Upcoming Events

Date Time Event

2025/09/24 15:30-17:00 Reading group

2025/09/26 15:30-17:00 NCTS Seminar in Algebraic Geometry

2025/10/01 15:30-17:00 Reading group

2025/10/08 15:30-17:00 Reading group

2025/10/09 13:30-15:00 NCTS Seminar in Algebraic Geometry

2025/10/09 15:30-17:00 NCTS Seminar in Algebraic Geometry

2025/10/13 13:30-15:30 Group meeting

2025/10/15 15:30-17:00 Reading group

2025/10/17 10:00-11:30 NCTS Seminar in Algebraic Geometry

2025/10/20 13:30-15:30 Group meeting

2025/11/10 ～ 2025/11/14 2025 Algebraic Geometry in East Asia

2026/01/12 ～ 2026/01/16 Tour de Formosa

2026/04/13 ～ 2026/04/17 2026 Higher Dimensional Algebraic Geometry

Reading group

2025.09.24 (Wednesday) 03:30PM-05:00PM

Location: Rm. 430, Astro-Math Bldg., NTU

NCTS Seminar in Algebraic Geometry

2025.09.26 (Friday) 03:30PM-05:00PM

Title: Signature 0 toric varieties, wall crossings, and cross polytope-like structures

Speaker: Soohyun Park (Hebrew University of Jerusalem)

Abstract: We describe the structure of simplicial locally convex fans associated to even-dimensional complete toric varieties with signature 0. They belong to the set of such toric varieties whose even degree Betti numbers yield a gamma vector equal to 0. The gamma vector is an invariant of palindromic polynomials whose nonnegativity lies between unimodality and real-rootedness. It is expected that the cases where the gamma vector is 0 form "building blocks'' among those where it is nonnegative. This means minimality with respect to a certain restricted class of blowups. However, this equality to 0 case is currently poorly understood. In the course of addressing this situation for such toric varieties, we find that the interpretation of the top component of the gamma vector as a signature encodes *intrinsic* combinatorial information on the fan in addition to compatibility with existing natural combinatorial examples as shown earlier. Our main method involves wall crossings. The links of the fan come from a repeated suspension of the maximal linear subspace in its realization in the ambient space of the fan. Conversely, the centers of these links containing any particular line form a cone or a repeated suspension of one. The intersection patterns between these "anchoring'' linear subspaces come from how far certain submodularity inequalities are from equality and parity conditions on their dimensions. This involves linear dependence and containment relations between them. We obtain these relations by viewing the vanishing of certain mixed volumes from the perspective of the exponents. Finally, these wall crossings yield a simple method of generating induced 4-cycles expected to cover the minimal objects described above. Note that this involves intersections of rational equivalence relations with 2-dimensional orbit closures instead of 1-dimensional ones as in most combinatorial applications.

Location: Rm. 515, NCTS (Cosmology Bldg., NTU) 

Reading group

2025.10.01 (Wednesday) 03:30PM-05:00PM

Location: Rm. 430, Astro-Math Bldg., NTU

Reading group

2025.10.08 (Wednesday) 03:30PM-05:00PM

Location: Rm. 430, Astro-Math Bldg., NTU

NCTS Seminar in Algebraic Geometry

2025.10.09 (Thursday) 03:30PM-05:00PM

Title: TBC

Speaker: Thibault Poiret (The University of St Andrews)

Abstract: TBC

Location: Rm. 515, NCTS (Cosmology Bldg., NTU) 

Reading group

2025.10.15 (Wednesday) 03:30PM-05:00PM

Location: Rm. 430, Astro-Math Bldg., NTU

Previous Events

Reading group

2025.09.17 (Wednesday) 03:30PM-05:00PM

Location: Rm. 430, Astro-Math Bldg., NTU

NCTS Seminar in Algebraic Geometry

2025.09.12 (Friday) 10:00AM-11:30AM

Title: Boundedness theorems for abelian fibrations

Speaker: Philip Engel (University of Illinois in Chicago) (video)

Abstract: I will discuss a proof that the number of deformation classes of symplectic varieties of fixed dimension, admitting a Lagrangian fibration, is finite (and analogous boundedness results for some other fibered K-trivial varieties). Conditional on the generalized semiampleness conjecture, we deduce a bound on the number of deformation classes of hyperkahler varieties in a fixed dimension, whose second Betti number is at least 5. This is joint work with Filipazzi, Greer, Mauri, and Svaldi.

Location: Rm. 515, NCTS (Cosmology Bldg., NTU) 

NCTS Seminar in Algebraic Geometry

2025.08.22 (Friday) 03:30PM-05:00PM

Title: Moduli spaces of threefolds on the Noether line

Speaker: Yong Hu (Shanghai Jiao Tong University) (video)

Abstract: In this talk, we will introduce the 3-dimensional Noether inequality and completely classify the canonical threefolds on the Noether line with $p_g \ge 5$ by studying their moduli spaces. For every such moduli space, we establish an explicit stratification, estimate the number of its irreducible components and prove the dimension formula. A new and unexpected phenomenon is that the number of irreducible components grows linearly with the geometric genus, while the moduli space of canonical surfaces on the Noether line with any prescribed geometric genus has at most two irreducible components of the same dimension. This is a joint work with S.Coughlan, R.Pignatelli and T.Zhang.

Location: Rm. 515, NCTS (Cosmology Bldg., NTU) 

NCTS Seminar in Algebraic Geometry

2025.06.20 (Friday) 10:00AM-11:30AM

Title: Stability of the cotangent bundle on some surfaces

Speaker: Jason Lo (California State University, Northridge) (video)

Abstract: In the 1980s, Donaldson and Uhlenbeck-Yau showed that on a smooth projective variety, the slope stability of a vector bundle is equivalent to the existence of solutions to the associated Hermitian-Yang-Mills equation. Recently, Collins and Yau asked whether a similar correspondence holds for line bundles, between Bridgeland stability conditions and the deformed Hermitian-Yang-Mills equation (or Leung-Yau-Zaslow equation). In this talk, I will report on progress on a similar question for the cotangent bundle on surfaces. This is joint work with Tristan Collins, Yun Shi, and Shing-Tung Yau.

