ZUMA-GT

The seminar will meet at 4:00 pm on Mondays in Room 204, Hai Na Yuan #2, Zijingang Campus （海纳苑2幢204室，浙大紫金港校区）, unless otherwise noted.

Spring 2026 Schedule

Sep 15, 2025 (SPECIAL LOCATION: the lecture room of IASM)

Speaker: Haohua Deng 邓昊骅 (Dartmouth College)
Pretalk: Projective varieties and their Hodge theory
In this pretalk I will briefly explain why Hodge-theoretic methods are fundamental in the study of projective varieties and their moduli. Elementary examples will be provided. No backgrounds beyond graduate-level complex analysis and algebraic topology will be assumed.
Research talk: Recent breakthroughs on completing general period mappings
Since Griffiths' question in the 70's, it is a long-standing problem to find a completion of general period mapping with significant geometric and Hodge-theoretic meaning. The classical theories on the compactification of locally symmetric varieties by Satake—Baily--Borel and Mumford et al provide such completions to a very limited set of "classical" cases, while the problem has been almost completely open for non-classical cases until recent years. I will report the latest progress in this direction including several of my papers. Collaborators include Chongyao Chen (IMFP Shanghai), Colleen Robles (Duke), Jacob Tsimerman (Toronto).

Sep 22, 2025

Speaker: TBA
Pretalk: TBA
TBA
Research talk: TBA
TBA

Sep 29, 2025

Speaker: Peng Du 杜鹏 (浙江师范大学 Zhejiang Normal University)
Pretalk: TBA
TBA
Research talk: Isotropic points in the Balmer spectrum of stable motivic homotopy categories
I will discuss the tensor-triangulated geometry of the stable motivic homotopy category SH(k) and a big family of the so-called isotropic realisation functors, parameterized by the choices of a Morava K-theory and an extension of the base field k (of characteristic zero). By studying the target category of such an isotropic realisation functor, we are able to construct the so-called isotropic Morava points of the Balmer spectrum Spc(SH(k)^c) of the stable motivic homotopy category SH(k). This is based on a joint work with A. Vishik.

Oct 6, 2025

国庆节休假

Oct 13, 2025

Speaker: Shuo Zhang 张硕 (Morningside Center 晨兴数学所)
Pretalk: Symplectic rigidity and counting curves
A symplectic structure is more rigid than a smooth structure but more flexible than Riemannian or complex structures. A central theme in symplectic topology is to develop tools for detecting different types of rigidity. In this talk, I will give a survey of pseudo-holomorphic curves and explain how they have become the most powerful tool for this purpose.
Research talk: Quilted TCFT and applications
Invariants defined by counting pseudo-holomorphic maps from Riemann surfaces with boundary are ubiquitous in symplectic geometry, low-dimensional topology, and mathematical physics. Examples include various types of Floer homologies, Fukaya categories, and Gromov–Witten theory. In this talk, I will survey a generalization developed by Wehrheim–Woodward, known as pseudo-holomorphic quilts. I will then present some applications of quilted invariants, including my proof of a conjecture of Seidel concerning the Floer homology of composed Dehn twists.

Oct 16, 2025 (SPECIAL TIME)

Speaker: Zhi Jiang 江智 (Fudan University, 复旦大学)
Pretalk: The Moduli space of curves
We discuss the classical way of parametrizing algebraic curves and the important work of Deligne-Mumford about the irreduciblity of the moduli spaces of curves.
Research talk: Surfaces of general type with the minimal holomorphic Euler characteristic
It is a very difficult task to classify varieties in higher dimensions, even for surfaces with small birational invariants. I will survey some recent progress towards understanding the structure of surfaces of general type whose holomorphic Euler characteristic is 1.

Oct 20, 2025 (Cancelled)

Speaker: TBA
Pretalk: TBA
TBA
Research talk: TBA
TBA

Oct 27, 2025

Speaker: Jingjun Han 韩京俊 (Fudan University, 复旦大学)
Pretalk: Log canonical thresholds and minimal log discrepancies
I will introduce definition and basic properties of log canonical thresholds and minimal log discrepancies.
Research talk: On boundedness in general type MMP
One of the main open problems in the Minimal Model Program (MMP) is the termination. Motivated by local volumes introduced by Chi Li, we introduce log canonical volume which is non-decreasing in any sequence of MMP for general type varieties. As a result, in such kind of MMP, we show that (1) the Cartier index of any Weil Q-Cartier is uniformly bounded; (2) every fiber of the extremal contractions or the flips is bounded (3) the set of minimal log discrepancies belongs to a finite set. This is a joint work with Lu Qi, and Ziquan Zhuang.

