Seminar information archive

15:30-16:40 Room #052 (Graduate School of Math. Sci. Bldg.)
Emanuele Guidotti (University of Milan)
Latest Development in yuimaGUI - Interactive Platform for Computational Statistics and Finance

[ Abstract ]
The yuimaGUI package provides a user-friendly interface for the yuima package, including additional tools related to Quantitative Finance. It greatly simplifies tasks such as estimation and simulation of stochastic processes, data retrieval, time series clustering, change point and lead-lag analysis. Today we are going to discuss the latest development in yuimaGUI, extending the Platform with multivariate modeling and simulation, Levy processes, Point processes, broader model selection tools and more general distributions thanks to the new yuima-Law object.

10:30-11:30 Room #056 (Graduate School of Math. Sci. Bldg.)
Qing Liu (Fukuoka University)
A discrete game interpretation for curvature flow equations with dynamic boundary conditions (日本語)

[ Abstract ]
A game-theoretic approach to motion by curvature was proposed by Kohn and Serfaty in 2006. They constructed a family of deterministic discrete games, whose value functions converge to the unique solution of the curvature flow equation. In this talk, we develop this method to provide an interpretation for the associated dynamic boundary value problems by including in the game setting a kind of nonlinear reflection near the boundary. We also discuss its applications to the fattening phenomenon. This talk is based on joint work with N. Hamamuki at Hokkaido University.

17:00-18:30 Room #056 (Graduate School of Math. Sci. Bldg.)
Doman Takata (The university of Tokyo)
An analytic index theory for infinite-dimensional manifolds and KK-theory (JAPANESE)

[ Abstract ]
The Atiyah-Singer index theorem is one of the monumental works in geometry and topology, which states the coincidence between analytic index and topological index on closed manifolds. The overall goal of my research is to formulate and prove an infinite dimensional version of this theorem. For this purpose, it is natural to begin with simple cases, and my current problem is the following: For infinite-dimensional manifolds equipped with a "proper and cocompact" action of the loop group of the circle, construct a loop group equivariant index theory, from the viewpoint of KK-theory. Although this project has not been completed, I have constructed several core objects for the analytic side of this problem, including a Hilbert space regarded as an "$L^2$-space", in arXiv:1701.06055 and arXiv:1709.06205. In this talk, I am going to report the progress so far.

15:30-17:00 Room #122 (Graduate School of Math. Sci. Bldg.)
Christopher Hacon (Utah/Kyoto)
Towards the termination of flips. (English)

[ Abstract ]
The minimal model program (MMP) predicts that if $X$ is a smooth complex projective variety which is not uniruled, then there is a finite sequence of "elementary" birational maps
$X=X_0-->X_1-->X_2-->...-->X_n$ known as divisorial contractions and flips whose output $\bar X=X_n$ is a minimal model so that $K_{\bar X}$ is a nef $Q$-divisor i.e it intersects all curves $C\subset \bar X$ non-negatively: $K_{\bar X}\cdot C\geq 0$.
The existence of these birational maps has been established, but in order to complete the MMP, it is necessary to show that flips terminate i.e. there are no infinite sequences of flips. In this talk we will discuss recent results towards the termination of flips.

[ Reference URL ]
https://www.math.utah.edu/~hacon/

13:30-15:00 Room #122 (Graduate School of Math. Sci. Bldg.)
Will Donovan (IPMU)
Perverse sheaves of categories and birational geometry (English)

[ Abstract ]
Kapranov and Schechtman have initiated a program to study perverse sheaves of categories, or perverse schobers. It is expected that examples arise from birational geometry, in particular from webs of flops. I explain progress towards constructing these objects for Grothendieck resolutions (work of the above authors with Bondal), and for 3-folds (joint work of myself and Wemyss).

10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Eiji Inoue (The University of Tokyo)
Kähler-Ricci soliton, K-stability and moduli space of Fano
manifolds (JAPANESE)

[ Abstract ]
Kähler-Ricci soliton is a kind of canonical metrics on Fano manifolds and is a natural generalization of Kähler-Einstein metric in
view of Kähler-Ricci flow.

