This is a reading seminar for two graduate students.) This talk studies the birational geometry of fibered surfaces, which are integral, projective, flat schemes of dimension 2 over a Dedekind scheme. In contrast to smooth projective curves, birational equivalence for surfaces does not imply isomorphism, which leads to the problem of understanding and selecting canonical representatives within a birational class. We first introduce basic tools for birational surface theory, including blowing-ups, contraction, and desingularization. We then explain how intersection theory on regular surfaces is used to analyze these operations and to identify exceptional curves. This perspective naturally leads to minimal surfaces and to applications of contraction criteria in the construction of canonical models.

(This is a reading seminar for two graduate students.) This talk studies the birational geometry of fibered surfaces, which are integral, projective, flat schemes of dimension 2 over a Dedekind scheme. In contrast to smooth projective curves, birational equivalence for surfaces does not imply isomorphism, which leads to the problem of understanding and selecting canonical representatives within a birational class. We first introduce basic tools for birational surface theory, including blowing-ups, contraction, and desingularization. We then explain how intersection theory on regular surfaces is used to analyze these operations and to identify exceptional curves. This perspective naturally leads to minimal surfaces and to applications of contraction criteria in the construction of canonical models.

The subfield of low-dimensional topology colloquially called "3.5-dimensional topology" studies closed 3-manifolds through the eyes of the 4-manifolds that they bound. This talk focusses on Casson's question of which rational homology 3-spheres bound rational homology 4-balls. Since rational homology 3-spheres bounding rational homology 4-balls are a rare phenomenon, we will discuss how to construct examples.

(This is a reading seminar for two graduate students.) This talk studies the birational geometry of fibered surfaces, which are integral, projective, flat schemes of dimension 2 over a Dedekind scheme. In contrast to smooth projective curves, birational equivalence for surfaces does not imply isomorphism, which leads to the problem of understanding and selecting canonical representatives within a birational class. We first introduce basic tools for birational surface theory, including blowing-ups, contraction, and desingularization. We then explain how intersection theory on regular surfaces is used to analyze these operations and to identify exceptional curves. This perspective naturally leads to minimal surfaces and to applications of contraction criteria in the construction of canonical models.

TBA

Asymptotically Locally Flat (ALF) Ricci-flat metrics are expected to model certain long-time singularities in four-dimensional Ricci flow, so understanding their stability is essential. In this talk, I will discuss that conformally Kähler, non-hyperkähler Ricci-flat ALF metrics are dynamically unstable under Ricci flow. Our work establishes three key tools in this setting: a Fredholm theory for the Laplacian on ALF metrics, the preservation of the ALF structure along the Ricci flow, and an extension of Perelman’s λ-functional to ALF metrics. This is joint work with Tristan Ozuch.

TBA

(The is a PhD student reading seminar to be given by Mr. Jaehong Kim.)

We see how smooth versions of peg problems give rise to constructions in symplectic topology. (No knowledge of symplectic topology is required).

We have a leisurely discussion of the Toeplitz Square peg problem and a little of its history.

Puncture–forgetting maps have been studied for a variety of objects, including Teichmüller spaces, mapping class groups, and closed curves. In this talk, we discuss several ideas of forgetting punctures in measured foliations, which give rise to upper semi-continuous maps between spaces of measured foliations. In the proof, we introduce complexes of pre-homotopic multicurves and show that they are hyperbolic CAT(0) cube complexes. We then study the action of point-pushing mapping classes on these complexes. This theory is motivated by applications to Teichmüller geodesics and the dynamics of post-critically finite rational maps. This is joint work with Jeremy Kahn.

(The is a PhD student reading seminar to be given by Mr. Jaehong Kim.)

https://wj-kim.com/2026-mini-togeda-workshop-at-kaist/

위상수학 및 기하학을 데이터 분석에 활용하는 데에 관심있는 젊은 한국인 연구자들을 위한 교류의 장을 만들고자 합니다. 2026.01.07~2026.01.08 이틀동안 진행됩니다. 자세한 정보는 다음 웹페이지 참조해주세요. https://wj-kim.com/2026-mini-togeda-workshop-at-kaist/

A fundamental problem in low-dimensional topology is to find the minimal genus of embedded surfaces in a 3-manifold or 4-manifold, in a given homology class. Ni and Wu solved a 3-dimensional minimal genus problem for rationally null-homologous knots. In this talk, we will discuss an analogous 4-dimensional minimal genus problem for rationally null-homologous knots. This is a joint work with Zhongtao Wu.