## Seminar information archive

Seminar information archive ～02/20｜Today's seminar 02/21 | Future seminars 02/22～

### 2012/06/04

#### Algebraic Geometry Seminar

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

Smooth P1-fibrations and Campana-Peternell conjecture (ENGLISH)

**Kiwamu Watanabe**(Saitama University)Smooth P1-fibrations and Campana-Peternell conjecture (ENGLISH)

[ Abstract ]

We give a complete classification of smooth P1-fibrations

over projective manifolds of Picard number 1 each of which admit another

smooth morphism of relative dimension one.

Furthermore, we consider relations of the result with Campana-Peternell conjecture

on Fano manifolds with nef tangent bundle.

We give a complete classification of smooth P1-fibrations

over projective manifolds of Picard number 1 each of which admit another

smooth morphism of relative dimension one.

Furthermore, we consider relations of the result with Campana-Peternell conjecture

on Fano manifolds with nef tangent bundle.

#### Seminar on Geometric Complex Analysis

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

Log-plurisubharmonicity of metric deformations induced by Schiffer and harmonic spans. (JAPANESE)

**Sachiko HAMANO**(Fukushima University)Log-plurisubharmonicity of metric deformations induced by Schiffer and harmonic spans. (JAPANESE)

### 2012/06/01

#### GCOE lecture series

14:00-15:30 Room #118 (Graduate School of Math. Sci. Bldg.)

Derived categories and cohomological invariants I (ENGLISH)

**Mihnea Popa**(University of Illinois at Chicago)Derived categories and cohomological invariants I (ENGLISH)

[ Abstract ]

(Abstract for both Parts I and II)

I will discuss results on the derived invariance of various cohomological quantities, like the Hodge numbers, a twisted version of Hochschild cohomology, the Picard variety, and cohomological support loci. I will include a small discussion of current work on orbifolds if time permits.

(Abstract for both Parts I and II)

I will discuss results on the derived invariance of various cohomological quantities, like the Hodge numbers, a twisted version of Hochschild cohomology, the Picard variety, and cohomological support loci. I will include a small discussion of current work on orbifolds if time permits.

### 2012/05/31

#### Seminar on Probability and Statistics

14:50-16:05 Room #006 (Graduate School of Math. Sci. Bldg.)

Holonomic gradient methods for likelihood computation (JAPANESE)

[ Reference URL ]

http://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2012/05.html

**SEI, Tomonari**(Department of Mathematics, Keio University)Holonomic gradient methods for likelihood computation (JAPANESE)

[ Reference URL ]

http://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2012/05.html

### 2012/05/30

#### Number Theory Seminar

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

Kernel of the monodromy operator for semistable curves (ENGLISH)

**Valentina Di Proietto**(University of Tokyo)Kernel of the monodromy operator for semistable curves (ENGLISH)

[ Abstract ]

For a semistable curve, we study the action of the monodromy operator on the first log-crystalline cohomology group. In particular we examine the relation between the kernel of the monodromy operator and the first rigid cohomology group, in the case of trivial coefficients, giving a new proof of a theorem of B. Chiarellotto and in the case of certain unipotent F-isocrystals as coefficients.

This is a joint work in progress with B. Chiarellotto, R. Coleman and A. Iovita.

For a semistable curve, we study the action of the monodromy operator on the first log-crystalline cohomology group. In particular we examine the relation between the kernel of the monodromy operator and the first rigid cohomology group, in the case of trivial coefficients, giving a new proof of a theorem of B. Chiarellotto and in the case of certain unipotent F-isocrystals as coefficients.

This is a joint work in progress with B. Chiarellotto, R. Coleman and A. Iovita.

#### Lectures

14:50-16:20 Room #123 (Graduate School of Math. Sci. Bldg.)

