March 2019, Seoul

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

March 2019, Seoul

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

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