Nov 3, 2025

Speaker: Habib Alizadeh (University of Science and Technology of China, 中国科技大学)
Pretalk: Barcodes in geometry
Barcode is a notion introduced first in Topological Data Analysis (TDA) and it captures the topology (holes) of a data set. In a different form this notion appeared long before TDA in the works of Morse where he uses functions on spaces to study their topology. Inspired by TDA and Morse, barcodes were re-introduced in geometry and are vastly studied with many significant applications, e.g., they can be used to detect periodic points of certain maps on manifolds; this is in the same spirit as the Morse inequality that states the number of critical points of a smooth non-degenerate function on a manifold is at least the sum of the Betti numbers of the manifold. In this talk we will define barcodes, using simple linear algebra that should be accessible by undergraduate students, and if time permits we will mention some applications of barcodes in geometry.
Research talk: Spectral diameter of a symplectic ellipsoid
Consider a diffeomorphism of an even-dimensional Euclidean space that is compactly supported in a given convex open subset X, and preserves the standard symplectic form; in dimension two in particular it preserves the area. Using barcodes we define an invariant of such a diffeomorphism that we call the spectral norm of the diffeomorphism. The space of such diffeomorphisms of X equipped with the spectral norm has a finite diameter which is called the spectral diameter of X. This number defines a symplectic capacity for X, an object defined axiomatically in symplectic geometry to capture the “symplectic size” of a domain; the first symplectic capacities were defined by Gromov using pseudo-holomorphic curves. In this talk, we compute the spectral diameter for all symplectic ellipsoids and polydisks, and in dimension four, for all convex toric domains. Exact computations of symplectic capacities are useful in obstructing symplectic embeddings.

Nov 10, 2025

Speaker: Langte Ma 马烺特 (Shanghai JiaoTong University,上海交通大学)
Pretalk: Generalized Anti-Self-Dual Instantons
ASD instantons are used by Donaldson and others in the 1980s to discover exotic smooth structures on 4-manifolds. In the late 1990s, Donaldson-Thomas proposed to study instantons over Riemannian manifolds with special homolony. I will introduce the notion of such instantons and explain their minimizing property for the Yang-Mills functional, which include HYM connections on Kahler manifolds as examples.
Research talk: Instantons on Product Manifolds
We study the generalized ASD instantons over product manifolds motivated by the fact that many examples of manifolds with special honolomy are built with blocks of product structures. In this talk, I will discuss a generalization of the notion of instanton charge on principal SU(r)-bundle over 4-manifolds to manifolds with special holonomy, and explain how the moduli spaces of instantons over product manifolds are related to this generalized charge, which leads to interaction with instantons on the product factors. This is joint work with Dylan Galt.

Nov 17, 2025

Speaker: TBA
Pretalk: TBA
TBA
Research talk: TBA
TBA

Nov 24, 2025

Speaker: Sheng Rao 饶胜 (Wuhan University, 武汉大学)
Pretalk: A rough introduction to deformation theory
I will introduce several important notions and theorems in the topics within my research in a rough way.
Research talk: Several Rigidity Theorems under Smooth Deformations
We report on several rigidity theorems concerning smooth deformations of compact complex manifolds. Two main theorems therein can be described as follows. Let Δ be the unit disk in the complex plane, and consider a smooth family of compact complex manifolds over Δ. We show that the subset of Δ over which the fibers are isomorphic to a fixed hyperbolic manifold is either a discrete subset or all of Δ. Furthermore, for a smooth Kähler family over Δ, we prove a similar rigidity result: the set of points where the fibers are isomorphic to a fixed projective manifold with semiample canonical line bundle is also either a discrete subset or the whole Δ. This talk is based on three preprints jointly authored with Jian Chen, Mu-Lin Li, I-Hsun Tsai, Kai Wang, and Mengjiao Wang.