Low-discrepancy sequences and algebraic curves over finite fields (III) (ENGLISH)

[ Reference URL ]

http://www.ms.u-tokyo.ac.jp/~matumoto/WORKSHOP/workshop2012.html

**Harald Niederreiter**(RICAM, Austrian Academy of Sciences)Low-discrepancy sequences and algebraic curves over finite fields (III) (ENGLISH)

[ Reference URL ]

http://www.ms.u-tokyo.ac.jp/~matumoto/WORKSHOP/workshop2012.html

### 2012/05/29

#### Tuesday Seminar on Topology

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

Triple linking numbers and triple point numbers

of torus-covering $T^2$-links

(JAPANESE)

**Inasa Nakamura**(Gakushuin University, JSPS)Triple linking numbers and triple point numbers

of torus-covering $T^2$-links

(JAPANESE)

[ Abstract ]

The triple linking number of an oriented surface link was defined as an

analogical notion of the linking number of a classical link. A

torus-covering $T^2$-link $\\mathcal{S}_m(a,b)$ is a surface link in the

form of an unbranched covering over the standard torus, determined from

two commutative $m$-braids $a$ and $b$.

In this talk, we consider $\\mathcal{S}_m(a,b)$ when $a$, $b$ are pure

$m$-braids ($m \\geq 3$), which is a surface link with $m$-components. We

present the triple linking number of $\\mathcal{S}_m(a,b)$ by using the

linking numbers of the closures of $a$ and $b$. This gives a lower bound

of the triple point number. In some cases, we can determine the triple

point numbers, each of which is a multiple of four.

The triple linking number of an oriented surface link was defined as an

analogical notion of the linking number of a classical link. A

torus-covering $T^2$-link $\\mathcal{S}_m(a,b)$ is a surface link in the

form of an unbranched covering over the standard torus, determined from

two commutative $m$-braids $a$ and $b$.

In this talk, we consider $\\mathcal{S}_m(a,b)$ when $a$, $b$ are pure

$m$-braids ($m \\geq 3$), which is a surface link with $m$-components. We

present the triple linking number of $\\mathcal{S}_m(a,b)$ by using the

linking numbers of the closures of $a$ and $b$. This gives a lower bound

of the triple point number. In some cases, we can determine the triple

point numbers, each of which is a multiple of four.

#### GCOE lecture series

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

Random walk on reductive groups. (ENGLISH)

**Yves Benoist**(CNRS, Orsay)Random walk on reductive groups. (ENGLISH)

[ Abstract ]

The asymptotic behavior of the sum of real numbers chosen independantly with same probability law is controled by many classical theorems: Law of Large Numbers, Central Limit Theorem, Law of Iterated Logarithm, Local Limit Theorem, Large deviation Principle, 0-1 Law,... In these introductory talks I will recall these classical results and explain their analogs for products of matrices chosen independantly with same probability law, when the action of the support of the law is semisimple. We will see that the dynamics of the corresponding action on the flag variety is a crucial tool for studying these non-commutative random walks.

The asymptotic behavior of the sum of real numbers chosen independantly with same probability law is controled by many classical theorems: Law of Large Numbers, Central Limit Theorem, Law of Iterated Logarithm, Local Limit Theorem, Large deviation Principle, 0-1 Law,... In these introductory talks I will recall these classical results and explain their analogs for products of matrices chosen independantly with same probability law, when the action of the support of the law is semisimple. We will see that the dynamics of the corresponding action on the flag variety is a crucial tool for studying these non-commutative random walks.

#### Lectures

14:50-16:20 Room #123 (Graduate School of Math. Sci. Bldg.)

Low-discrepancy sequences and algebraic curves over finite fields (II) (ENGLISH)

[ Reference URL ]

http://www.ms.u-tokyo.ac.jp/~matumoto/WORKSHOP/workshop2012.html

**Harald Niederreiter**(RICAM, Austrian Academy of Sciences)Low-discrepancy sequences and algebraic curves over finite fields (II) (ENGLISH)

[ Reference URL ]

http://www.ms.u-tokyo.ac.jp/~matumoto/WORKSHOP/workshop2012.html

### 2012/05/28

#### Seminar on Geometric Complex Analysis

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

Local cohomology and hypersurface isolated singularities II (JAPANESE)

**Shinichi TAJIMA**(University of Tsukuba)Local cohomology and hypersurface isolated singularities II (JAPANESE)

[ Abstract ]

局所コホモロジーの孤立特異点への応用として

・$\mu$-constant-deformation の Tjurina 数

・対数的ベクトル場の構造と構成法

・ニュートン非退化な超曲面に対する Kouchnirenko の公式

について述べる.

局所コホモロジーの孤立特異点への応用として

・$\mu$-constant-deformation の Tjurina 数

・対数的ベクトル場の構造と構成法

・ニュートン非退化な超曲面に対する Kouchnirenko の公式

について述べる.

