Seminar information archive

Seminar information archive ~05/25Today's seminar 05/26 | Future seminars 05/27~

2011/11/22

Operator Algebra Seminars

16:30-18:00   Room #126 (Graduate School of Math. Sci. Bldg.)

Spyridon Michalakis
( Institute for Quantum Information and Matter (Caltech))
Stability of topological phases of matter (ENGLISH)
[ Abstract ]
The first lecture will be an introduction to quantum mechanics and a proof of Lieb-Robinson bounds for constant range interaction Hamiltonians. The second lecture will build on the first to prove a powerful lemma on the transformation of the interactions of generic gapped Hamiltonians to a new set of rapidly-decaying interactions that commute with the groundstate subspace. I call this "The Energy Filtering Lemma". Then, the third lecture will be on the construction of the Spectral Flow unitary (Quasi-adiabatic evolution) and its properties; in particular, the perfect simulation of the evolution of the groundstate subspace within a gapped path. I will end with a presentation of the recent result on the stability of the spectral gap for frustration-free Hamiltonians, highlighting how the previous three lectures fit into the proof.

Tuesday Seminar on Topology

16:30-18:00   Room #056 (Graduate School of Math. Sci. Bldg.)
Toshitake Kohno (The University of Tokyo)
Quantum and homological representations of braid groups (JAPANESE)
[ Abstract ]
Homological representations of braid groups are defined as
the action of homeomorphisms of a punctured disk on
the homology of an abelian covering of its configuration space.
These representations were extensively studied by Lawrence,
Krammer and Bigelow. In this talk we show that specializations
of the homological representations of braid groups
are equivalent to the monodromy of the KZ equation with
values in the space of null vectors in the tensor product
of Verma modules when the parameters are generic.
To prove this we use representations of the solutions of the
KZ equation by hypergeometric integrals due to Schechtman,
Varchenko and others.

In the case of special parameters these representations
are extended to quantum representations of mapping
class groups. We describe the images of such representations
and show that the images of any Johnson subgroups
contain non-abelian free groups if the genus and the
level are sufficiently large. The last part is a joint
work with Louis Funar.

Lie Groups and Representation Theory

16:30-18:00   Room #002 (Graduate School of Math. Sci. Bldg.)
Takayuki Okuda (東京大学大学院 数理科学研究科)
Smallest complex nilpotent orbit with real points (JAPANESE)
[ Abstract ]
Let $\\mathfrak{g}$ be a non-compact simple Lie algebra with no complex
structures.
In this talk, we show that there exists a complex nilpotent orbit
$\\mathcal{O}^{G_\\mathbb{C}}_{\\text{min},\\mathfrak{g}}$ in
$\\mathfrak{g}_\\mathbb{C}$ ($:=\\mathfrak{g} \\otimes \\mathbb{C}$)
containing all of real nilpotent orbits in $\\mathfrak{g}$ of minimal
positive dimension.
For many $\\mathfrak{g}$, the orbit
$\\mathcal{O}^{G_\\mathbb{C}}_{\\text{min},\\mathfrak{g}}$ is just the
complex minimal nilpotent orbit in $\\mathfrak{g}_\\mathbb{C}$.
However, for the cases where $\\mathfrak{g}$ is isomorphic to
$\\mathfrak{su}^*(2k)$, $\\mathfrak{so}(n-1,1)$, $\\mathfrak{sp}(p,q)$,
$\\mathfrak{e}_{6(-26)}$ or $\\mathfrak{f}_{4(-20)}$,
the orbit $\\mathcal{O}^{G_\\mathbb{C}}_{\\text{min},\\mathfrak{g}}$ is not
the complex minimal nilpotent orbit in $\\mathfrak{g}_\\mathbb{C}$.
We also determine $\\mathcal{O}^{G_\\mathbb{C}}_{\\text{min},\\mathfrak{g}}$
by describing the weighted Dynkin diagrams of these for such cases.

