KIAS Topology Seminar

About

The KIAS Topology seminar is one of the regular group seminars at Korea Institute for Advanced Study (KIAS). The goal is to invite researchers working on topology to give seminar talks and share their expertise. The topics include low-dimensional topology, symplectic and contact topology, algebraic topology, toric topology, Homotopy Algebra, DG Geometry, Poisson Geometry, algebraic K-theory, topological quantum field theory, category theory, algebraic geometry, and any other related subjects. For more information about the seminar, contact the webmaster.

**The Organizers:** Dongwook Choa, Hakho Choi and Jongbaek Song.
Schedule, Year 2022

11 August 2022 16:00--17:00, Online (**Zoom link**, Zoom Meeting ID: 525 820 5033, Passcode: topology)

** The homotopy classification of gauge groups of principal bundles over 4- and 6-dimensional manifolds **

Tseleung So (University of Western Ontario)

Let G be a Lie group and let P be a principal G-bundle over a manifold M. The gauge group of P is the topological group consisting of equivariant automorphisms of P that fix M. Over last thirty years extensive work has been studying their topology and classifying gauge groups up to homotopy equivalence. In this seminar I will talk about the classification of homotopy types of gauge groups when M is a 4- and 6-manifold.

05 August 2022 10:00--12:00, Online (**Zoom link**, Zoom Meeting ID: 886 2150 0783, Passcode: 611724)

** Cluster categories from symplectic geometry **

Wonbo Jeong(SNU, QSMS)

Let M be a plumbing of cotangent bundles of n-sphere (n>2) along a tree T. We show that a derived wrapped Fukaya category W, a derived compact Fukaya category F and the cocore disks of M form a Calabi-Yau triple. This implies that the quotient category W/F becomes the Amiot-Guo-Keller cluster category. When the tree T is of Dynkin type, we compute the morphism spaces between cocores in W/F as a path algebra of specific quiver. This is a joint work with Hanwool Bae and Jongmyeong Kim

09 February 2022 14:00--16:00, Online (**Zoom link**, Zoom Meeting ID: 854 4475 8975, Passcode: 172671)

** Cheeger-Gromov rho-invariant and Cha inequality **

Geunho Lim (University of California, Santa Barbara, USA)

In this talk, we will discuss quantitative bounds for Cheeger-Gromov rho-invariants. Cha proved the existence of universal bounds for rho-invariants for topological manifolds and provided explicit linear bounds for 3-manifolds. We give a new result of linear bounds for high dimensional manifolds. A key idea is to construct (4k)-cobordisms pi_1-injectively bounded by (4k-1)-manifolds, using relative hyperbolization. This talk is based on a recent joint work with Shmuel Weinberger.

Archive

**2021**
**2020**
**2019**
**2018** **2017** **2016**

Venue

**Address:** 85 Hoegiro Dongdaemungu, Seoul 02455, Republic of Korea

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