Location: Rm. 505, NCTS (Cosmology Bldg., NTU) 

NCTS Seminar in Algebraic Geometry

2025.05.27 (Friday) 03:30PM-05:00PM

Title: Berkovich compactifications of complex analytic varieties

Speaker: Jérôme Poineau (Université de Caen Normandie) (video)

Abstract: Let X be a complex algebraic variety. We explain how to produce a canonical compactification of its analytification X(C) by adding a Berkovich space at the boundary (the later being defined over the field C endowed with the trivial absolute value), building on earlier work by Morgan-Shalen, Berkovich, Favre, Thuillier, Fantini, Boucksom-Jonsson, etc. Our construction takes place in the setting of hybrid Berkovich spaces, which allows to get a compactification that is a locally ringed space and preserves several properties such as normality, regularity, etc. When the variety X is a moduli space of Riemann surfaces, we obtain a space related to Amini-Nicolussi’s hybrid compactification, which may be used to study the asymptotic behavior of families of Arakelov-Bergmann measures or Green functions. This last part is work in progress with Robert Wilms.

Location: Rm. 515, NCTS (Cosmology Bldg., NTU) 

NCTS Seminar in Algebraic Geometry

2025.04.25 (Friday) 03:30PM-05:00PM

Title: Categorical Torelli for cyclic covers

Speaker: Hannah Dell (University of Bonn) (video)

Abstract: Since any Fano variety can be recovered from its derived category up to isomorphism, we ask whether less information determines the variety - this is called a categorical Torelli question. In this talk, we consider an n-fold cover X → Y ramified in a divisor Z. The cyclic group of order n acts on X. We study how a certain subcategory of Db(X) (the Kuznetsov component) behaves under this group action. We combine this with techniques from topological K-theory and Hodge theory to prove that this subcategory determines X for two new classes of Fano threefolds which arise as double covers of (weighted) projective spaces. This is joint work with Augustinas Jacovskis and Franco Rota (arXiv:2310.13651).

Location: Rm. 515, NCTS (Cosmology Bldg., NTU) 

NCTS Seminar in Algebraic Geometry

2025.04.07 (Monday) 03:30PM-05:00PM

Title: On the birational geometry of algebraically integrable foliations

Speaker: Paolo Cascini (Imperial College London) (video)

Abstract: I will review recent progress on extending the Minimal Model Program to algebraically integrable foliations. My focus will be on applications such as the canonical bundle formula and recent results toward the boundedness of Fano foliations.

Location: Rm. 515, NCTS (Cosmology Bldg., NTU) 

NCTS Seminar in Algebraic Geometry

2025.03.21 (Friday) 03:30PM-05:00PM

Title: K3 surfaces associated with varieties of generalized Kummer type

Speaker: Salvatore Floccari (Universität Bielefeld) (video)

Abstract: Varieties of generalized Kummer type (Kum^n-type) are one of the two infinite series of known hyper-Kähler varieties, the other one being given by deformations of Hilbert schemes of points of K3 surfaces. Via Hodge theory and the Torelli theorem, it is possible to associate a K3 surface S_K with any variety K of Kum^n type, naturally defined as the K3 surface whose transcendental lattice is Hodge isometric to that of K with the form rescaled by a factor 2.
In my talk I will explain how K and the associated K3 surface are related geometrically through a moduli space of sheaves on S_K. Building upon the work of O'Grady, Markman, Voisin and Varesco, we are able to prove the Hodge conjecture for all powers of these K3 surfaces. As a corollary we obtain the Hodge conjecture for all powers of any abelian fourfold of Weil type with discriminant 1, strenghtening a result of Markman.

Location: Rm. 505, NCTS (Cosmology Bldg., NTU) 

NCTS Seminar in Algebraic Geometry

2025.03.07 (Friday) 03:30PM-05:00PM

Title: Finite group actions and duality on Picard stacks

Speaker: Guillermo Gallego (FU Berlin) (video)

Abstract: Picard stacks are commutative group objects in the 2-category of stacks. Examples include commutative group schemes and abelian varieties, but also classifying stacks BG, for G a commutative group scheme. More generally, for such G over a scheme X, the stack of G-torsors Bun(G/X) is also a Picard stack. There is a natural notion of duality inside Picard stacks, given by considering maps to BGm, where Gm denotes the multiplicative group. This duality generalizes both Cartier duality and the duality of abelian varieties. There is also a notion of Fourier-Mukai transform associated a Picard stack, which gives an equivalence of categories when the Picard stack is "good". A particularly interesting class of good Picard stacks is formed by Beilinson 1-motives, which are objects essentially of the form M x A x BG, for M a finitely generated abelian group, A an abelian variety, and G a commutative group scheme.
In this talk, we review this theory, and consider the actions of finite groups on Picard stacks. This leads us to construct the appropriate notions of "invariants" and "coinvariants" on Picard stacks, which are linked to group cohomology and homology, respectively. This allows us to recover the SYZ mirror symmetry over the generic locus of the Hitchin fibration developed by Hausel-Thaddeus, Donagi-Pantev and Chen-Zhu and give a slight generalization of their results, which allows us to explore similar structures in other fibrations related to the Hitchin fibration.

