I am an associate professor working at Kyoto University (Department of Mathematics, Graduate School of Science, Kyoto University). My main research fields are low dimensional topology and gauge theory. My Ph.D. advisor was Professor. Mikio Furuta.
The email address has been changed since April 2023.
E-mail: masaki.taniguchi"at"math.kyoto-u.ac.jp
Address: Kitashirakawa Oiwake-cho, Sakyo-ku, Kyoto 606-8502, Japan
My research interests range over 3- and 4-dimensional topology and gauge theory. In particular, I'm interested in homology cobordisms, concordances, (filtered/equivariant/orbifold/real) Floer theory and gauge theory for non-compact 4-manifolds.
Yang-Mills, Seiberg-WItten gauge theory, Donaldson, Seiberg-Witten invariant, Donaldson's diagonalization theorem, Instanton, monopole Floer homology, h-invariant, Seiberg-Witten Floer homotopy type, spaces of Morse trajectories, gauge theory on 4-manifolds with periodic ends, 10/8-inequality, positive scalar curvature, the 3-dimensional homology cobordism group, Seifert hypersurface of 2-knots, Chern-Simons functional for 2-knots, knot group, codimension-1 embedding of 3-manifolds, groups of diffeomorphisms and homeomorphisms of 4-manifolds, Seiberg-Witten Floer homotopy contact invariant, spin symplectic filling, K-theoretic contact invariant, Bauer-Furuta type invariant of Kronheimer-Mworka's invariant for 4-manifold with boundary, adjunction inequality, symplectic cap, H-sliceness in general 4-manifolds, exotic pairs of 4-manifolds with boundary, branched covering spaces of knots and surfaces, involutions on 3- and 4-manifolds, Floer homotopy type for knots and involutions, Floer K-theory for knots and involutions, 10/8-inequality for knots and involutions, relative genus bounds, extension problems of involutions, real Seiberg-Witten theory, stabilizing numbers for knots, exotic diffeomorphisms of 4-manifolds, exotic surfaces in 4-manifolds, exotic codimension-1 embeddings in 4-manifolds, generalized Thurston-Bennequin type inequality, singular instanton knot theory, local equivalence theory with Chern-Simons filtration, satellite operations on the knot concordance group, stabilization of exotic embeddings of 3-manifolds into 4-manifolds, small exotic 4-manifolds, strong cork detections, non-smoothable diffeomorphisms on 4-manifolds, exotic Dehn twits along Seifert 3-manifolds, exotic diffeomorphisms which survive after stabilizations, exotic diffeomorphism on a contractible 4-manifold, involutive (S^1-family ver) instanton Floer homology, strong corks which survive after definite stabilization, linear independence of surgeries of slice knots in the homology bordism group of diffeomorphisms, transverse knot invariants from Floer homotopy, symplectic surfaces, quasi-positivity of Montesinos knots, slice torus invariant from equivariant Seiberg-Witten theory, (2n,1)-cables, sliceness, equivariant lattice homotopy type
Here is a description of the field for students and postdoctoral researchers who are interested in my laboratory.
Schedule of talks (overseas):
Travel schedule (overseas):
22-25, Jun, 2026, Korea, the International Conference for the 80th Anniversary of the Korean Mathematical Society
Conferences and seminars I'm organizing:
Nandemo seminar, an informal seminar at Kyoto University
PCMI, 2026, summer, "Knotted Surfaces in Four-Manifolds", (Park City Mathematics Institute, Research Program Organizer), link
京都大学 大学院理学研究科 数学教室の准教授です. ゲージ理論を用いた低次元トポロジーの研究に興味があります. 4次元におけるホモロジー同境・結び目コンコーダンス, 付随する幾何学的な問題意識, これらを扱う種々のFloer理論を研究してきました. また, 非コンパクト4次元多様体上のゲージ理論の展開, およびその応用にも興味があります.
Yang-Millsゲージ理論, Donaldson, Seiberg-Witten不変量, Donaldsonの対角化定理, インスタントン・モノポール Floerホモロジー, h-不変量, Floer ホモトピー型, Morse trajectoriesの空間,周期的端を持つ多様体に対するゲージ理論, Seiberg-Witten理論, 10/8不等式, 正スカラー曲率の障害, ホモロジー同境群, 2次元結び目のSeifert 超曲面, 2次元結び目のChern-Simons汎関数, 結び目群, 3次元多様体の余次元1の埋め込み, 4次元多様体の(微分)同相群, Seiberg-Witten Floer コンタクト不変量, K理論的コンタクト不変量, 接触構造, シンプレクティック充填, Kronheimer-Mworka's不変量のBauer-Furuta型refinement, adjunction不等式, symplectic cap, 結び目のH-スライス性, 境界付き4次元多様体の微分構造, 結び目の分岐被覆, 対合および結び目に対するFloer homotopy型, 対合および結び目に対するFloer K理論, 対合および結び目に対する10/8不等式, 実Seiberg-Witten理論, 相対種数評価, 対合の拡張問題, エキゾチックな微分同相写像, 4次元多様体内のエキゾチックな曲面・3次元多様体, 一般化されたThurston-Bennequin型不等式, 結び目特異インスタントンFloer理論, 定量的局所同型理論, 結び目同境, 結び目同境群上のサテライト写像, エキゾチック性の安定化, スモールエキゾチック4次元多様体, strongコルク, αβγを用いた種数評価, exotic Dehnツイスト, stabilizationで生き残るエキゾチック微分同相, 可縮な4次元多様体上のエキゾチック微分同相, involutiveインスタントンFloerホモロジー, strong corkのstabilization problem, 微分同相のホモロジー同境群, transverse結び目不変量, symplectic曲面, Montesinos結び目のquasipositivity, (2n,1)-ケーブル, 同変格子ホモトピー型
私の研究室に興味のある学生やポスドクの方向けの分野紹介の文章はここにあります.
メールアドレス: masaki.taniguchi"at"math.kyoto-u.ac.jp
部屋: 理学部3号館225
Researchmap, Research Gate, arXiv
所属学会: 日本数学会
講演予定の集会・セミナー(国内)：
微分トポロジー26, 大谷大学, link
参加予定の集会・セミナー：
京大の情報
世話人をしているセミナー, 集会