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BEGIN:VEVENT
DTSTART;VALUE=DATE:20250301
DTEND;VALUE=DATE:20260216
DTSTAMP:20260416T064042
CREATED:20250304T080834Z
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SUMMARY:Ngoc Cuong Nguyen (KAIST)
DESCRIPTION:Ngoc Cuong Nguyen\nVisitor (2025.3.1-2026.2.15) from KAIST\nOffice: B248
URL:https://ccg.ibs.re.kr/event/250301-260215/
CATEGORIES:Visitors
ATTACH;FMTTYPE=image/jpeg:https://ccg.ibs.re.kr/wp-content/uploads/2025/03/ncnguyen_rescaled-1.jpg
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BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20260121T150000
DTEND;TZID=Asia/Seoul:20260121T160000
DTSTAMP:20260416T064042
CREATED:20260115T053810Z
LAST-MODIFIED:20260116T045714Z
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SUMMARY:Torsion points on holomorphic sections of elliptic surfaces
DESCRIPTION:    Speaker\n\n\nSui-Chung Ng\nECNU\n\n\n\n\n\n\nA complex algebraic surface is called an elliptic surface if it is a fiber surface whose general fibers are elliptic curves. An elliptic surface can also be regarded as an elliptic curve $E$ over the function field $K$ of an algebraic curve. The holomorphic sections of that elliptic surface can then be regarded as $K$-rational points of $E$. In the 90s\, N. Mok proposed and started to use differential geometry to study these $K$-rational points (as holomorphic sections). In this talk\, we will discuss how to study the torsions points on such holomorphic sections within this framework. This is based on a joint work with N. Mok.
URL:https://ccg.ibs.re.kr/event/tba/
LOCATION:B236-1\, IBS\, Korea\, Republic of
CATEGORIES:Several Complex Variables Seminar
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BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20260121T163000
DTEND;TZID=Asia/Seoul:20260121T173000
DTSTAMP:20260416T064042
CREATED:20260115T053615Z
LAST-MODIFIED:20260115T053842Z
UID:4354-1769013000-1769016600@ccg.ibs.re.kr
SUMMARY:On the rank of Hermitian polynomials and the SOS Conjecture
DESCRIPTION:    Speaker\n\n\nYun Gao\nShanghai Jiao Tong U\n\n\n\n\n\n\nHilbert’s 17-th problem asked whether a non-negative polynomial in several real variables must be a sum of squares of rational functions. There is also a quantitative version of Hilbert’s 17th problem which asks how many squares are needed. D’Angelo extend this problem to more general case which is called Hermitian or complex variable analogues of Hilbert’s problem. Let $z\in\mathbb C^n$ and $\|z\|$ be its Euclidean norm. Ebenfelt proposed a conjecture regarding the possible ranks of the Hermitian polynomials in $z\,\bar z$ of the form $A(z\,\bar z)\|z\|^2$\, known as the SOS Conjecture\, where SOS stands for “sums of squares”. In this talk\, we will introduce a dimension formula for local holomorphic mappings. As an application\, we use this formula to study this conjecture and its generalizations to arbitrary signatures for a Hermition forms on $\mathbb C^n$. It is joint work with Sui-Chung Ng.
URL:https://ccg.ibs.re.kr/event/on-the-rank-of-hermitian-polynomials-and-the-sos-conjecture/
LOCATION:B236-1\, IBS\, Korea\, Republic of
CATEGORIES:Several Complex Variables Seminar
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