#### Algebraic Geometry Seminar

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

Generic vanishing and linearity via Hodge modules (ENGLISH)

**Mihnea Popa**(University of Illinois at Chicago)Generic vanishing and linearity via Hodge modules (ENGLISH)

[ Abstract ]

I will explain joint work with Christian Schnell, in which we extend the fundamental results of generic vanishing theory (for instance for the canonical bundle of a smooth projective variety) to bundles of holomorphic forms and to rank one local systems, where parts of the theory have eluded previous efforts. To achiever this, we bring all of the old and new results under the same roof by enlarging the scope of generic vanishing theory to the study of filtered D-modules associated to mixed Hodge modules. Besides Saito's vanishing and direct image theorems for Hodge modules, an important input is the Laumon-Rothstein Fourier transform for bundles with integrable connection.

I will explain joint work with Christian Schnell, in which we extend the fundamental results of generic vanishing theory (for instance for the canonical bundle of a smooth projective variety) to bundles of holomorphic forms and to rank one local systems, where parts of the theory have eluded previous efforts. To achiever this, we bring all of the old and new results under the same roof by enlarging the scope of generic vanishing theory to the study of filtered D-modules associated to mixed Hodge modules. Besides Saito's vanishing and direct image theorems for Hodge modules, an important input is the Laumon-Rothstein Fourier transform for bundles with integrable connection.

#### Lectures

14:50-16:20 Room #123 (Graduate School of Math. Sci. Bldg.)

Low-discrepancy sequences and algebraic curves over finite fields (I) (ENGLISH)

http://www.ms.u-tokyo.ac.jp/~matumoto/WORKSHOP/workshop2012.html

**Harald Niederreiter**(RICAM, Austrian Academy of Sciences)Low-discrepancy sequences and algebraic curves over finite fields (I) (ENGLISH)

[ Abstract ]

This is the second of the four lectures. The first one is Colloquium talk on May 25th 16:30--17:30 at 002.

Abstract from Colloquium:

Quasi-Monte Carlo (QMC) methods are deterministic analogs of statistical Monte Carlo

methods in computational mathematics. QMC methods employ evenly distributed

low-discrepancy sequences instead of the random samples used in Monte Carlo methods.

For many types of computational problems, QMC methods are more efficient than

Monte Carlo methods. After a general introduction to QMC methods, the talk focuses

on the problem of constructing low-discrepancy sequences which has fascinating links

with subjects such as finite fields, error-correcting codes, and algebraic curves.

[ Reference URL ]This is the second of the four lectures. The first one is Colloquium talk on May 25th 16:30--17:30 at 002.

Abstract from Colloquium:

Quasi-Monte Carlo (QMC) methods are deterministic analogs of statistical Monte Carlo

methods in computational mathematics. QMC methods employ evenly distributed

low-discrepancy sequences instead of the random samples used in Monte Carlo methods.

For many types of computational problems, QMC methods are more efficient than

Monte Carlo methods. After a general introduction to QMC methods, the talk focuses

on the problem of constructing low-discrepancy sequences which has fascinating links

with subjects such as finite fields, error-correcting codes, and algebraic curves.

http://www.ms.u-tokyo.ac.jp/~matumoto/WORKSHOP/workshop2012.html

### 2012/05/26

#### Harmonic Analysis Komaba Seminar

13:30-17:00 Room #128 (Graduate School of Math. Sci. Bldg.)

The Takagi function - a survey (JAPANESE)

Dyadic, classical and martingale harmonic analysis II (JAPANESE)

**Kiko Kawamura**(University of North Texas) 13:30-15:00The Takagi function - a survey (JAPANESE)

[ Abstract ]

More than a century has passed since Takagi published his simple example of a continuous but nowhere differentiable function,

yet Takagi's function -- as it is now commonly referred

to despite repeated rediscovery

by mathematicians in the West -- continues to inspire, fascinate and puzzle researchers as never before.

In this talk, I will give not only an overview of the history and known characteristics of the function,

but also discuss some of the fascinating applications it has found -- some quite recently! -- in such diverse areas of mathematics as number theory, combinatorics, and analysis.

More than a century has passed since Takagi published his simple example of a continuous but nowhere differentiable function,

yet Takagi's function -- as it is now commonly referred

to despite repeated rediscovery

by mathematicians in the West -- continues to inspire, fascinate and puzzle researchers as never before.

