## Colloquiums

### Department Colloquium (01/06/2017)

2017.05.24 Wed up
Date: June 1st, 2017, 16:30–
Place: Colloquium Room, West Wing
Speakers:  1. Tetsuya Abe(Ritsumeikan University),  2. Andrea Collevecchio (Monash University)

### Colloquium [June 23, 2016]

2016.06.17 Fri up

June 23, 2016 @BKC, West Wing 6F, Colloquium room 17:30-18:30

Time: 17:30-18:30

Mouez Dimassi (University of Bordeaux and Ritsumeikan University)

TitleSemiclassical Trace Formula for Systems of h-Pseudodifferential Operators and Application to the Spectral Shift Function

AbstractIn this talk we give a microlocal trace formula for a system of h-pseudodiifferential operators.

We apply this trace formula to the asymptotic of the counting function of the number of eigenvalues and to the asymptotics of the spectral shift function of the semiclassical Schrödinger operator with matrix valued potential.
Our proofs are based  on a time independent method.
This a joint work with S. Fujiié  and M. Assal.

### Colloquium [May 27, 2016]

2016.05.17 Tue up

May 27, 2016 @BKC, Forest House F105, 16:30-18:00

1. Time: 16:30-17:10

Keita Owari (Ritsumeikan University)

Title: On Convex Functions on Orlicz Spaces with $\Delta_2$-Conjugates

Abstract: We show that in an Orlicz space $$L^\Phi$$ with the conjugate Young function $$\Psi$$ being $$\Delta_2$$ (so $$L^\Phi$$ is the dual of $$L^\Psi$$), a proper convex function has a $$\langle L^\Phi,L^\Psi\rangle$$-dual representation iff it is order lower semicontinuous; more precisely, a convex set $$C\subset L^\Phi$$ is $$\sigma(L^\Phi,L^\Psi)$$-closed iff for each order interval $$[-\eta,\eta]=\{\xi:-\eta\leq \xi\leq \eta\}$$ ($$0\leq \eta\in L^\Phi$$), the intersection $$C\cap [-\eta,\eta]$$ is closed in $$L^0$$. The result is based on the following technical lemma: for any norm bounded sequence $$(\xi_n)_n$$ in $$L^\Phi$$ which converges in probability to $$0$$, there exist forward convex combinations $$\zeta_n\in \mathrm{conv}(\xi_n,\xi_{n+1},…)$$ as well as an element $$\eta\in L^\Phi_+$$ such that $$\zeta_n\rightarrow 0$$ and $$|\zeta_n|\leq \eta$$. We show also that a finite-valued convex function on $$L^\Phi$$ is $$\tau(L^\Phi,L^\Psi)$$-continuous iff it is sequentially $$\tau(L^\Phi,L^\Psi)$$-continuous on order intervals, and the condition is equivalent to the order continuity of the function.
This is a Joint work with Freddy Delbaen (ETH Zürich and Univ. Zürich).

2. Time: 17:20-18:00

Daisuke Tarama (Ritsumeikan University)

Title: Elliptic brations associated to free rigid bodies

Abstract: The free rigid body dynamics stands for a dynamical system describing the rotational motion of a rigid body under no external force, which is a typical solvable example in analytical mechanics. Mathematically, the dynamics is formulated as a Hamiltonian system on the cotangent bundle of the three-dimensional rotation group. One can also regard it as the geodesic flow on the rotation group with respect to a left-invariant metric. Because of its symmetry, the dynamics can essentially be described by Euler equation on the threedimensional Euclidean space, which is completely integrable. The integral curve of this equation is in fact a smooth elliptic curve. It is also known that one can associate a Lax equation whose spectral curve is again a smooth elliptic curve.
Varying the parameters of the system, one obtains two elliptic fibrations over threedimensional projective space. In this talk, the singular fibres and the monodromy of these fibrations, as well as their mutual relation, are analysed and the link to Birkhoff normal forms, introduced from the viewpoint of Hamiltonian systems, will be also mentioned.

This talks is based on the joint works with Isao Naruki and Jean-Pierre Françoise.

### Colloquium [January 25, 2016]

2016.01.06 Wed up

January 25, 2016 @BKC campus, West Wing 7F, Mathematics Lab 1, 16:30-18:00

1. Time: 16:30-17:10

2. Time: 17:20-18:00

### Colloquium [October 30, 2015]

2015.10.15 Thu up
Date: 16:30–17:30, October 30, 2015
Place: BKC, Forest House F104
Speaker: Shin Harase (Ritsumeikan University)
Title : Implementing 64-bit maximally equidistributed Mersenne Twisters
Abstract: CPUs and operating systems are moving from 32 to 64 bits, and hence it is important to have good pseudorandom number generators designed to fully exploit these word lengths. However, existing 64-bit very long period generators based on linear recurrences modulo 2 are not completely optimized in terms of the equidistribution properties. In this talk, we develop 64-bit maximally equidistributed pseudorandom number generators that are optimal in this respect and have speeds equivalent to 64-bit Mersenne Twisters. This talk is based on a joint work with Takamitsu Kimoto at Recruit Holdings Co., Ltd.

