Nagoya Univ.)On uniform K-stability (Japanese)

[ Abstract ]

It is a joint work with Sébastien Boucksom and Mattias Jonsson. We first introduce functionals on the space of test configurations, as non-Archimedean analogues of classical functionals on the space of Kähler metrics. Then, uniform K-stability is defined as a counterpart of K-energy's coercivity condition. Finally, reproving and strengthening Y. Odaka's results, we study uniform K-stability of Kähler-Einstein manifolds.

It is a joint work with Sébastien Boucksom and Mattias Jonsson. We first introduce functionals on the space of test configurations, as non-Archimedean analogues of classical functionals on the space of Kähler metrics. Then, uniform K-stability is defined as a counterpart of K-energy's coercivity condition. Finally, reproving and strengthening Y. Odaka's results, we study uniform K-stability of Kähler-Einstein manifolds.

#### Algebraic Geometry Seminar

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

Good reduction of K3 surfaces (日本語 or English)

https://www.ms.u-tokyo.ac.jp/~ymatsu/index_j.html

**Yuya Matsumoto**(University of Tokyo)Good reduction of K3 surfaces (日本語 or English)

[ Abstract ]

We consider degeneration of K3 surfaces over a 1-dimensional base scheme

of mixed characteristic (e.g. Spec of the p-adic integers).

Under the assumption of potential semistable reduction, we first prove

that a trivial monodromy action on the l-adic etale cohomology group

implies potential good reduction, where potential means that we allow a

finite base extension.

Moreover we show that a finite etale base change suffices.

The proof for the first part involves a mixed characteristic

3-dimensional MMP (Kawamata) and the classification of semistable

degeneration of K3 surfaces (Kulikov, Persson--Pinkham, Nakkajima).

For the second part, we consider flops and descent arguments. This is a joint work with Christian Liedtke.

[ Reference URL ]We consider degeneration of K3 surfaces over a 1-dimensional base scheme

of mixed characteristic (e.g. Spec of the p-adic integers).

Under the assumption of potential semistable reduction, we first prove

that a trivial monodromy action on the l-adic etale cohomology group

implies potential good reduction, where potential means that we allow a

finite base extension.

Moreover we show that a finite etale base change suffices.

The proof for the first part involves a mixed characteristic

3-dimensional MMP (Kawamata) and the classification of semistable

degeneration of K3 surfaces (Kulikov, Persson--Pinkham, Nakkajima).

For the second part, we consider flops and descent arguments. This is a joint work with Christian Liedtke.

https://www.ms.u-tokyo.ac.jp/~ymatsu/index_j.html

#### Tokyo Probability Seminar

16:50-18:20 Room #128 (Graduate School of Math. Sci. Bldg.)

A finite diameter theorem on RCD spaces

**Yu Kitabeppu**(Graduate School of Sciences, Kyoto University)A finite diameter theorem on RCD spaces

### 2015/05/21

#### Lectures

16:00-17:00 Room #056 (Graduate School of Math. Sci. Bldg.)

The Shape of Data

(ENGLISH)

http://faculty.ms.u-tokyo.ac.jp/Carlsson.html

**Gunnar Carlsson**(Stanford University, Ayasdi INC)The Shape of Data

(ENGLISH)

[ Abstract ]

There is a tremendous amount of attention being paid to the notion of

"Big Data". In many situations, however, the problem is not so much the

size of the data but rather its complexity. This observation shows that

it is now important to find methods for representing complex data in a

compressed and understandable fashion. Representing data by shapes

turns out to be useful in many situations, and therefore topology, the

mathematical sub discipline which studies shape, becomes quite

relevant. There is now a collection of methods based on topology for

analyzing complex data, and in this talk we will discuss these methods,

with numerous examples.

[ Reference URL ]There is a tremendous amount of attention being paid to the notion of

"Big Data". In many situations, however, the problem is not so much the

size of the data but rather its complexity. This observation shows that

it is now important to find methods for representing complex data in a

compressed and understandable fashion. Representing data by shapes

turns out to be useful in many situations, and therefore topology, the

mathematical sub discipline which studies shape, becomes quite

relevant. There is now a collection of methods based on topology for

analyzing complex data, and in this talk we will discuss these methods,

with numerous examples.

http://faculty.ms.u-tokyo.ac.jp/Carlsson.html

### 2015/05/20

#### Number Theory Seminar

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

Colmez' conjecture in average (English)

**Shou-Wu Zhang**(Princeton University)Colmez' conjecture in average (English)

[ Abstract ]

This is a report on a joint work with Xinyi Yuan on a conjectured formula of Colmez about the Faltings heights of CM abelian varieties. I will sketch a deduction of this formula in average of CM types from our early work on Gross-Zagier formula. When combined with a recent work of Tsimerman, this result implies the Andre-Oort conjecture for the moduli of abelian varieties.

Our method is different than a recently announced proof of a weaker form of the average formula by Andreatta, Howard, Goren, and Madapusi Pera: we use neither high dimensional Shimura varieties nor Borcherds' liftings.