Dec 1, 2025

Speaker: Qizheng Yin 訚琪峥 (北京大学)
Pretalk: Global Torelli theorem for K3 surfaces
Research talk: A user's guide to Markman's hyperholomorphic bundles
We discuss several applications of Markman’s recent construction of hyperholomorphic bundles on products of hyper-Kähler varieties of K3^[n] type. These include the algebraicity of certain natural Hodge classes (Markman’s own work), the D-equivalence conjecture (joint work with Davesh Maulik, Junliang Shen, and Ruxuan Zhang), and, potentially, a better understanding of the Chow ring of K3^[n] type varieties.

Dec 8, 2025

Speaker: Yu Li 李宇 (University of Science and Technology of China, 中国科技大学几何物理中心)
Pretalk: Gromov–Hausdorff Convergence and Łojasiewicz Inequalities
In this pretalk, I will review basic properties and results of Gromov–Hausdorff convergence. I will also give a brief introduction to the Łojasiewicz inequality and highlight its applications across several geometric settings.
Research talk: Strong Uniqueness of Cylindrical Tangent Flows in Ricci Flow and Applications
I will present a recent result establishing strong uniqueness of cylindrical tangent flows in Ricci flow via a Łojasiewicz inequality for the pointed entropy. As applications, I will discuss consequences for the singular set of noncollapsed Ricci-flow limit spaces—obtained as Gromov–Hausdorff limits of closed Ricci flows with uniformly bounded entropy. In particular, we derive an L^1 curvature estimate for four-dimensional closed Ricci flows and resolve Perelman’s bounded diameter conjecture. This is joint work with Hanbing Fang.

Dec 15, 2025

Speaker: Jie Min 闵捷 (河套数学与交叉学科研究院 HIMIS)
Pretalk: Introduction to almost toric fibrations
In this pretalk, I will cover the basics of toric actions and almost toric fibrations, visible symplectic and Lagrangian submanifolds, blow-up and blow-down operations.
Research talk: Symplectic log Calabi-Yau divisors and almost toric fibrations
Lagrangian fibrations sit at the crossroads of integrable systems, toric symplectic geometry and mirror symmetry. A particularly simple and interesting class of Lagrangian fibrations is called almost toric fibrations, whose total spaces are symplectic 4-manifolds. In this talk I will introduce almost toric fibrations over disks and their boundary preimages, which are symplectic divisors representing the first Chern class, called symplectic log Calabi-Yau divisors. I will then talk about joint work with Tian-Jun Li and Shengzhen Ning, showing that given a symplectic log Calabi-Yau divisor, an almost toric fibration can be constructed. I will also outline an application of this construction to understanding Lagrangian spheres in rational surfaces.

Dec 22, 2025

Speaker: Yuan Gao 高原 (南京大学 Nanjing University)
Pretalk: Descent in Hamiltonian Floer theory
The Mayer–Vietoris sequence is an instance of computing Čech cohomology with respect to a good cover. As it turns out, Hamiltonian Floer cohomology, one of the central cohomology theories studied in symplectic geometry, comes with a default notion of a “good cover.” In the pretalk, I will review the theory of symplectic cohomology with support introduced by Varolgunes, recall its sheaf property, and discuss its generalizations to the open-string case.
Research talk: Local-to-global mirror symmetry: a new look at a classical example
The Strominger–Yau–Zaslow perspective has provided a conceptual picture for understanding mirror symmetry, yet functorial proofs of Homological Mirror Symmetry (HMS) based on it have not been completely established. In this talk, I will discuss a different approach—based on joint work-in-progress with Umut Varolgunes—to constructing the mirror space and the HMS functor using Floer theory with support, modeling on a symplectic counterpart to the Gross–Siebert toric degeneration. The majority of this talk will focus on implementing the strategy on the classical example of an elliptic curve, originally approached by Polishchuk and Zaslow.

