Kisun Lee, Introduction to Numerical Algebraic Geometry

B236-1 IBS, Korea, Republic of

    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

Kisun Lee, Numerical Certification and Certified Homotopy Tracking

B236-1 IBS, Korea, Republic of

    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

Euisung Park, On Rank 3 Quadratic Equations of Projective Varieties

B236-1 IBS, Korea, Republic of

    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.

Changho Han, Trigonal Curves and Associated K3 Surfaces

B236-1 IBS, Korea, Republic of

    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

Justin Lacini, On Log del Pezzo Surfaces in Positive Characteristic

B236-1 IBS, Korea, Republic of

    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

Naoto Yotsutani, Bott Manifolds with the Strong Calabi Dream Structure

B236-1 IBS, Korea, Republic of

    Speaker Naoto Yotsutani Kagawa university We prove that if the Futaki invariant of a polarized Bott manifold (X, L) for any ample line bundle L vanishes, then X is isomorphic to the products of the projective lines. This talk is based on a work joint with Kento Fujita (algebro-geometrical approach), and another independent

Giancarlo Urzua, The Birational Geometry of Markov Numbers

B236-1 IBS, Korea, Republic of

    Speaker Giancarlo Urzua Pontificia Universidad Catolica de Chile The projective plane is rigid. However, it may degenerate to surfaces with quotient singularities. After the work of Bădescu and Manetti, Hacking and Prokhorov 2010 classified these degenerations completely. They are Q-Gorenstein partial smoothings of P(a2, b2, c2), where a, b, c satisfy the Markov

Izzet Coskun, The Geometry of Moduli Spaces of Sheaves on P2

B236-1 IBS, Korea, Republic of

    Speaker Izzet Coskun University of Illinois Chicago In this talk, I will explain how to use Bridgeland stability conditions to compute the ample and effective cones of moduli spaces of sheaves on the projective plane. I will describe the birational geometry of these moduli spaces and give applications to the higher rank interpolation

Izzet Coskun, The Higher Rank Brill-Noether Problem on Surfaces

B236-1 IBS, Korea, Republic of

    Speaker Izzet Coskun University of Illinois Chicago In this talk, I will explain how to use Bridgeland stability conditions to compute the cohomology of a general stable sheaf on a K3 or abelian surface. This talk is based on joint work with Howard Nuer and Kota Yoshioka.

Luca Schaffler, An Explicit Wall Crossing for the Moduli Space of Hyperplane Arrangements

B236-1 IBS, Korea, Republic of

    Speaker Luca Schaffler Roma Tre University The moduli space of hyperplanes in projective space has a family of geometric and modular compactifications that parametrize stable hyperplane arrangements with respect to a weight vector. Among these, there is a toric compactification that generalizes the Losev-Manin moduli space of points on the line. We study

Yen-An Chen, Toric Fano Foliations

B236-1 IBS, Korea, Republic of

    Speaker Yen-An Chen National Taiwan University In recent years, there are significant developments of the minimal model program for foliated varieties. It is intriguing to ask if Fano foliations form a bounded family. It is anticipated that Borisov-Alexeev-Borisov conjecture also holds in the context of foliations. In this talk, I will discuss the

Luca Schaffler, Unimodal Singularities and Boundary Divisors in the KSBA Moduli of a Class of Horikawa Surfaces

B236-1 IBS, Korea, Republic of

    Speaker Luca Schaffler Roma Tre University Smooth minimal surfaces of general type with K2=1, pg=2, and q=0 constitute a fundamental example in the geography of algebraic surfaces, and the 28-dimensional moduli space M of their canonical models admits a modular compactification M via the minimal model program. We describe eight new irreducible boundary

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