Sunday, June 23, 2024

2024-06-28 / 11:00 ~ 12:00

학과 세미나/콜로퀴엄 - 기타: Introduction to Milnor K-theory and its historical perspectives

by 사킵 무쉬타크 샤(Indian Statistical Institute - Bangalore)

Mr. Saqib Mushtaq Shah, a KAIX visiting graduate student from ISI Bangalore who will stay at KAIST for 8 weeks, is going to give a series of weekly talks on the Milnor K-theory from the beginning. It is part of his KAIX summer internship works.

2024-06-28 / 16:30 ~ 17:30

IBS-KAIST 세미나 - 이산수학: Skein relations for punctured surfaces

by Wonwoo Kang(University of Illinois, Urbana-Champaign)

Since the introduction of cluster algebras by Fomin and Zelevinsky in 2002, there has been significant interest in cluster algebras of surface type. These algebras are particularly noteworthy due to their ability to construct various combinatorial structures like snake graphs, T-paths, and posets, which are useful for proving key structural properties such as positivity or the existence of bases. In this talk, we will begin by presenting a cluster expansion formula that integrates the work of Musiker, Schiffler, and Williams with contributions from Wilson, utilizing poset representatives for arcs on triangulated surfaces. Using these posets and the expansion formula as tools, we will demonstrate skein relations, which resolve intersections or incompatibilities between arcs. Topologically, a skein relation replaces intersecting arcs or arcs with self-intersections with two sets of arcs that avoid the intersection differently. Additionally, we will show that all skein relations on punctured surfaces include a term that is not divisible by any coefficient variable. Consequently, we will see that the bangles and bracelets form spanning sets and exhibit linear independence. This work is done in collaboration with Esther Banaian and Elizabeth Kelley.

2024-06-24 / 16:00 ~ 17:00

학과 세미나/콜로퀴엄 - 미분기하 세미나:

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In this talk we present homogeneous nonprime ideals that can be used to produce, via an unprojection process, homogeneous prime ideals of high Castelnuovo-Mumford regularity. We thus provide counterexamples to the Eisenbud-Goto regularity conjecture other than those given by the Rees-like algebra method of J. McCullough and I. Peeva. Their construction was inspired by G. Caviglia (2004), J. Beder et al. (2011), and K. Borna-A. Mohajer (2015, arXiv).

2024-06-25 / 10:00 ~ 18:00

학과 세미나/콜로퀴엄 - 위상수학 세미나:

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This is a one-day workshop with young geometric topologists. Follow the link for more details
https://sites.google.com/site/hrbaik85/workshop-and-conferences-at-kaist/yggt-at-kaist?authuser=0

2024-06-24 / 17:00 ~ 18:00

학과 세미나/콜로퀴엄 - 대수기하학:

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Let G be a numerical semigroup. We prove an upper bound for the Betti numbers of the semigroup ring of G which depends only on the width of G, that is, the difference between the largest and the smallest generators of G. In this way, we make progress towards a conjecture of Herzog and Stamate. Moreover, for 4-generated numerical semigroups, the first significant open case, we prove the Herzog-Stamate bound for all but finitely many values of the width. This is a joint work with A. Moscariello and A. Sammartano.

2024-06-27 / 16:00 ~ 18:00

학과 세미나/콜로퀴엄 - 위상수학 세미나:

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It has been well known that any closed, orientable 3-manifold can be obtained by performing Dehn surgery on a link in S^3. One of the most prominent problems in 3-manifold topology is to list all the possible lens spaces that can be obtained by a Dehn surgery along a knot in S^3, which has been solved by Greene. A natural generalization of this problem is to list all the possible lens spaces that can be obtained by a Dehn surgery from other lens spaces. Besides, considering surgeries between lens spaces is also motivated from DNA topology. In this talk, we will discuss distance one surgeries between lens spaces L(n, 1) with n ≥ 5 odd and lens spaces L(s, 1) for nonzero s and the corresponding band surgeries from T(2, n) to T(2, s), by using our Heegaard Floer d-invariant surgery formula, which is deduced from the Heegaard Floer mappping cone formula. We give an almost complete classification of the above surgeries.

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