Location: Rm. 515, NCTS (Cosmology Bldg., NTU) 

NCTS Seminar in Algebraic Geometry

2025.02.07 (Friday) 03:30PM-05:00PM

Title: Length of triangulated categories

Speaker: Yuki Hirano (Tokyo University of Agriculture and Technology) (video)

Abstract: Composition series is fundamental in the study of finite groups and finite dimensional modules.
One of the most important properties of such composition series is the Jordan-Hölder property, and this implies the property that all composition series have the same length (we call this the Jordan--Dedekind property).
In this talk, I will introduce the notion of composition series for triangulated categories, and discuss composition series of derived categories of certain finite dimensional algebras and smooth projective varieties. In particular, I will explain that the Jordan--Dedekind property does not hold for derived categories of certain finite dimensional algebras of finite global dimension and certain smooth projective toric surfaces. This talk is based on joint work with Kalck and Ouchi.

Location: Rm. 515, NCTS (Cosmology Bldg., NTU) 

NCTS Seminar in Algebraic Geometry

2025.01.03 (Friday) 03:30PM-05:00PM

Title: On the Nash Problem over 3-fold Terminal Singularities

Speaker: Keng-Hung Lin (Oklahoma University) (video)

Abstract: Let X be a singular variety over complex numbers. Nash proposed an approach to use families of arcs based the singular locus of X, inducing the so-called Nash valuations, to characterize divisorial valuations appearing in every resolution of singularities over X, which are called essential valuations. In particular, Nash prove that every Nash valuation is essential, so it’s natural to ask if every essential valuation is corresponded by some Nash valuation, which is called the Nash problem over X.
In this talk, I will briefly introduce the Nash problem, including the backgrounds/developments, and then talk about my current works(in progress) on the Nash problem over 3-fold terminal singularities.  

Location: Rm. 515, NCTS (Cosmology Bldg., NTU) 

NCTS Seminar in Algebraic Geometry

2024.11.22 (Friday) 03:30PM-05:00PM

Title: Automorphisms with Zariski dense orbits of Calabi-Yau threefolds with birational $c_2$-contraction

Speaker: Keiji Oguiso (The University of Tokyo) (video)

Abstract: We work over ${\mathbf C}$ or $\overline{\mathbf Q}$. In algebraic geometry and algebraic dynamics, for given a projective variety $V$ and a birational selfmap $g \in {\rm Bir}\, (V)$, it is natural to study (i) dynamical degrees of $g$  (ii) the existence of Zariski dense orbit of $g$, (iii) non-existence of equivariant non-trivial rational fibration with respect to $g$ (primitivity of $g$) and, (iv) non-existence of invariant rational functions with respect to $g$.
After explaining some back ground, motivation of the problem from algebraic geometry, algebraic and arithmetic dynamics, I would like to consider these four properies of an automorphism $f$ of a Calabi-Yau threefold $X$, with some hidden roles of the second Chern class $c_2(X)$ in this study.
First, I would like to deduce that, under two notorious but natural conjectures, there are exactly two Calabi-Yau threefolds with an automorphism of Zariski dense orbit.
Then, I would like to show the (unconditional) relations among properties (i) -(iv) on automorphisms of these two Calabi-Yau threefolds, with an explicit description of their automorphism groups, some idea of proof and explicit examples.

Location: Rm. 515, NCTS (Cosmology Bldg., NTU) 

NCTS Seminar in Algebraic Geometry

2024.11.11 (Monday) 03:30PM-05:00PM

Title: Smooth Weighted Blowdowns

Speaker: Giovanni Inchiostro (University of Washington) (video)

Abstract: An analogue of blow-ups are weighted blow-ups. Those are transformations, in nature similar to blow-ups, which are a bit more flexible. For example, weighted blow-ups give better algorithms for resolving singularities of algebraic varieties, and often appear in moduli spaces of interest. The price that one has to pay for the extra flexibility is that the result of a weighted blow-up might no longer be a variety, but rather an algebraic stack.
Therefore one natural question is: when is an algebraic stack a weighted blow-up of a simpler space? My coauthors and I give some criteria for when this question has a positive answer. This is a joint work with Arena, Di Lorenzo, Mathur, Obinna and Pernice.

Location: Rm. 515, NCTS (Cosmology Bldg., NTU) 

NCTS Seminar in Algebraic Geometry

2024.10.11 (Friday) 03:30PM-05:00PM

Title: Hyperbolicity of Projective Hypersurfaces Via Green-Griffiths Jet Differentials

Speaker: Benoît Cadorel (University of Lorraine) (video)

Abstract: A complex projective variety X is said to be (Brody) hyperbolic if it admits no entire curve, i.e. no non-constant holomorphic map starting from the complex plane. The Kobayashi conjecture asserts that a generic hypersurface of high degree should be Brody hyperbolic (we even expect the bound on the degree to be linear in the dimension). The first complete proof of this conjecture was only given by Brotbek in 2017, with a very high bound on the degree. It has become clear in the last few years that an efficient way of proving hyperbolicity results for hypersurfaces is to apply jet differential techniques, via Siu's so called strategy of slanted vector fields : this strategy has been refined by many authors (Diverio-Merker-Rousseau, Darondeau, Brotbek, Deng, Demailly, Riedl-Yang...). Until quite recently, the best known bounds on the degree were at least exponential in the dimension.
A core part of the strategy of slanted vector fields consists in picking an adequate jet space above the hypersurface, before studying the base locus of a natural tautological line bundle on it. Quite recently, Bérczi-Kirwan have managed to construct a new jet space via techniques of non-reductive GIT, which allowed them to spectacularly improve the previously known bounds, to a polynomial in the dimension.
Another candidate for jet spaces has existed for quite a long time, but seems to have been a bit overlooked in this problem: the Green-Griffiths jet space, introduced by these authors around 1980. As we will explain, the latter can also be used in the strategy above, and, surprisingly enough, it again gives a polynomial bound.