Dec 29, 2025 (SPECIAL TIME and LOCATION: 10.30 AM in the lecture room of IASM)

Speaker: Trung Nghiem (Université Claude Bernard Lyon 1)
Pretalk: Introduction to toric Calabi--Yau cones
A toric variety is a normal algebraic variety that contains an algebraic torus as a dense set, whose action extends to the whole variety. Since their conception, the varieties have provided many insightful examples for important conjectures in algebraic geometry. This pretalk aims to introduce the concept of complex affine toric varieties with Gorenstein singularities; their classification in terms of rational polytopes; and their equivalent metric characterization as toric Calabi--Yau cones (i.e. Ricci-flat Kähler cone metrics with toric isometry).
Research talk: An effective construction of asymptotically conical Calabi--Yau manifolds
An asymptotically conical Calabi--Yau manifold is a Ricci-flat Kähler manifold whose shape, when zoomed out towards infinity, looks like a Calabi--Yau cone. A recent work of Conlon--Hein shows that an AC Calabi--Yau manifold is obtained either by algebraic deformations or crepant resolution in a reversible and exhaustive process. In terms of the metric on the cone, the behavior of the AC Calabi--Yau metric is said to be quasi-regular or irregular. Examples of the latter are notoriously rare in the literature: in fact the only such example before our work was built by Conlon--Hein using ad-hoc computations; but so far there has been no explicit way to obtain them, and an open question in their paper was whether there exist more metrics of the same kind. In my research talk, I'll present an effective strategy to construct irregular AC Calabi--Yau manifolds via Altmann's deformation theory of isolated toric Gorenstein singularities (i.e. toric Calabi--Yau cones by the previous talk). This is a joint work with Ronan Conlon (University of Texas, Dallas).

Jan 6, 2026 (SPECIAL TIME and LOCATION: 2.30 PM in the lecture room of IASM)

Speaker: Xuan Yao 姚萱 (Princeton University)
Pretalk: Schoen-Yau’s minimal slicing technique and its applications on the positive scalar curvature problem.
We introduce Schoen-Yau’s minimal slicing technique and their proof of Geroch conjecture in low dimensions.
Research talk: Capillary minimal slicing and scalar curvature rigidity in dimension 4
We develop a capillary minimal slicing technique and use it to prove a scalar curvature rigidity result in dimension 4. This is a joint work with Dongyeong Ko.

Jan 12, 2026 (SPECIAL TIME and LOCATION: 10:30 AM in the lecture room of IASM)

Speaker: Si-Yang Liu 刘思阳 (University of Bonn 波恩大学)
Pretalk: Categorification of Fixed Points
One important goal of classical mechanics is to understand periodic orbits of motions of particles. Via Hamiltonian formalism, this can be rephrased as fixed points of certain self-diffeomorphisms of a given manifold. There are conjectures relating such fixed points to the topology of spaces, which were resolved via “categorifying fixed points.”
Research talk: Symplectic Geometry of Degenerations
Degeneration of algebraic varieties is a classical but powerful way of studying algebraic and symplectic geometry. While algebraic structures vary in a family, their de Rham cohomologies remain locally constant, leading to Schmid’s construction of mixed Hodge structures that essentially describes the geometry of the degenerate variety. Symplectic structures behave similarly, and one expects a parallel localization formula relating the symplectic geometry of a smooth fiber to that of a degenerate fiber. In this talk, I will discuss a special case where this philosophy can be translated into concrete statements and some applications. This is based on joint work in preparation with Sheel Ganatra, Wenyuan Li, and Peng Zhou.

Collapse Fall 2025 Schedule

Mar 3

Speaker: Wenhao Ou 欧文浩 (中科院数学所)
Pretalk: Rational curves in complex manifolds
We review some classical results in birational geometry, particularly on rational curves in complex manifolds.
Research talk: A characterization of uniruled Kaehler manifolds
We adapt Bost's algebraicity characterization to the situation of a germ in a compact Kaehler manifold. As a consequence, we extend the algebraic integrability criteria of Campana-Paun and of Druel to foliations on compact Kaehler manifolds. As an application, we prove that a compact Kaehler manifold is uniruled if and only if its canonical line bundle is not pseudoeffective.