2011/11/21

Seminar on Geometric Complex Analysis

10:30-12:00   Room #128 (Graduate School of Math. Sci. Bldg.)
Hisashi Kasuya (University of Tokyo)
Techniques of computations of Dolbeault cohomology of solvmanifolds (JAPANESE)

Seminar on Mathematics for various disciplines

13:30-14:30   Room #056 (Graduate School of Math. Sci. Bldg.)
Ernie Esser (University of California, Irvine)
A convex model for non-negative matrix factorization and dimensionality reduction on physical space (ENGLISH)
[ Abstract ]
A collaborative convex framework for factoring a data matrix X into a non-negative product AS, with a sparse coefficient matrix S, is proposed. We restrict the columns of the dictionary matrix A to coincide with certain columns of the data matrix X, thereby guaranteeing a physically meaningful dictionary and dimensionality reduction. We focus on applications of the proposed framework to hyperspectral endmember and abundances identification and also show an application to blind source separation of NMR data.
This talk is based on joint work with Michael Moeller, Stanley Osher, Guillermo Sapiro and Jack Xin.

Kavli IPMU Komaba Seminar

16:30-18:00   Room #002 (Graduate School of Math. Sci. Bldg.)
Siu-Cheong Lau (IPMU)
Enuemerative meaning of mirror maps for toric Calabi-Yau manifolds (ENGLISH)
[ Abstract ]
For a mirror pair of smooth manifolds X and Y, mirror symmetry associates a complex structure on Y to each Kaehler structure on X, and this association is called the mirror map. Traditionally mirror maps are defined by solving Picard-Fuchs equations and its geometric meaning was unclear. In this talk I explain a recent joint work with K.W. Chan, N.C. Leung and H.H. Tseng which proves that mirror maps can be obtained by taking torus duality (the SYZ approach) and disk-counting for a class of toric Calabi-Yau manifolds in any dimensions. As a consequence we can compute disk-counting invariants by solving Picard-Fuchs equations.

2011/11/19

Monthly Seminar on Arithmetic of Automorphic Forms

10:15-12:30   Room #117 (Graduate School of Math. Sci. Bldg.)
Jiro Sekiguchi (Tokyo Univ. of Agriculture) 10:15-11:15
Hyperelliptic integrals related with dihedral groups (JAPANESE)
Yoshihiro Ohnishi (Yamanashi University) 11:30-12:30
Survey on the generalized Bernoulli-Hurwitz numbers for a higher genus algebraic function, and some problems (JAPANESE)

2011/11/18

Lectures

15:00-16:00   Room #052 (Graduate School of Math. Sci. Bldg.)
Hiroshi Isozaki (University of Tsukuba)
Inverse problems for heat equations with discontinuous conductivities
(JAPANESE)
[ Abstract ]
In a bounded domain $\\Omega \\subset {\\bf R}^n$, consider the heat
equation $\\partial_tu = \\nabla(\\gamma(t,x)\\nabla u)$. The heat
conductivity is assumed to be piecewise constant : $\\gamma = k^2$ on
$\\Omaga_1(t) \\subset\\subset \\Omega$, $\\gamma(t,x) = 1$ on
$\\Omega\\setminus\\Omega_1(t)$. In this talk, we present recent results
for the inverse problems of reconstructing $\\gamma(t,x)$ from the
Dirichlet-to-Neumann map :
$u(t)|_{\\partial\\Omega} \\to $\\partial_{\\nu}u|_{\\partial\\Omega}$ for a time
interval $(0,T)$. These are the joint works with P.Gaitan, O.Poisson,
S.Siltanen, J.Tamminen.

2011/11/17

GCOE lecture series

17:00-18:00   Room #370 (Graduate School of Math. Sci. Bldg.)
Oleg Emanouilov (Colorado State University)
Recovery of weakly coupled system from partial Cauchy data (ENGLISH)
[ Abstract ]
We consider the inverse problem for recovery of coefficients of weakly coupled system of elliptic equations in a bounded 2D domain.

