[English]
16:30 -- 18:00 Ȋwȓ(wLpX)
Tea: 16:00 -- 16:30 R[

Last updated August 3, 2012
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410 -- 056, 16:30 -- 18:00

t (ww@Ȋw)

On homology of symplectic derivation Lie algebras of the free associative algebra and the free Lie algebra

Abstract: We discuss homology of symplectic derivation Lie algebras of the free associative algebra and the free Lie algebra with particular stress on their abelianizations (degree 1 part). Then, by using a theorem of Kontsevich, we give some applications to rational cohomology of the moduli spaces of Riemann surfaces and metric graphs. This is a joint work with Shigeyuki Morita and Masaaki Suzuki.

417 -- 056, 16:30 -- 18:00

Eriko Hironaka (Florida State University)

Pseudo-Anosov mapping classes with small dilatation

Abstract: A mapping class is a homeomorphism of an oriented surface to itself modulo isotopy. It is pseudo-Anosov if the lengths of essential simple closed curves under iterations of the map have exponential growth rate. The growth rate, an algebraic integer of degree bounded with respect to the topology of the surface, is called the dilatation of the mapping class. In this talk we will discuss the minimization problem for dilatations of pseudo-Anosov mapping classes, and give two general constructions of pseudo-Anosov mapping classes with small dilatation.

424 -- 056, 16:30 -- 18:00

Dylan Thurston (Columbia University)

Combinatorial Heegaard Floer homology

Abstract: Heegaard Floer homology is a powerful invariant of 3- and 4-manifolds. In 4 dimensions, Heegaard Floer homology (together with the Seiberg-Witten and Donaldson equations, which are conjecturally equivalent), provides essentially the only technique for distinguishing smooth 4-manifolds. In 3 dimensions, it provides much geometric information, like the simplest representatives of a given homology class.
In this talk we will focus on recent progress in making Heegaard Floer homology more computable, including a complete algorithm for computing it for knots.

51 -- 056, 16:30 -- 18:00

J v (ww@Ȋw)

Minimal models, formality and hard Lefschetz property of solvmanifolds with local systems

Abstract: For a simply connected solvable Lie group G with a cocompact discrete subgroup {\Gamma}, we consider the space of differential forms on the solvmanifold G/{\Gamma} with values in certain flat bundle so that this space has a structure of a differential graded algebra(DGA). We construct Sullivan's minimal model of this DGA. This result is an extension of Nomizu's theorem for ordinary coefficients in the nilpotent case. By using this result, we refine Hasegawa's result of formality of nilmanifolds and Benson-Gordon's result of hard Lefschetz properties of nilmanifolds.

58 -- 056, 16:30 -- 18:00

Ε (ww@Ȋw, {wpU)

Infinite examples of non-Garside monoids having fundamental elements

Abstract: The Garside group, as a generalization of Artin groups, is defined as the group of fractions of a Garside monoid. To understand the elliptic Artin groups, which are the fundamental groups of the complement of discriminant divisors of the semi-versal deformation of the simply elliptic singularities E_6~, E_7~ and E_8~, we need to consider another generalization of Artin groups. In this talk, we will study the presentations of fundamental groups of the complement of complexified real affine line arrangements and consider the associated monoids. It turns out that, in some cases, they are not Garside monoids. Nevertheless, we will show that they satisfy the cancellation condition and carry certain particular elements similar to the fundamental elements in Artin monoids. As a result, we will show that the word problem can be solved and the center of them are determined.

522 -- 056, 17:10 -- 18:10

J (sw)

Gamma Integral Structure in Gromov-Witten theory

Abstract: The quantum cohomology of a symplectic manifold undelies a certain integral local system defined by the Gamma characteristic class. This local system originates from the natural integral local sysmem on the B-side under mirror symmetry. In this talk, I will explain its relationships to the problem of analytic continuation of Gromov-Witten theoy (potentials), including crepant resolution conjecture, LG/CY correspondence, modularity in higher genus theory.

529 -- 056, 16:30 -- 18:00

ɓ썹 (wK@w, {wpU)

Triple linking numbers and triple point numbers of torus-covering $T^2$-links

Abstract: The triple linking number of an oriented surface link was defined as an analogical notion of the linking number of a classical link. A torus-covering $T^2$-link $\mathcal{S}_m(a,b)$ is a surface link in the form of an unbranched covering over the standard torus, determined from two commutative $m$-braids $a$ and $b$. In this talk, we consider $\mathcal{S}_m(a,b)$ when $a$, $b$ are pure $m$-braids ($m \geq 3$), which is a surface link with $m$-components. We present the triple linking number of $\mathcal{S}_m(a,b)$ by using the linking numbers of the closures of $a$ and $b$. This gives a lower bound of the triple point number. In some cases, we can determine the triple point numbers, each of which is a multiple of four.