In this talk, I will give not only an overview of the history and known characteristics of the function,

but also discuss some of the fascinating applications it has found -- some quite recently! -- in such diverse areas of mathematics as number theory, combinatorics, and analysis.

**Yutaka Terasawa**(The University of Tokyo) 15:30-17:00Dyadic, classical and martingale harmonic analysis II (JAPANESE)

[ Abstract ]

In a filtered measure space, we investigate the characterization of weights for which positive operators and maximal operators are bounded.

For this, a refinement of Carleson embedding theorem is introduced in this setting. Sawyer type characterization of weights for which a two-weight norm inequality for a generalized Doob's maximal operator holds is established by an application of our Carleson embedding theorem. If time permits, we would like to mention Hyt\\"onen-P\\'erez type sharp one-weight estimate of Doob's

maximal operator which is derived from our two-weight characterization.

This talk is based on a joint work with Professor Hitoshi Tanaka

(The University of Tokyo).

In a filtered measure space, we investigate the characterization of weights for which positive operators and maximal operators are bounded.

For this, a refinement of Carleson embedding theorem is introduced in this setting. Sawyer type characterization of weights for which a two-weight norm inequality for a generalized Doob's maximal operator holds is established by an application of our Carleson embedding theorem. If time permits, we would like to mention Hyt\\"onen-P\\'erez type sharp one-weight estimate of Doob's

maximal operator which is derived from our two-weight characterization.

This talk is based on a joint work with Professor Hitoshi Tanaka

(The University of Tokyo).

### 2012/05/25

#### Colloquium

16:30-17:30 Room #002 (Graduate School of Math. Sci. Bldg.)

Quasi-Monte Carlo methods: deterministic is often better than random (ENGLISH)

http://www.ms.u-tokyo.ac.jp/~matumoto/WORKSHOP/workshop2012.html

**Harald Niederreiter**(RICAM, Austrian Academy of Sciences)Quasi-Monte Carlo methods: deterministic is often better than random (ENGLISH)

[ Abstract ]

Quasi-Monte Carlo (QMC) methods are deterministic analogs of statistical Monte Carlo methods in computational mathematics. QMC methods employ evenly distributed low-discrepancy sequences instead of the random samples used in Monte Carlo methods. For many types of computational problems, QMC methods are more efficient than Monte Carlo methods. After a general introduction to QMC methods, the talk focuses on the problem of constructing low-discrepancy sequences which has fascinating links with subjects such as finite fields, error-correcting codes, and algebraic curves.

This talk also serves as the first talk of the four lecture series. The other three are on 5/28, 5/29, 5/30, 14:50-16:20 at room 123.

[ Reference URL ]Quasi-Monte Carlo (QMC) methods are deterministic analogs of statistical Monte Carlo methods in computational mathematics. QMC methods employ evenly distributed low-discrepancy sequences instead of the random samples used in Monte Carlo methods. For many types of computational problems, QMC methods are more efficient than Monte Carlo methods. After a general introduction to QMC methods, the talk focuses on the problem of constructing low-discrepancy sequences which has fascinating links with subjects such as finite fields, error-correcting codes, and algebraic curves.

This talk also serves as the first talk of the four lecture series. The other three are on 5/28, 5/29, 5/30, 14:50-16:20 at room 123.

http://www.ms.u-tokyo.ac.jp/~matumoto/WORKSHOP/workshop2012.html

#### GCOE lecture series

14:00-15:30 Room #118 (Graduate School of Math. Sci. Bldg.)

Generic vanishing theory and connections with derived categories (ENGLISH)

**Mihnea Popa**(University of Illinois at Chicago)Generic vanishing theory and connections with derived categories (ENGLISH)

[ Abstract ]

I will give a basic introduction to the main results regarding the cohomology of deformations of the canonical bundle, and explain a connection with certain t-structures on the derived categories of Picard varieties. (This will also serve as an introduction for the talk at AG seminar on 5/28, 15:30-17:00.)

I will give a basic introduction to the main results regarding the cohomology of deformations of the canonical bundle, and explain a connection with certain t-structures on the derived categories of Picard varieties. (This will also serve as an introduction for the talk at AG seminar on 5/28, 15:30-17:00.)

