복소기하학연구단
Speaker Jungkai Chen National Taiwan University The minimal model program works pretty well in dimension three. However, the explicit classification of divisorial contractions to points was completed quite recently thanks to the work of Kawamata, Hayakawa, Kawakita and more. In this talk, we are going to describe threefold divisorial contractions to curves. We …
Speaker Shigeru Mukai RIMS, Kyoto University I will discuss the moduli space of abelian surfaces with bi-level structure of type (1, d) for d = 2, 3, 4, 5. Part 1: Their Satake compactification is the projective 3-space P3 for d = 2, 3, 4. Part 2: It is a small contraction of …
Speaker Shigeru Mukai RIMS, Kyoto University I will discuss the moduli space of abelian surfaces with bi-level structure of type (1, d) for d = 2, 3, 4, 5. Part 1: Their Satake compactification is the projective 3-space P3 for d = 2, 3, 4. Part 2: It is a small contraction of …
Speaker Sung Rak Choi Yonsei University In this talk, we define and study a triple called a potential triple which consists of a pair (X, Δ) and a polarizing pseudoeffective divisor D. To such a triple, we define a so-called potential multiplier ideal sheaf which gives a simultaneous generalization of the multiplier ideal …
Zoom ID: 880 6763 5837 PW: 312515 Speaker Minyoung Jeon University of Georgia Prym varieties are abelian varieties constructed from etale double covers of algebraic curves. In 1985, Welters equipped Prym varieties with Brill-Noether loci. In this talk, we will describe the Prym-Brill-Noether loci with special vanishing at up to two marked points …
Speaker Eric Sommers University of Massachusetts Among the nilpotent orbits in a simple Lie algebra are the special nilpotent orbits, which play an important role in representation theory. Some of the geometry of the closure of a nilpotent orbit can be understood by taking a transverse slice to a smaller orbit in the …
Speaker Cheol Hyun Cho Seoul National University The variation operator in singularity theory maps relative homology cycles to compact cycles in the Milnor fiber using the monodromy. We construct its symplectic analogue for an isolated singularity. We define a new Floer cohomology, called monodromy Lagrangian Floer cohomology, which provides categorifications of the standard …
Zoom ID: 880 6763 5837 PW: 312515 Speaker Myeongjae Lee Stony Brook University Strata of differentials are interesting objects studied in various fields such as Teichmuller dynamics, topology and algebraic geometry. Generalized strata are subsets of the strata of meromorphic differentials, where certain sets of residues summing up to zero. We present the …
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 …