2016年4月 -- 7月
[English]
[過去のプログラム]
17:00 -- 18:30 数理科学研究科棟(東京大学駒場キャンパス)
Tea: 16:30 -- 17:00 コモンルーム
Last updated September 9, 2016
世話係
河野 俊丈
河澄 響矢
北山 貴裕
逆井 卓也
4月5日 -- 056号室, 17:00 -- 18:30
北山 貴裕 (東京大学大学院数理科学研究科)
Torsion invariants and representation varieties for non-positively curved cube complexes
Abstract:
Applications of torsion invariants and representation varieties have been extensively studied for 3-manifolds.
Twisted Alexander polynomials are known to detect the Thurston norm and fiberedness of a 3-manifold.
Ideal points of character varieties are known to detect essential surfaces in a
3-manifold in a certain extension of Culler-Shalen theory.
In view of cubulation of 3-manifolds one can expect that these results naturally extend to a wider framework and,
in particular, the case of virtually special cube complexes.
We formulate and discuss such analogous questions for non-positively curved cube complexes.
4月12日 -- 056号室, 17:00 -- 18:30
Aniceto Murillo (Universidad de Malaga)
Homotopy theory of differential graded Lie algebras
Abstract:
Having as motivation the Deligne's principle by which every deformation functor is governed by a differential graded Lie algebra,
we build a homotopy theory for these algebras which extend the classical Quillen approach and let us model any
(non necessarily 1-connected nor path connected) complex.
This is joint work with Urtzi Buijs, Yves Félix and Daniel Tanré.
4月19日 -- 056号室, 17:00 -- 18:30
Błażej Szepietowski (Gdansk University)
Topological rigidity of finite cyclic group actions on compact surfaces
Abstract:
Two actions of a group on a surface are called topologically equivalent if they are conjugate by a homeomorphism of the surface.
I will describe a method of enumeration (and classification)
of topological equivalence classes of actions of a finite group on a compact surface,
based on the combinatorial theory of noneuclidean crystallographic groups (NEC groups in short)
and a relationship between the outer automorphism group of an NEC group and certain mapping class group.
By this method we study topological equivalence of actions of a finite cyclic group on a compact surface,
in the situation where the order of the group is large relative to the genus of the surface.
4月26日 -- 056号室, 17:00 -- 18:30
植木 潤 (東京大学大学院数理科学研究科)
Arithmetic topology on branched covers of 3-manifolds
Abstract:
The analogy between 3-dimensional topology and number theory was first pointed out by Mazur in the 1960s,
and it has been studied systematically by Kapranov, Reznikov, Morishita, and others.
In their analogies, for example, knots and 3-manifolds correspond to primes and number rings respectively.
The study of these analogies is called arithmetic topology now.
In my talk, based on their dictionary of analogies, we study analogues of idelic class field theory,
Iwasawa theory, and Galois deformation theory in the context of 3-dimensional topology,
and establish various foundational analogies in arithmetic topology.
5月10日 -- 056号室, 17:00 -- 18:30
小鳥居 祐香 (東京大学大学院数理科学研究科)
On Milnor's link-homotopy invariants for handlebody-links
Abstract:
A handlebody-link is a disjoint union of handlebodies embedded in $S^3$
and HL-homotopy is an equivalence relation on handlebody-links generated by self-crossing changes.
A. Mizusawa and R. Nikkuni classified the set of HL-homotopy classes of
2-component handlebody-links completely using the linking numbers for handlebody-links.
In this talk, by using Milnor's link-homotopy invariants,
we construct an invariant for handlebody-links
and give a bijection between the set of HL-homotopy classes of n-component handlebody-links
with some assumption and a quotient of the action of the general linear group on a tensor product of modules.
This is joint work with Atsuhiko Mizusawa at Waseda University.
5月17日 -- 056号室, 17:00 -- 18:30
正井 秀俊 (東京大学大学院数理科学研究科)
Some dynamics of random walks on the mapping class groups
Abstract:
The dynamics of random walks on the mapping class groups on closed surfaces of genus >1 will be discussed.
We define the topological entropy of random walks.
Then we prove that the drift with respect to Thurston or
Teichmüller metrics and the Lyapunov exponent all coincide with the topological entropy.
This is a "random version" of pseudo-Anosov dynamics observed by Thurston and
I will begin this talk by recalling the work of Thurston.
5月24日 -- 056号室, 17:00 -- 18:30
田中 心 (東京学芸大学)
Independence of Roseman moves for surface-knot diagrams
Abstract:
Roseman moves are seven types of local modifications for surface-knot diagrams in 3-space
which generate ambient isotopies of surface-knots in 4-space.
In this talk, I will discuss independence among the seven Roseman moves.
In particular, I will focus on Roseman moves involving triple points and on those involving branch points.
The former is joint work with Kanako Oshiro (Sophia University) and Kengo Kawamura (Osaka City University),
and the latter is joint work with Masamichi Takase (Seikei University).