65 -- 056, 16:30 -- 18:00

v Y (Ócmw)

A generalization of Dehn twists

Abstract: We introduce a generalization of Dehn twists for loops which are not necessarily simple loops on an oriented surface. Our generalization is an element of a certain enlargement of the mapping class group of the surface. A natural question is whether a generalized Dehn twist is in the mapping class group. We show some results related to this question. This talk is partially based on a joint work with Nariya Kawazumi (Univ. Tokyo).

612 -- 056, 16:30 -- 18:00

j (sw ͌, {wpU)

Topological interpretation of the quandle cocycle invariants of links

Abstract: Carter et al. introduced many quandle cocycle invariants combinatorially constructed from link-diagrams. For connected quandles of finite order, we give a topological meaning of the invariants, without some torsion parts. Precisely, this invariant equals a sum of "knot colouring polynomial" and of a Z-equivariant part of the Dijkgraaf-Witten invariant. Moreover, our approach involves applications to compute "good" torsion subgroups of the 3-rd quandle homologies and the 2-nd homotopy groups of rack spaces.

619 -- 056, 17:10 -- 18:10

{ Kv (wK@w)

On the universal degenerating family of Riemann surfaces over the D-M compactification of moduli space

Abstract: It is usually understood that over the Deligne- Mumford compactification of moduli space of Riemann surfaces of genus > 1, there is a family of stable curves. However, if one tries to construct this family precisely, he/she must first take a disjoint union of various types of smooth families of stable curves, and then divide them by their automorphisms to paste them together. In this talk we will show that once the smooth families are divided, the resulting quotient family contains not only stable curves but virtually all types of degeneration of Riemann surfaces, becoming a kind of universal degenerating family of Riemann surfaces.

710 -- 056, 16:30 -- 18:00

Marcus Werner (Kavli IPMU)

Topology in Gravitational Lensing

Abstract: General relativity implies that light is deflected by masses due to the curvature of spacetime. The ensuing gravitational lensing effect is an important tool in modern astronomy, and topology plays a significant role in its properties. In this talk, I will review topological aspects of gravitational lensing theory: the connection of image numbers with Morse theory; the interpretation of certain invariant sums of the signed image magnification in terms of Lefschetz fixed point theory; and, finally, a new partially topological perspective on gravitational light deflection that emerges from the concept of optical geometry and applications of the Gauss-Bonnet theorem.

717 -- 056, 16:30 -- 18:00

rY (ȑw)

Abstract: A strongly non-degenerate mixed function has a Milnor open book structures on a sufficiently small sphere. We introduce the notion of a holomorphic-like mixed function and we will show that a link defined by such a mixed function has a canonical contact structure. Then we will show that this contact structure for a certain holomorphic-like mixed function is carried by the Milnor open book.

724 -- 056, 16:30 -- 18:00

Greg McShane (Institut Fourier, Grenoble)

Orthospectra and identities

Abstract: The orthospectra of a hyperbolic manifold with geodesic boundary consists of the lengths of all geodesics perpendicular to the boundary.
We discuss the properties of the orthospectra, asymptotics, multiplicity and identities due to Basmajian, Bridgeman and Calegari. We will give a proof that the identities of Bridgeman and Calegari are the same.

94 -- 002, 17:00 -- 18:00

Piotr Nowak (the Institute of Mathematics, Polish Academy of Sciences)

Poincaré inequalities, rigid groups and applications

Abstract: Kazhdanfs property (T) for a group G can be expressed as a fixed point property for affine isometric actions of G on a Hilbert space. This definition generalizes naturally to other normed spaces. In this talk we will focus on the spectral (aka geometric) method for proving property (T), based on the work of Garland and studied earlier by Pansu, Zuk, Ballmann-Swiatkowski, Dymara-Januszkiewicz (glambda_1>1/2h conditions) and we generalize it to to the setting of all reflexive Banach spaces. As applications we will show estimates of the conformal dimension of the boundary of random hyperbolic groups in the Gromov density model and present progress on Shalomfs conjecture on vanishing of 1-cohomology with coefficients in uniformly bounded representations on Hilbert spaces.

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