日時: 2026年4月10日（金), 16:00-17:30
場所: 学習院大学(目白キャンパス) 南1号館103教室
講演者: Feng Luo 氏 (Rutgers University)
講演題目: Rigidity of Convex Sets in Hyperbolic 3-Space
ABSTRACT:
Pogorelov's rigidity theorem states that a compact convex body in the hyperbolic 3-space is determined up to isometry by the intrinsic path metric on its boundary. In this talk, we show that the intrinsic path metric on the boundary determines a closed non-compact convex set up to isometry, provided that the set of limit points of the convex set at infinity of the hyperbolic 3-space has vanishing 1-dimensional Hausdorff measure, i.e., zero length. Furthermore, this zero-length condition is optimal. This can be considered as an analogue of the Painleve removable singularity theorem in complex analysis, which states that compact sets of zero length are removable for bounded holomorphic functions. This is a joint work with Yanwen Luo and Zhenghao Rao.
日時：2025年12月19日(金）16:00~17:30
会場：早稲田大学, 理工キャンパス, 51号館18階02教室
講演者：Teng Fei (Rutgers大学)
題目："Degeneration of Calabi-Yau 3-folds and 3-forms"
ABSTRACT:
We study the geometries associated to various 3-forms on a symplectic 6-manifold of different orbital types. As an application, we demonstrate how this can be used to find Lagrangian foliations and other geometric structures of interest arising from certain degeneration of Calabi-Yau 3-folds.
日時：2025年7月24日（木）16:00~17:30
会場：学習院大学(目白キャンパス) 南1号館103教室
講演者： Gilbert Weinstein 氏 (Ariel University)
題目："The mass angular momentum inequality"
ABSTRACT:
We show that either there is a counterexample to black hole uniqueness, in the form of a regular axisymmetric stationary vacuum spacetime with an asymptotically flat end and multiple degenerate horizons which is ‘ADM stable’, or the following statement holds. Complete, simply connected, maximal initial data sets for the Einstein equations with multiple ends that are either asymptotically flat or asymptotically cylindrical, admit an ADM mass lower bound given by the square root of total angular momentum, under the assumption of nonnegative energy density and axisymmetry. Moreover, equality is achieved bound only for a constant time slice of an extreme Kerr spacetime. The proof is based on a novel flow of singular harmonic maps with hyperbolic plane target, under which the renormalized harmonic energy is monotonically nonincreasing. Relevant properties of the flow are achieved through a refined asymptotic analysis of solutions to the linearized harmonic map equations. This is joint work with Qing Han, Marcus Khuri, and Jingang Xiong
日時：2023年3月13日（月）14:00~15:30
会場：学習院大学(目白キャンパス) 南1号館103教室
Speaker： Gilbert Weinstein 氏 (Ariel University)
TItle："Asympototic Analysis of Harmonic Maps with Prescribed Singularities"
ABSTRACT:
Motivated by stationary axially symmetric solutions of the Einstein field equations, we study harmonic maps with prescribed singularities from domains in 3-d Euclidean space into the hyperbolic plane. The boundary conditions require these to be singular near the z-axis and asymptotic to extreme Kerr harmonic maps near punctures on the z-axis, corresponding to degenerate event horizons. It is proven that every such map admits a unique tangent map at each such puncture. The possible tangent maps are classified and shown to be maps into geodesics in the hyperbolic plane, depending on two parameters, angular momentum and conical singularity. The rate of convergence to the tangent map is established. A similar expansion is also obtained at the asymptotically flat end. Together with earlier results, this provides a complete regularity theory for these harmonic maps with prescribed singularities. These results are in preparation of a study of the mass-angular-momentum inequality for axially symmetric vacuum data with multiple black holes.
This is joint work with Marcus Khuri, Qing Han, and Jingang Xiong.
