Tuesday Seminar on Topology

[Japanese]   [Past Programs]
17:00 -- 18:30 Graduate School of Mathematical Sciences, The University of Tokyo (with live streaming on Zoom)
or
17:00 -- 18:00 Online seminar on Zoom.

Last updated April 16, 2024
Information :　
Kazuo Habiro
Nariya Kawazumi
Takahiro Kitayama
Takuya Sakasai

Pre-registration is required.
Once you register, you can attend all our seminars until the end of March, 2024.
The zoom meeting will be opened 15 minutes before start.
Making audio and video recordings is prohibited.
April 9, 17:00-18:30 -- Room 056 with live streaming on Zoom

Shouhei Honda (The University of Tokyo)

Topological stability theorem and Gromov-Hausdorff convergence

Abstract: Gromov-Hausdorff distance defines a distance on the set of all isometry classes of compact metric spaces. It is natural to ask about topological relationships between two compact metric spaces whose Gromov-Hausdorff distance is small. Cheeger-Colding provided a striking result about this question, under a (lower) curvature bound on Ricci curvature. In this talk we will improve this result sharply. This is a joint work with Yuanlin Peng (Tohoku University). If time permits, along this direction, we will also discuss a recent work about a topological stability result to flat tori via harmonic maps, where this is a joint work with Christian Ketterer (University of Freiburg), Ilaria Mondello (Université de Paris Est Créteil), Chiara Rigoni (University of Vienna) and Raquel Perales (CIMAT).

April 16, 17:00-18:30 -- Online on Zoom

Hiroaki Karuo (Gakushuin University)

Skein algebras and quantum tori in view of pants decompositions

Abstract: To understand the algebraic structures of skein algebras and their generalizations, we usually try to embed these algebras into quantum tori using ideal triangulations of a surface and the splitting map. However, such a construction does not work for the skein algebras of closed surfaces and the Roger-Yang skein algebras of punctured surfaces.
In the talk, we define filtrations on these algebras using pants decompositions and embed the associated graded algebras into quantum tori. As a consequence, Roger-Yang skein algebras are quantizations of decorated Teichmuller spaces. This talk is based on a joint work with Wade Bloomquist (Morningside University) and Thang Le (Georgia Institute of Technology).

April 23, 17:00-18:30 -- Room 056 with live streaming on Zoom

Tatsumasa Suzuki (Meiji University)

Pochette surgery on 4-manifolds and the Ozsváth-Szabó d-invariants of Brieskorn homology 3-spheres

Abstract: This talk consists of the following two research contents:
I. The boundary sum of S1×D3 and D2×S2 is called a pochette. The pochette surgery, which is a generalization of Gluck surgery and a special case of torus surgery, was discovered by Zjuñici Iwase and Yukio Matsumoto in 2004. For a pochette P embedded in a 4-manifold X, a pochette surgery on X is the operation of removing the interior of P and gluing P by a diffeomorphism of the boundary of P. In this talk, we focus on the fact that pochette surgery is a surgery with a cord and the 2-sphere S2, and attempt to classify the diffeomorphism type of pochette surgery on the 4-sphere S4.
II. In 2003, Peter Ozsváth and Zoltán Szabó introduced a homology cobordism invariant for homology 3-spheres called a d-invariant. In this talk, we present new computable examples by refining the Karakurt--Şavk formula for any Brieskorn homology 3-sphere ∑(p,q,r) with p is odd and pq+pr-qr=1. Furthermore, by refining the Can-Karakurt formula for the d-invariant of any ∑(p,q,r), we also introduce the relationship with the d-invariant of ∑(p,q,r) and those of lens spaces. This talk includes contents of joint work with Motoo Tange (University of Tsukuba).

May 7, 17:00-18:30 -- Online on Zoom

Ingrid Irmer (Southern University of Science and Technology)

The Thurston spine and the Systole function of Teichmüller space

Abstract: The systole function fsys on Teichmüller space Tg of a closed genus g surface is a piecewise-smooth map Tg → R whose value at any point is the length of the shortest geodesic on the corresponding hyperbolic surface. It is known that fsys gives a mapping class group-equivariant handle decomposition of Tg via an analogue of Morse Theory. This talk explains the relationship between this handle decomposition and the Thurston spine of Tg.