In this talk, I will explain the following good geometric features of Fano manifolds admitting Kähler-Ricci solitons:
1. Volume minimization, reductivity and uniqueness results established by Tian&Zhu.
2. Relation to algebraic (modified) K-stability estabilished by Berman&Witt-Niström and Datar&Székelyhidi.
3. Moment map picture for Kähler-Ricci soliton (‘real side’)
4. Moduli stack (‘virtual side’) and moduli space of them

A result in 1 is indispensable for the formulation in 3 and 4, and explains why we should consider solitons, beyond Einstein metrics. I also show an essential idea in the construction of the moduli space of Fano manifolds admitting Kähler-Ricci solitons and give some remarks on technical key point.

14:45-15:45 Room #122 (Graduate School of Math. Sci. Bldg.)
M.M. Lavrentʼev, Jr. (Novosibirsk State University)
Some strongly degenerate parabolic equations (joint with Prof. A. Tani) (ENGLISH)

[ Abstract ]
We consider some nonlinear 1D parabolic equations with the positive leading coefficient which is not away from zero. "Hyperbolic phenomena" (gradient blowing up phenomena) were reported in literature for such models. We describe special cases of regular solvability for degenerate equations under study.

[ Reference URL ]
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_MMLavrentev.pdf

17:00-18:30 Room #056 (Graduate School of Math. Sci. Bldg.)
Mutsuo Oka (Tokyo University of Science)
On the singularity theory of mixed hypersurfaces and some conjecture (JAPANESE)

[ Abstract ]
Consider a real algebraic variety of real codimension 2 defined by $V:=\{g(\mathbf x,\mathbf y)=h(\mathbf x,\mathbf y)=0\}$ in $\mathbb C^n=\mathbb R^n\times \mathbb R^n$. Put $\mathbf z=\mathbf x+i\mathbf y$ and consider complex valued real analytic function $f=g+ih$. Replace the variables $x_1,y_1\dots, x_n,y_n$ using the equality $x_j=(z_j+\bar z_j)/2,\, y_j=(z_j-\bar z_j)/2i$. Then $f$ can be understood to be an analytic functions of $z_j,\bar z_j$. We call $f$ a mixed function. In this way, $V=\{f(\mathbf z,\bar{\mathbf z})=0\}$ and we can use the techniques of complex analytic functions and the singularity theory developed there. In this talk, we explain basic properties of the singularity of mixed hyper surface $V(f)$ and give several open questions.

10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Sumio Yamada (Gakushuin University)
Harmonic map and the Einstein equation in five dimension (JAPANESE)

[ Abstract ]
We present a new method in constructing 5-dimensional stationary solutions to the vacuum Einstein equation. In 1917, H. Weyl expressed the Schwarzschild black hole solution using a cylindical coordinate system, and consequently realized that the metric is completely determined by a harmonic function. Since then, the relation between harmonic maps and the Einstein equation has been explored mostly by physicists, which they call the sigma model of the Einstein equation. In this talk, after explaining the historical background, we demonstrate that in 5D, the Einstein spacetimes can have a wide range of black hole horizons in their topological types. In particular we establish an existence theorem of harmonic maps, which subsequently leads to constructions of 5D spacetimes with black hole horizons of positive Yamabe types, namely $S^3$, $S^2 \times S^1$, and the lens space $L(p,q)$. This is a joint work with Marcus Khuri and Gilbert Weinstein.

16:00-17:30 Room #126 (Graduate School of Math. Sci. Bldg.)
Takuya MURAYAMA (Graduate School of Science, Kyoto University)
Chordal Komatu-Loewner equation for a family of continuously growing hulls (JAPANESE)

15:00-17:00 Room #123 (Graduate School of Math. Sci. Bldg.)
Sug Woo Shin (University of California, Berkeley)
Introduction to the Langlands-Rapoport conjecture (ENGLISH)