5月31日 -- 056号室, 17:00 -- 18:30
Benoît Guerville-Ballé (東京学芸大学)
A linking invariant for algebraic curves
Abstract:
We construct a topological invariant of algebraic plane curves,
which is in some sense an adaptation of the linking number of knot theory.
As an application, we show that this invariant distinguishes a new Zariski pair of curves
(ie a pair of curves having same combinatorics, yet different topology).
6月7日 -- 056号室, 17:00 -- 18:30
早野 健太 (慶應義塾大学)
Topology of holomorphic Lefschetz pencils on the four-torus
Abstract:
In this talk, we will show that two holomorphic Lefschetz pencils on the four-torus are
(smoothly) isomorphic if they have the same genus and divisibility.
The proof relies on the theory of moduli spaces of polarized abelian surfaces.
We will also give vanishing cycles of some holomorphic pencils of the four-torus explicitly.
This is joint work with Noriyuki Hamada (The University of Tokyo).
6月14日 -- 056号室, 17:00 -- 18:30
粕谷 直彦 (青山学院大学)
Non-Kähler complex structures on R^4
Abstract:
We consider the following problem. "Is there any non-Kähler complex structure on R^{2n}?"
If n=1, the answer is clearly negative. On the other hand,
Calabi and Eckmann constructed non-Kähler complex structures on R^{2n} for n ≥ 3.
In this talk, I will construct uncountably many non-Kähler complex structures on R^4,
and give the affirmative answer to the case where n=2.
For the construction, it is important to understand the genus-one achiral Lefschetz fibration
S^4 → S^2 found by Yukio Matsumoto and Kenji Fukaya.
This is a joint work with Antonio Jose Di Scala and Daniele Zuddas.
6月21日 -- 056号室, 17:00 -- 18:30
伊藤 昇 (東京大学大学院数理科学研究科)
Spaces of chord diagrams of spherical curves
Abstract:
In this talk, the speaker introduces a framework to obtain (possibly infinitely many)
new topological invariants of spherical curves under local homotopy moves (several types of Reidemeister moves).
They are defined by chord diagrams, each of which is a configurations of even paired points on a circle.
We see that these invariants have useful properties.
6月28日 -- 056号室, 17:00 -- 18:30
見村 万佐人 (東北大学)
Strong algebraization of fixed point properties
Abstract:
バナッハ空間（ないしは族）を固定したとき，有限生成群のそれ上の等長作用が常に大域的固定点を持つ，
という性質を固定点性質と呼ぶ．
ヒルベルト空間全体のなす族を考えたときの固定点性質は，「Kazhdan の性質
(T)」と呼ばれる群の剛性と同値であることが知られている．
離散群の線型表現の分類は連続群と違い，群が少しでも複雑になると手に負えない．
これが原因で，離散群の固定点性質を直接示すことは当面の間著しく困難であった．
Y. Shalom は1999年の論文（Publ. IHES）で，固定点性質を部分群に分けて，
最後に“パッチワーク”する，という手法を応用し，上の困難に対し初のブレイクスルーをもたらした．
しかし，Shalomのパッチワーク戦略では群の部分群による「有界生成（Bounded Generation）」という厄介な要請が本質的であって
（後述するように実はこれは気のせいだったのだが，長年そう信じられてきたように講演者には思われる），
この要請がShalomの手法を適用する際の致命的な弱点となっていた．
今回，講演者はShalomのパッチワーク（1999,2006）の思想を発展させて，
「有界生成」条件を舞台から追いやることに成功した．講演者の条件は，
部分群たちを広げていくある“ゲーム”の必勝戦略として記述される．
講演ではこの“ゲーム”の内容・証明のあらすじをお話したい．
これにより，「有界生成」の成立がわからないような状況でもパッチワーク戦略を適用できうるようになった．
系として，いろいろな離散群が強い固定点性質をもつことを示せ，しかも証明も非常にコンセプチュアルである．
こうした応用面についても概観したい．
7月12日 -- 056号室, 17:00 -- 18:30
John Parker (Durham University)
Non-arithmetic lattices
Abstract:
In this talk I will discuss arithmetic and non-arithmetic lattices
and I will give a history of the problem of finding non-arithmetic lattices.
I will also briefly describe the construction of new non-arithmetic lattices in SU(2,1)
found in my joint workwith Martin Deraux and Julien Paupert.
7月19日 -- 056号室, 17:00 -- 18:30
渡邊 陽介 (University of Hawaii)
The geometry of the curve graphs and beyond
Abstract:
The curve graphs are locally infinite.
However, by using Masur-Minsky's tight geodesics, one could view them as locally finite graphs.
Bell-Fujiwara used a special property of tight geodesics and showed that the asymptotic dimension of the curve graphs is finite.
In this talk, I will introduce a new class of geodesics which also has the property.
If time permits, I will explain how such geodesics can be adapted in Out(F_n) setting.