Location: Rm. 515, NCTS (Cosmology Bldg., NTU) 

NCTS Seminar in Algebraic Geometry

2024.09.20 (Friday) 10:00AM-11:30AM

Title: Quantum Cohomology of Toric Bundles

Speaker: Yuki Koto (Academia Sinica) (video)

Abstract: Quantum cohomology of a smooth projective variety X is a deformation of a ring structure on usual cohomology H*(X) defined by virtual counting of rational curves on X. It is known to be deeply related to various fields, including mirror symmetry, enumerative geometry and birational geometry. When X is a fiber bundle, the relationship between cohomology of a base/fiber and cohomology of the total space is well understood. While it is natural to expect a similar phenomenon in quantum cohomology, it remains unclear in a general situation. In this talk, I will explain the progress in this problem when the fiber is a smooth (semi)projective toric variety. This work is partially based on joint work with Iritani.

Location: Rm. 515, NCTS (Cosmology Bldg., NTU) 

NCTS Seminar in Algebraic Geometry

2024.08.26 (Monday) 03:30PM-05:00PM

Title: On the Hodge Structures of Global Smoothings of Normal Crossing Varieties

Speaker: Kuan-Wen Chen (Columbia University) (video)

Abstract: Suppose we are given a one-parameter semistable degeneration of (possibly non-Kähler) compact complex manifolds such that each component of the central fiber is Kähler. Then, we provide a criterion for the cohomology of the general fiber to have Hodge decomposition in terms of the topology of the central fiber. If this is the case, we also give a formula of the Hodge index on the middle cohomology of the general fiber in terms of the invariants of the central fiber.
If time permits, we will also discuss the application of the theorem to the global smoothing of m-fold ODPs, Hashimoto-Sano’s non-Kähler Calabi-Yau threefolds, and Sano’s non- Kähler Calabi-Yau m-folds.

Location: Rm. 505, NCTS (Cosmology Bldg., NTU) 

Seminar in Hodge Theory

2024.08.05 (Monday) 01:30PM-05:00PM

Title: Mixed Hodge structures on the cohomology of an open variety

Speaker: 黃建順(video)

Title: Monodromy and VHS

Speaker: Pedro Núñez (video)

Location: Rm. 505, NCTS (Cosmology Bldg., NTU) 

Seminar in Hodge Theory

2024.07.22 (Monday) 01:30PM-05:00PM

Title: Hodge structures II

Speaker: 張志煥(video)

Title: Deformations of complex manifolds

Speaker: 林俊廷(video)

Location: Rm. 515, NCTS (Cosmology Bldg., NTU) 

Seminar in Hodge Theory

2024.07.08 (Monday) 01:30PM-05:00PM

Title: Kodaira dimension of smooth projective fibrations

Speaker: 張繼剛(video)

Title: Kodaira dimension of smooth projective fibrations II

Speaker: 黃語庭(video)

Location: Rm. 440, NCTS (Astro-Math Bldg., NTU) 

Group Meeting

2024.06.03 (Monday) 02:00PM-04:00PM

Speakers: 中橋一萌(video)、張志煥(video)

Location: Rm. 509, NCTS (Cosmology Bldg., NTU) 

Group Meeting

2024.05.27 (Monday) 02:00PM-04:00PM

Speakers: 張繼剛(video)、蔡以恆(video)

Location: Rm. 509, NCTS (Cosmology Bldg., NTU) 

Group Meeting

2024.05.13 (Monday) 02:00PM-04:00PM

Speakers: 張宏彬(video)、陳毅鴻(video)

Location: Rm. 509, NCTS (Cosmology Bldg., NTU) 

Group Meeting

2024.05.06 (Monday) 02:00PM-04:00PM

Speakers: 蘇品丞(video)、張志煥(video)

Location: Rm. 509, NCTS (Cosmology Bldg., NTU) 

NCTS Seminar in Algebraic Geometry

2024.04.26 (Friday) 03:30PM-05:00PM

Speaker: Roberto Pignatelli (University of Trento) (video)

Title: Fibrations in (1,2)-Surfaces

Abstract: The content of this seminar stems from an ongoing collaboration with S. Coughlan, Y. Hu, and T. Zhang. By "(1,2)-surfaces" we denote complex algebraic surfaces with canonical singularities, ample canonical system, volume 1, and geometric genus 2. This is a class of surfaces that played a significant role in the theory of surfaces of general type in the last century and has shown in this century to also play an important role in the theory of 3-dimensional varieties, particularly in the recent proof of the 3-dimensional Noether inequality obtained by J. Chen, M. Chen, and C. Jiang. In fact, 3-dimensional varieties fibred in surfaces of type (1,2) play a role in this proof similar to that played by fibrations in curves of genus 2 in lower dimensions. In this seminar, I will introduce the concept of "simple" fibration in surfaces of type (1,2) and explain how through this concept we obtained a complete classification of 3-folds that satisfy the  equality in the aforementioned inequality. I will also discuss analogies and differences with the 2-dimensional case. Finally, I will mention some open problems that we are currently investigating.

Location: Rm. 515, NCTS (Cosmology Bldg., NTU) 

NCTS Seminar in Algebraic Geometry

2024.04.19 (Friday) 03:30PM-05:00PM

Speaker: Iacopo Brivio (Harvard University) (video)

Title: Antiitaka conjecture for tame fibrations in positive characteristic

Abstract: A famous conjecture by Iitaka predicts that, given a fibration $f\colon X\to Y$ of smooth complex varieties with general fiber $F$, then the inequality $\kappa(K_X)\geq \kappa(K_F)+\kappa(K_Y)$ holds. It was recently shown by Chang that, when the stable base locus $\mathbb{B}(-K_X)$ is $f$-vertical, then a similar inequality holds for the anticanonical divisor: $\kappa(-K_X)\leq \kappa(-K_F)+\kappa(-K_Y)$. Over fields of positive characteristic it is known that both Iitaka's conjecture and Chang's theorem can fail. However the expectation is that, when $F$ is sufficiently well-behaved with respect to the Frobenius morphism, then these results should hold. In this talk I will show that this is the case for Chang's theorem. This is based on joint work with M. Benozzo and C.-K. Chang.