[ Abstract ]
In 1970s Langlands envisioned a program to compute the Hasse-Weil zeta functions of Shimura varieties as an alternating product of automorphic L-functions, which in particular implies the meromorphic continuation and functional equation for the zeta functions. In 1987, Langlands and Rapoport formulated a precise and far-reaching conjecture describing the set of points of Shimura varieties modulo p as an essential step towards the goal. The program has been largely carried out by Langlands, Kottwitz, and others for PEL-type Shimura varieties with striking applications to the local and global Langlands correspondences (which in turn led to further applications). We have started to understand the more general Hodge-type and abelian-type cases only recently, thanks to Kisin's work on the Langlands-Rapoport conjecture in the good reduction case. The lecture aims to give a gentle introduction to his seminal paper. After a brief introduction, the lecture is divided into four parts.
(i) Shimura varieties: We introduce Shimura varieties of Hodge type and abelian type and their integral models.
(ii) Statement of the conjecture: After setting up the language of
Galois gerbs, we state the Langlands-Rapoport conjecture.
(iii) Sketch of Kisin's proof: We sketch Kisin's proof of the conjecture for Shimura varieties of Hodge type.
(iv) Counting fixed points: Following forthcoming work of Kisin, Y. Zhu, and the speaker, we explain how to apply the Langlands-Rapoport conjecture to count fixed-points of
Hecke-Frobenius correspondences.

[ Reference URL ]
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_SugWooShin.pdf

13:00-14:00 Room #123 (Graduate School of Math. Sci. Bldg.)
Alex Youcis (University of California, Berkeley)
The Langlands-Kottwitz method for deformation spaces of Hodge type

[ Abstract ]
Cohomology of global Shimura varieties is an object of universal importance in the Langlands program. Given a Shimura datum (G,X) and a (sufficiently nice) representation ¥xi of G, one obtains an l-adic sheaf F_{¥xi,l} on Sh(G,X) with a G(A_f)-structure. Thus, in the standard way, the cohomology group H^*(Sh(G,X),F_¥xi) has an admissible action of Gal(¥overline{E}/E) ¥times G(A_f), where E=E(G,X) is the reflex field of (G,X). Extending work of Kottwitz, Scholze, and others we discuss a method for computing the traces of this action, more specifically of an element ¥tau ¥times g where ¥tau ¥in W_{E_¥mathfrak{p}} for some prime ¥mathfrak{p} of E dividing p and g ¥in G(A_f^p) ¥times G(Z_p), in terms of a weighted point count on the Shimura variety's special fiber, as well as the traces of various local Shimura varieties over E_¥mathfrak{p}, at least in the case when (G,X) is a abelian-type Shimura datum unramified at p.

15:30-16:30 Room #056 (Graduate School of Math. Sci. Bldg.)
Kei IRIE (The University of Tokyo)
Generic density theorems for periodic Reeb orbits and minimal hypersurfaces (日本語)

15:00-17:00 Room #123 (Graduate School of Math. Sci. Bldg.)
Sug Woo Shin (University of California, Berkeley)
Introduction to the Langlands-Rapoport conjecture (ENGLISH)

[ Abstract ]
In 1970s Langlands envisioned a program to compute the Hasse-Weil zeta functions of Shimura varieties as an alternating product of automorphic L-functions, which in particular implies the meromorphic continuation and functional equation for the zeta functions. In 1987, Langlands and Rapoport formulated a precise and far-reaching conjecture describing the set of points of Shimura varieties modulo p as an essential step towards the goal. The program has been largely carried out by Langlands, Kottwitz, and others for PEL-type Shimura varieties with striking applications to the local and global Langlands correspondences (which in turn led to further applications). We have started to understand the more general Hodge-type and abelian-type cases only recently, thanks to Kisin's work on the Langlands-Rapoport conjecture in the good reduction case. The lecture aims to give a gentle introduction to his seminal paper. After a brief introduction, the lecture is divided into four parts.
(i) Shimura varieties: We introduce Shimura varieties of Hodge type and abelian type and their integral models.
(ii) Statement of the conjecture: After setting up the language of
Galois gerbs, we state the Langlands-Rapoport conjecture.
(iii) Sketch of Kisin's proof: We sketch Kisin's proof of the conjecture for Shimura varieties of Hodge type.
(iv) Counting fixed points: Following forthcoming work of Kisin, Y. Zhu, and the speaker, we explain how to apply the Langlands-Rapoport conjecture to count fixed-points of
Hecke-Frobenius correspondences.

