TBA (Osamu Iyama)

• Osamu Iyama

Room: Lecture Hall

TBA (Shinnosuke Okawa)

• Shinnosuke Okawa

Room: Lecture Hall

TBA (Lutz Hille)

• Lutz Hille

Room: Lecture Hall

Finiteness of Orlov spectra of singularity categories

• Ryo Takahashi

Room: Lecture Hall The Orlov spectrum of a triangulated category is the set of generation times of strong generators. Ballard, Favero and Katzarkov proved that the singularity category of a hypersurface isolated singularity has finite Orlov spectrum. In this talk, we will introduce the new notion of uniformly dominant local rings. We will show that the singularity category of a uniformly dominant isolated singularity has finite Orlov spectrum, and consider when a given local ring is uniformly dominant.

Semi-infinite Hodge structure associated with hyperbolic root systems

• Kyoji Saito

Room: Lecture Hall It is well-known that there exist semi-infinite Hodge structure associated to finite or elliptic root systems (which describes the lattice of vanishing cycles for either simple or elliptic root systems). Recently, we found that the semi-infinite Hodge structure exist for hyperbolic root systems of rank 2. This is a surprise, since the hyperbolic root systems do not have geometric origin so the they behaves quite differently than the above classical cases (e.g. some eigenvalues of monodromy are not root of unity but real). In the present talk, we will describe the construction down to the earth.

TBA (Atsushi Takahashi)

• Atsushi Takahashi

Room: Lecture Hall

Fukaya category of Landau-Ginzburg model via Witten equation

• Huijun Fan

Room: Lecture Hall Landau-Ginzburg model has become a cornerstone theory of global mirror symmetry. The closed string A-theory of a LG model has already been built, and is well-known as the quantum singularity theory (or FJRW theory). An open string theory of a LG model has also been treated in the paper “Fukaya Category of Landau-Ginzburg model, arXiv:18012.11748v1”, but with not much attention. In this talk, I will recall the construction in this paper, which is related to the boundary value problem of the Witten equations arising from Landau-Ginzburg model, and mention the Maurer- Cartan element conjecture proposed by Gaiotto-Moore-Witten (or Kapranov- Kontsevich-Soibelman).

Genus-0 permutation-equivariant KGW invariants of the point

• Todor Milanov

Room: Lecture Hall K-theoretic Gromov--Witteh (KGW) theory was introduced by Givental and Y.P. Lee as a generalization of Gromov--Witten theory. Recently, Givental realised that if we want to compute KGW invariants via fixed-point localization methods, we have to consider a more general theory, i.e., the permutation equivariant version of KGW theory. I would like to give an introduction to this topic and to explain how to compute the invariants in genus-0 for the simplest possible target -- the point.

Effective characterizations of semi-abelian varieties

• Sofia Tirabassi

Room: Lecture Hall I will show how three logaritmic plurigenera and the logarithic irregularity are enough to characterize semi-abelian surfaces among the quasi-projective surfaces. I will also present some results for higher dimensional varieties in a very special case. This is joint work with Mendes Lopes and Pardini and a work in progress with J. Baudin.

Derived equivalence for the simple flop of type $G_2^{\dagger}$

• Wahei Hara

Room: Lecture Hall In this talk we discuss an example of a simple flop that was found by Kanemitsu, from the point of view of derived categories. A simple flop is a flop between two smooth varieties that is connected by one smooth blow-up and one smooth blow- down, and those flops were partially classified by Kanemitsu, using Dynkin data. The exceptional divisor of the blow-ups has two projective bundle structures of the same rank, and is called a roof. The simple flop of type $G_2^{\dagger}$, which we discuss in this talk, is the only known example of a simple flop that has the non- homogeneous roof. The main theorem of the talk is that the simple flop of type $G_2^{\dagger}$ gives a derived equivalence. The proof is done by using tilting bundles, and hence it also produces a noncommutative crepant resolution that is derived equivalent to both sides of the flop. Despite its Dynkin label, the construction of the tilting bundles is related to rational homogeneous manifolds of Dynkin type $B_3$ and $D_4$.

TBA (Mikhail Kapranov)

• Mikhail Kapranov

Room: Lecture Hall

TBA (Rina Anno)

• Rina Anno

Room: Lecture Hall

Dolbeault Geometric Langlands conjecture via quasi-BPS categories

• Yukinobu Toda

Room: Lecture Hall In this talk, I will introduce the notion of `limit category' for cotangents of smooth stacks, which is expected to give a categorical degeneration of the category of D-modules on them. I show that the limit category for the moduli stack of Higgs bundles admits a semiorthogonal decomposition into products of quasi-BPS categories, which are categorifications of BPS invariants of some non-compact Calabi-Yau 3-folds. I propose the formulation of Dolbeault Geometric Langlands conjecture using the limit category, which is regarded as a classical limit of Geometric Langlands correspondence. I also show that the limit category admits Hecke operators. This is a joint work in progress with Tudor Padurariu.

TBA (Timothy Logvinenko)

• Timothy Logvinenko

Room: Lecture Hall

TBA (Katherine A. Maxwell)

• Katherine A. Maxwell

Room: Lecture Hall

TBA (Alexei Lvov)

• Alexei Lvov

Room: Lecture Hall

Wrapped and compact Fukaya categories of plumbings

• Dogancan Karabas

Room: Lecture Hall Given any finite quiver Q, where each vertex corresponds to a fixed Lagrangian $L_v$, I will describe an associated symplectic manifold known as the plumbing of $T^*L_v$'s along Q. Using a local-to-global approach, I will explain how their wrapped Fukaya category can be expressed as a Ginzburg dg algebra with based loop space coefficients or a derived multiplicative preprojective algebra. In the second part of my talk, I will demonstrate that microlocal sheaves on the union of $L_v$'s recover the compact Fukaya category of the plumbing, generalising the Nadler-Zaslow correspondence for cotangent bundles. The first part is joint work with Sangjin Lee (arXiv:2405.10783), and the second part is ongoing work with Sangjin Lee and Wonbo Jeong.

Hodge microsheaves on cotangent bundles and plumbings

• Tatsuki Kuwagaki

Room: Lecture Hall The theory of Hodge microsheaves aims at generalizing the theory of mixed Hodge modules in twofold: (1) "infinite-dimensional" like wrapped sheaves of Nadler, (2) "microlocal" in the style of Bezrukavnikov-Kapranov. In this talk, I'll explain some background philosophy and some nontrivial computational results in the theory, based on joint work with Takahiro Saito.