過去の記録 ~12/05本日 12/06 | 今後の予定 12/07~


16:30-18:00   数理科学研究科棟(駒場) 128号室
酒匂宏樹 氏 (東大数理)
Recent results for amalgamated free products of type II$_1$ factors



14:40-16:10   数理科学研究科棟(駒場) 128号室
竹崎正道 氏 (UCLA)
冨田竹崎理論とその応用 (5)



14:40-16:10   数理科学研究科棟(駒場) 128号室
竹崎正道 氏 (UCLA)
冨田竹崎理論とその応用 (4)


16:30-18:00   数理科学研究科棟(駒場) 056号室
Tea: 16:00 - 16:30 コモンルーム
Alexander Getmanenko 氏 (IPMU)
Resurgent analysis of the Witten Laplacian in one dimension
[ 講演概要 ]
I will recall Witten's approach to the Morse theory through properties of a certain differential operator. Then I will introduce resurgent analysis -- an asymptotic method used, in particular, for studying quantum-mechanical tunneling. In conclusion I will discuss how the methods of resurgent analysis can help us "see" pseudoholomorphic discs in the eigenfunctions of the Witten Laplacian.


Kavli IPMU Komaba Seminar

16:30-18:00   数理科学研究科棟(駒場) 002号室
Makoto Sakurai 氏 (東京大学大学院数理科学研究科)
Differential Graded Categories and heterotic string theory
[ 講演概要 ]
The saying "category theory is an abstract nonsense" is even physically not true.
The schematic language of triangulated category presents a new stage of string theory.

To illuminate this idea, I will draw your attention to the blow-up minimal model
of complex algebraic surfaces. This is done under the hypothetical assumptions
of "generalized complex structure" of cotangent bundle due to Hitchin school.
The coordinate transformation Jacobian matrices of the measure of sigma model
with spin structures cause one part of the gravitational "anomaly cancellation"
of smooth Kahler manifold $X$ and Weyl anomaly of compact Riemann surface $\\Sigma$.

$Anom = c_1 (X) c_1 (\\Sigma) \\oplus ch_2 (X)$,

in terms of 1st and 2nd Chern characters. Note that when $\\Sigma$ is a puctured disk
with flat metric, the chiral algebra is nothing but the ordinary vertex algebra.

Note that I do not explain the complex differential geometry,
but essentially more recent works with the category of DGA (Diffenreial Graded Algebra),
which is behind the super conformal field theory of chiral algebras.

My result of "vanishing tachyon" (nil-radical part of vertex algebras)
and "causality resortation" in compactified non-critical heterotic sigma model
is physically a promising idea of new solution to unitary representation of operator algebras.
This idea is realized in the formalism of BRST cohomology and its generalization
in $\\mathcal{N} = (0,2)$ supersymmetry, that is, non-commutative geometry
with non-linear constraint condition of pure spinors for covariant quantization.



13:30-16:00   数理科学研究科棟(駒場) 117号室
Andrei Marshakov 氏 (Lebedev Physical Institute) 13:30-14:30
Tau-functions of Toda theories, partitions and conformal blocks
[ 講演概要 ]
I discuss the class of tau-functions,
corresponding to special solutions of integrable systems,
related to Hurwitz numbers and supersymmetric Yang-Mills
theories. Their natural generalization turn to coincide with
the conformal blocks of two-dimensional conformal
field theories. In special case these conformal
blocks turn into the scalar products of certain ``coherent
states'' in the highest-weight module of the Virasoro
algebra, generalizing the matrix elements
for the well-known coherent states in Fock spaces.
TBA 氏 (TBA) 15:00-16:00
[ 講演概要 ]



16:20-17:50   数理科学研究科棟(駒場) 056号室
藤原 洋 氏 (インターネット総合研究所代表取締役所長)


16:00-17:30   数理科学研究科棟(駒場) 002号室
大西 勇 氏 (広島大学大学院理学研究科)
A Mathematical Aspect of the One-Dimensional Keller and Rubinow Model for Liesegang Bands
[ 講演概要 ]
In 1896, colloid-chemist R.E. Liesegang [4] observed strikingly
regular patterns in precipitation-reaction processes, which are referred to as Liesegang bands or rings, according to their shape. In this talk I introduce an attempt to understand from a mathematical viewpoint the experiments in which regularized structures with spatially distinct bands of precipitated material are exhibited, with clearly visible scaling properties. This study is a result [1] of a collaboration with Professors D. Hilhorst, R. van der Hout, and M. Mimura.