日時：2022年6月8日（水）16:00~17:30
会場：学習院大学(目白キャンパス) 南1号館103教室
Speaker：Prof. John Loftin (Rutgers University)
Title："Cubic Differentials, Harmonic Maps, and Real Buildings"
ABSTRACT:
Consider a Riemann surface S of genus g at least 2 equipped with a holomorphic cubic differential U. This pair (S,U) induces, via the theory of Higgs bundles, a rank-3 bundle with a flat connection, which induces a representation of the fundamental group into SL(3,R), and these representations comprise the Hitchin component. In addition, there is a harmonic map, equivariant under this representation, from the universal cover of S into the symmetric space SL(3,R)/SO(3). This parametrization of the Hitchin component is not explicit but involves the a system of PDEs. For nonzero U, we study the case sU as s approaches infinity. In particular, we show the geometry in this limit can be read off explicitly from U, in terms of an embedding of the universal cover of S into the real building given by the asymptotic cone of the symmetric space SL(3,R)/SO(3). We are able to provide explicit pictures for most triangle groups.
日時：2018年4月9日（月）16:00~17:30
会場：学習院大学(目白キャンパス) 南1号館303教室
Speaker：Prof. Wilderich Tuschmann (Karlsruhe Institute of Technology)
Title："On Spaces and Moduli Spaces of Nonnegatively Curved Riemannian Metrics”
ABSTRACT:
I will report on general results and questions about spaces and moduli spaces of Riemannian metrics with non-negative Ricci or non-negative sectional curvature on closed and open manifolds, and present recent joint work with Michael Wiemeler. In particular, we construct the first classes of manifolds for which these spaces have non-trivial rational homotopy, homology and cohomology groups.
日時：2017年10月23日（月）17:00~18:00
会場：学習院大学(目白キャンパス) 南1号館304教室
Speaker：Prof. Athanase Papadopoulos (IRMA, Univ. Strasbourg/CNRS)
Title："On some theorems on spherical geometry from Menelaus' Spherics ”
ABSTRACT:
The « Spherics » by Menelaus of Alexandria (1st-2nd c. A.D.) is the most important book ever written on spherical geometry. It is a profound work. It contains 91 propositions, and some of them are very difficult to prove. An edition, from Arabic texts (the Greek original does not survive), is being published now by De Gruyter, in their series Scientia Graeco-Arabica, No.21.
https://www.degruyter.com/view/product/496630
This publication contains in particular the first English translation of Menelaus' treatise. In this talk, I will explain some of the major theorems on spherical geometry contained in this work.
日時：2017年7月3日（月）16:00~16:40 Part 1 (introductory) 16:45~17:30 Part 2 (advanced)
会場：学習院大学(目白キャンパス) 南1号館303教室
Speaker：Prof. Claus Hertling (University of Mannheim)
Title："Marked singularities, their moduli spaces, period maps and Stokes structures ”
ABSTRACT:
Holomorphic functions with isolated singularities can be considered in analogy to compact holomorphic curves. The topology is much richer. But for singularities with fixed topological data, there is also a moduli space, a period map to a space of generalizations of Hodge structures, and a Torelli problem. The talk will present results and conjectures on this, for unmarked and for marked singularities. It will also say something new on generic members of universal unfoldings and their Stokes structures.
日時：2017年7月3日（月）16:00~16:40 Part 1 (introductory) 16:45~17:30 Part 2 (advanced)
会場：学習院大学(目白キャンパス) 南1号館303教室
Speaker：今城洋 亮 (Kavli IPMU)
Title："Special Lagrange部分多様体の特異点 ”
ABSTRACT:
Special Lagrange部分多様体はHarvey--Lawsonが導入した概念で、ある特殊なクラスの（高次元）極小曲面である。幾何学的測度論によりSpecial Lagrange部分多様体の特異点が自然に定義される。一方4次元Yang--Mills gauge theoryやSymplectic多様体のPseudo-Holomorphic curveについては特異点の扱いがわかっている。しかしSpecial Lagrange部分多様体の特異点はより複雑である。もう一方String Theoryとの関係から深谷圏の研究が進んでおり、その結果をSpecial Lagrange部分多様体の特異点の研究に応用することもできる。ただし深谷圏のObjectは今の所Non-singular Lagrangian（あるいは赤穂JoyceのImmersed Lagrangian）に限られ、両者の関係はまだ明らかでない。本講演ではいくつか具体的なSingularityに関する私の結果を紹介する。
日時：2017年4月24日（月）16:00~16:30 coffee / tea
16:30~17:10 Part 1 (introductory)
17:15~18:00 Part 2 (advanced)
会場：早稲田大学理工キャンパス 51号館18階 06教室
Speaker：Mao-Pei Tsui (National Taiwan University)
Title："Stability and Uniqueness of Minimal Surface Systems ”
ABSTRACT:
It is well-known that the solution to minimal surface equation subject to the Dirichlet boundary condition is unique and stable in codimension one case. However in the higher codimension case, Lawson and Osserman discovered a remarkable counterexample to the uniqueness and stability of solutions of the minimal surface systems. In this talk, we explain some recent results about the stability and uniqueness of minimal surface systems. This is joint work with Yng-Ing Lee and Yuan Shyong Ooi.