Operator Algebra Seminars

16:30-18:00   Room #117 (Graduate School of Math. Sci. Bldg.)
Takehiko Yamanouchi (Tokyo Gakugei University)
Hecke pairs in ergodic measured equivalence relations (JAPANESE)

2011/11/16

Seminar on Geometric Complex Analysis

16:30-18:00   Room #128 (Graduate School of Math. Sci. Bldg.)
Franc Forstneric (University of Ljubljana)
Disc functionals and Siciak-Zaharyuta extremal functions on singular varieties (ENGLISH)
[ Abstract ]
A disc functional on a complex space, $X$, is a function P that assign a real number $P(f)$ (possibly minus infinity) to every analytic disc $f$ in $X$. An examples is the Poisson functional $P_u$ of an upper semicontinuous function $u$ on $X$: in that case $P_u(f)$ is the average of u over the boundary curve of the disc $f$. Other natural examples include the Lelong and the Riesz functionals. The envelope of a disc functional $P$ is a function on $X$ associating to every point $x$ of $X$ the infimum of the values $P(f)$ over all analytic discs $f$ in $X$ satisfying $f(0)=x$. The main point of interest is that the envelopes of many natural disc functionals are plurisubharmonic functions solving certain extremal problems. In the classical case when $X=\mathbf{C}^n$ this was first discovered by E. Poletsky in the early 1990's. In this talk I will discuss recent results on plurisubharmonicity of envelopes of all the classical disc functional mentioned above on locally irreducible complex spaces. In the second part of the talk I will give formulas expressing the classical Siciak-Zaharyuta maximal function of an open set in an affine algebraic variety as the envelope of certain disc functionals. We establish plurisubharmonicity of envelopes of certain classical disc functionals on locally irreducible complex spaces, thereby generalizing the corresponding results for complex manifolds. We also find new formulae expressing the Siciak-Zaharyuta extremal function of an open set in a locally irreducible affine algebraic variety as the envelope of certain disc functionals, similarly to what has been done for open sets in $\mathbf{C}^n$ by Lempert and by Larusson and Sigurdsson.

GCOE Seminars

10:00-11:00   Room #270 (Graduate School of Math. Sci. Bldg.)
Alfred Ramani (Ecole Polytechnique)
All you never really wanted to know about QRT, but were foolhardy enough to ask (ENGLISH)
[ Abstract ]
We discuss various extensions of the famous QRT second order, first degree, integrable mapping. We show how these extensions can be combined. A discussion of integrable correspondences related to these extended QRT mappings is also presented.

2011/11/15

Tuesday Seminar on Topology

16:30-18:00   Room #056 (Graduate School of Math. Sci. Bldg.)
Francois Laudenbach (Univ. de Nantes)
Singular codimension-one foliations
and twisted open books in dimension 3.
(joint work with G. Meigniez)
(ENGLISH)
[ Abstract ]
The allowed singularities are those of functions.
According to A. Haefliger (1958),
such structures on manifolds, called $\\Gamma_1$-structures,
are objects of a cohomological
theory with a classifying space $B\\Gamma_1$.
The problem of cancelling the singularities
(or regularization problem)
arise naturally.
For a closed manifold, it was solved by W.Thurston in a famous paper
(1976), with a proof relying on Mather's isomorphism (1971):
Diff$^\\infty(\\mathbb R)$ as a discrete group has the same homology
as the based loop space
$\\Omega B\\Gamma_1^+$.
For further extension to contact geometry, it is necessary
to solve the regularization problem
without using Mather's isomorphism.
That is what we have done in dimension 3. Our result is the following.

{\\it Every $\\Gamma_1$-structure $\\xi$ on a 3-manifold $M$ whose
normal bundle
embeds into the tangent bundle to $M$ is $\\Gamma_1$-homotopic
to a regular foliation
carried by a (possibily twisted) open book.}

The proof is elementary and relies on the dynamics of a (twisted)
pseudo-gradient of $\\xi$.

All the objects will be defined in the talk, in particular the notion
of twisted open book which is a central object in the reported paper.


