## Seminar information archive

Seminar information archive ～05/21｜Today's seminar 05/22 | Future seminars 05/23～

### 2012/06/13

#### Number Theory Seminar

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

Singular homologies of non-Archimedean analytic spaces and integrals along cycles (JAPANESE)

**Tomoki Mihara**(University of Tokyo)Singular homologies of non-Archimedean analytic spaces and integrals along cycles (JAPANESE)

#### Lectures

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

A KPZ equation for zero-range interactions (ENGLISH)

**Sunder Sethuraman**(University of Arizona)A KPZ equation for zero-range interactions (ENGLISH)

[ Abstract ]

We derive a type of KPZ equation, in terms of a martingale problem, as a scaling limit of fluctuation fields in weakly asymmetric zero-range processes. Joint work (in progress) with Milton Jara and Patricia Goncalves.

We derive a type of KPZ equation, in terms of a martingale problem, as a scaling limit of fluctuation fields in weakly asymmetric zero-range processes. Joint work (in progress) with Milton Jara and Patricia Goncalves.

#### Lectures

11:00-15:30 Room #128 (Graduate School of Math. Sci. Bldg.)

Workshop for Quasi-Monte Carlo and Pseudo Random Number Generation (ENGLISH)

[ Reference URL ]

http://sites.google.com/a/craft.titech.ac.jp/workshop-on-qmc-and-prng-2012-utms/

**S. Harase, et. al.**(Tokyo Institute of Technology/JSPS)Workshop for Quasi-Monte Carlo and Pseudo Random Number Generation (ENGLISH)

[ Reference URL ]

http://sites.google.com/a/craft.titech.ac.jp/workshop-on-qmc-and-prng-2012-utms/

### 2012/06/12

#### Tuesday Seminar on Topology

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

Topological interpretation of the quandle cocycle invariants of links (JAPANESE)

**Takefumi Nosaka**(RIMS, Kyoto University, JSPS)Topological interpretation of the quandle cocycle invariants of links (JAPANESE)

[ Abstract ]

Carter et al. introduced many quandle cocycle invariants

combinatorially constructed from link-diagrams. For connected quandles of

finite order, we give a topological meaning of the invariants, without

some torsion parts. Precisely, this invariant equals a sum of "knot

colouring polynomial" and of a Z-equivariant part of the Dijkgraaf-Witten

invariant. Moreover, our approach involves applications to compute "good"

torsion subgroups of the 3-rd quandle homologies and the 2-nd homotopy

groups of rack spaces.

Carter et al. introduced many quandle cocycle invariants

combinatorially constructed from link-diagrams. For connected quandles of

finite order, we give a topological meaning of the invariants, without

some torsion parts. Precisely, this invariant equals a sum of "knot

colouring polynomial" and of a Z-equivariant part of the Dijkgraaf-Witten

invariant. Moreover, our approach involves applications to compute "good"

torsion subgroups of the 3-rd quandle homologies and the 2-nd homotopy

groups of rack spaces.

#### Lie Groups and Representation Theory

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

Conformally invariant systems of differential operators of non-Heisenberg parabolic type (ENGLISH)

**Toshihisa Kubo**(the University of Tokyo)Conformally invariant systems of differential operators of non-Heisenberg parabolic type (ENGLISH)

[ Abstract ]

The wave operator in Minkowski space is a classical example of a conformally invariant differential operator.

Recently, the notion of conformality of one operator has been

generalized by Barchini-Kable-Zierau to systems of differential operators.

Such systems yield homomrophisms between generalized Verma modules. In this talk we build such systems of second-order differential operators in the maximal non-Heisenberg parabolic setting.

If time permits then we will discuss the corresponding homomorphisms between generalized Verma modules.

The wave operator in Minkowski space is a classical example of a conformally invariant differential operator.

Recently, the notion of conformality of one operator has been

generalized by Barchini-Kable-Zierau to systems of differential operators.

Such systems yield homomrophisms between generalized Verma modules. In this talk we build such systems of second-order differential operators in the maximal non-Heisenberg parabolic setting.