日時：2016年1月16日（月）16:00~16:40 Part 1 (introductory)
16:45~17:30 Part 2 (advanced)
Venue： Gakushuin Univ., South Building 1-303
Speaker：Prof. Marc Troyanov (スイス連邦工科大学ローザンヌ校 (EPFL))
Title：" The Binet-Legendre metric in Finsler geometry and some applications”
ABSTRACT:
The Binet-Legendre metric is a canonical Riemannian metric associated to a given metric on a given manifold; it has a well controlled behaviorunder isometries, conformal transformations or bi-Lipschitz deformations that makes it an efficient tool to solve problems in Finsler geometry by reducing them to their Riemannian counterpart.
In this talk I will survey some recent applications of the Binet-Legendre metrics to solve some specific Finslerian problems. This is joint work with V. Matveev.
日時：2016年11月28日（月）16:00~16:40 Part 1 (introductory)
16:45~17:30 Part 2 (advanced)
Venue： Gakushuin Univ., South Building 1-303
Speaker：Prof. Chikako Mese (Johns Hopkins)
Title：" Harmonic maps, bubbling and application to the non-smooth uniformization problem”
ABSTRACT:
We will discuss the Sacks and Uhlenbeck Theorem regarding the "bubbling phenomena" for harmonic maps in the singular setting. Specifically, we have the following dichotomy: given a finite energy map from a Riemann surface into a compact locally CAT(k) space X, either there exists a harmonic map homotopic to the given map or there exists a bubble, i.e. a conformal harmonic map from the standard 2-sphere to X. As an application, we give a harmonic maps approach to the non-smooth uniformization problem of finding a conformal or quasiconformal map between the standard 2-phere and a metric space homeomorphic to a 2-sphere.
日時：2016年10月31日（月）15:30~16:00 coffee / tea
16:00~16:40 Part 1 (introductory)
16:45~17:30 Part 2 (advanced)
会場：早稲田大学理工キャンパス 51号館18階 18-12教室
講演者：金沢 篤 氏 (京都大学)
題目："Tyurin予想とSYZミラー対称性 ”
概要：
本講演では主にCalabi-Yau多様体とFano多様 体の ミ ラー対称性をSYZミラー対称性の視点からお話します。まずCalabi-Yau多様体が Fano多様体の和に退化する状況は代数幾何において基本的です。このときCalabi-Yau多様体の幾何と退化先のFano多様体の 幾何の間の関係を 問うものにTyurin予想があります。SYZミラー対称性のアイデアがTyurin予想とどのように関係するのか、講演者の最近の結果 を交えて解説します。
日時：2016年10月3日（月）16:00~16:40 Part 1 (introductory)
16:45~17:30 Part 2 (advanced)
会場：学習院大学(目白キャンパス) 南1号館303教室
講演者： 西納武男氏 (立教大学)
題目："多 様体の退化と変形理論 ”
概要：
複素多様体の内部の正則曲線の挙動を調べる際, 存在と変形を知ることは重要な課題である。特定の正則曲線の構成のために変形理論を用いることはよくあるが, 価値の高い正則曲線を得るには変形理論の方も難しくなり, 特に障害がある場合には一般に困難が生じる。また, 変形を始める際に用いる正則曲線をうまく構成することもまた別の問題である。この講演では, 多様体の退化を用いてこれらの問題を考察する手法について説明したい。
日時：2016年6月17日（金）15:30~16:00 coffee / tea
16:00~16:40 Part 1 (introductory)