Lie Groups and Representation Theory

16:30-18:00   Room #126 (Graduate School of Math. Sci. Bldg.)
Laurant Demonet (Nagoya University)
Categorification of cluster algebras arising from unipotent subgroups of non-simply laced Lie groups (ENGLISH)
[ Abstract ]
We introduce an abstract framework to categorify some antisymetrizable cluster algebras by using actions of finite groups on stably 2-Calabi-Yau exact categories. We introduce the notion of the equivariant category and, with similar technics as in [K], [CK], [GLS1], [GLS2], [DK], [FK], [P], we construct some examples of such categorifications. For example, if we let Z/2Z act on the category of representations of the preprojective algebra of type A2n-1 via the only non trivial action on the diagram, we obtain the cluster structure on the coordinate ring of the maximal unipotent subgroup of the semi-simple Lie group of type Bn [D]. Hence, we can get relations between the cluster algebras categorified by some exact subcategories of these two categories. We also prove by the same methods as in [FK] a conjecture of Fomin and Zelevinsky stating that the cluster monomials are linearly independent.

References
[CK] P. Caldero, B. Keller, From triangulated categories to cluster algebras, Invent. Math. 172 (2008), no. 1, 169--211.
[DK] R. Dehy, B. Keller, On the combinatorics of rigid objects in 2-Calabi-Yau categories, arXiv: 0709.0882.
[D] L. Demonet, Cluster algebras and preprojective algebras: the non simply-laced case, C. R. Acad. Sci. Paris, Ser. I 346 (2008), 379--384.
[FK] C. Fu, B. Keller, On cluster algebras with coefficients and 2-Calabi-Yau categories, arXiv: 0710.3152.
[GLS1] C. Geiss, B. Leclerc, J. Schröer, Rigid modules over preprojective algebras, Invent. Math. 165 (2006), no. 3, 589--632.
[GLS2] C. Geiss, B. Leclerc, J. Schröer, Cluster algebra structures and semicanoncial bases for unipotent groups, arXiv: math/0703039.
[K] B. Keller, Categorification of acyclic cluster algebras: an introduction, arXiv: 0801.3103.
[P] Y. Palu, Cluster characters for triangulated 2-Calabi--Yau categories, arXiv: math/0703540.

2011/11/14

GCOE lecture series

17:00-18:00   Room #470 (Graduate School of Math. Sci. Bldg.)
Oleg Emanouilov (Colorado State University)
Recovery of weakly coupled system from partial Cauchy data (ENGLISH)
[ Abstract ]
We consider the inverse problem for recovery of coefficients of weakly coupled system of elliptic equations in a bounded 2D domain.

Algebraic Geometry Seminar

15:30-17:00   Room #122 (Graduate School of Math. Sci. Bldg.)
Kiwamu Watanabe (University of Tokyo)
On projective manifolds swept out by cubic varieties (JAPANESE)
[ Abstract ]
The structures of embedded complex projective manifolds swept out by varieties with preassigned properties have been studied by several authors. In this talk, we study structures of embedded projective manifolds swept out by cubic varieties.

2011/11/10

GCOE lecture series

17:00-18:00   Room #370 (Graduate School of Math. Sci. Bldg.)
Oleg Emanouilov (Colorado State University)
Inverse boundary value problem for Schroedinger equation in two dimensions (ENGLISH)
[ Abstract ]
We relax the regularity condition on potentials of Schroedinger equations in uniqueness results on the inverse boundary value problem recently proved in A.Bukhgeim (2008) and O. Imanuvilov, G.Uhlmann and M. Yamamoto (2010).

Applied Analysis

15:00-16:00   Room #128 (Graduate School of Math. Sci. Bldg.)
Yoichiro Mori (University of Minnesota )
Mathematical Modeling of Cellular Electrodiffusion and Osmosis (JAPANESE)

Applied Analysis

16:30-17:30   Room #128 (Graduate School of Math. Sci. Bldg.)
Bernold Fiedler (Free University of Berlin)
Schoenflies spheres in Sturm attractors (ENGLISH)
[ Abstract ]
In gradient systems on compact manifolds the boundary of the unstable manifold of an equilibrium need not be homeomorphic to a sphere, or to any compact manifold.
For scalar parabolic equations in one space dimension, however, we can exlude complications like Reidemeister torsion and the Alexander horned sphere. Instead the boundary is a Schoenflies embedded sphere. This is due to Sturm nodal properties related to the Matano lap number.