Mar 4 (SPECIAL TIME/LOCATION: TUESDAY in the lecture room of IASM)

Speaker: Jihao Liu 刘济豪 (北京大学)
Pretalk: An Introduction to Foliations and the Minimal Model Program
This pretalk will provide an overview of foliations from the perspective of birational geometry, along with an introduction to the minimal model program for foliations. We will discuss foundational concepts and set the stage for the main talk, which explores recent advances in the field.
Research talk: Boundedness of Algebraically Integrable Fano Foliations
In this talk, I will discuss a recent joint work with Paolo Cascini, Jingjun Han, Fanjun Meng, Calum Spicer, Roberto Svaldi, and Linyao Xie. We establish two key results: (1) the existence of good minimal models for klt algebraically integrable adjoint foliated structures of general type, and (2) the boundedness of \epsilon-lc Fano algebraically integrable adjoint foliated structures. These results are analogues of the BCHM and BAB theorems respectively in the context of algebraically integrable foliations/adjoint foliated structures.

Mar 10

Speaker: Yalong Cao 曹亚龙 (中科院晨兴数学中心)
Pretalk: Why critical loci are important
We review why critical loci are important.
Research talk: Quasimaps to critical loci
Critical loci are fundamental objects in geometry, physics, and representation theory. In this talk, we will introduce their quantum K-theory by counting quasimaps from curves. Joint work with Yukinobu Toda and Gufang Zhao.

Mar 24

Speaker: Shi Wang 汪湜 (上海科技大学)
Pretalk: Basics in nonpositive curvature
We review basics in nonpositive curvature.
Research talk: The natural flow and the critical exponent
For a complete Riemannian manifold of nonpositive curvature, we introduce a flow. We give an upper bound on the k-Jacobian of the flow in terms of the critical exponent of the fundamental group. We also give several applications connecting the geometry and topology of the manifold, which include the linear isoperimetric inequality, the homological vanishing theorem, and the non-existence of compact complex subvarieties in certain complex hyperbolic manifolds. This is joint work with Chris Connell and Ben McReynolds.

Mar 31

Speaker: Lars Andersson (BIMSA)
Pretalk: General Relativity and Geometry
I will give a brief introduction to the Einstein equation of general relativity and mention some open problems related to it.
Research talk: Gravitational instantons and special geometry
Gravitational instantons are Ricci flat complete Riemannian 4-manifolds with at least quadratic curvature decay. Classical examples include the Taub-NUT and the Euclidean Kerr instanton. In this talk I will present some recent results on classification, stability, and conservation laws, for instantons with special geometry.

Apr 7

Speaker: Zheng Hua 华诤 (香港大学)
Pretalk: On Modular Poisson structures
We will briefly recall Poisson structures in the algebraic geometry context. We will focus on two main classes of examples: moduli space of sheaves on del Pezzo surfaces and semi-classical limits of noncommutative deformations.
Research talk: Symplectic foliation of modular Poisson structures
We will give a unified construction of the algebraic Poisson structures mentioned in the first part of the talk, via the moduli space of complexes on degeneration of elliptic curves. Our construction leads to a neat description of the symplectic leaves. We will discuss several applications on deformations of Hilbert schemes and positroid varieties.

Apr 8 (SPECIAL TIME/LOCATION: TUESDAY in the lecture room of IASM)

Speaker: Yuji Odaka 尾高悠志 (京都大学)
Pretalk: Canonical torus action on (holomorphic) symplectic singularities
Symplectic singularities arise from e.g., nilpotent orbit closure, compact hyperKahler varieties, quiver varieties, and so on. These have been studied actively recently, not only in algebraic geometry, but from geometric representation theoretic or string theoretic perspectives. 2-dimensional case is the classical orbifolds, the so-called Klein / ADE singularity. D. Kaledin conjectured around 2000 that they are always quasi-homogeneous, i.e., admit local good C^*-action. We prove the conjecture conditionally by a new approach, i.e., using complex differential geometry and related algebraic geometry with Poisson structures. In particular, we obtain a canonical action with DG interpretation. Joint with Yoshinori Namikawa.
Research talk: Tangent cone, bubbling, compactness and algebraic geometry
In the latter half, we talk about more general or technical aspects. First main aspect of our approach to the Kaledin’s conjecture to interpret the predicted conical structure as metric tangent cone, after the Donaldson-Sun theory which revealed general algebro-geometric structure underlying the general metric tangent cone of klt singularities with local singular Kahler-Einstein metrics (the second aspect is understanding of Poisson deformations). Their method is extended to understanding the bubbling of the metric family with euclidean volume growths e.g., Kronheimer ALE space. As in the case of (metric) tangent cones, these bubblings, or "older" Gromov-Hausdorff limit of compact Kahler-Einstein manifolds (singular Q-Fano var, by Donaldson-Sun I) etc are all some differential geometric limits which turn out to be varieties. I plan to explain key ideas and methods of how their underlying limit varieties can be algebro-geometrically re-constructed or recovered in a somewhat unified deformation theoretic manner (without any technical prerequisites in algebraic geometry).

