## Seminar information archive

#### Lie Groups and Representation Theory

17:00-18:30   Room #122 (Graduate School of Math. Sci. Bldg.)
Anton Evseev (University of Birmingham)
RoCK blocks, wreath products and KLR algebras (English)
[ Abstract ]
The so-called RoCK (or Rouquier) blocks play an important role in representation theory of symmetric groups over a finite field of characteristic $p$, as well as of Hecke algebras at roots of unity. Turner has conjectured that a certain idempotent truncation of a RoCK block is Morita equivalent to the principal block $B_0$ of the wreath product $S_p\wr S_d$ of symmetric groups, where $d$ is the "weight" of the block. The talk will outline a proof of this conjecture, which generalizes a result of Chuang-Kessar proved for $d < p$. The proof uses an isomorphism between a Hecke algebra at a root of unity and a cyclotomic Khovanov-Lauda-Rouquier algebra, the resulting grading on the Hecke algebra and the ideas behind a construction of R-matrices for modules over KLR algebras due to Kang-Kashiwara-Kim.

#### Tuesday Seminar on Topology

17:00-18:30   Room #056 (Graduate School of Math. Sci. Bldg.)
Akishi Kato (The University of Tokyo)
Quiver mutation loops and partition q-series (JAPANESE)
[ Abstract ]
Quivers and their mutations are ubiquitous in mathematics and
mathematical physics; they play a key role in cluster algebras,
wall-crossing phenomena, gluing of ideal tetrahedra, etc.
Recently, we introduced a partition q-series for a quiver mutation loop
(a loop in a quiver exchange graph) using the idea of state sum of statistical
mechanics. The partition q-series enjoy some nice properties such
as pentagon move invariance. We also discuss their relation with combinatorial
Donaldson-Thomas invariants, as well as fermionic character formulas of
certain conformal field theories.
This is a joint work with Yuji Terashima.

### 2015/05/18

#### Seminar on Geometric Complex Analysis

10:30-12:00   Room #126 (Graduate School of Math. Sci. Bldg.)
Masanori Adachi (Tokyo Univ. of Science)
On a global estimate of the Diederich–Fornaess index of Levi-flat real hypersurfaces (Japanese)
[ Abstract ]
We give yet another proof for a global estimate of the Diederich-Fornaess index of relatively compact domains with Levi-flat boundary, namely, the index must be smaller than or equal to the reciprocal of the dimension of the ambient space. Although the Diederich-Fornaess index is originally defined for relatively compact domains in complex manifolds, our formulation reveals that it makes sense for abstract Levi-flat CR manifolds.

#### Algebraic Geometry Seminar

15:30-17:00   Room #122 (Graduate School of Math. Sci. Bldg.)
Will Donovan (IPMU)
Twists and braids for general 3-fold flops (English)
[ Abstract ]
When a 3-fold contains a floppable rational curve, a theorem of Bridgeland provides a derived equivalence between the 3-fold and its flop. I will discuss recent joint work with Michael Wemyss, showing that these flop functors satisfy Coxeter-type braid relations. Using this result, we construct an action of a braid-type group on the derived category of the 3-fold. This group arises from the topology of a certain simplicial hyperplane arrangement, determined by the local geometry of the curve. I will give examples and explain key elements in the construction, including the noncommutative deformations of curves introduced in our previous work.
[ Reference URL ]
http://db.ipmu.jp/member/personal/4007en.html

#### Numerical Analysis Seminar

16:30-18:00   Room #056 (Graduate School of Math. Sci. Bldg.)
Katsuhisa Ozaki (Shibaura Institute of Technology)
Accurate matrix multiplication by error-free transformation (日本語)

#### Tokyo Probability Seminar

16:50-18:20   Room #128 (Graduate School of Math. Sci. Bldg.)
Lu Xu (Graduate School of Mathematical Sciences, The University of Tokyo)
Central limit theorem for stochastic heat equations in random environments

### 2015/05/14

#### Applied Analysis

16:00-17:30   Room #128 (Graduate School of Math. Sci. Bldg.)
Masahito Ohta (Tokyo University of Science)
Strong instability of standing waves for some nonlinear Schr\"odinger equations (Japanese)

### 2015/05/13

#### Operator Algebra Seminars

16:45-18:15   Room #122 (Graduate School of Math. Sci. Bldg.)
Yosuke Kubota (Univ. Tokyo)
Controlled topological phases and the bulk-edge correspondence for
topological insulators (English)

