Dates: April 4 (Friday) - April 6 (Sunday), 2025
Location: Room 108, Natural Science Building 5, Department of Mathematics, Kangwon National University (Chuncheon)
April 4 (Friday)
14:00 - 14:50 TaeHeon KIM
15:00 - 15:50 Hyunggi KIM
16:10 - 17:00 Ju A LEE
18:00 - 20:00 Dinner
April 5 (Saturday)
09:30 - 10:20 Woohyeok JO - 1
10:40 - 11:30 Woohyeok JO - 2
12:00 - 13:30 Lunch
14:00 - 14:50 Discussion by Jongil PARK - 1
16:00 - 17:00 Discussion by Jongil PARK - 2
18:00 - 20:00 Dinner
April 6 (Sunday)
09:30 - 10:20 Kyungbae PARK
10:40 - 11:30 Ki-Heon YUN
12:00 - 13:30 Lunch
TaeHeon KIM (Seoul National University)
Title: Negative Spheres in Blow-ups of Elliptic Surfaces
Abstract: We study negative spheres in blow-ups of elliptic surfaces using multisections and specific singular fibers. Following the work of Stipsicz and Szabó, we attempted to find spheres with larger negative self-intersection and an infinite family of such spheres.
Hyunggi KIM (Seoul National University)
Title: Finding Lefschetz fibration on a resolution of a quotient of product space
Abstract: Lefschetz fibration is widely studied object in mathematics, particularly in complex surfaces, symplectic 4-manifold theory. Lefschetz fibration is closely related to a word factorization of a trivial element in mapping class groups, called a monodromy factorization of Lefschetz fibration. There are some ways for finding such factorization on given LF, and in this talk I want to introduce a Matsumoto’s method to finding monodromy factorization of LF from the quotient of S^2 \times \Sigma_2. Also I want to explain my recent studies, total space of resolution of a quotient of S^2 \times \Sigma_g and finding monodromy factorization.
Ju A LEE (Seoul National University)
Title: Lefschetz pencils on a complex projective plane from a topological viewpoint
Abstract: In this talk, we present a differential topological construction of symplectic Lefschetz pencils of genus (d-1)(d-2)/2} with d^2 base points and 3(d-1)^2 critical points for arbitrary d≥4, analogous to holomorphic Lefschetz pencils of curves of degree d in P^2. Moreover, for the case d=4, we derive an explicit monodromy factorization of the genus 3 holomorphic Lefschetz pencil on P^2 based on the braid monodromy technique and prove that it can also be topologically constructed by breeding the monodromy relations of the genus 1 holomorphic Lefschetz pencils.
Woohyeok JO (Seoul National University)
Title: On the Euler characteristic for orbifolds
Abstract: In 1957, Satake introduced the notion of "V-manifolds", which is now called orbifolds, as a generalization of manifolds, and defined the Euler characteristic of a compact orbifold as the alternating sum of inverses of the orders of isotropy subgroups of simplices. In this talk, we discuss various equivalent ways to define the orbifold Euler characteristic, and observe how the orbifold Euler characteristic is related to the three fibers conjecture and the Montgomery-Yang problem.
Kyungbae PARK (Kangwon National University)
Title: The Alexander polynomial of twisted torus knots
Abstract: Twisted torus knots are a generalization of torus knots, obtained by introducing additional full twists to adjacent strands of the torus knots. In this talk, we present an explicit formula for the Alexander polynomial of twisted torus knots. Our approach utilizes a presentation of the knot group of twisted torus knots combined with Fox’s free differential calculus. As applications, we provide a lower bound for the genus of certain families of twisted torus knots and identify families of twisted torus knots that are not L-space knots.
Ki-Heon YUN (Sungshin Women's University)
TBA
박경배(강원대), 박종일(서울대)
NRF-중견연구지원사업(박종일 교수)