Apr 14

Speaker: Yifei Zhu 朱一飞 (南方科技大学)
Pretalk: Quantum materials, Higgs bundles, and geometric Langlands correspondence
With motivation from condensed matter physics and materials science in collaboration with physicists, I’ll discuss explicit examples of eigenbundles associated to both gapped and gapless quantum mechanical systems, that is, to families of matrices with prescribed symmetry, as well as their homotopical classifications. These include Hopf bundles and, more generally, certain rank-2 and rank-3 Higgs bundles. The geometry and topology of such mathematical objects and their moduli spaces shed light on questions in physics, namely, hyperbolic band theory (after A. J. Kollár et al.) and bulk–edge correspondence, which I will at least indicate.
Research talk: Spheres, spectral algebraic geometry, and Jacquet–Langlands correspondence
The ring spectrum of spheres plays a similar role in spectral algebraic geometry that the ring of integers does for classical algebraic geometry. It recovers the latter in a natural way while encoding additional higher-homotopical information. With motivation from structure and computation centered around the homotopy groups of spheres, I’ll explain joint work with Xuecai Ma of Westlake University. We define relative effective Cartier divisors for a spectral Deligne–Mumford stack. We then apply the representability of their moduli to questions at the crossroad of algebraic topology and arithmetic geometry.

Apr 18 (SPECIAL TIME/LOCATION: FRIDAY in the lecture room of IASM)

Speaker: Jian Xiao 肖建 (清华大学)
Pretalk: Examples on log-concavity
We present several examples on log-concavity in geometry and combinatorics, behind which is the Hodge index theorem.
Research talk: Extremals in log-concavity: an algebro-geometric viewpoint
We show how to formulate the extremal problem in log-concavity in the framework of algebraic geometry, and discuss some of our progress towards the conjectural picture. Based on joint work with Jiajun Hu.

Apr 21

Speaker: Guchuan Li 李谷川 (北京大学)
Pretalk: Bott Periodicity and topological K-theory
We will assume Bott Periodicity and use it to define a generalized cohomology theory: topological K-theory.
Research talk: Real Bott periodicity at higher chromatic heights
Real Bott periodicity shows that the homotopy groups of real topological K-theory is 8-periodic. From chromatic homotopy theory perspective, Real topological K-theory is a height 1 theory, and for each natural number n, there are height n periodic cohomology theories. Important examples include 192 periodic topological modular forms at height 2 and Hill-Hopkins-Ravenel’s 256 periodic Kervarie detection spectrum at height 4. In this talk, we give a general formula for the periodicity for all heights. This is joint work with Zhipeng Duan, Mike Hill, Yutao Liu, Danny XiaoLin Shi, Guozhen Wang, and Zhouli Xu.

Apr 28

Speaker: Rixin Fang 方日鑫 (复旦大学)
Pretalk: Introduction to K-theory and Hochschild Homology
We introduce low dimensional K-theory first, and briefly explain Quillen's plus construction. Then we recall the Hochschild homology of an algebra, and its relation with K-theory. If time permits, we give a briefly introduction on stable homotopy theory, and $v_n$-periodicity.
Research talk: Chromatic redshift and Segal conjecture
The Lichtenbaum--Quillen property comes with an arithmetic background, Waldhausen reformulated this property as a telescopic homotopy problem. The chromatic redshift introduced by Rognes generalized this idea to higher height ring spectra. And algebraic K-theory for ring spectra can be well understood by trace method, we will briefly recall the trace method. By the work of J. Hahn, D. Wilson, et al., the redshift problem can be reduced to Segal conjecture and (weak) canonical vanishing problem. We recall the techniques to prove Segal conjecture, and we present examples that Segal conjecture holds. We use the cyclic decomposition to demonstrate some examples that Segal conjecture fails, and thus Lichtenbaum--Quillen property fails also.

