Pak Tung Ho, The Weighted Yamabe Problem
B236-1 IBS, Korea, Republic ofSpeaker Pak Tung Ho Sogang University In this talk, I will explain what the weighted Yamabe problem is, and mention some related results that Jinwoo Shin (KIAS) and I obtained.
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Aeryeong Seo, TBA
B266 and on-lineSpeaker Aeryeong Seo Kyungpook National University TBA
Jinhyun Park, A Reciprocity Theorem Arising from a Family of Algebraic Curves
B236-1 IBS, Korea, Republic ofSpeaker Jinhyun Park KAIST The classical reciprocity theorem, also called the residue theorem, states that the sum of the residues of a rational (meromorphic) differential form on a compact Riemann surface is zero. Its generalization to smooth projective curves over a field is often called the Tate reciprocity theorem. There is a different …
Jaewoo Jeong, Hankel Index of Smooth Non-ACM Curves of Almost Minimal Degree
B236-1 IBS, Korea, Republic ofSpeaker Jaewoo Jeong IBS CCG The Hankel index of a real variety is a semi-algebraic invariant that quantifies the (structural) difference between nonnegative quadrics and sums of squares on the variety. Note that the Hankel index of a variety is difficult to compute and was computed for just few cases. In 2017, …
Livia Campo, Fano 3-folds and Equivariant Unprojections
B266 IBS, Korea, Republic ofSpeaker Livia Campo KIAS The classification of terminal Fano 3-folds has been tackled from different directions: for instance, using the Minimal Model Program, via explicit Birational Geometry, and via Graded Rings methods. In this talk I would like to introduce the Graded Ring Database - an upper bound to the numerics of Fano …
Junho Choe, Constructions of Counterexamples to the Regularity Conjecture
B266 IBS, Korea, Republic ofSpeaker Junho Choe KIAS Castelnuovo-Mumford regularity, simply regularity, is one of the most interesting invariants in projective algebraic geometry, and the regularity conjecture due to Eisenbud and Goto says that the regularity can be controlled by the degree for any projective variety. But counterexamples to the conjecture have been constructed by some methods. …
Joaquín Moraga, Coregularity of Fano Varieties
on-lineSpeaker Joaquín Moraga UCLA In this talk, we will introduce the absolute coregularity of Fano varieties. The coregularity measures the singularities of the anti-pluricanonical sections. Philosophically, most Fano varieties have coregularity 0. In the talk, we will explain some theorems that support this philosophy. We will show that a Fano variety of coregularity …
Andrea Petracci, A 1-dimensional Component of K-moduli of Del Pezzo Surfaces
on-lineSpeaker Andrea Petracci Università di Bologna Fano varieties are algebraic varieties with positive curvature; they are basic building blocks of algebraic varieties. Great progress has been recently made by Xu et al. to construct moduli spaces of Fano varieties by using K-stability (which is related to the existence of Kähler-Einstein metrics). These moduli …
JongHae Keum, Fake Projective Planes I
B236-1 IBS, Korea, Republic ofSpeaker JongHae Keum KIAS Fake projective planes (abbreviated as FPPs) are 2-dimensional complex manifolds with the same Betti numbers as the projective plane, but not isomorphic to it. FPPs can be uniformized by a complex 2-ball. In other words, they are ball quotients having the minimum possible Betti numbers. The existence of such …
JongHae Keum, Fake Projective Plane II
B236-1 IBS, Korea, Republic ofSpeaker JongHae Keum KIAS Fake projective planes (abbreviated as FPPs) are 2-dimensional complex manifolds with the same Betti numbers as the projective plane, but not isomorphic to it. FPPs can be uniformized by a complex 2-ball. In other words, they are ball quotients having the minimum possible Betti numbers. The existence of such …
Kangjin Han, Secant variety and its singularity I
B266 IBS, Korea, Republic ofSpeaker Kangjin Han DGIST Secant variety (or more generally Join) construction is one of the main methods to construct a new geometric object from the original one in classical algebraic geometry. In this series of talks, we first consider some general facts on secant varieties and then focus on a specific topic, i.e. …