2011/11/09

Number Theory Seminar

18:00-19:00   Room #056 (Graduate School of Math. Sci. Bldg.)
Atsushi Shiho (University of Tokyo)
On extension and restriction of overconvergent isocrystals (ENGLISH)
[ Abstract ]
First we explain two theorems concerning (log) extension of overconvergent isocrystals. One is a p-adic analogue of the theorem of logarithmic extension of regular integrable connections, and the other is a p-adic analogue of Zariski-Nagata purity. Next we explain a theorem which says that we can check certain property of overconvergent isocrystals by restricting them to curves.

(本講演は「東京パリ数論幾何セミナー」として、インターネットによる東大数理とIHESとの双方向同時中継で行います。)

2011/11/08

Tuesday Seminar on Topology

16:30-18:00   Room #056 (Graduate School of Math. Sci. Bldg.)
Shoji Yokura (Kagoshima University )
Fiberwise bordism groups and related topics (JAPANESE)
[ Abstract ]
We have recently introduced the notion of fiberwise bordism. In this talk, after a quick review of some of the classical (co)bordism theories, we will explain motivations of considering fiberwise bordism and some results and connections with other known works, such as M. Kreck's bordism groups of orientation preserving diffeomorphisms and Emerson-Meyer's bivariant K-theory etc. An essential motivation is our recent work towards constructing a bivariant-theoretic analogue (in the sense of Fulton-MacPherson) of Levine-Morel's or Levine-Pandharipande's algebraic cobordism.

Tuesday Seminar of Analysis

16:30-18:00   Room #128 (Graduate School of Math. Sci. Bldg.)
Yutaka Terasawa (Graduate School of Mathematical Sciences,
The University of Tokyo (JSPS Research Fellow))
Stochastic Power-Law Fluid equations: Existence and Uniqueness of weak solutions (joint work with Nobuo Yoshida) (JAPANESE)

Seminar on Mathematics for various disciplines

16:30-17:30   Room #052 (Graduate School of Math. Sci. Bldg.)
Ralph Bruckschen (ベルリン工科大学、MATHEON)
Interactive Data Visualization challenges, approaches and examples (ENGLISH)
[ Abstract ]
Data visualization is probably the most important method to analyze scientific datasets. In the time of petaflop supercomputers and high resolution sensors, the visualization of such datasets became a challenge because of the sheer magnitude. Using the latest technology I will describe some of the challenges and approaches to visualize large and massive datasets. The main bottle necks will be explained, as some algorithms and data structures to widen them. Finally I will show some examples of data visualization using a CAVE environment and virtual prototyping from the 3D Labor at the Technical University of Berlin.

2011/11/07

GCOE lecture series

17:00-18:00   Room #470 (Graduate School of Math. Sci. Bldg.)
Oleg Emanouilov (Colorado State University)
Inverse boundary value problem for Schroedinger equation in two dimensions (ENGLISH)
[ Abstract ]
We relax the regularity condition on potentials of Schroedinger equations in uniqueness results on the inverse boundary value problem recently proved in A.Bukhgeim (2008) and O. Imanuvilov, G.Uhlmann and M. Yamamoto (2010).

Algebraic Geometry Seminar

15:30-17:00   Room #122 (Graduate School of Math. Sci. Bldg.)
Atsushi Ito (University of Tokyo)
Okounkov bodies and Seshadri constants (JAPANESE)
[ Abstract ]
Okounkov bodies, which are convex bodies associated to big line bundles, have rich information of the line bundles. On the other hand, Seshadri constants are invariants which measure the positivities of line bundles. In this talk, I will explain a relation between Okounkov bodies and Seshadri constants.

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