May 12

Speaker: Siqi He 何思奇 (中科院晨兴数学中心)
Pretalk: The Analytic Compactification of SL(2,C) Character Varieties
In the pretalk, we will introduce Taubes’ work on the analytic compactification of the SL(2,C) character variety of 3- and 4-manifolds from a gauge theory perspective. We will discuss the construction of the compactification, and understanding the boundary of the compactified space.
Research talk: The Deformation Problem for Z/2 Harmonic 1-Forms over Kähler Manifolds
Z/2 harmonic 1-forms, introduced by Taubes, describe the boundary behavior of moduli spaces arising from gauge-theoretic equations. The Hitchin–Simpson equations on a Kähler manifold are first-order nonlinear equations for a pair consisting of a connection on a Hermitian vector bundle and a 1-form valued in the endomorphism bundle. We study the behavior of solutions to the Hitchin–Simpson equations as the norm of the 1-form becomes unbounded, and explore its relationship with Z/2 harmonic 1-forms. In addition, we will discuss the deformation problem of Z/2 harmonic 1-forms in the Kähler setting.

May 19

Speaker: Honghao Gao 高鸿灏 (清华大学丘成桐数学中心)
Pretalk: Legendrian knots and its invariants
Knots are loops in Euclidean 3 space. On top of that, Legendrian knots additionally satisfy a particular differential equation, imposing constraints to the tangent direction at a certain point. Understanding Legendrian knots is one of the central topics in a subject called contact topology. In this pretalk, we will explain how to describe Legendrian knots through (a lot of) pictures, and introduce some algebraic invariants that are used to study Legendrian knots.
Research talk: Legendrian knots and Lagrangian fillings
Lagrangian fillings are surfaces bounding Legendrian knots, which live in a 4-dimensional space called symplectization. Different Lagrangian fillings can be distinguished by cluster charts in a moduli space associated to the Legendrian knots. In this talk, I will explain the joint work with Roger Casals, on how to construct a Lagrangian filling from a given cluster chart.

May 26

Speaker: Yu Zhang 张宇 (天津大学)
Pretalk: Gröbner Bases: The Linear Algebra of Polynomial Ideals
This talk explores Gröbner bases as the nonlinear analog of Gaussian elimination and row echelon form in linear algebra. By comparing polynomial ideals to linear subspaces, we’ll see how Gröbner bases enable systematic solutions to systems of polynomial equations. Using intuitive examples and analogies, we demystify the core principles of Gröbner basis theory.
Research talk: Extensive Computations of the Adams Spectral Sequence E_2-Page at Odd Primes
The Adams spectral sequence of the sphere is a cornerstone of stable homotopy theory, yet explicit computations remain notoriously difficult due to prohibitive computational complexity. In this talk, we focus on the case of odd primes, which exhibits distinct structural features compared to the p=2 setting. By leveraging insights from computational algebra, we (1) construct a tailored extension of Gröbner basis theory for the noncommutative Steenrod algebra at odd primes, and (2) develop a novel algorithmic framework using this generalized theory to compute the E_2-page of the Adams spectral sequence in significantly higher degrees than previously achievable. These advances not only expand the algorithmic toolkit for spectral sequence computations but also open new avenues for exploring stable homotopy groups of spheres. This is joint work with Weinan Lin.

Jun 2

端午节

Jun 9

Speaker: Zhipeng Duan 段志鹏 (南京师范大学)
Pretalk: Atiyah’s Real K-theory and Slice Spectral Sequences
In this pre-talk, we will introduce Atiyah’s Real K-theory and explain its connections to complex and real K-theory. We will then apply the slice spectral sequence to compute its homotopy groups.
Research talk: Vanishing lines and periodicities of higher real K-theories
In this talk, we generalize computations in Atiyah’s Real K-theory to broader classes of groups and to higher chromatic heights. We will present two key structural results arising from these developments: a vanishing line result and a periodicity result. These results enable a more effective approach to computing homotopy fixed point spectral sequences and slice spectral sequences. We will also discuss an interesting geometric application that follows from these structural insights. This talk is based on a combination of several joint works with Mike Hill, Hana Jia Kong, Guchuan Li, Yutao Liu, Yunze Lu, Xiaolin Danny Shi, Guozhen Wang, and Zhouli Xu.

Collapse Spring 2025 Schedule

Spring 2026 Schedule

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