[ Reference URL ]
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_SugWooShin.pdf

11:00-12:00 Room #123 (Graduate School of Math. Sci. Bldg.)
Alexander Bertoloni Meli (University of California, Berkeley)
The Cohomology of Rapoport-Zink Spaces of EL-Type

[ Abstract ]
I will discuss Rapoport-Zink spaces of EL-type and how to explicitly compute a certain variant of their cohomology in terms of the local Langlands correspondence for general linear groups. I will then show how this computation can be used to resolve certain cases of a conjecture of Harris.

17:30-18:30 Room #056 (Graduate School of Math. Sci. Bldg.)
Sug Woo Shin (University of California, Berkeley)
Endoscopy and cohomology of U(n-1,1) (ENGLISH)

[ Abstract ]
We apply the endoscopic classification of automorphic representations for inner forms of unitary groups to bound the growth of cohomology in congruence towers of locally symmetric spaces associated with U(n-1,1). Our bound is sharper than the bound predicted by Sarnak-Xue for general locally symmetric spaces. This is joint work with Simon Marshall.

15:00-17:00 Room #123 (Graduate School of Math. Sci. Bldg.)
Sug Woo Shin (University of California, Berkeley)
Introduction to the Langlands-Rapoport conjecture (ENGLISH)

[ Abstract ]
In 1970s Langlands envisioned a program to compute the Hasse-Weil zeta functions of Shimura varieties as an alternating product of automorphic L-functions, which in particular implies the meromorphic continuation and functional equation for the zeta functions. In 1987, Langlands and Rapoport formulated a precise and far-reaching conjecture describing the set of points of Shimura varieties modulo p as an essential step towards the goal. The program has been largely carried out by Langlands, Kottwitz, and others for PEL-type Shimura varieties with striking applications to the local and global Langlands correspondences (which in turn led to further applications). We have started to understand the more general Hodge-type and abelian-type cases only recently, thanks to Kisin's work on the Langlands-Rapoport conjecture in the good reduction case. The lecture aims to give a gentle introduction to his seminal paper. After a brief introduction, the lecture is divided into four parts.
(i) Shimura varieties: We introduce Shimura varieties of Hodge type and abelian type and their integral models.
(ii) Statement of the conjecture: After setting up the language of
Galois gerbs, we state the Langlands-Rapoport conjecture.
(iii) Sketch of Kisin's proof: We sketch Kisin's proof of the conjecture for Shimura varieties of Hodge type.
(iv) Counting fixed points: Following forthcoming work of Kisin, Y. Zhu, and the speaker, we explain how to apply the Langlands-Rapoport conjecture to count fixed-points of
Hecke-Frobenius correspondences.

[ Reference URL ]
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_SugWooShin.pdf

16:45-18:15 Room #126 (Graduate School of Math. Sci. Bldg.)
Yusuke Isono (RIMS, Kyoto Univ.)
Factoriality, Connes' invariants and fullness of amalgamated free products (English)

15:00-17:00 Room #123 (Graduate School of Math. Sci. Bldg.)
Sug Woo Shin (University of California, Berkeley)
Introduction to the Langlands-Rapoport conjecture (ENGLISH)

[ Abstract ]
In 1970s Langlands envisioned a program to compute the Hasse-Weil zeta functions of Shimura varieties as an alternating product of automorphic L-functions, which in particular implies the meromorphic continuation and functional equation for the zeta functions. In 1987, Langlands and Rapoport formulated a precise and far-reaching conjecture describing the set of points of Shimura varieties modulo p as an essential step towards the goal. The program has been largely carried out by Langlands, Kottwitz, and others for PEL-type Shimura varieties with striking applications to the local and global Langlands correspondences (which in turn led to further applications). We have started to understand the more general Hodge-type and abelian-type cases only recently, thanks to Kisin's work on the Langlands-Rapoport conjecture in the good reduction case. The lecture aims to give a gentle introduction to his seminal paper. After a brief introduction, the lecture is divided into four parts.
(i) Shimura varieties: We introduce Shimura varieties of Hodge type and abelian type and their integral models.
(ii) Statement of the conjecture: After setting up the language of
Galois gerbs, we state the Langlands-Rapoport conjecture.
(iii) Sketch of Kisin's proof: We sketch Kisin's proof of the conjecture for Shimura varieties of Hodge type.
(iv) Counting fixed points: Following forthcoming work of Kisin, Y. Zhu, and the speaker, we explain how to apply the Langlands-Rapoport conjecture to count fixed-points of
Hecke-Frobenius correspondences.