[1] Hilhorst, D., van der Hout, R., Mimura, M., and Ohnishi, I.: A Mathematical Study of the One-Dimensional Keller and Rubinow Model for Liesegang Bands. J. Stat Phys 135: 107-132 (2009)
[2] Kai, S., Muller, S.C.: Spatial and temporal macroscopic structures in chemical reaction system: precipitation patterns and interfacial motion. Sci. Form 1, 8-38 (1985)
[3] Keller, J.B., Rubinow, S.I.: Recurrent precipitation and Liesegang rings. J. Chem. Phys. 74, 5000-5007 (1981)
[4] Liesegang, R.E.: Chemische Fernwirkung. Photo. Archiv 800, 305-309 (1896)
[5] Mimura, M., Ohnishi, I., Ueyama, D.: A mathematical aspect of Liesegang phenomena in two space dimensions. Res. Rep. Res. Inst. Math. Sci. 1499, 185-201 (2006)
[6] Ohnishi, I.,Mimura, M.: A mathematical aspect of Liesegang phenomena. In: Proceedings of Equadiff-11, pp. 343-352 (2005).



16:30-18:00   数理科学研究科棟(駒場) 128号室
同じ週の木・金に柏キャンパスで開催されるIMPU workshopの講演内容に関係しています。 http://faculty.ms.u-tokyo.ac.jp/~topology/IPMU/workshop.html
Gert Heckman 氏 (IMAPP, Faculty of Science, Radboud University Nijmegen)
Birational Hyperbolic Geometry
[ 講演概要 ]
We study compactifications for complex ball quotients.
We first recall the Satake-Bailey-Borel compactification and the Mumford resolution.
Then we discuss compactifications of ball quotients minus a totally geodesic divisor.
These compactifications turn up for a suitable class of period maps.
[ 参考URL ]



16:40-18:10   数理科学研究科棟(駒場) 126号室
Gerard van der Geer 氏 (Universiteit van Amsterdam)
Cohomology of moduli spaces of curves and modular forms
[ 講演概要 ]
The Eichler-Shimura theorem expresses cohomology of local systems
on the moduli of elliptic curves in terms of modular forms. The
cohomology of local systems can be succesfully explored by counting
points over finite fields. We show how this can be applied to
obtain a lot of information about the cohomology of other moduli spaces
of low genera and also about Siegel modular forms of genus 2 and 3.
This is joint work with Jonas Bergstroem and Carel Faber.



16:20-17:50   数理科学研究科棟(駒場) 117号室
辻 芳彦 氏 ((社)日本アクチュアリー会事務局事務局長)


15:00-16:00   数理科学研究科棟(駒場) 370号室
Shuai Lu 氏 (Johann Radon Institute)
Regularized total least squares: computational aspects and error bounds
[ 講演概要 ]
For solving linear ill-posed problems, regularization methods are required when the right hand side and/or the operator are corrupted by some noise. In the present talk, regularized solutions are constructed using regularized total least squares and dual regularized total least squares. We discuss computational aspects and provide order optimal error bounds that characterize the accuracy of the regularized solutions. The results extend earlier results where the operator is exactly given. We also present some numerical experiments, which shed light on the relationship between RTLS, dual RTLS and the standard Tikhonov regularization.



