Title and Abstract

Feb. 17 Monday

11:00 -- 12:30 Yukinobu Toda I

Title: Introduction to Bridgeland stability conditions

Abstract: I will give a general introduction to Bridgeland stability conditions for non-experts.

14:00 -- 15:30 Arend Bayer I

Title: Wall-crossing for Bridgeland stability conditions and birational geometry of moduli spaces

Abstract: I will explain a construction that systematically relates wall-crossing for moduli spaces of Bridgeland-stable objects to the birational geometry of the moduli space. Technically, this construction is given as a numerically positive divisor class on the moduli space naturally associated to the stability condition.

Both talks (I and II) are based on joint work with Emanuele Macrì.

16:00 -- 17:30 Kota Yoshioka I

Title: Bridgeland stability on abelian surfaces

Abstract: I will explain some results on the moduli of stable objects on abelian surfaces which were obtained a few years ago. This is a joint work with H. Minamide and S. Yanagida.

Feb. 18Tuesday

11:00 -- 12:30 Arend Bayer II

Title: Wall-crossing for Bridgeland stability conditions and birational geometry of moduli spaces

Abstract: I will explain how the construction explained in talk I can be used in the case of moduli spaces of sheaves on K3 surfaces. The results give an essentially complete description of their birational geometry, including a description of their nef cones (answering questions by Hassett-Tschinkel), their birational models, and Lagrangian fibrations (proving a well-known conjecture that predicts when these exist). Both talks (I and II) are based on joint work with Emanuele Macrì.

14:00 -- 15:30 Yukinobu Toda II

Title:Gepner type stability conditions on graded matrix factorizations

Abstract: I will discuss conjectural stability conditions on graded matrix factorizations. I will focus on the case of homogeneous polynomials which define general cubic fourfolds containing a plane.

16:00 -- 17:30 Kota Yoshioka II

Title: Bridgeland stability on abelian surfaces

Abstract: I will explain some results on the moduli of stable objects on abelian surfaces which were obtained a few years ago. This is a joint work with H. Minamide and S. Yanagida.

Feb. 19 Wednesday

11:00 -- 12:30 Matthew Ballard I

Title: Stratifications under group actions and derived categories

Abstract: Let X be a variety admitting an action by an algebraic group G. I will describe natural stratifications on X often associated to stability questions in GIT. Then I will discuss how these stratifications can be used to extract information on derived categories of quotients of X by G. This relates to joint work with David Favero and Ludmil Katzarkov.

14:00 -- 15:30 David Favero I

Title: VGIT, HMS, Constructible sheaves, and Lagrangian Skeleta

Abstract: I will discuss variation of geometric invariant theory quotients from the perspective of Lagrangian skeleta and constructible sheaves following Fang, Liu, Treumann, and Zaslow. The proposal is that the non-proper toric stacks necessary to describe wall-crossing phenomena in derived categories are mirror to wrapped Fukaya categories where the Hamiltonian flow is the distance to the Lagrangian skeleton. This is joint work in progress with Ballard, Diemer, Katzarkov, Kerr, and Kontsevich.

16:00 -- 17:30 Kentaro Hori I

Title: Grade Restriction Rule and D-brane Central Charge

Abstract: I will provide an introduction to linear sigma models, and present a result on the "hemisphere partition function". The partition function turns out to agree with the central charge of the brane placed at the boundary. It is an analytic function on (a cover of) the quantum Kahler moduli space that approaches the expected form at various limits, including large volume limits where the Gamma class shows up as well as the Landau-Ginzburg orbifold(or Gepner) points. The grade restriction rule plays the central role in the analytic continuation across phase boundaries. Based on a joint work with Mauricio Romo.

Feb. 20 Thursday

11:00 -- 12:30 Howard Nuer

Title: Calabi-Yau 3-folds containing Enriques surfaces and degenerations to a strange family

Abstract: We give several constructions of Calabi-Yau 3-folds containing Enriques surfaces. For each family we describe several birational models, and for one of these families we can identify all of its minimal models, exhibiting interesting behavior from the point of view of MMP. Using an alternative description of this family, we find two degenerations which admit crepant resolutions. One of these degenerations is a 1-parameter family of Calabi-Yau 3-folds that has very strange properties from the point of view of mirror symmetry. We discuss these strange features as well as some possible explanations for their occurrence.

14:00 -- 15:15 David Favero II

Title: Homological Projective Duality and LG-models

Abstract: Homological Projective Duality, as the name indicates, is a relationship between the derived category of a variety X and its (homological) projective dual. The subject was introduced by Kuznetsov and has yielded many nontrivial examples of derived equivalences. I will give an introduction to Homological Projective Duality and explain how one can obtain a large class of Homological Projective Duals which are LG-models by varying Geometric Invariant Theory quotients.

15:30 -- 16:45 Matthew Ballard II

Title: Towards Homological Projective Duality for Grassmannians

Abstract: Using the tools of variation of GIT quotients and derived categories of Landau-Ginzburg models, I will give a description of a triangulated category serving as a type of Homological Projective Dual of a Grassmannian. The relation of this to the duals given by Kuznetsov and recent work of Addington-Donovan-Segal will be discussed. This is work (very much) in progress with Dragos Deliu, M. Umut Isik, David Favero, and Ludmil Katzarkov.

17:00 -- 18:30 Sergey Galkin

Title: An explicit construction of Miura's varieties

Abstract: In 1301.7632 Makoto Miura studied Calabi-Yau threefolds obtained as a linear sections of a Schubert cycle in the Cayley plane. He computed the BPS numbers, and conjectured that these threefolds should have non-trivial Fourier-Mukai partners. We'll give an explicit construction of the threefolds predicted by Miura. In fact, both families fit into series that "extend" Grassmannian-Pfaffian duality: varieties that parametrise pairs of a skew-symmetric form and a vector in its kernel. This is work in progress with Alexander Kuznetsov and Michael Movshev.

Feb. 21 Friday

10:00 -- 11:30 Michal Kapustka

Title: Calabi-Yau threefolds in P^6

Abstract: Calabi-Yau threefolds in P^6, so-called Pfaffian Calabi-Yau threefolds, are a special class of Calabi-Yau threefolds which on one hand have often precise descriptions in terms of equations and on the other are hard to study from the point of view of mirror symmetry. In this talk, we shall review the theory of these manifolds and present directions for possible future investigation. This is joint work with G. Kapustka.

11:45 -- 13:00 Kentaro Hori II

Title: Linear Sigma Models with Strongly Coupled Phases

Abstract: Linear sigma models with physically interesting phases ("strongly coupled phases") yield interesting mathematical correspondences, such as Rodland correspondence (Pfaffian vs Grassmannian) as well as Hosono-Takagi correspondence (double symmetric determinantal variety vs Reye congruence). I will try to explain the underlying gauge theory duality,and provide more examples of correspondences, with some surprises. Bases on a joint work with Johanna Knapp.