Location: Rm. 515, NCTS (Cosmology Bldg., NTU) 

NCTS Seminar in Algebraic Geometry

2024.04.12 (Friday) 03:30PM-05:00PM

Speaker: Jie Liu (AMSS) (video)

Title: Kawamata-Miyaoka type inequality for canonical Q-Fano varieties

Abstract: An irreducible normal projective variety is called Q-Fano if it has Q-factorial singularities, with Picard number one and ith ample anti-canonical divisor. According to the minimal model program, Q-Fano varieties with canonical singularities are one of the building blocks of algebraic varieties. In this talk I will show that the second Chern class of a canonical Q-Fano variety is effectively bounded from below by its first Chern class. This is joint work with Haidong Liu.

Location: Rm. 515, NCTS (Cosmology Bldg., NTU) 

Group Meeting

2024.03.25 (Monday) 2:00PM-4:00PM

Speakers: 吳沂騰(video)、陳毅鴻(video)

Location: Rm. 509, NCTS (Cosmology Bldg., NTU) 

Group Meeting

2024.03.11 (Monday) 2:00PM-4:00PM

Speakers: 張繼剛(video)、蘇品丞

Location: Rm. 509, NCTS (Cosmology Bldg., NTU) 

NCTS Seminar in Algebraic Geometry

2024.02.23 (Friday) 11:00AM-12:00PM

Speaker: Fei Yu Chen (University of California, Berkeley) (video)

Title: Deformation theory and coalgebras

Abstract: Deformation theory aims to classify infinitismal deformations of mathematical objects. For many geometric objects, this comes out to understanding the Lie algebra structure on their tangent spaces. A key technique in proving these arguments is Koszul duality, which gives the cotangent complex of an algebra the extra structure of a Lie coalgebra, then you take a linear dual to get the Lie algebra structure on the tangent space. My work currently aims to understand the role of coalgebras in deformation theory. We develop a theory of a tangent complex and a coalgebraic version of formal moduli problems, and relate them to the algebraic theories. On the way we also need to understand the problem of rectification of coalgebras: relating the model structure of coalgebras with the infinity categorical definition of coalgebras, which unlike with algebras is not true in many cases.

Location: Rm. 515, NCTS (Cosmology Bldg., NTU) 

NCTS Seminar in Algebraic Geometry

2024.02.19 (Monday) 02:30PM-03:30PM

Speaker: Kento Fujita (Osaka University) (video)

Title: On the Calabi problem for Fano varieties

Abstract: I will give a survey on the recent progresses on the K-stability of Fano varieties. Especially, I will present the history of the Calabi problem, the original definition of K-stability, a valuative criterion for the K-stability of Fano varieties, Abban--Zhuang's theory, 3-dimensional application, and so on.

Location: Rm. 515, NCTS (Cosmology Bldg., NTU) 

NCTS Seminar in Algebraic Geometry

2024.01.08 (Monday) 03:30PM-05:00PM

Speaker: Weichung Chen (The University of Tokyo) (video)

Title: Ascending Chain Condition for Minimal Log Discrepancies for Bounded Generalized Pairs

Abstract: Minimal log discrepancy (mld) is an invariant of variety or log pair singularities that measures how singular they are. The ascending chain condition (acc) for mlds of singularities of a fixed dimension is conjectured to hold by Shokurov. On the other hand, generalized pairs play an important role in Birkar's proof of the Borisov-Alexeev-Borisov conjecture (BBAB theorem), which says that Fano varieties of a fixed dimension with a fixed lower bound of mlds form a bounded family. We show that the ACC conjecture holds for bounded families of generalized pairs. Applying BBAB theorem, we show that the ACC conjecture holds for generalized Fano pair.

Location: Rm. 515, NCTS (Cosmology Bldg., NTU) 

Student Seminar

2024.01.04 (Thursday) 10:00AM-11:00AM

Speaker: 張繼剛 (video)

Location: Rm. 509, NCTS (Cosmology Bldg., NTU) 

Student Seminar

2023.12.27 (Wednesday) 01:20PM-03:10PM

Speaker: 中橋一萌 (video)

Location: Rm. 509, NCTS (Cosmology Bldg., NTU) 

NCTS Seminar in Algebraic Geometry

2023.12.15 (Friday) 03:30PM-05:00PM

Speaker: Kentaro Mitsui (Kobe University) (video)

Title: Deformation of α_p-actions to Z/pZ-actions on Surfaces

Abstract: We study α_p-actions and Z/pZ-actions on surfaces and their quotient singularities in positive characteristic p. We can connect some singularities such as non-taut rational double points via deformation of these actions. We also try to classify additive derivations, which correspond to α_p-actions. This is joint work with Hiroyuki Ito and Nobuo Sato.

Location: Rm. 440, NCTS (Astro-Math Bldg., NTU) 

Student Seminar

2023.12.08 (Friday) 03:20PM-05:10PM

Speakers: 張宏彬 (video)、蘇品丞 (video)

Location: Rm. 509, NCTS (Cosmology Bldg., NTU) 

NCTS Seminar in Algebraic Geometry

2023.11.24 (Friday) 03:30PM-05:00PM

Speaker: Alexandra Kuznetsova (Steklov Math. Institute) (video)

Title: Automorphisms of families in abelian varieties

Abstract: We consider a fibration X whose general fiber is an abelian variety and fix a fiberwise birational automorphism f of X. Then f restricts into a regular automorphism of a general fiber of the fibration since abelian varieties do not contain rational curves. Thus, f induces a family of regular automorphisms of abelian varieties. However sometimes f does not induce a regular automorphism on any birational model of the whole variety X i.e. there is no regularization of f. In my talk I will show that the existence of the regularization depends on the dynamical properties of f. The talk is based on the joint work with Charles Favre.

