【講演題目】On diffeomorphisms of irreducible 4-manifolds
【開催期間】11月28日(金) 15:30〜16:30
【場所】W1-D-313 （数理談話会＋幾何学セミナー＋トポロジーセミナー合同セミナー）
※15:00〜15:30にティータイム（談話室，C-515）があります．
【講師】今野北斗氏（東京大学）
【講演要旨】可微分閉4次元多様体が既約 (irreducible) とは，それが非自明な連結和分解を持たないことをいう．その定義から，既約な4次元多様体は4次元トポロジーにおけるbuilding blockであり，また典型的には (minimalな) シンプレクティック4次元多様体や複素曲面のunderlyingな可微分多様体として表れる．重要なクラスの4次元多様体であるが，その微分同相群について知られていることは最近まで大変少なかった．この対象に対する微分位相幾何やシンプレクティック幾何の基本的な問題が，族のゲージ理論で解決できることを説明する．
【講演題目】Constraint qualification for generic parameter families of constraints in optimization
【開催期間】11月21日(金) 16:00〜17:00
【場所】W1-C-514 （トポロジーセミナー）
【講師】早野健太氏（慶應義塾大学）
【講演要旨】Constrained optimization is a problem of minimizing objective functions within the feasible set that is described by the system of equalities and inequalities of constraint functions. A fundamental tool for characterizing solutions is the Karush–Kuhn–Tucker (KKT) condition, which requires the existence of suitable Lagrange multipliers. In unconstrained optimization, this reduces to the familiar first-order condition, which every local minimizer satisfies. In constrained problems, by contrast, the existence of multipliers does not automatically follow from local minimality. This fact is precisely what motivates constraint qualifications: they are assumptions placed only on the constraint system, ensuring the validity of the KKT condition at all local minimizers. In this talk, we first introduce a classification result on the map-germs that appear in generic parameter families of constrained functions, obtained by applying techniques from singularity theory. We then explain when the map-germs arising in this classification satisfy several well-known constraint qualifications.
【講演題目】Links of mixed singularities with "nice" properties
【開催期間】11月14日(金) 16:00〜17:00
【場所】W1-C-514 （トポロジーセミナー）
【講師】Raimundo Araujo dos Santos 氏 (University of Sao Paulo, Brazil)
【講演要旨】こちら(pdf ファイル) をご覧ください．以下は TeX 用の原文です．
Given a non-constant holomorphic map germ $f: (\C^{2},0)\to (\C,0)$ it was proved by J. Milnor that, there exists a smooth locally trivial fibration, with projection given by $\arg(f):=\dfrac{f}{\|f\|}:S^{3}_{\epsilon}\setminus (\{f=0\}\cap S_{\epsilon}^{3}) \to S^1,$ for all $\epsilon>0$ small enough. It was called later {\bf the Milnor fibration associated to the singularity $f.$}
In the special case where the singular locus of $f$ is only the origin, $Sing (f)=\{0\},$ it is well known that the isotopy type of $K_{f}:=\{f=0\}\cap S_{\epsilon}^{3}$ does not depend on the choice of $\epsilon$ again, if it is chosen small enough. Hence, one may also associate to the singularity $f$ this interesting topological object $K_{f}$ which is a link on the 3-sphere, in the classical sense of algebraic topology (i.e., {\bf an embedding of finite many disjoint union of $S^1$ into $S^{3}$}).
Now, for a mixed polynomial map germ (to be introduced along the talk) $f: (\C^{2},0)\to (\C,0)$ the Milnor fibration as above is not defined in general, for several many different reasons.
In this talk, with the help of the Newton polyhedron, we will introduce a special class of mixed singularities where one can guarantee the existence of a Milnor fibration (but with projection {\bf not} necessarily given by $arg(f)$ as in the holomorphic case), where somehow is possible to describe the behavior of its associated links $K_{f}:=\{f=0\}\cap S_{\epsilon}^{3}.$
【講演題目】Apparent contours of simplicial maps of closed surfaces into the plane and its Applications
【開催期間】2025年10月6日(月) 16:00〜17:00（注意！！いつもと曜日が異なります）
【場所】W1-C-514 （トポロジーセミナー）
【講師】山本卓宏氏（東京学芸大学）
【講演要旨】可微分写像の特異点論の基本的な研究対象である曲面間のジェネリックな写像は，特異点として折り目特異点，カスプ特異点のみを許容し，その像を写像による曲面の apparent contour と呼ぶ．曲面が閉曲面である場合，apparent contour はカスプ付きつの単純閉曲線になる．閉曲面の apparent contour のうち"単純な"形状に関して，R. Pignoni に始まり，S. Demoto, 亀之園淳, 萩原黎弥, 山本等により研究されてきた．
本講演では，曲面間のジェネリックな可微分写像を援用し，閉曲面から平面への単体写像にジェネリックというクラスを導入する．さらに，閉曲面から平面へのジェネリックな単体写像を用いて閉曲面の apparent contour のうち"単純な" apparent contour を導入し，いくつかの閉曲面に対してその形を決定する．
【講演題目】Leafwise Hodge decomposition
【開催期間】7月11日(金) 16:00～17:30
【場所】W1-C-413 オーディトリアム （幾何学・トポロジー合同セミナー）（注意！！いつもと部屋が異なります）
【講師】Jesús A. Álvarez López 氏（University of Santiago de Compostela/立命館大学）
【講演要旨】First, I will recall the leafwise Hodge decomposition for Riemannian foliations, obtained in collaboration with Yuri Kordyukov in 2000. Next, I will recall two examples of foliations, by Guillemin and by Deninger and Singhoff, where the leafwise Hodge decomposition fails, and even a trace formula for foliated flows fails in the second example. Finally, I’ll explain a different type of leafwise Hodge decomposition that is true in those examples, and how an additional term for the trace formula appears, making it true in the second example. This is a work in progress.