This is a report on a joint work with Xinyi Yuan on a conjectured formula of Colmez about the Faltings heights of CM abelian varieties. I will sketch a deduction of this formula in average of CM types from our early work on Gross-Zagier formula. When combined with a recent work of Tsimerman, this result implies the Andre-Oort conjecture for the moduli of abelian varieties.

Our method is different than a recently announced proof of a weaker form of the average formula by Andreatta, Howard, Goren, and Madapusi Pera: we use neither high dimensional Shimura varieties nor Borcherds' liftings.

#### Operator Algebra Seminars

16:45-18:15 Room #122 (Graduate School of Math. Sci. Bldg.)

Unique prime factorization and bicentralizer problem for a class of type III factors

**Yusuke Isono**(RIMS, Kyoto Univ.)Unique prime factorization and bicentralizer problem for a class of type III factors

### 2015/05/19

#### PDE Real Analysis Seminar

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

Convex bodies and geometry of some associated Minkowski functionals (日本語)

**Sumio Yamada**(Gakushuin University)Convex bodies and geometry of some associated Minkowski functionals (日本語)

[ Abstract ]

In this talk, we will investigate the construction of so-called Hilbert metric, as well as Funk metric, defined on convex set from a new variational viewpoint. The local and global aspects of the geometry of the resulting Minkowski functionals will be contrasted. As an application, some remarks on the Perron-Frobenius theorem will be made. Part of the project is a joint work with Athanase Papadopoulos (Strasbourg).

In this talk, we will investigate the construction of so-called Hilbert metric, as well as Funk metric, defined on convex set from a new variational viewpoint. The local and global aspects of the geometry of the resulting Minkowski functionals will be contrasted. As an application, some remarks on the Perron-Frobenius theorem will be made. Part of the project is a joint work with Athanase Papadopoulos (Strasbourg).

#### Lie Groups and Representation Theory

17:00-18:30 Room #122 (Graduate School of Math. Sci. Bldg.)

RoCK blocks, wreath products and KLR algebras (English)

**Anton Evseev**(University of Birmingham)RoCK blocks, wreath products and KLR algebras (English)

[ Abstract ]

The so-called RoCK (or Rouquier) blocks play an important role in representation theory of symmetric groups over a finite field of characteristic $p$, as well as of Hecke algebras at roots of unity. Turner has conjectured that a certain idempotent truncation of a RoCK block is Morita equivalent to the principal block $B_0$ of the wreath product $S_p\wr S_d$ of symmetric groups, where $d$ is the "weight" of the block. The talk will outline a proof of this conjecture, which generalizes a result of Chuang-Kessar proved for $d < p$. The proof uses an isomorphism between a Hecke algebra at a root of unity and a cyclotomic Khovanov-Lauda-Rouquier algebra, the resulting grading on the Hecke algebra and the ideas behind a construction of R-matrices for modules over KLR algebras due to Kang-Kashiwara-Kim.

The so-called RoCK (or Rouquier) blocks play an important role in representation theory of symmetric groups over a finite field of characteristic $p$, as well as of Hecke algebras at roots of unity. Turner has conjectured that a certain idempotent truncation of a RoCK block is Morita equivalent to the principal block $B_0$ of the wreath product $S_p\wr S_d$ of symmetric groups, where $d$ is the "weight" of the block. The talk will outline a proof of this conjecture, which generalizes a result of Chuang-Kessar proved for $d < p$. The proof uses an isomorphism between a Hecke algebra at a root of unity and a cyclotomic Khovanov-Lauda-Rouquier algebra, the resulting grading on the Hecke algebra and the ideas behind a construction of R-matrices for modules over KLR algebras due to Kang-Kashiwara-Kim.

#### Tuesday Seminar on Topology

17:00-18:30 Room #056 (Graduate School of Math. Sci. Bldg.)

Quiver mutation loops and partition q-series (JAPANESE)

**Akishi Kato**(The University of Tokyo)Quiver mutation loops and partition q-series (JAPANESE)

[ Abstract ]

Quivers and their mutations are ubiquitous in mathematics and

mathematical physics; they play a key role in cluster algebras,

wall-crossing phenomena, gluing of ideal tetrahedra, etc.

Recently, we introduced a partition q-series for a quiver mutation loop

(a loop in a quiver exchange graph) using the idea of state sum of statistical

mechanics. The partition q-series enjoy some nice properties such

as pentagon move invariance. We also discuss their relation with combinatorial

Donaldson-Thomas invariants, as well as fermionic character formulas of

certain conformal field theories.

This is a joint work with Yuji Terashima.

Quivers and their mutations are ubiquitous in mathematics and

mathematical physics; they play a key role in cluster algebras,

wall-crossing phenomena, gluing of ideal tetrahedra, etc.

Recently, we introduced a partition q-series for a quiver mutation loop

(a loop in a quiver exchange graph) using the idea of state sum of statistical

mechanics. The partition q-series enjoy some nice properties such

as pentagon move invariance. We also discuss their relation with combinatorial

Donaldson-Thomas invariants, as well as fermionic character formulas of

certain conformal field theories.