### 2015/05/12

#### Tuesday Seminar of Analysis

16:30-18:00   Room #126 (Graduate School of Math. Sci. Bldg.)
Keisuke Takasao (Graduate School of Mathematical Sciences, the University of Tokyo)
Convergence of the Allen-Cahn equation with constraint to Brakke's mean curvature flow (Japanese)
[ Abstract ]
In this talk we consider the Allen-Cahn equation with constraint. In 1994, Chen and Elliott studied the asymptotic behavior of the solution of the Allen-Cahn equation with constraint. They proved that the zero level set of the solution converges to the classical solution of the mean curvature flow under the suitable conditions on initial data. In 1993, Ilmanen proved the existence of the mean curvature flow via the Allen-Cahn equation without constraint in the sense of Brakke. We proved the same conclusion for the Allen-Cahn equation with constraint.

#### Tuesday Seminar on Topology

17:30-18:30   Room #056 (Graduate School of Math. Sci. Bldg.)
Masayuki Asaoka (Kyoto University)
Growth rate of the number of periodic points for generic dynamical systems (JAPANESE)
[ Abstract ]
For any hyperbolic dynamical system, the number of periodic
points grows at most exponentially and the growth rate
reflects statistic property of the system. For dynamics far
from hyperbolicity, the situation is different. In 1999,
Kaloshin proved genericity of super-exponential growth in the
region where dense set of dynamical systems exhibits homoclinic
tangency (so called the Newhouse region).

How does the number of periodic points grow for generic
partially hyperbolic dynamical systems? Such systems are known
to be far from homoclinic tangency. Is the growth at most
exponential like hyperbolic system, or super-exponential by
a mechanism different from homoclinic tangency?

The speaker, Katsutoshi Shinohara, and Dimitry Turaev proved
super-exponential growth of the number of periodic points for
generic one-dimensional iterated function systems under some
reasonable conditions. Such systems are models of dynamics
of partially hyperbolic systems in neutral direction. So, we
expect genericity of super-exponential growth in a region of
partially hyperbolic systems.

In this talk, we start with a brief history of the problem on
growth rate of the number of periodic point and discuss two
mechanisms which lead to genericity of super-exponential growth,
Kaloshin's one and ours.

### 2015/05/11

#### Seminar on Geometric Complex Analysis

10:30-12:00   Room #126 (Graduate School of Math. Sci. Bldg.)
Kengo Hirachi (The Univ. of Tokyo)
Integral Kahler Invariants and the Bergman kernel asymptotics for line bundles
[ Abstract ]
On a compact Kahler manifold, one can define global invariants by integrating local invariants of the metric. Assume that a global invariant thus obtained depends only on the Kahler class. Then we show that the integrand can be decomposed into a Chern polynomial (the integrand of a Chern number) and divergences of one forms, which do not contribute to the integral. We apply this decomposition formula to describe the asymptotic expansion of the Bergman kernel for positive line bundles and to show that the CR Q-curvature on a Sasakian manifold is a divergence. This is a joint work with Spyros Alexakis (U Toronto).

#### Tokyo Probability Seminar

16:50-18:20   Room #128 (Graduate School of Math. Sci. Bldg.)
Naoyuki Ichihara (College of Science and Engineering, Aoyama Gakuin University)
Phase transitions for controlled Markov chains on infinite graphs (JAPANESE)

#### Algebraic Geometry Seminar

15:30-17:00   Room #122 (Graduate School of Math. Sci. Bldg.)
Taro Sano (Kyoto University)
Deformations of weak Fano varieties (日本語 or English)
[ Abstract ]
A smooth projective variety often has obstructed deformations.
Nevertheless, important varieties such as Fano varieties and
Calabi-Yau varieties have unobstructed deformations.
In this talk, I explain about unobstructedness of deformations of weak
Fano varieties, in particular a weak Q-Fano 3-fold.
I also present several examples to show delicateness of this unobstructedness.
[ Reference URL ]

### 2015/05/08

#### Geometry Colloquium

10:00-11:30   Room #126 (Graduate School of Math. Sci. Bldg.)
Masashi Ishida (Osaka University)
On Perelman type functionals for the Ricci Yang-Mills flow (Japanese)
[ Abstract ]
In his works on the Ricci flow, Perelman introduced two functionals with monotonicity
formulas under the Ricci flow. The monotonicity formulas have many remarkable geometric applications. On the other hand, around 2007, Jeffrey Streets and Andrea Young independently and simultaneously introduced a new geometric flow which is called the Ricci Yang-Mills flow. The new flow can be regarded as the Ricci flow coupled with the Yang-Mills
heat flow. In this talk, we will introduce new functionals with monotonicity formulas under the Ricci Yang-Mills flow and discuss its applications.