If time permits then we will discuss the corresponding homomorphisms between generalized Verma modules.

#### Lectures

09:50-17:10 Room #118 (Graduate School of Math. Sci. Bldg.)

Workshop for Quasi-Monte Carlo and Pseudo Random Number Generation (ENGLISH)

[ Reference URL ]

http://sites.google.com/a/craft.titech.ac.jp/workshop-on-qmc-and-prng-2012-utms/

**Josef Dick, et. al.**(Univ. New South Wales)Workshop for Quasi-Monte Carlo and Pseudo Random Number Generation (ENGLISH)

[ Reference URL ]

http://sites.google.com/a/craft.titech.ac.jp/workshop-on-qmc-and-prng-2012-utms/

### 2012/06/11

#### Kavli IPMU Komaba Seminar

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

Quantum cohomology of flag varieties (ENGLISH)

**Changzheng Li**(Kavli IPMU)Quantum cohomology of flag varieties (ENGLISH)

[ Abstract ]

In this talk, I will give a brief introduction to the quantum cohomology of flag varieties first. Then I will introduce a Z^2-filtration on the quantum cohomology of complete flag varieties. In the end, we will study the quantum Pieri rules for complex/symplectic Grassmannians, as applications of the Z^2-filtration.

In this talk, I will give a brief introduction to the quantum cohomology of flag varieties first. Then I will introduce a Z^2-filtration on the quantum cohomology of complete flag varieties. In the end, we will study the quantum Pieri rules for complex/symplectic Grassmannians, as applications of the Z^2-filtration.

#### Seminar on Geometric Complex Analysis

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

Differential forms on complete intersections (ENGLISH)

**Damian BROTBEK**(University of Tokyo)Differential forms on complete intersections (ENGLISH)

[ Abstract ]

Brückmann and Rackwitz proved a vanishing result for particular types of differential forms on complete intersection varieties. We will be interested in the cases not covered by their result. In some cases, we will show how the space $H^0(X,S^{m_1}\Omega_X\otimes \cdots \otimes S^{m_k}\Omega_X)$ depends on the equations defining $X$, and in particular we will prove that the theorem of Brückmann and Rackwitz is optimal. The proofs are based on simple, combinatorial, cohomology computations.

Brückmann and Rackwitz proved a vanishing result for particular types of differential forms on complete intersection varieties. We will be interested in the cases not covered by their result. In some cases, we will show how the space $H^0(X,S^{m_1}\Omega_X\otimes \cdots \otimes S^{m_k}\Omega_X)$ depends on the equations defining $X$, and in particular we will prove that the theorem of Brückmann and Rackwitz is optimal. The proofs are based on simple, combinatorial, cohomology computations.

### 2012/06/09

#### Harmonic Analysis Komaba Seminar

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

Resent topics on the Cauchy integrals (the works of Muscalu and others) (JAPANESE)

Ill-posedness for the nonlinear Schr\\"odinger equations in one

space dimension

(JAPANESE)

**Yasuo Furuya**(Tokai University) 13:30-15:00Resent topics on the Cauchy integrals (the works of Muscalu and others) (JAPANESE)

**Tsukasa Iwabuchi**(Chuo University) 15:30-17:00Ill-posedness for the nonlinear Schr\\"odinger equations in one

space dimension

(JAPANESE)

[ Abstract ]

In this talk, we consider the Cauchy problems for the nonlinear Schr\\"odinger equations. In particular, we study the ill-posedness by showing that the continuous dependence on initial data does not hold. In the known results, Bejenaru-Tao (2006) considered the problem in the Sobolev spaces $H^s (\\mathbb R)$ and showed the ill-posedness when $s < -1 $. In this talk, we study the ill-posedness in the Besov space for one space dimension and in the Sobolev spaces for two space dimensions.