This is a joint work with Yuji Terashima.

### 2015/05/18

#### Seminar on Geometric Complex Analysis

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

On a global estimate of the Diederich–Fornaess index of Levi-flat real hypersurfaces (Japanese)

**Masanori Adachi**(Tokyo Univ. of Science)On a global estimate of the Diederich–Fornaess index of Levi-flat real hypersurfaces (Japanese)

[ Abstract ]

We give yet another proof for a global estimate of the Diederich-Fornaess index of relatively compact domains with Levi-flat boundary, namely, the index must be smaller than or equal to the reciprocal of the dimension of the ambient space. Although the Diederich-Fornaess index is originally defined for relatively compact domains in complex manifolds, our formulation reveals that it makes sense for abstract Levi-flat CR manifolds.

We give yet another proof for a global estimate of the Diederich-Fornaess index of relatively compact domains with Levi-flat boundary, namely, the index must be smaller than or equal to the reciprocal of the dimension of the ambient space. Although the Diederich-Fornaess index is originally defined for relatively compact domains in complex manifolds, our formulation reveals that it makes sense for abstract Levi-flat CR manifolds.

#### Algebraic Geometry Seminar

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

Twists and braids for general 3-fold flops (English)

http://db.ipmu.jp/member/personal/4007en.html

**Will Donovan**(IPMU)Twists and braids for general 3-fold flops (English)

[ Abstract ]

When a 3-fold contains a floppable rational curve, a theorem of Bridgeland provides a derived equivalence between the 3-fold and its flop. I will discuss recent joint work with Michael Wemyss, showing that these flop functors satisfy Coxeter-type braid relations. Using this result, we construct an action of a braid-type group on the derived category of the 3-fold. This group arises from the topology of a certain simplicial hyperplane arrangement, determined by the local geometry of the curve. I will give examples and explain key elements in the construction, including the noncommutative deformations of curves introduced in our previous work.

[ Reference URL ]When a 3-fold contains a floppable rational curve, a theorem of Bridgeland provides a derived equivalence between the 3-fold and its flop. I will discuss recent joint work with Michael Wemyss, showing that these flop functors satisfy Coxeter-type braid relations. Using this result, we construct an action of a braid-type group on the derived category of the 3-fold. This group arises from the topology of a certain simplicial hyperplane arrangement, determined by the local geometry of the curve. I will give examples and explain key elements in the construction, including the noncommutative deformations of curves introduced in our previous work.

http://db.ipmu.jp/member/personal/4007en.html

#### Numerical Analysis Seminar

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

Accurate matrix multiplication by error-free transformation (日本語)

**Katsuhisa Ozaki**(Shibaura Institute of Technology)Accurate matrix multiplication by error-free transformation (日本語)

#### Tokyo Probability Seminar

16:50-18:20 Room #128 (Graduate School of Math. Sci. Bldg.)

Central limit theorem for stochastic heat equations in random environments

**Lu Xu**(Graduate School of Mathematical Sciences, The University of Tokyo)Central limit theorem for stochastic heat equations in random environments

### 2015/05/14

#### Applied Analysis

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

Strong instability of standing waves for some nonlinear Schr\"odinger equations (Japanese)

**Masahito Ohta**(Tokyo University of Science)Strong instability of standing waves for some nonlinear Schr\"odinger equations (Japanese)

### 2015/05/13

#### Operator Algebra Seminars

16:45-18:15 Room #122 (Graduate School of Math. Sci. Bldg.)

Controlled topological phases and the bulk-edge correspondence for

topological insulators (English)

**Yosuke Kubota**(Univ. Tokyo)Controlled topological phases and the bulk-edge correspondence for

topological insulators (English)

### 2015/05/12

#### Tuesday Seminar of Analysis

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

Convergence of the Allen-Cahn equation with constraint to Brakke's mean curvature flow (Japanese)

**Keisuke Takasao**(Graduate School of Mathematical Sciences, the University of Tokyo)Convergence of the Allen-Cahn equation with constraint to Brakke's mean curvature flow (Japanese)

[ Abstract ]

In this talk we consider the Allen-Cahn equation with constraint. In 1994, Chen and Elliott studied the asymptotic behavior of the solution of the Allen-Cahn equation with constraint. They proved that the zero level set of the solution converges to the classical solution of the mean curvature flow under the suitable conditions on initial data. In 1993, Ilmanen proved the existence of the mean curvature flow via the Allen-Cahn equation without constraint in the sense of Brakke. We proved the same conclusion for the Allen-Cahn equation with constraint.

In this talk we consider the Allen-Cahn equation with constraint. In 1994, Chen and Elliott studied the asymptotic behavior of the solution of the Allen-Cahn equation with constraint. They proved that the zero level set of the solution converges to the classical solution of the mean curvature flow under the suitable conditions on initial data. In 1993, Ilmanen proved the existence of the mean curvature flow via the Allen-Cahn equation without constraint in the sense of Brakke. We proved the same conclusion for the Allen-Cahn equation with constraint.

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