16:45~17:30 Part 2 (advanced)
会場：早稲田大学理工キャンパス 51号館18階 18-06教室
講演者：山田澄生氏 (学習院大学)
題目："Einstein方程式およびEinstein-Maxwell方 程式 の幾 何学 ”
概要：
一般相対性理論の最も大きな未解決問題であ る宇 宙検 閲官予想と関連して、ペンローズ不等式という時空の幾何学と時空の漸近的不変量との間に成立する関係が ある。真空または電磁場が存在する時空を表すアインシュタイン方程式の厳密解を、ペンローズ不等式の剛性と解釈することで一般的な時 空が、ペンロース不等 式の意味で変分的に特徴付けられることを解説する。ここで紹介する結果は、Marcus Khuri氏およびGilbert Weinstein氏との15年来の共同研究である。
日時：2016年5月13日（金）16:00~16:40 Part 1 (introductory)
16:45~17:30 Part 2 (advanced)
会場：学習院大学(目白キャンパス) 南1号館303教室
講演者： 三石 史人氏 (学習院大学)
題目："アレクサンドロフ空間の良い被覆とその応用 ”
概要：
アレクサンドロフ空間とは, 曲率の下限の概念を備えた完備距離空間であり,リーマン多様体の列の適切な意味の極限空間や,リーマン多様体の(固定点を持ち得る) 等長群作用の商空間とし て自然に現れます.私自身は当面は, アレクサンドロフ空間を徹底的に調べつくすという事に興味があります.今回は最近の山口孝男氏との共同研究を通じて得られた一連の結 果のうち,アレクサン ドロフ空間の距離空間としての良い性質及び,その性質と非崩壊極限との相性の良さを紹介します.
日時：2016年4月15日（金）15:30~16:00 coffee / tea
16:00~16:40 Part 1 (introductory)
16:45~17:30 Part 2 (advanced)
Venue：早稲田大学理工キャンパス 51号館18階 18-12教室
Speaker：Uwe Semmelmann (University of Stuttgart)
Title："Almost complex structures on quaternionic Kähler manifolds and symmetric spaces”
ABSTRACT:
In my talk I will explain how to prove the non-existence of almost complex structures on certain classes of manifolds, e.g. quaternion Kähler manifolds and homogeneous spaces of non vanishing Euler characteristic. The proof is based on the Atiyah-Singer index theorem and elementary calculations with characteristic classes. This is a joint work with Paul Gauduchon and Andrei Moroianu.
日時：2016年4月15日（金）15:30~16:00 coffee / tea
16:00~16:40 Part 1 (introductory)
16:45~17:30 Part 2 (advanced)
会場：早稲田大学理工キャンパス 51号館18階 18-12教室
講演者：河井 公大朗 氏 (東大数理)
題目："Cohomogeneity one coassociative submanifolds ”
日時：2015年12月7日（月）16:00~16:40 Part 1 (introductory)
16:45~17:30 Part 2 (advanced)
会場：学習院大学(目白キャンパス) 南1号館103教室
Speaker： Richard Schoen (UC Irvine, Stanford University)
Title："Extremal eigenvalue problems and minimal surfaces ”
ABSTRACT:
It turns out that the metrics that arise from certain classes of minimal surfaces are extremal for eigenvalues in the space of all metrics on the surface. We will describe this connection for minimal surfaces in spheres and for free boundary minimal surfaces in the ball. We will then summarize the results which have been obtained in solving such extremal problems.
日時：2015年10月26日（月）15:30~16:00 coffee / tea
16:00~16:40 Part 1 (introductory)
16:45~17:30 Part 2 (advanced)
会場：早稲田大学理工キャンパス 55号館N棟1階 第一会議室
講演者：宮岡礼子 氏（東北大学）
題目："Hamiltonian non-displaceability of the Gauss image of isoparametric hypersurfaces”