Location: Rm. 515, NCTS (Cosmology Bldg., NTU) 

NCTS Seminar in Algebraic Geometry

2023.11.17 (Friday) 03:30PM-05:00PM

Speaker: Chih-Wei Chang (NTU) (video)

Title: Tropical Linear Series and Their Applications

Abstract: Let K be an algebraically closed valued field with valuation ring R, and let C be a curve over K. A semistable model of C over Spec R gives rise to a metric graph \Gamma. Baker proved the Specialization Lemma relating ranks of divisors on curves to those on graphs, envisioning tropical methods to prove results about divisors on algebraic curves, such as the Brill-Noether and Gieseker-Petri Theorems. David Jensen and Sam Payne defined the notions of tropical linear series and tropical dependence on graphs, which are closely related to problems concerning possibly incomplete linear series on algebraic curves, such as the maximal rank theorem. In this talk, I will review the story and discuss our recent progress in this direction. Based on joint work with David Jensen, Sam Payne, Dagan Karp, Jayden Wang, and Hernan Iriarte.  

Location: Rm. 515, NCTS (Cosmology Bldg., NTU) 

NCTS Seminar in Algebraic Geometry

2023.11.10 (Friday) 03:30PM-05:00PM

Speaker: Kenta Hashizume (Niigata University) (video)

Title: Minimal model theory for log canonical pairs and log canonical loci

Abstract: The minimal model theory is a fundamental tool to construct a variety with good geometrical properties. The theory is indispensable to recent development of birational geometry. In this talk, I will start with the motivation of the minimal model theory, and then I will explain the recent development of the minimal model theory for log canonical pairs. After that, I will introduce a recent result on minimal model program for normal pairs along log canonical loci. 

Location: Rm. 515, NCTS (Cosmology Bldg., NTU) 

NCTS Seminar in Algebraic Geometry

2023.10.27 (Friday) 03:30PM-05:00PM

Speaker: Ruijie Yang (Humboldt-Universität zu Berlin) (video)

Title: The geometric Riemann-Schottky problem and Hodge theory

Abstract: It is a classical problem in algebraic geometry, dated back to Riemann, to characterize Jacobians of smooth projective curves among all principally polarized abelian varieties. In 2012, Casalaina-Martin proposed a conjecture in terms of singularities of theta divisors. In this talk, I will present a partial solution of this conjecture using Hodge theory and D-modules. We also show that this conjecture can be deduced from a conjecture of Pareschi and Popa on GV sheaves and minimal cohomology classes.
To achieve this, we develop a theory of higher multiplier ideals, which is a Hodge-theoretic refinement of the theory of multiplier ideals in birational geometry. This new theory relies on the Hodge theory of Kashiwara-Malgrange V-filtration, Sabbah-Schnell’s theory of complex mixed Hodge modules and the language of twisted D-modules by Beilinson and Bernstein. This is based on the joint work with Christian Schnell.

Location: Rm. 515, NCTS (Cosmology Bldg., NTU) 

NCTS Seminar in Algebraic Geometry

2023.10.20 (Friday) 03:30PM-05:00PM

Speaker: Pedro Núñez (NTU) (video)

Title: Indecomposability of derived categories of hyperelliptic manifolds

Abstract: The MMP aims at classifying algebraic varieties up to birational equivalence, and derived categories are rich homological invariants of algebraic varieties that see a lot of their birational geometry. The basic operations of the MMP are reflected as semiorthogonal decompositions in the derived category, and minimal varieties of non-zero geometric genus are conjectured to have indecomposable derived categories. Hyperelliptic surfaces are an interesting example, because they show that the converse of the conjecture does not hold. In this talk, we discuss a generalization of the indecomposability of hyperelliptic surfaces to higher dimensional hyperelliptic manifolds, which is current joint work in progress with Pieter Belmans and Andreas Demleitner.
The talk will be roughly divided into three parts. First, an introductory part in which derived categories are briefly introduced, focusing on their relation to birational geometry. Then, an overview of semiorthogonal decompositions and their relation to the MMP. And lastly, a more detailed discussion of the semiorthogonal indecomposability question.

Location: Rm. 515, NCTS (Cosmology Bldg., NTU) 

NCTS Seminar in Algebraic Geometry

2023.10.13 (Friday) 03:30PM-05:00PM

Speaker: Keita Goto (NTU) (video)

Title: An Introduction to Berkovich Geometry and Kontsevich-Soibelman Conjecture

Abstract: Originally, Berkovich Geometry was known as one of the theories studying Non-Archimedean Geometry which is a branch to study analytic spaces over a non-Archimedean field.
However, a framework of Berkovich Geometry enables us to study analytic spaces over not only a non-Archimedean field but also a certain Banach ring.
In this talk, I'll introduce such a concept and fundamental facts of Berkovich Geometry.
Besides, I'll explain Kontsevich-Soibelman Conjecture as its application.
An SYZ fibration is often studied in the SYZ mirror symmetry context.
This conjecture predicts a certain equivalence between SYZ fibration and a non-Archimedean analog of SYZ fibration.
The latter half of my talk will be devoted to describing my joint work with Yuji Odaka, which partially proves this conjecture.

Location: Rm. 515, NCTS (Cosmology Bldg., NTU) 

Student Seminar

2023.10.02 (Monday) 01:20PM-03:10PM

Speakers: 蘇品丞 (video)、張宏彬

Location: Rm. 509, NCTS (Cosmology Bldg., NTU) 

NCTS Seminar in Algebraic Geometry

2023.09.22 (Friday) 03:30PM-05:00PM

Speaker: Kuan-Wen Lai (Academia Sinica) (video)

Title: Bijective Cremona Transformations of the Plane

Abstract: Cremona transformations are invertible maps from a projective space to itself defined by polynomials. We say a Cremona transformation is "bijective" if it induces a bijection on the set of rational points. For example, over a finite field, the set of rational points is finite, thus every such transformation induces a permutation in the usual sense, and it is natural to ask whether one can realize all possible permutations among these points this way. In this talk, I will present the answer for projective planes.
At least half of this talk is intended for a general audience in mathematics. This is joint work with Shamil Asgarli, Masahiro Nakahara, and Susanna Zimmermann, published on Selecta Mathematica, New Series 28, 53 (2022).

