Colloquium (2018)

Speaker Kengo Kawamura (OCAMI)
Title On surface-knots and their diagrams
Date November 28 (Wed.) 2018, 16:30~17:30
Place Dept. of Mathematics, Faculty of Science Bldg., E408
Abstract A surface-knot is a connected closed surface in a 4-space, which is generalization of a knot as a connected closed curve in a 3-space. A diagram of a knot is a projection image of the knot into a 2-plane. It is usual to use a diagram in knot theory. Similarly, a diagram of a surface-knot is defined to be a projection image of the surface-knot into a 3-space. A study of surface-knots together with diagrams has developed since the late 1990s. In this talk, I introduce similarities and differences between surface-knot diagrams and knot diagrams. Also, I show my recent results on the triple point number of a surface-knot.
Speaker Hiroshi Tamaru (Osaka City University)
Title Symmetric spaces, submanifold geometry, and left-invariant metrics.
Date OCTOBER 17 (Wed.) 2018, 16:30~17:30
Place Dept. of Mathematics, Faculty of Science Bldg., E408
Abstract It is an important problem in geometry to study whether a given manifold admit some nice geometric structures. As a Lie group version of this problem, there is a problem to study whether a given Lie group admit some nice left-invariant Riemannian metrics, which has recently been studied actively. For this problem, we propose an approach from the viewpoint of submanifolds in symmetric spaces, and have obtained some results. In this talk, we illustrate our approach, and also survey some previous results on submanifolds in symmetric spaces and also on Einstein solvmanifolds.
Speaker Takuji Nakamura (Osaka Electro-Communication University)
Title On local moves for knots, virtual knots, and welded knots.
Date SEPTEMBER 12 (Wed.) 2018, 16:00~17:00
Place Dept. of Mathematics, Faculty of Science Bldg., E408
Abstract A knot is an embedded circle in the 3-sphere. A knot diagram is a projection image of a knot into the 2-sphere which has only transversal double points equipped with upper/lower information. A local move on a knot diagram is a replacement of a part of the diagram with another partial diagram. Local moves play an important role in Knot theory such as the study on the complexity for knots, the study on geometric/algebraic properties for knots about a given local move, and so on. On the other hand, virtual knots or welded knots are studied as generalizations of ordinary knots. They are defined in terms of a new type of crossings, say virtual crossings and new equivalence relations. In this talk, we introduce several famous local moves for knots, and show some properties about the local moves for knots, virtual knots, and welded knots.
Speaker Hiraku Atobe (The University of Tokyo)
Title On the Ramanujan conjecture for automorphic representations and several liftings
Date JULY 4 (Wed.) 2018, 16:30~17:30
Place Dept. of Mathematics, Faculty of Science Bldg., E408
Abstract Automorphic forms and representations are essential tools in the modern number theory. The Ramanujan conjecture, proven by Deligne, is an important result to treat holomorphic cuspidal automorphic representations of GL(2). For higher rank groups, the same assertion of the Ramanujan conjecture no longer holds. In fact, the Saito-Kurokawa liftings and Duke-Imamoglu-Ibukiyama-Ikeda liftings are counterexamples. In this talk, I will talk about these liftings from the perspective of automorphic representations.
Speaker Toshiaki Hishida (Nagoya University)
Title Asymptotic structure of the steady Navier-Stokes flow in the exterior of a moving obstacle in 2D
Date JUNE 6 (Wed.) 2018, 16:30~17:30
Place Dept. of Mathematics, Faculty of Science Bldg., E408
Abstract Analysis of the steady Navier-Stokes flow in 2D exterior domains is much harder than 3D case and the issue is always the asymptotic behevior of solutions at spatial infinity. The most difficult feature particularly in the case where the obstacle (rigid body) is at rest is the Stokes paradox, which prevents us from the linearization method. In this talk I would like to clarify why the motion (translation/rotation) of the obstacle leads to resolution of the Stokes paradox and how it affects the structure of the flow. Those are interpreted in terms of the asymptotic representation of the flow at infinity which exhibits the leading profile together with its coefficient.
Last Modified on 2018.11.2