## 今後の予定

### 2016年02月15日(月)

#### FMSPレクチャーズ

17:00-18:00   数理科学研究科棟(駒場) 118号室
Patricia Gaitan 氏 (Aix-Marseille University)
Probing for inclusions for heat conductive bodies time independent and time dependent cases (ENGLISH)
[ 講演参考URL ]
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Gaitan.pdf

### 2016年02月16日(火)

#### トポロジー火曜セミナー

17:00-18:30   数理科学研究科棟(駒場) 056号室
Tea : Common Room 16:30 -- 17:00
Luc Menichi 氏 (University of Angers)
String Topology, Euler Class and TNCZ free loop fibrations (ENGLISH)
[ 講演概要 ]
Let $M$ be a connected, closed oriented manifold.
Chas and Sullivan have defined a loop product and a loop coproduct on
$H_*(LM;¥mathbb{F})$, the homology of the
free loops on $M$ with coefficients in the field $¥mathbb{F}$.
By studying this loop coproduct, I will show that if the free loop
fibration
$¥Omega M¥buildrel{i}¥over¥hookrightarrow LM¥buildrel{ev}¥over¥twoheadrightarrow M$
is homologically trivial, i.e. $i^*:H^*(LM;¥mathbb{F})¥twoheadrightarrow H^*(¥Omega M;¥mathbb{F})$ is onto,
then the Euler characteristic of $M$ is divisible by the characteristic
of the field $¥mathbb{F}$
(or $M$ is a point).

#### FMSPレクチャーズ

10:00-11:00   数理科学研究科棟(駒場) 002号室
This lecture will be given as part of “Workshop on L^2 Extension Theorems”.
Dror Varolin 氏 (Stony Brook)
L^2 Extension and its applications: A survey (1) (ENGLISH)
[ 講演概要 ]
We discuss certain aspects of the theory of L^2 extension, going back to the famous and fundamental work of Ohsawa and Takegoshi, and even further back to work of Donnelly and Fefferman.
The first of three lectures will recall a number of L^2 extension theorems, to some extent following an incomplete history (as I see it), and ending with a sketch of a proof of one of these theorems.
The second lecture will discuss a number of my favorite applications of L^2 extension, from Bergman kernels to deformation invariance of plurigenera.
The third lecture will discuss a new proof of the extension theorem, due to Berndtsson and Lempert. The key tool is a theorem of Berndtsson on the positivity of direct images, which we will review. Berndtsson's theorem permits the introduction of degeneration techniques, whose surprising application to L^2 extension represents one of the most beautiful and fundamental recent breakthroughs in the subject.
[ 講演参考URL ]
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Varolin.pdf

### 2016年02月17日(水)

#### FMSPレクチャーズ

10:00-11:00   数理科学研究科棟(駒場) 002号室
This lecture will be given as part of “Workshop on L^2 Extension Theorems”.
Dror Varolin 氏 (Stony Brook)
L^2 Extension and its applications: A survey (2) (ENGLISH)
[ 講演概要 ]
We discuss certain aspects of the theory of L^2 extension, going back to the famous and fundamental work of Ohsawa and Takegoshi, and even further back to work of Donnelly and Fefferman.
The first of three lectures will recall a number of L^2 extension theorems, to some extent following an incomplete history (as I see it), and ending with a sketch of a proof of one of these theorems.
The second lecture will discuss a number of my favorite applications of L^2 extension, from Bergman kernels to deformation invariance of plurigenera.
The third lecture will discuss a new proof of the extension theorem, due to Berndtsson and Lempert. The key tool is a theorem of Berndtsson on the positivity of direct images, which we will review. Berndtsson's theorem permits the introduction of degeneration techniques, whose surprising application to L^2 extension represents one of the most beautiful and fundamental recent breakthroughs in the subject.
[ 講演参考URL ]
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Varolin.pdf

### 2016年02月18日(木)

#### FMSPレクチャーズ

10:00-11:00   数理科学研究科棟(駒場) 002号室
This lecture will be given as part of “Workshop on L^2 Extension Theorems”.
Dror Varolin 氏 (Stony Brook)
L^2 Extension and its applications: A survey (3) (ENGLISH)
[ 講演概要 ]
We discuss certain aspects of the theory of L^2 extension, going back to the famous and fundamental work of Ohsawa and Takegoshi, and even further back to work of Donnelly and Fefferman.
The first of three lectures will recall a number of L^2 extension theorems, to some extent following an incomplete history (as I see it), and ending with a sketch of a proof of one of these theorems.
The second lecture will discuss a number of my favorite applications of L^2 extension, from Bergman kernels to deformation invariance of plurigenera.
The third lecture will discuss a new proof of the extension theorem, due to Berndtsson and Lempert. The key tool is a theorem of Berndtsson on the positivity of direct images, which we will review. Berndtsson's theorem permits the introduction of degeneration techniques, whose surprising application to L^2 extension represents one of the most beautiful and fundamental recent breakthroughs in the subject.
[ 講演参考URL ]
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Varolin.pdf

