Saturday, June 14, 2025

2025-06-18 / 16:00 ~ 18:00

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An n-dimensional k-handlebody is an n-manifold obtained from an n-ball by attaching handles of index up to k, where n ≥ k. We will discuss that for any n ≥ 2k + 1, any n-dimensional k-handlebody is diffeomorphic to the product of a 2k-dimensional k-handlebody and an (n − 2k)-ball. For example, a 2025-dimensional 6-handlebody is the product of an 12-dimensional 6-handlebody and a 2013-ball. We also introduce (n,k)-Kirby diagrams for some n-dimensional k-handlebodies. Here (4,2)-Kirby diagrams correspond to the classical Kirby diagrams for 4-dimensional 2-handlebodies.

2025-06-20 / 14:00 ~ 16:00

학과 세미나/콜로퀴엄 - 기타: Chow groups and intersection products #1

by 김재홍(KAIST)

(This is a reading seminar talk by a graduate student, Mr. Jaehong Kim.) This talk is a reading seminar about basic intersection theory, following chapter 1 to 6 of the book of William Fulton. The main objects to be dealt with are Chow groups, pullback/pushforward, pseudo-divisors, divisor intersection, Chern/Segre classes, deformation to the normal cone and intersection products.

2025-06-17 / 16:30 ~ 17:30

IBS-KAIST 세미나 - 이산수학: The Quantitative Fractional Helly Theorem

by Attila Jung(Eötvös Loránd University)

Two celebrated extensions of Helly’s theorem are the Fractional Helly theorem of Katchalski and Liu (1979) and the Quantitative Volume theorem of Barany, Katchalski, and Pach (1982). Improving on several recent works, we prove an optimal combination of these two results. We show that given a family $F$ of $n$ convex sets in $\mathbb{R}^d$ such that at least $\alpha \binom{n}{d+1}$ of the $(d+1)$-tuples of $F$ have an intersection of volume at least 1, then one can select $\Omega_{d,\alpha}(n)$ members of $F$ whose intersection has volume at least $\Omega_d(1)$. Joint work with Nora Frankl and Istvan Tomon.

2025-06-17 / 14:30 ~ 15:30

학과 세미나/콜로퀴엄 - 위상수학 세미나:

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In this talk, we study several computational problems related to knots and links. We investigate lower bounds on the computational complexity of theoretical knot theory problems. Unknotting number is one of the most interesting knot invariants, and various research has been done to find unknotting numbers of knots. However, compared to its simple definition, it is generally hard to find the unknotting number of a knot, and it is known for only some knots. There is no algorithm for determining unknotting numbers yet. First, we show that for an arbitrary positive integer n, a non-torus knot exists with the unknotting number n. Second, we show that the computational complexity of the diagrammatic un-knotting number problem is NP-hard. We construct a Karp reduction from 3-SAT to the diagrammatic unknotting number problem. Third, we also prove that the prime sublink problem is NP-hard by making a Karp reduction from the known NP-complete problem, the non-tautology problem.

2025-06-19 / 10:30 ~ 11:30

SAARC 세미나 - SAARC 세미나:

by 지홍창()

General linear model concerns the statistical problem of estimating a vector x from the vector of measurements y=Ax+e, where A is a given design matrix whose rows correspond to individual measurements and e represents errors in measurements. Popular iterative algorithms, e.g. message passing, used in this context requires a "warm start", meaning they must be initialized better than a random guess. In practice, it is often the case that a spectral estimator, i.e. the principal component of a certain matrix built from Y, serves as such an initialization. In this talk, we discuss the theoretical aspect of the spectral estimator and present a theorem on its performance guarantee. Our result gives a threshold for the sample complexity, that is, how many measurements are needed for a warm start to be obtainable, as well as a concrete estimator. If time permits, we will also discuss our method based on (vector-valued) Approximate Message Passing.

2025-06-20 / 14:00 ~ 16:00

IBS-KAIST 세미나 - 수리생물학:

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In this talk, we discuss the paper “Large language models for scientific discovery in molecular property prediction” by Yizhen Zheng et.al., nature machine intelligence, 2025.

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