過去の記録

代数学コロキウム

16:30-18:45   数理科学研究科棟(駒場) 056号室

Elementary computation of ramified component of the Jacobi sum
[ 講演概要 ]
R. Coleman and W. McCallum calculated the Jacobi sum Hecke characters using their computation of the stable reduction of the Fermat curve in 1988. In my talk, we give an elementary proof of the main result of them without using rigid geometry or the stable model of the Fermat curve.
Christopher Deninger 氏 (Universität Münster) 17:45-18:45
P-divisible groups and the p-adic Corona problem

2009年11月17日(火)

トポロジー火曜セミナー

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

On the $SO(N)$ and $Sp(N)$ free energy of a closed oriented 3-manifold
[ 講演概要 ]
We give an explicit formula of the $SO(N)$ and $Sp(N)$ free energy
of a lens space and show that the genus $g$ terms of it are analytic
in a neighborhood at zero, where we can choose the neighborhood
independently of $g$.
Moreover, it is proved that for any closed oriented 3-manifold $M$
and any $g$, the genus $g$ terms of $SO(N)$ and $Sp(N)$ free energy
of $M$ coincide up to sign.

2009年11月16日(月)

複素解析幾何セミナー

10:30-12:00   数理科学研究科棟(駒場) 128号室

Weighted Green functions of polynomial skew products on C^2

代数幾何学セミナー

16:40-18:10   数理科学研究科棟(駒場) 126号室
Colin Ingalls 氏 (University of New Brunswick and RIMS)
Rationality of the Brauer-Severi Varieties of Skylanin algebras
[ 講演概要 ]
Iskovskih's conjecture states that a conic bundle over
a surface is rational if and only if the surface has a pencil of
rational curves which meet the discriminant in 3 or fewer points,
(with one exceptional case). We generalize Iskovskih's proof that
such conic bundles are rational, to the case of projective space
bundles of higher dimension. The proof involves maximal orders
and toric geometry. As a corollary we show that the Brauer-Severi
variety of a Sklyanin algebra is rational.

2009年11月14日(土)

保型形式の整数論月例セミナー

13:30-16:00   数理科学研究科棟(駒場) 117号室

On weak endoscopic lift (117号室)
[ 講演概要 ]
rank 2のsymplectic 群の保型表現$\\pi$の spinor L-関数(4次)が殆どの素点で楕円保型形式のL-関数の積になっているものをweak ndoscopic liftと呼びます. $\\pi$がtemperedならば, 全てのweak endoscopic liftはrank 4のtheta関数(theta lift)でかける事がBrooks Roberts氏により知られています.

Derivations and Automorphisms on the noncommutative algebra of power series.

[ 講演概要 ]
We discuss a relationship between a class of derivations and a class of automorphisms on the noncommutative algebra of formal power series in two variables. Each class relates bijectively by exponential and logarithm maps. In this talk we define a specific class of derivations, which generates a noncommutaive Lie algebra whose defining relations are related to a classical Witt algebra. The main claim is the explicit description of the
automorphisms which are corresponding to the derivations via exponential map.

2009年11月12日(木)

講演会

10:40-12:10   数理科学研究科棟(駒場) 128号室

作用素環セミナー

16:30-18:00   数理科学研究科棟(駒場) 128号室

Recent results for amalgamated free products of type II$_1$ factors

2009年11月11日(水)

講演会

14:40-16:10   数理科学研究科棟(駒場) 128号室

2009年11月10日(火)

講演会

14:40-16:10   数理科学研究科棟(駒場) 128号室

トポロジー火曜セミナー

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.

2009年11月09日(月)

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.

2009年11月07日(土)

東京無限可積分系セミナー

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
TBA
[ 講演概要 ]
TBA

2009年11月05日(木)

GCOE社会数理講演シリーズ

16:20-17:50   数理科学研究科棟(駒場) 056号室

応用解析セミナー

16:00-17:30   数理科学研究科棟(駒場) 002号室

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.

References:

[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).

2009年11月04日(水)

Lie群論・表現論セミナー

16:30-18:00   数理科学研究科棟(駒場) 128号室

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.
[ 講演参考URL ]
http://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar.html

2009年11月02日(月)

代数幾何学セミナー

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.

2009年10月30日(金)

GCOE社会数理講演シリーズ

16:20-17:50   数理科学研究科棟(駒場) 117号室

アクチュアリーの役割Ⅱ

GCOEセミナー

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.

2009年10月29日(木)

作用素環セミナー

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

講演会

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

2009年10月28日(水)

講演会

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

2009年10月27日(火)

トポロジー火曜セミナー

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.

2009年10月26日(月)

複素解析幾何セミナー

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

2009年10月23日(金)

GCOE社会数理講演シリーズ

16:20-17:50   数理科学研究科棟(駒場) 117号室

アクチュアリーの役割Ⅰ

談話会・数理科学講演会

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)

p進エタール層のp進Hodge理論
[ 講演概要 ]