### 2015/05/07

#### Tuesday Seminar on Topology

17:00-18:30   Room #056 (Graduate School of Math. Sci. Bldg.)
Patrick Dehornoy (Univ. de Caen)
The group of parenthesized braids (ENGLISH)
[ Abstract ]
We describe a group B obtained by gluing in a natural way two well-known
groups, namely Artin's braid group B_infty and Thompson's group F. The
elements of B correspond to braid diagrams in which the distances
between the strands are non uniform and some rescaling operators may
change these distances. The group B shares many properties with B_infty:
as the latter, it can be realized as a subgroup of a mapping class
group, namely that of a sphere with a Cantor set removed, and as a group
of automorphisms of a free group. Technically, the key point is the
existence of a self-distributive operation on B.

### 2015/05/02

#### Harmonic Analysis Komaba Seminar

13:30-17:00   Room #128 (Graduate School of Math. Sci. Bldg.)
Hitoshi Tanaka (Univ Tokyo) 13:30-15:00
Two-weight Morrey norm inequality and the sequential testing
(日本語)
[ Abstract ]
In this talk we extend Sawyer's two-weight theory to Morrey spaces and give a characterization of two-weight Morrey norm inequalities for the (general) Hardy-Littlewood maximal operators in terms of the sequential testing due to H\"{a}nninen, Hyt\"{o}nen and Li.
We also introduce the description of the K\"othe dual of Morrey type spaces generated by a basis of measurable functions.
The second topic is based on a joint work with Professors Sawano (Tokyo Metropolitan University) and Masty{\l}o (Adam Mickiewicz University and Institute of Mathematics).
Yoshihiro Sawano (Tokyo Metropolitan University.) 15:30-17:00
The topology of the dual space of ${\mathcal S}_0$
(日本語)
[ Abstract ]
Based on the notation of my Japanese book, I will consider the topology of ${\mathcal S}_0'$, the dual of ${\mathcal S}_0$.
In view of the linear isomorphism ${\mathcal S}_0' \sim {\mathcal S}/{\mathcal P}$, we can consider two different topologies;

1) the weak-* topology
and
2) the quotient topology in ${\mathcal S}/{\mathcal P}$.

We aim to show that these two topologies are the same. This will be an errortum of my Japanese book.
This work is done jointly with Takahiro Noi and Shohei Nakamura in Tokyo Metropolitan University.

### 2015/04/28

#### Tuesday Seminar on Topology

17:00-18:30   Room #056 (Graduate School of Math. Sci. Bldg.)
Hidetoshi Masai (The University of Tokyo, JSPS)
Verify hyperbolicity of 3-manifolds by computer and its applications. (JAPANESE)
[ Abstract ]
In this talk I will talk about the program called HIKMOT which
rigorously proves hyperbolicity of a given triangulated 3-manifold. To
prove hyperbolicity of a given triangulated 3-manifold, it suffices to
get a solution of Thurston's gluing equation. We use the notion called
interval arithmetic to overcome two types errors; round-off errors,
and truncated errors. I will also talk about its application to
exceptional surgeries along alternating knots. This talk is based on
joint work with N. Hoffman, K. Ichihara, M. Kashiwagi, S. Oishi, and
A. Takayasu.

#### Lie Groups and Representation Theory

17:00-18:30   Room #122 (Graduate School of Math. Sci. Bldg.)
Bent Orsted (Aarhus University and the University of Tokyo)
Restricting automorphic forms to geodesic cycles (English)
[ Abstract ]
We find estimates for the restriction of automorphic forms on hyperbolic manifolds to compact geodesic cycles in terms of their expansion into eigenfunctions of the Laplacian. Our method resembles earlier work on products of automorphic forms by Bernstein and Reznikov, and it uses Kobayashi's new symmetry-breaking kernels. This is joint work with Jan M\"o{}llers.