Location: Rm. 515, NCTS (Cosmology Bldg., NTU) 

2023.06.30 (Friday)

03:30PM-05:00PM

Speaker: 蘇品丞 (video)

Reference: (Coughlan and Pignatelli, arXiv:2207.06845) Simple fibrations in (1, 2)-surfaces

Location: Rm. 515, NCTS (Cosmology Bldg., NTU) 

2023.06.09 (Friday)

03:30PM-05:00PM

Speaker: 張志煥 (video)

Reference: (arXiv: 2108.01506) Moduli Spaces of Quasi-Trivial Sheaves

Location: Rm. 509, NCTS (Cosmology Bldg., NTU) 

2023.05.25 (Thursday)

03:30PM-05:30PM

Lecture 8. Full exceptional collections ([3, Note 5, Lecture 10])

Speaker: 中橋一萌 (video)

Lecture 9. Grothendieck Riemann-Roch ([3, Note 6, Lecture 11])

Speaker: 張志煥 (video)

Reference: [3] Prof. Hsueh-Yung Lin’s note

Location: Rm. 509, NCTS (Cosmology Bldg., NTU) 

2023.05.11 (Thursday)

03:30PM-05:30PM

Lecture 5. Derived Functors in algebraic geometry, I ([1, Sec 3.3])

Speaker: 黃建順 (video)

Lecture 6. Derived Functors in algebraic geometry, II ([1, Sec 3.3])

Speaker: 陳毅鴻 (video)

Reference: [1] D. Huybrechts, Fourier-Mukai Transforms in Algebraic Geometry

Location: Rm. 509, NCTS (Cosmology Bldg., NTU) 

2023.04.20 (Thursday)

03:30PM-05:30PM

Lecture 1. Triangulated categories and exact functors ([1, Sec 1.2, 1.3])

Speaker: 林俊廷 (video)

Lecture 2. Derived Categories of abelian categories ([1, Sec 2.1])

Speaker: 施政邦 (video) (4/27 video)

Reference: [1] D. Huybrechts, Fourier-Mukai Transforms in Algebraic Geometry

Location: Rm. 509, NCTS (Cosmology Bldg., NTU) 

2023.03.31 (Friday) NCTS Seminar in Algebraic Geometry

03:30PM-04:30PM

Speaker: Yujiro Kawamata (video)

Title: NC deformations, semi-orthogonal decompositions and Q-Gorenstein smoothing

Abstract: I will explain how NC deformations of coherent sheaves can sometimes be used to produce locally free sheaves.
I will also explain some consequences on semi-orthogonal decompositions of derived categories and singularity categories.

Location: Rm. 515, NCTS (Cosmology Bldg., NTU) 

2023.03.02 (Thursday)

03:30PM-05:30PM

Lecture 9. Negativity Lemma (Lemma 3.38-3.41)

Speaker: Hajime Nakahashi (video)

Lecture 10. Running the MMP (Section 3.7)

Speaker: Jheng-Jie Chen (video)

Reference: [1] J. Kollár, S. Mori, Birational Geometry of Algebraic Varieties

Location: Rm. 440, NCTS (Astro-Math Bldg., NTU) 

2023.02.16 (Thursday)

02:30PM-05:30PM

Lecture 4. Existence of the Minimal Model Program (section 2.2 of [1])

Speaker: 張宏彬 (video)

Lecture 5. Discrepancies (section 2.3 of [1], up to subsection 2.33)

Speaker: 陳毅鴻 (video)

Lecture 6. Singularities in MMP (section 2.3 of [1], after subsection 2.34)

Speaker: 蘇品丞 (video)

Reference: [1] J. Kollár, S. Mori, Birational Geometry of Algebraic Varieties

Location: Rm. 509, NCTS (Cosmology Bldg., NTU) 

2023.02.09 (Thursday)

03:30PM-05:30PM

Lecture 2. Ampleness Criterion (1.5 of [1])

Speaker: 施政邦 (viedo)

Lecture 3. Minimal Model of Surfaces and an Overview of Higher Dimensional Varieties (1.4 of [1] and Prop. 2.5, Example 2.7, subsection 2.14 in section 2.1 of [1])

Speaker: 鄭容濤 (video)

Reference: [1] J. Kollár, S. Mori, Birational Geometry of Algebraic Varieties

Location: Rm. 509, NCTS (Cosmology Bldg., NTU) 

2023.02.06 (Monday)

03:00PM-04:00PM

Speaker: Pedro Núñez (University of Freiburg) (video)

Title: Adapted differentials on Campana orbifolds

Abstract: Adapted differentials play an important role in Campana's birational classification program. In this talk we will discuss two results concerning them. These differential forms are usually only defined over suitably ramified covers, and the first result shows that they can be seen as a qfh-sheaf on the whole category of schemes over the orbifold. The second result ensures that we can extend (reflexive) adapted differential 1-forms on such a suitably ramified cover to a resolution of singularities of the cover, provided that the orbifold is klt. As an application, we construct the Albanese of a Campana orbifold with quotient singularities.