16:30-18:00   数理科学研究科棟(駒場) 128号室
Robert Coquereaux 氏 (CNRS/CPT, Marseille)
Fusion graphs for Lie groups at level k and quantum symmetries


16:30-17:30   数理科学研究科棟(駒場) 270号室
Michael I. Tribelsky 氏 (MIREA (Technical University), Moscow, Russia)
Spectral properties of Nikolaevskiy chaos



16:30-17:30   数理科学研究科棟(駒場) 370号室
Michael Ruzhansky 氏 (Imperial College, London)
Dispersive and Strichartz estimates for hyperbolic equations of general form



16:30-18:00   数理科学研究科棟(駒場) 056号室
Tea: 16:00 - 16:30 コモンルーム
Alex Bene 氏 (IPMU)
A new appearance of the Morita-Penner cocycle
[ 講演概要 ]
In this talk, I will recall the Morita-Penner cocycle on the dual fatgraph complex for a surface with one boundary component. This cocycle, when restricted to paths representing elements of the mapping class group, represents the extended first Johnson homomorphism \\tau_1, thus can be viewed as a (in some specific sense canonical) "groupoid extension" of \\tau_1. There are now several different contexts in which this cocycle can be constructed, and in this talk I will briefly review several of them, including one discovered in the context of finite type invariants of homology cylinders in joint work with J.E. Andersen, J-B. Meilhan, and R.C. Penner.



10:30-12:00   数理科学研究科棟(駒場) 128号室
Pietro Corvaja 氏 (Università di Udine)
On Vojta's conjecture in the split function field case



16:20-17:50   数理科学研究科棟(駒場) 117号室
辻 芳彦 氏 ((社)日本アクチュアリー会事務局事務局長)


16:30-17:30   数理科学研究科棟(駒場) 002号室
お茶&Coffee&お菓子: 16:00~16:30 (コモンルーム)
辻 雄 氏 (東京大学大学院数理科学研究科)
[ 講演概要 ]
複素や実の多様体の特異コホモロジーを微分形式の言葉で記述する理論として、de Rhamの定理やHodge理論が良く知られている。p進Hodge理論は、これらの類似をp進体上の代数多様体のp進エタール・コホモロジーで考える理論である。p進エタール・コホモロジーにはp進体の絶対ガロア群が非常に複雑に作用しており、この作用を分かりやすい別の言葉で記述する理論の構築が、p進Hodge理論における大きな課題となっている。前半でp進Hodge理論の研究の歴史や背景について概観した後、後半ではp進体の絶対ガロア群のp進表現の相対版である、p進体上定義された代数多様体上のp進エタール層についての最近の研究を紹介する。


15:00-16:10   数理科学研究科棟(駒場) 128号室
Vladimir Bogachev 氏 (Moscow State University)
On invariant measures of diffusion processes with unbounded drifts
[ 参考URL ]



16:30-18:00   数理科学研究科棟(駒場) 128号室
Adam Skalski 氏 (Lancaster University)
On some questions related to Voiculescu's noncommutative topological entropy


10:40-12:10   数理科学研究科棟(駒場) 128号室
竹崎正道 氏 (UCLA)
冨田竹崎理論とその応用 (3)


16:30-17:40   数理科学研究科棟(駒場) 122号室
深澤 正彰 氏 (大阪大学 金融・保険教育研究センター)
[ 講演概要 ]
The notion of asymptotic efficiency for discrete hedging is introduced and a discretizing strategy which is asymptotically efficient is given explicitly. A lower bound for asymptotic risk of discrete hedging is given, which is attained by a simple discretization scheme. Numerical results for delta hedging in the Black-Scholes model are also presented.
[ 参考URL ]


13:00-14:15   数理科学研究科棟(駒場) 122号室
深澤 正彰 氏 (大阪大学 金融・保険教育研究センター)
Asymptotic Analysis for Stochastic Volatility (確率的ボラティティの漸近解析)



15:30-17:00   数理科学研究科棟(駒場) 122号室
Jean-Dominique Deuschel 氏 (TU Berlin)
Mini course on the gradient models, Ⅲ: Non convex potentials at high temperature
[ 講演概要 ]
In the non convex case, the situation is much more complicated. In fact Biskup and Kotecky describe a non convex model with several ergodic components. We investigate a model with non convex interaction for which unicity of the ergodic component, scaling limits and large deviations can be proved at sufficiently high temperature. We show how integration can generate strictly convex potential, more precisely that marginal measure of the even sites satisfies the random walk representation. This is a joint work with Codina Cotar and Nicolas Petrelis.

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