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E6-1 #4415
Tensor and Geometry with application 미니 워크숍

E6-1 #4415

### Organizers

곽시종날짜: 2023년 8월 10일~11일

장소: E6-1 #4415호

Time table

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8월 10일 오후 3:00 - 3:50 / 문현석 (KIAS)

8월 10일 오후 4:10 - 5:00 / 이기선 (UCSD)

저녁식사 5시40분

8월 11일 오전 10:00 - 10:50 / 한강진 (DGIST)

8월 11일 오후 11:10 - 12:00 / 최준호 (KIAS)

점심식사 12시 30분

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논문제목 및 초록

문현석

Title: On the rank index of some quadratic varieties

Abstract: A projective variety X is said to satisfy property QR(k) if its homogeneous ideal can be generated by quadratic polynomials of rank at most k. We define the rank index of X to be the smallest integer k such that X satisfies property QR(k). Many classical varieties, such as Segre-Veronese embeddings, rational normal scrolls and curves of high degree, satisfy property QR(4). Recently, it is shown in the previous paper that every Veronese embedding has rank index 3 if the base field has characteristic ̸= 2, 3. In this talk, we explain the rank index of X when it is some other classical projective variety such as rational normal scrolls, Segre varieties, Plucker embeddings of the Grassmannians of lines and del Pezzo varieties.

이기선

Title: Algorithms, applications and certification in numerical nonlinear algebra

Abstract: Nonlinear algebra is the name of franchising various kinds of interests in applied algebraic geometry. Especially, numerical nonlinear algebra employs numerical techniques for problems in nonlinear algebra. This talk begins with a question reminding the meaning of solving a (polynomial) equation in algebraic geometry and overviews the homotopy continuation as a method for finding solutions to a system of polynomial equations. After problems from algorithmic and application points of view in numerical nonlinear algebra are introduced, we discuss how the results from numerical techniques can be certified. No pre-knowledge from graduate-level algebraic geometry is assumed.

한강진

Title: Sullivant-Talaska ideal of the cyclic Gaussian Graphical Model

Abtract: In this talk, we introduce a conjecture due to Sturmfels and Uhler concerning generation of the prime ideal of the variety associated to the Gaussian graphical model of any cycle graph and explain how to prove it. Our methods are general and applicable to a large class of ideals with radical initial ideals. This work is done jointly with A. Conner and M. Michalek

최준호

Title: A generalization of the gonality conjecture

Abstract: Let $C$ be a linearly normal smooth projective curve and suppose that its degree is sufficiently large. Then the gonality conjecture settled by Ein-Lazarsfeld and Rathmann says that the gonality of $C$ can be computed by syzygies of $C$. In this talk we show that syzygies of higher secant varieties to $C$ completely determines the gonality sequence of $C$. This is a joint work with Prof. Sijong Kwak and Prof. Jinhyung Park.

### Organizers

Jae Kyoung Kim (KAIST/IBS, Korea) and Krešimir Josić (U of Houston, USA)*https://sites.google.com/view/iciam-2023-stocmodelbio/home?authuser=0*