[ Reference URL ]
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_SugWooShin.pdf

17:00-18:30 Room #056 (Graduate School of Math. Sci. Bldg.)
Dan Cristofaro-Gardiner (University of California, Santa Cruz)
Beyond the Weinstein conjecture (ENGLISH)

[ Abstract ]
The Weinstein conjecture states that any Reeb vector field on a closed manifold has at least one closed orbit. The three-dimensional case of this conjecture was proved by Taubes in 2007, and Hutchings and I later showed that in this case there are always at least 2 orbits. While examples exist with exactly two orbits, one expects that this lower bound can be significantly improved with additional assumptions. For example, a theorem of Hofer, Wysocki, and Zehnder states that a generic nondegenerate Reeb vector field associated to the "standard" contact structure on $S^3$ has either 2, or infinitely many, closed orbits. We prove that any nondegenerate Reeb vector field has 2 or infinitely many closed orbits as long as the associated contact structure has torsion first Chern class. This is joint work with Mike Hutchings and Dan Pomerleano.

15:30-17:00 Room #122 (Graduate School of Math. Sci. Bldg.)
Taku Suzuki (Utsunomiya)
Higher order families of lines and Fano manifolds covered by linear
spaces
(Japanese (writing in English))

[ Abstract ]
In this talk, for an embedded Fano manifold $X$, we introduce higher
order families of lines and a new invariant $S_X$. They are line
versions of higher order minimal families of rational curves and the
invariant $N_X$ which were introduced in my previous talk on 4th
November 2016. In addition, $S_X$ is related to the dimension of
covering linear spaces. Our goal is to classify Fano manifolds $X$ which
have large $S_X$.

13:00-14:00 Room #122 (Graduate School of Math. Sci. Bldg.)
Sander Mack-Crane (University of California, Berkeley)
Langlands-Rapoport for the Modular Curve

[ Abstract ]
We discuss a concrete version of the Langlands-Rapoport conjecture in the case of the modular curve, and use this case to illuminate some of the more abstract features of the Langlands-Rapoport conjecture for general (abelian type) Shimura varieties.

16:50-18:20 Room #002 (Graduate School of Math. Sci. Bldg.)
Norikazu Saito (University of Tokyo)
Various aspects of numerical analysis (Japanese)

15:00-16:10 Room #052 (Graduate School of Math. Sci. Bldg.)

10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Atsushi Hayashimoto (National Institute of Technology, Nagano College)
Proper holomorphic mappings and generalized pseudoellipsoids (JAPANESE)

[ Abstract ]
We study the classification of proper holomorphic mappings between generalized pseudoellipsoids of different dimensions.

Huang proved some classification theorems of proper holomorphic mappings between balls of different dimensions, which are called gap theorems. Our present theorems are their weakly pseudoconvex versions.

In the theorem, classified mapping is so-called a variables splitting mapping and each component is derived from a homogeneous proper polynomial mapping between balls.

The essential methods are the ''good'' decompositions of CR vector bundle and reduction the mapping under consideration to the mapping of balls. By this reduction, we can apply Huang's gap theorem.

Seminar on Probability and Statistics

2018/05/22

PDE Real Analysis Seminar

Tuesday Seminar on Topology

2018/05/21

Algebraic Geometry Seminar

Algebraic Geometry Seminar

Seminar on Geometric Complex Analysis

2018/05/16

FMSP Lectures

2018/05/15

Tuesday Seminar on Topology

2018/05/14

Seminar on Geometric Complex Analysis

Tokyo Probability Seminar

2018/05/11

FMSP Lectures

Lectures

Colloquium

2018/05/10

FMSP Lectures

Lectures

2018/05/09

Number Theory Seminar

FMSP Lectures

Operator Algebra Seminars

2018/05/08

FMSP Lectures

Tuesday Seminar on Topology

Algebraic Geometry Seminar

Lectures

Numerical Analysis Seminar

Seminar on Probability and Statistics

2018/05/07

Seminar on Geometric Complex Analysis