복소기하학연구단
Speaker Kisun Lee Clemson University Numerical algebraic geometry employs numerical techniques for problems in algebraic geometry. This talk begins with a question reminding the meaning of solving a (polynomial) equation. It overviews the homotopy continuation as a method for finding solutions to a system of polynomial equations. After problems from algorithmic and application …
Speaker Kisun Lee Clemson University A certified algorithm produces a solution and a certificate of correctness to a problem. Numerical certification studies certified algorithms for results obtained from numerical methods in algebraic geometry. In this talk, we discuss why numerical certification is needed in numerical algebraic geometry and introduce the Krawczyk homotopy as …
Speaker Euisung Park Korea University Many projective varieties are ideal-theoretically cut out by quadratic polynomials of rank less than or equal to 4. Classical constructions in projective geometry like rational normal scrolls and Segre-Veronese varieties are examples. Regarding this phenomenon, I would like to talk about the following two results in this talk. …
Speaker Jiewon Park KAIST Various monotonicity formulae have profound applications in many different problems in geometric analysis. Quite often these formulae can be derived from pointwise Hessian estimates, also known as Li-Yau-Hamilton estimates or matrix Harnack inequalities. In this talk we will focus on this connection building upon Hessian estimates for the Green …
Invited Speakers Dongwook Choa (KIAS, Seoul) Young-Jun Choi (Pusan National Univ.) Siarhei Finski (École Polytechnique) Hervé Gaussier (Univ. Grenoble-Alpes) Masafumi Hattori (Kyoto Univ.) Siqi He (AMSS, Beijing) Ludmil Katzarkov (Univ. Miami) Yusuke Kawamoto (ETH, Zurich) Takayuki Koike (Osaka Metropolitan Univ.) Yu-Shen Lin (Boston Univ.) George Marinescu (Univ. Köln) Yuichi Nohara (Meiji Univ.) Semon Rezchikov (Princeton …
Speaker Sheng Meng East China Normal University Let X be a normal projective variety over C. Let f be a surjective endomorphism of X. In this talk, I will try to explain our current program on the classification and the building blocks of (f, X), involving two main tools: equivariant minimal model program …
Speaker Chuyu Zhou Yonsei University In this lecture, I will recall some basic knowledge on K-stability and some background on wall crossing in proportional setting. Then we plan to conduct a comparison between proportional case and non-proportional case. Under the comparison, we will define several domains associated to a family of couples and …
Speaker Chuyu Zhou Yonsei University In this lecture, we will talk about two properties of K-semistable domains in non-proportional setting. One is the finiteness criterion, which states that the number of domains is finite for a family of couples. The other is about the shape of each domain, which states that they are …
Speaker Xiaojun Huang Rutgers Univ Let M be a smooth real codimension two compact submanifold in a Stein manifold. We will prove the following theorem: Suppose that M has two elliptic complex tangents and suppose CR points are non-minimal. Assume further that M is contained in a bounded strongly pseudoconvex domain. Then M …
Changho Han (한창호) Visitor (2024.10.13-2024.10.14) from Korea University Office: -
Speaker Changho Han Korea university K3 surfaces, as a generalization of elliptic curves, have a rich amount of geometric properties. Recalling that elliptic curves are double covers of rational curves branched over 4 distinct points, there are K3 surfaces that are cyclic triple covers of rational surfaces; Artebani and Sarti classified such generic …
Speaker Justin Lacini Princeton university A log del Pezzo surface is a normal surface with only Kawamata log terminal singularities and anti-ample canonical class. Over the complex numbers, Keel and McKernan have classified all but a bounded family of log del Pezzo surfaces of Picard number one. In this talk we will extend …