Location: Rm. 515, NCTS (Cosmology Bldg., NTU) 

2023.01.12 (Thursday)

Part A. 02:00PM-04:00PM

Speaker1: 張宏彬 (video)

Speaker2: 施政邦 (video)

Part B. 04:00PM-05:00PM

Speaker: 陳毅鴻 (video)

Location: Rm. 509, NCTS (Cosmology Bldg., NTU) 

2022.12.30 (Friday)

04:00PM-0.5:00PM

Speaker: Geoffrey Mboya (University of Oxford) (video)

Title: Singular threefold families of K3 surfaces

Abstract: This talk will be on the classification problem of projective fibrations f:X->P^1 over the projective line, where the general fibre of f is one of the  “famous 95” list of Fletcher–Reid K3 hypersurfaces in weighted projective spaces; and the fibration f : X → P^1 embeds into a weighted projective bundle as an anticanonical hypersurface with at most Ordinary Double Point singularities. I will demonstrate how to construct twisting data on F, leading to finite lists of mildly singular CY3s. I will also comment on a projective version of deformations of these CY3s that revisit earlier works of Gross and Ruan. This is part of my submitted DPhil thesis and joint work arXiv:2210.10559 with Balazs Szendroi.

Location: Rm. 505, NCTS (Cosmology Bldg., NTU) 

2022.12.19 (Monday)

04:00PM-0.5:00PM

Speaker: Chuyu Zhou (EPFL) (video)

Title: On multiplicities of fibers of Fano fibrations.

Abstract: In this talk, we will focus on a conjecture on multiplicities of fibers of Fano fibrations, and present that several important conjectures in birational geometry (including Mckernan-Shokurov conjecture and boundedness conjecture for RC Calabi-Yau varieties) could be reduced to this multiplicity conjecture.

Location: Rm. 505, NCTS (Cosmology Bldg., NTU) 

2022.12.08 (Thursday)

Part A. 03:30PM-04:30PM

Speaker: Hajime Nakahashi (video)

Part B. 04:30PM-05:30PM

Speaker: 陳毅鴻 (video)

Location: Rm. 509, NCTS (Cosmology Bldg., NTU) 

2022.11.17 (Thursday)

Part A. 03:30PM-04:30PM

Speaker: 張志煥 (video)

Part B. 04:30PM-05:30PM

Speaker: 施政邦 (video)

Location: Rm. 509, NCTS (Cosmology Bldg., NTU) 

2022.11.3 (Thursday)

Part A. 03:30PM-04:30PM

Speaker: 蘇品丞 (video)

Part B. 04:30PM-05:30PM

Speaker: 黃建順 (video)

Location: Rm. 509, NCTS (Cosmology Bldg., NTU) 

2022.10.13 (Thursday)

Part A. 03:30PM-04:30PM

Speaker: Hajime Nakahashi (video)

Title: Mumford's numerical criterion

Part B. 04:30PM-05:30PM

Speaker: 黃建順 (video)

Title: spectral sequence

Ref. Steenbrink's book, 3.4-3.5

Location: Rm. 509, NCTS (Cosmology Bldg., NTU) 

2022.09.29 (Thursday)

Part A. 03:30PM-04:30PM

Speaker: 張志煥 (video)

Ref. Mukai's book Chapter 6

Part B. 04:30PM-05:30PM

Speaker: 黃建順 (video)

Ref. Steenbrink's book, 2.3-2.4

Location: Rm. 509, NCTS (Cosmology Bldg., NTU) 

2022.09.15 (Thursday)

Part A. 03:30PM-04:30PM

Speaker: Hong-Bin Chang (張宏彬) (video)

Title:  Examples of invariants and moduli

Ref. Mukai's book Chapter 1

Part B. 04:30PM-05:30PM

Speaker: Yi-Hong Chen (陳毅鴻) (video)

Title:  Classical Hodge theory

Ref. Steenbrink's book, 1.1-1.2

Location: Rm. 509, NCTS (Cosmology Bldg., NTU) 

2022.04.29

Apr. 29 (Friday) 09:00AM-10:00AM

Speaker: Jayan Mukherjee (Brown University)

Title: Deformations and moduli of irregular canonical covers with $K^2=4p_g-8$

Abstract: In this article, we study the  moduli of irregular surfaces of general type with at worst canonical singularities satisfying $K^2 = 4p_g-8$, for any even integer $p_g \geq 4$. These surfaces also have unbounded irregularity $q$. We carry out our study by investigating the deformations of the canonical morphism $\varphi: X \to \mathbb{P}^N$, where $\varphi$ is a quadruple Galois cover of a smooth surface of minimal degree. As a result, we show the existence of infinitely many moduli spaces, satisfying the strict Beauville inequality $p_g > 2q-4$, with an irreducible component that has a proper "quadruple" sublocus where the degree of the canonical morphism jumps up. The existence of jumping subloci is a contrast with the moduli of surfaces with $K^2 = 2p_g- 4$, studied by Horikawa. These irreducible moduli components with a jumping sublocus also present a similarity and a difference to the moduli of curves of genus $g\geq 3$, for, like in the case of curves, the degree of the canonical morphism goes down outside a closed sublocus but, unlike in the case of curves, it is never birational.

Location: Rm. 515, NCTS (Cosmology Bldg., NTU) 

2022.04.15

Apr. 15 (Friday) 03:00PM-04:00PM

Speaker: Meng Chen (Fudan University)

Title:  On explicit birational geometry of higher dimensional varieties 

Abstract:  In this seminar, I will talk about some new progress on estimating the lower bound of canonical volumes and the upper bound of canonical stability indices for higher dimensional varieties of general type. I will mainly introduce the construction of examples with small volumes and a general machinery of studying the canonical stability index. 

Location: Rm. 515, NCTS (Cosmology Bldg., NTU) 

2022.03.25

Mar. 25 (Friday) 09:00AM-10:00AM

Speaker: Shihoko Ishii (The University of Tokyo)

Title:  A bound of the number of weighted blow-ups to compute the minimal log discrepancy for smooth 3-folds 

Abstract:  In the talk I will show that the minimal log discrepancy of every pair consisting of a smooth 3-fold and a "general" real ideal is computed by the divisor obtained by at most two weighted blow ups.

Our proof suggests the following conjecture: Every pair consisting of a smooth N-fold and a "general” real ideal is computed by a divisor obtained by at most N-1 weighted blow ups.

This is regarded as a weighted blow up version of Mustata-Nakamura’s conjecture.