### Colloquium [July 14, 2015]

2015.07.01 Wed up
Date: 16:30–17:30, July 14, 2015
Place: BKC, Forest House F111
Speaker: Fabrice Baudoin (Perdue University)
Title : Hypocoercive diffusions
Abstract: In this talk, we will present a new method to study the convergence to equilibrium of hypocoercive diffusions. The method is based on local computations and parallels the Bakry-Emery approach to hypercontractivity.

### Colloquium [June 26, 2015]

2015.06.16 Tue up
Date: 16:30–17:30, June 26, 2015
Place: BKC, Forest House F111
Speaker: Vania Sordoni(University of Bologna)
Title : Gevrey microhyperbolicity and FBI transform.
Abstract:
We  study the  Gevrey singularities of the solution of  microhyperbolic  equations by using exponential weighted estimates in the phase space. In particular, we recover  some known results on the propagation of Gevrey regularity  in a elementary way, using microlocal exponential estimates.

### Colloquium [May 28, 2015]

2015.05.18 Mon up

May 28, 2015 @BKC campus, Forest House F107, 16:30-18:00

1. Time: 16:30-17:10

Freddy Delbaen
(ETH and UNIZH)

Title: Risk Measures, Orlicz Spaces and Mackey Topology

Abstract: For a risk measure defined on $$L^\infty$$, there is a stronger continuity property which can be translated as (sequential) continuity on the bounded sets for the Mackey topology induced by $$L^1$$.  This is a more complicated way of saying that the risk measure satisfies a dominated convergence theorem.  It was proved (by Cheridito and Li) that this implies a continuity property on the whole space (not just on bounded sets).  One can ask whether such a phenomenon exists for convex functions defined on the dual of an arbitrary Banach space.  There are several extensions possible.  The general result, although straightforward in convex function theory,  seems new.  Whether sequential continuity implies continuity is related to a property called strongly weakly compactly generated (SWCG).  There are counterexamples for spaces not satisfying the SWCG property.   In the talk I will put emphasis on the relation between risk measures, Orlicz spaces and Mackey topology.  I will not make the excursion to Banach space theory.

2. Time: 17:20-18:00

André Martinez(University of Bologna and Ritsumeikan University)

Title: Optimal estimates for Helmholtz resonators with straight neck in any dimension.

Abstract: This is a joint work with Alain Grigis and Thomas Duykaerts where we obtain an optimal bound on the width of the lowest resonance for a general Helmholtz resonators with straight neck. Such a resonator consists of a bounded cavity, connected with the exterior by a thin tube. The frequency of the sounds it produces are determined by the shape of the cavity, and one expects that their duration is related to the length of the tube and to the diameter of its section. From a mathematical point of view, this phenomena is described by the resonances of the Dirichlet Laplacian on the domain consisting of the union of the cavity, the tube, and the exterior. Here, we obtain an asymptotic estimate on the duration of the sounds when the width of the tube tends to zero. This estimate shows that this duration is exponentially large, with a rate that is proportional to the length of the tube, and inversely proportional to its width. The proof is based on previous results obtained by Hislop-Martinez and Martinez-Nédélec, and on a recent version of Carleman estimates due to Kenig-Sjostrand-Uhlman.

### Colloquium [April 23, 2015]

2015.04.15 Wed up
April 23, 2015 @BKC campus, Forest House F109, 16：30–18:00

1. Time: 16:30 — 17:10
Seung-Hyeok Kye;（Seoul National University）
Title  :Positive bi-linear maps as tri-partite entanglement witnesses
abstract:

We introduce various notions of positivity for bi-linear maps in operator systems. They are witnesses for various notions of tri-partite entanglement when the domains and ranges are matrix algebras. We present concrete examples of witnesses for three qubit entanglement.

2. Time: 17:20 — 18:00
Kazuki Utsumi （Ritsumeikan University）
Title  : Classification problems of Jacobian fibrations on K3 surfaces

abstract :
Jacobian fibrations on K3 surfaces can be regarded as elliptic curves over the rational function field. We introduce classification problems and their answers for some K3 surfaces.

contact:
Hiraku Nozawa ; e-mail <hnozawa AT fc.ritsumei.ac.jp>
Yuri Imamura ; e-mail <imamuray AT fc.ritsumei.ac.jp>

### Colloquium [January 16, 2015]

2015.01.08 Thu up
Date: 17:00–17:50, January 16, 2015
Place: The 1st Lab. of Math. on the 7th floor of West Wing
Speaker: Jens Wittsten　(Ritsumeikan University)
Title : An interpolation problem arising in seismic imaging
Abstract:
In seismic imaging, one wishes to use knowledge of reflected seismic waves to make an image of the Earth’s sub-surface. However, in marine seismic surveys (such as towed streamers), the obtained data is typically undersampled or has missing traces. The aim of this talk is to (briefly) discuss the mathematics behind the seismic imaging method, and to describe one way to interpolate the known data in case of missing traces, using a type of anisotropic diffusion to fill in the gaps. This is based on joint work with F. Andersson and Y. Morimoto.