March 2019, Seoul

**Title:** Derived Categories of Sextic Du Val del Pezzo surfaces II

March 2019, Seoul

**Title:** Derived Categories of Sextic Du Val del Pezzo surfaces II

February 2019, Seoul

**Title:** Derived Categories of Sextic Du Val del Pezzo surfaces I

January 2019, Seoul

**Title:** Instanton Bundles on Quartic del Pezzo Threefold

December 2018, Seoul

**Title:** Instanton Bundles on Fano Threefolds II

December 2018, Seoul

**Title:** Instanton Bundles on Fano Threefolds I

November 2019, Moscow

**Title:** The variety of semistable del Pezzo surfaces

**Abstract:**

Kollar introduced a generalization of GIT stability for hypersurfaces: stability over rings. This notion is useful for finding good reductions to finite characterstic and for finding good (semistable) birational models of fibrations. I will talk about extending this notion to del Pezzo surfaces of degree 1 and 2. These surfaces are hypersurfaces in weighted projective spaces, where GIT techniques do not work. On the other hand embeddings into the projective spaces are not complete intersections and are difficult to work with. I will talk about generalizations of stability in both of these settings. In particular, I will talk about parameter spaces of del Pezzo surfaces of degrees 1 and 2

October 2018, Seoul

**Title:** Indroduction to Derived Categories IV

October 2018, Gunsan

**Title:** Stability of del Pezzo surfaces over rings

**Abstract:**

Kollar introduced a generalization of GIT stability for hypersurfaces: stability over rings. This notion is useful for finding good reductions to finite characterstic and for finding good (semistable) birational models of fibrations. I will talk about extending this notion to del Pezzo surfaces of degree 1 and 2. These surfaces are hypersurfaces in weighted projective spaces, where GIT techniques do not work. On the other hand embeddings into the projective spaces are not complete intersections and are difficult to work with. I will talk about generalizations of stability in both of these settings. In particular, I will talk about parameter spaces of del Pezzo surfaces of degrees 1 and 2.

September 2018, Seoul

**Title:** Indroduction to Derived Categories I

August 2018, Seoul

**Title:** Semistability of del Pezzo surfaces, good models and reductions

**Abstract:**

Kollar has introduces a notion of stability of a hypersurface in projective space over a ring. This notion can be used to find good reductions of hypersurfaces to finite characteristic. It also has application to birational geometry. If a cubic fibration over an affine curve is a semistable cubic surface over the coordinate ring of the base, then the fibration is a Mori fiber space and the total space has only Gorenstein singularities. This is an improvment over an existing result of Corti, whose version gave models with also Gorenstein but worse singularities. On the other hand, Corti’s method allowed to prove similar result for del Pezzo fibrations of degree 2. I will talk about extending the results of Kollar to del Pezzo surfaces of degree 2 and 1. As a corollary we improve Corti’s result and prove an analogue in degree 1.