### 2016年03月08日(火)

#### 作用素環セミナー

16:45-18:15   数理科学研究科棟(駒場) 118号室
Roberto Longo 氏 (ローマ大学)
Localisation of infinite spin particles (英語)

### 2016年03月11日(金)

#### 作用素環セミナー

16:45-18:15   数理科学研究科棟(駒場) 118号室
Bas Jordans 氏 (Univ. Oslo)
Convergence to the boundary for random walks on discrete quantum groups
(English)

### 2016年03月16日(水)

#### PDE実解析研究会

16:00-17:00   数理科学研究科棟(駒場) 056号室

Boris Khesin 氏 (University of Toronto)
Fluids, vortex membranes, and skew-mean-curvature flows (English)
[ 講演概要 ]
We show that an approximation of the hydrodynamical Euler equation describes the skew-mean-curvature flow on vortex membranes in any dimension. This generalizes the classical binormal, or vortex filament, equation in 3D. We present a Hamiltonian framework for dynamics of higher-dimensional vortex filaments and vortex sheets as singular 2-forms (Green currents) with support of codimensions 2 and 1, respectively.

### 2016年03月29日(火)

#### 代数学コロキウム

17:30-18:30   数理科学研究科棟(駒場) 002号室

Matthew Morrow 氏 (Universität Bonn)
Motivic cohomology of formal schemes in characteristic p
(English)
[ 講演概要 ]
The logarithmic Hodge-Witt sheaves of Illusie, Milne, Kato, et al. of a smooth variety in characteristic p provide a concrete realisation of its p-adic motivic cohomology, thanks to results of Geisser-Levine and Bloch-Kato-Gabber which link them to algebraic K-theory. I will explain an analogous theory for formal schemes, as well as applications to algebraic cycles, such as a weak Lefschetz theorem for formal Chow groups.

(本講演は「東京北京パリ数論幾何セミナー」として, インターネットによる東大数理, Morningside Center of MathematicsとIHESの双方向同時中継で行います.)

### 2016年04月11日(月)

#### 代数幾何学セミナー

15:30-17:00   数理科学研究科棟(駒場) 122号室
Piotr Pragacz 氏 (Institute of Mathematics, Polish Academy of Sciences )
Diagonals of flag bundles (English)
[ 講演概要 ]
TBA
[ 講演参考URL ]
https://www.impan.pl/~pragacz/main.htm

### 2016年04月12日(火)

#### Lie群論・表現論セミナー

17:00-18:30   数理科学研究科棟(駒場) 126号室
Piotr Pragacz 氏 (Institute of Mathematics, Polish Academy of Sciences)
Universal Gysin formulas for flag bundles
[ 講演概要 ]
We give generalizations of the formula for the push-forward of a power of the hyperplane class in a projective bundle to flag bundles of type A, B, C, D. The formulas (and also the proofs) involve only the Segre classes of the original vector bundles and characteristic classes of universal bundles. This is a joint work with Lionel Darondeau.

### 2016年04月27日(水)

#### PDE実解析研究会

15:00-16:00   数理科学研究科棟(駒場) 056号室

Elijah Liflyand 氏 (Bar-Ilan University, Israel)
Fourier transform versus Hilbert transform (English)
[ 講演概要 ]
We present several results in which the interplay between the Fourier transform and the Hilbert transform is of special form and importance.
1. In 50-s (Kahane, Izumi-Tsuchikura, Boas, etc.), the following problem in Fourier Analysis attracted much attention: Let $\{a_k\},$ $k=0,1,2...,$ be the sequence of the Fourier coefficients of the absolutely convergent sine (cosine) Fourier series of a function $f:\mathbb T=[-\pi,\pi)\to \mathbb C,$ that is $\sum |a_k|<\infty.$ Under which conditions on $\{a_k\}$ the re-expansion of $f(t)$ ($f(t)-f(0)$, respectively) in the cosine (sine) Fourier series will also be absolutely convergent?
We solve a similar problem for functions on the whole axis and their Fourier transforms. Generally, the re-expansion of a function with integrable cosine (sine) Fourier transform in the sine (cosine) Fourier transform is integrable if and only if not only the initial Fourier transform is integrable but also the Hilbert transform of the initial Fourier transform is integrable.
2. The following result is due to Hardy and Littlewood: If a (periodic) function $f$ and its conjugate $\widetilde f$ are both of bounded variation, their Fourier series converge absolutely.
We generalize the Hardy-Littlewood theorem (joint work with U. Stadtmüller) to the Fourier transform of a function on the real axis and its modified Hilbert transform. The initial Hardy-Littlewood theorem is a partial case of this extension, when the function is taken to be with compact support.
3. These and other problems are integrated parts of harmonic analysis of functions of bounded variation. We have found the maximal space for the integrability of the Fourier transform of a function of bounded variation. Along with those known earlier, various interesting new spaces appear in this study. Their inter-relations lead, in particular, to improvements of Hardy's inequality.
There are multidimensional generalizations of these results.
[ 講演参考URL ]
http://u.math.biu.ac.il/~liflyand/