### 2012/05/23

#### PDE Real Analysis Seminar

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

$L^p$ Estimates of the Vector Fields and their Applications (ENGLISH)

**Xingfei Xiang**(East China Normal University)$L^p$ Estimates of the Vector Fields and their Applications (ENGLISH)

[ Abstract ]

For $1< p < \\infty$, the estimates of $W^{1,p}$ norm of the vector fields in bounded domains in $\\mathbb R^3$ in terms of their divergence and curl have been well studied. In this talk, we shall present the $L^{{3}/{2}}$ estimates of vector fields with the $L^1$ norm of the $\\curl$ in bounded domains. By a similar discussion, we establish the $L^p$ estimates of the vector fields for $1 < p < \\infty$. As an application of the $L^p$ estimates, the Global $\\dv-\\curl$ lemma in Sobolev spaces of negative indices is given.

For $1< p < \\infty$, the estimates of $W^{1,p}$ norm of the vector fields in bounded domains in $\\mathbb R^3$ in terms of their divergence and curl have been well studied. In this talk, we shall present the $L^{{3}/{2}}$ estimates of vector fields with the $L^1$ norm of the $\\curl$ in bounded domains. By a similar discussion, we establish the $L^p$ estimates of the vector fields for $1 < p < \\infty$. As an application of the $L^p$ estimates, the Global $\\dv-\\curl$ lemma in Sobolev spaces of negative indices is given.

#### Number Theory Seminar

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

Simply connected elliptic surfaces (JAPANESE)

**Kentaro Mitsui**(University of Tokyo)Simply connected elliptic surfaces (JAPANESE)

[ Abstract ]

We characterize simply connected elliptic surfaces by their singular fibers in any characteristic case. To this end, we study orbifolds of curves, local canonical bundle formula, and resolutions of multiple fibers. The result was known for the complex analytic case. Our method can be applied to the rigid analytic case.

We characterize simply connected elliptic surfaces by their singular fibers in any characteristic case. To this end, we study orbifolds of curves, local canonical bundle formula, and resolutions of multiple fibers. The result was known for the complex analytic case. Our method can be applied to the rigid analytic case.

### 2012/05/22

#### Tuesday Seminar of Analysis

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

Viscosity solutions for nonlinear elliptic-parabolic problems (ENGLISH)

**Norbert Pozar**(Graduate School of Mathematical Sciences, The University of Tokyo)Viscosity solutions for nonlinear elliptic-parabolic problems (ENGLISH)

[ Abstract ]

We introduce a notion of viscosity solutions for a general class of

elliptic-parabolic phase transition problems. These include the

Richards equation, which is a classical model in filtration theory.

Existence and uniqueness results are proved via the comparison

principle. In particular, we show existence and stability properties

of maximal and minimal viscosity solutions for a general class of

initial data. These results are new even in the linear case, where we

also show that viscosity solutions coincide with the regular weak

solutions introduced in [Alt&Luckhaus 1983]. This talk is based on a

recent work with Inwon Kim.

We introduce a notion of viscosity solutions for a general class of

elliptic-parabolic phase transition problems. These include the

Richards equation, which is a classical model in filtration theory.

Existence and uniqueness results are proved via the comparison

principle. In particular, we show existence and stability properties

of maximal and minimal viscosity solutions for a general class of

initial data. These results are new even in the linear case, where we

also show that viscosity solutions coincide with the regular weak

solutions introduced in [Alt&Luckhaus 1983]. This talk is based on a

recent work with Inwon Kim.

#### Numerical Analysis Seminar

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

The DtN finite element method and the Schwarz method for multiple scattering problems (JAPANESE)

[ Reference URL ]

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

**Daisuke Koyama**(The University of Electro-Communications)The DtN finite element method and the Schwarz method for multiple scattering problems (JAPANESE)

[ Reference URL ]

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

#### Tuesday Seminar on Topology

17:10-18:10 Room #056 (Graduate School of Math. Sci. Bldg.)

Gamma Integral Structure in Gromov-Witten theory (JAPANESE)

**Hiroshi Iritani**(Kyoto University)Gamma Integral Structure in Gromov-Witten theory (JAPANESE)

[ Abstract ]

The quantum cohomology of a symplectic

manifold undelies a certain integral local system

defined by the Gamma characteristic class.