### 2015/04/27

#### Seminar on Geometric Complex Analysis

10:30-12:00   Room #126 (Graduate School of Math. Sci. Bldg.)
Sachiko Hamano (Fukushima Univ.)
Variational formulas for canonical differentials and application (Japanese)
[ Abstract ]
We prove the variational formulas of the second order for $L_1$- and $L_0$-canonical differentials, which with the remarkable contrast are our first example in the case of the deforming non-planar open Riemann surface. As a direct application, we show the rigidity of the Euclidean radius of the moduli disk on open torus under pseudoconvexity. The main part of this talk is a joint work with Masakazu Shiba and Hiroshi Yamaguchi.

#### Algebraic Geometry Seminar

15:30-17:00   Room #122 (Graduate School of Math. Sci. Bldg.)
Genki Ouchi (University of Tokyo/IPMU)
Lagrangian embeddings of cubic fourfolds containing a plane (日本語)

#### Numerical Analysis Seminar

16:30-18:00   Room #056 (Graduate School of Math. Sci. Bldg.)
Akitoshi Takayasu (Waseda University)
A method of verified computations for solutions to semilinear parabolic equations using an analytic semigroup (日本語)

### 2015/04/24

#### Geometry Colloquium

10:00-11:30   Room #126 (Graduate School of Math. Sci. Bldg.)
Kento Fujita (Kyoto University)
On K-stability and the volume functions of Q-Fano varieties (JAPANESE)
[ Abstract ]
For Fano manifolds X, it is known that X admits K\"ahler-Einstein metrics if and only if the polarized pair
(X, -K_X) is K-polystable. In this talk, I will introduce a new effective stability named "divisorial stability" for Fano manifolds, which is weaker than K-stability and stronger than slope stability along divisors. I will show that:
1. We can easily test divisorial stability via the volume functions.
2. There is a relationship between divisorial stability and the structure property of Okounkov bodies of anti-canonical divisors.
3. For toric Fano manifolds, the existence of K\"ahler-Einstein metrics is equivalent to divisorial semistability.

#### Colloquium

16:50-17:50   Room #123 (Graduate School of Math. Sci. Bldg.)
Bent Oersted (Aarhus University and University of Tokyo)
Rigidity of conformal functionals on spheres (ENGLISH)
[ Abstract ]
On a compact smooth manifold one may construct a Riemannian metric in many different ways. Each metric gives rise to natural elliptic operators such as the Laplace-Beltrami operator and corresponding spectral invariants, e.g. the eigenvalues, the trace of the heat semigroup, and the zeta function. In
this lecture we shall consider such functionals on the space of metrics on the sphere, combining conformal differential geometry and representation theory of semisimple Lie groups to obtain results about local extremal properties of special functionals. This is based on joint work with Niels Martin Moeller.

### 2015/04/23

#### Applied Analysis

16:00-17:30   Room #128 (Graduate School of Math. Sci. Bldg.)
Bernold Fiedler (Free University of Berlin)
The importance of being just late (ENGLISH)
[ Abstract ]
Delays are a ubiquitous nuisance in control. Delays increase finite-dimensional phase spaces to become infinite-dimensional. But, are delays all that bad?

Following an idea of Pyragas, we attempt noninvasive and model-independent stabilization of unstable p-periodic phenomena $u(t)$ by a friendly delay $r$ . Our feedback only evaluates differences $u(t-r)-u(t)$. When the time delay $r$ is chosen to be an integer multiple $np$ of the minimal period $p$, the difference and the feedback vanish alike: the control strategy becomes noninvasive on the target periodic orbit.

We survey promise and limitations of this idea, including applications and an example of delay control of delay equations.

The results are joint work with P. Hoevel, W. Just, I. Schneider, E. Schoell, H.-J. Wuensche, S. Yanchuk, and others. See also

http://dynamics.mi.fu-berlin.de/

#### Infinite Analysis Seminar Tokyo

17:00-18:30   Room #002 (Graduate School of Math. Sci. Bldg.)
Hideya Watanabe (Department of Mathematics, Tokyo Institute of Technology, Graduate school of science and Engineering)
Parabolic analogue of periodic Kazhdan-Lusztig polynomials (JAPANESE)
[ Abstract ]
We construct a parabolic analogue of so-called periodic modules, which are modules over the Hecke algebra
associated with an affine Weyl group.
These modules have a basis similar to Kazhdan-Lusztig basis.
Our construction enables us to see the relation between (ordinary)periodic KL-polynomials and parabolic ones.