In this talk, we consider the Cauchy problems for the nonlinear Schr\\"odinger equations. In particular, we study the ill-posedness by showing that the continuous dependence on initial data does not hold. In the known results, Bejenaru-Tao (2006) considered the problem in the Sobolev spaces $H^s (\\mathbb R)$ and showed the ill-posedness when $s < -1 $. In this talk, we study the ill-posedness in the Besov space for one space dimension and in the Sobolev spaces for two space dimensions.

### 2012/06/08

#### GCOE lecture series

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

Derived categories and cohomological invariants II (ENGLISH)

**Mihnea Popa**(University of Illinois at Chicago)Derived categories and cohomological invariants II (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.

#### Kavli IPMU Komaba Seminar

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

Period Integrals and Tautological Systems (ENGLISH)

**Bong Lian**(Brandeis University)Period Integrals and Tautological Systems (ENGLISH)

[ Abstract ]

We develop a global Poincar\\'e residue formula to study

period integrals of families of complex manifolds. For any compact

complex manifold $X$ equipped with a linear system $V^*$ of

generically smooth CY hypersurfaces, the formula expresses period

integrals in terms of a canonical global meromorphic top form on $X$.

Two important ingredients of this construction are the notion of a CY

principal bundle, and a classification of such rank one bundles.

We also generalize the construction to CY and general type complete

intersections. When $X$ is an algebraic manifold having a sufficiently

large automorphism group $G$ and $V^*$ is a linear representation of

$G$, we construct a holonomic D-module that governs the period

integrals. The construction is based in part on the theory of

tautological systems we have developed earlier. The approach allows us

to explicitly describe a Picard-Fuchs type system for complete

intersection varieties of general types, as well as CY, in any Fano

variety, and in a homogeneous space in particular. In addition, the

approach provides a new perspective of old examples such as CY

complete intersections in a toric variety or partial flag variety. The

talk is based on recent joint work with R. Song and S.T. Yau.

We develop a global Poincar\\'e residue formula to study

period integrals of families of complex manifolds. For any compact

complex manifold $X$ equipped with a linear system $V^*$ of

generically smooth CY hypersurfaces, the formula expresses period

integrals in terms of a canonical global meromorphic top form on $X$.

Two important ingredients of this construction are the notion of a CY

principal bundle, and a classification of such rank one bundles.

We also generalize the construction to CY and general type complete

intersections. When $X$ is an algebraic manifold having a sufficiently

large automorphism group $G$ and $V^*$ is a linear representation of

$G$, we construct a holonomic D-module that governs the period

integrals. The construction is based in part on the theory of

tautological systems we have developed earlier. The approach allows us

to explicitly describe a Picard-Fuchs type system for complete

intersection varieties of general types, as well as CY, in any Fano

variety, and in a homogeneous space in particular. In addition, the

approach provides a new perspective of old examples such as CY

complete intersections in a toric variety or partial flag variety. The

talk is based on recent joint work with R. Song and S.T. Yau.

### 2012/06/05

#### Tuesday Seminar on Topology

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

A generalization of Dehn twists (JAPANESE)

**Yusuke Kuno**(Tsuda College)A generalization of Dehn twists (JAPANESE)

[ Abstract ]

We introduce a generalization

of Dehn twists for loops which are not

necessarily simple loops on an oriented surface.

Our generalization is an element of a certain

enlargement of the mapping class group of the surface.

A natural question is whether a generalized Dehn twist is

in the mapping class group. We show some results related to this question.

This talk is partially based on a joint work

with Nariya Kawazumi (Univ. Tokyo).

We introduce a generalization

of Dehn twists for loops which are not

necessarily simple loops on an oriented surface.

Our generalization is an element of a certain

enlargement of the mapping class group of the surface.

A natural question is whether a generalized Dehn twist is

in the mapping class group. We show some results related to this question.

This talk is partially based on a joint work

with Nariya Kawazumi (Univ. Tokyo).

#### GCOE lecture series

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

Random walk on reductive groups II (ENGLISH)

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

#### Lie Groups and Representation Theory

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

Random walk on reductive groups (ENGLISH)

**Yves Benoist**(CNRS and 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.

### 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.

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