Speaker |
Atsushi Takeuchi (Osaka City University) |
Title |
Stochastic calculus for Hawkes processes |
Date |
FEBRUARY 20 (Wed.) 2019, 16:30~17:30
|
Place |
Dept. of Mathematics, Faculty of Science Bldg., E408 |
Abstract |
Jump processes with c\’ad-l\’ag sample paths, that is, the right-
continuous ones with left hand limits, are often used in our daily
life, in order to describe various models such as the ones in
mathematical finance. Hawkes processes are self-exciting point
processes depending on the past histories. In this talk, the integration
by parts formulas on the marked Hawkes process and the related
topics shall be introduced from the viewpoint of the recent joint works
on the Malliavin calculus with A. Kohatsu-Higa (Ritsumeikan University,
JAPAN). |
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 2019.2.5