This local system originates from the natural integral

local sysmem on the B-side under mirror symmetry.

In this talk, I will explain its relationships to the problem

of analytic continuation of Gromov-Witten theoy (potentials),

including crepant resolution conjecture, LG/CY correspondence,

modularity in higher genus theory.

The quantum cohomology of a symplectic

manifold undelies a certain integral local system

defined by the Gamma characteristic class.

This local system originates from the natural integral

local sysmem on the B-side under mirror symmetry.

In this talk, I will explain its relationships to the problem

of analytic continuation of Gromov-Witten theoy (potentials),

including crepant resolution conjecture, LG/CY correspondence,

modularity in higher genus theory.

### 2012/05/21

#### Algebraic Geometry Seminar

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

Characterizations of projective spaces and hyperquadrics

(JAPANESE)

**Taku Suzuki**(Waseda University)Characterizations of projective spaces and hyperquadrics

(JAPANESE)

[ Abstract ]

After Mori's works on Hartshorne's conjecture, many results to

characterize projective spaces and hyperquadrics in terms of

positivity properties of the tangent bundle have been provided.

Kov\\'acs' conjecture states that smooth complex projective

varieties are projective spaces or hyperquadrics if the $p$-th

exterior product of their tangent bundle contains the $p$-th

exterior product of an ample vector bundle. This conjecture is

the generalization of many preceding results. In this talk, I will

explain the idea of the proof of Kov\\'acs' conjecture for varieties

with Picard number one by using a method of slope-stabilities

of sheaves.

After Mori's works on Hartshorne's conjecture, many results to

characterize projective spaces and hyperquadrics in terms of

positivity properties of the tangent bundle have been provided.

Kov\\'acs' conjecture states that smooth complex projective

varieties are projective spaces or hyperquadrics if the $p$-th

exterior product of their tangent bundle contains the $p$-th

exterior product of an ample vector bundle. This conjecture is

the generalization of many preceding results. In this talk, I will

explain the idea of the proof of Kov\\'acs' conjecture for varieties

with Picard number one by using a method of slope-stabilities

of sheaves.

#### Seminar on Geometric Complex Analysis

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

Local cohomology and hypersurface isolated singularities I (JAPANESE)

**Shinichi TAJIMA**(University of Tsukuba)Local cohomology and hypersurface isolated singularities I (JAPANESE)

#### Kavli IPMU Komaba Seminar

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

Topological Strings on Elliptic Fibrations (ENGLISH)

**Emanuel Scheidegger**(The University of Freiburg)Topological Strings on Elliptic Fibrations (ENGLISH)

[ Abstract ]

We will explain a conjecture that expresses the BPS invariants

(Gopakumar-Vafa invariants) for elliptically fibered Calabi-Yau

threefolds in terms of modular forms. In particular, there is a

recursion relation which governs these modular forms. Evidence comes

from the polynomial formulation of the higher genus topological string

amplitudes with insertions.

We will explain a conjecture that expresses the BPS invariants

(Gopakumar-Vafa invariants) for elliptically fibered Calabi-Yau

threefolds in terms of modular forms. In particular, there is a

recursion relation which governs these modular forms. Evidence comes

from the polynomial formulation of the higher genus topological string

amplitudes with insertions.

### 2012/05/19

#### Monthly Seminar on Arithmetic of Automorphic Forms

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

TBA (JAPANESE)

TBA (JAPANESE)

**Takashi Taniguchi**(Kobe Univeristy) 13:30-14:30TBA (JAPANESE)

**Masao Tsuzuki**(Sophia University) 15:00-16:00TBA (JAPANESE)

### 2012/05/18

#### Seminar on Probability and Statistics

14:50-16:00 Room #006 (Graduate School of Math. Sci. Bldg.)

PAC-Bayesian Bound for Gaussian Process Regression and Multiple Kernel Additive Model (JAPANESE)

[ Reference URL ]

http://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2012/04.html

**SUZUKI, Taiji**(University of Tokyo)PAC-Bayesian Bound for Gaussian Process Regression and Multiple Kernel Additive Model (JAPANESE)

[ Reference URL ]

http://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2012/04.html

< Previous 123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960616263646566676869707172737475767778798081828384858687888990919293949596979899100101102103104105106107108109110111112113114115116117118119120121122123124125126127128129130131132133 Next >