Plenary Talks

 

  Monday

      Uhi Rinn Suh (Seoul National University)

Title : Vertex Algebras: Natural Complexity from CFT and Recent Developments

 

Abstract : Vertex algebras, mathematically formulated by Borcherds, are known to provide a rigorous framework for describing two-dimensional conformal field theory (CFT). In this talk, I will explain how the definition and inherent complexity of vertex algebras arise naturally from the perspective of CFT. We will then introduce several approaches that have been developed to overcome these complexities and to achieve a deeper understanding of vertex algebras. Finally, we will present recent results obtained within this viewpoint, emphasizing ongoing progress and directions in the study of vertex algebras.

 

  Tuesday

      Yoji Akama (Tohoku University)

Title : Classifications of tessellations and spherical tilings

 

Abstract : We study graphs on surfaces with positive curvature from two perspectives. First, for graphs with positive Forman curvature on all edges under certain tessellation conditions, we establish a complete classification and a new finiteness proof using medial graphs (joint work with B. Hua, Y. Su, and Y. Zhang). Second, we classify graphs on surfaces with positive corner curvature, with a specific focus on the tilings of the sphere by congruent polygons (joint work with M. Yan and his students).

 

  Wednesday

      Jin-Cheng Jiang (National Tsing Hua University)

Title : On the small data Cauchy problem for the Boltzmann equation

 

Abstract : In this talk, we will review some progress on the small data Cauchy problem for the Boltzmann equation. The classical result requires that the initial data has exponential decay in spatial or velocity variable. We proved the well-posedness result when the initial data is small in L3 space for the hard sphere, cutoff hard potential, Maxwellain molecule and part of soft potential models. We will also discuss the difficulty we meet when studying the very soft potential. The results presented here are based on the joint work with LingBing He, Hung-Wen Kuo and Meng-Hao Liang.

 

  Thursday

      Hao Wu (Fudan University)

Title : On a Navier-Stokes-Cahn-Hilliard system with chemotaxis, mass transport and nonlocal interaction

 

Abstract : We consider a diffuse interface model for viscous incompressible two-phase flows where the mechanisms of chemotaxis, mass transport and nonlocal interaction of Oono's type are taken into account. The evolution system couples the Navier-Stokes equations for the volume-averaged fluid velocity, a convective Cahn-Hilliard equation for the phase-field variable, and an advection-diffusion equation for the density of a chemical substance. This system can be viewed as a thermodynamically consistent extension of the well-known “Model H” for incompressible binary fluids. For the initial-boundary value problem with a physically relevant singular potential in three dimensions, we report some recent results on the well-posedness, regularity propagation of global weak solutions and their long-time behavior.

 

Parallel Session A

 

  Monday

      Ting-Wei Chang (National Tsing Hua University)

Title : Gauss sums and Gross-Koblitz formula

 

Abstract : Gauss sums are ubiquitous algebraic numbers in number theory. In this talk, we give a brief introduction to these numbers and discuss some of their arithmetic properties. We then focus on the classical Gross-Koblitz formula, which relates Gauss sums to special p-adic gamma values. Finally, we turn to the function field side and present our main result concerning analogous of Gauss sums in this setting.

 

      Siyong Tao (Tsinghua University)

Title : Bernstein-Sato roots and test module filtrations for Cartier pairs in positive characteristics

 

Abstract : The Bernstein-Sato polynomial is an important invariant of an ideal $J$ in a polynomial ring over the complex field $\mathbb{C}$, which measures the singularities of the zero-locus of $J$.

Work of M. Musta\c{t}\u{a}, later extended by T. Bitoun and E. Quinlan-Gallego, provides an analogous Bernstein-Sato theory for an ideal $I$ in a regular $F$-finite ring $R$ of positive characteristic. M. Blickle and A. Stäbler generalized M. Musta\c{t}\u{a}'s constructions and defined a family of Bernstein-Sato polynomials for a $F$-regular Cartier module associated with a principal ideal.

Now let $I$ be an ideal of a regular $F$-finite ring $R$ of characteristic $p>0$, and let $(M,\mathcal{C})$ be an $R$-Cartier pair. We define the Bernstein-Sato roots for the triple $(M,\mathcal{C},I)$ under some certain conditions. And we prove that these roots are non-positive, rational, and closely related to the jumping numbers of the non-increasing right-continuous filtration, the test module filtration $\{\tau(M,\mathcal{C}^{I(t)})\}_{t\geq 0}$, which is an analogue of $V$-filtration in the complex case.

 

      Zhirun Zhan (Kyoto University)

Title : Uniqueness of mild solutions to the Navier-Stokes equations in weak-type $L^d$ space 

 

Abstract : This talk deals with the uniqueness of mild solutions to the forced Navier-Stokes equations. It is known that the uniqueness of mild solutions to the unforced Navier-Stokes equations holds in $L^{\infty}(0,T;L^d(\mathbb{R}^d))$ when $d\geq 4$, and in $C([0,T];L^d(\mathbb{R}^d))$ when $d\geq3$. As for the forced Navier-Stokes equations, when $d\geq3$, the uniqueness holds in $C([0,T];L^{d,\infty}(\mathbb{R}^d))$ with force and initial data in appropriate Lorentz spaces. In this talk we show that for $d\geq3$, the uniqueness of mild solutions to the forced Navier-Stokes equations holds in a wider scale-critical space.

 

      Xinyao He (Fudan University)

Title : Dimensional Entropy in Amenable Group Actions and Its Applications

 

Abstract : As an analogue of Hausdorff dimension in fractal geometry, dimensional entropy plays an important role in the complexity theory of dynamical system. For amenable group actions, we establish connections between dimensional entropy and several dynamical quantities, namely, weak expansiveness, topological entropy relative to a factor map, and metric mean dimension. These are joint works with Dou Dou, Guohua Zhang, and Ruifeng Zhang.

 

      Ping-Hsun Chuang (National Taiwan University)

Title : Generalized Arithmetic Picard-Lefschetz Formula

 

Abstract : In SGA 7 II, Deligne established the Picard–Lefschetz formula describing the action of the inertia group on the vanishing cycles of a proper flat family X → Spec R over a Henselian discrete valuation ring R whose special fiber has only isolated ordinary quadratic singularities. In this talk, I will present a generalization of this formula to families whose special fibers have isolated singularities of diagonal type. Moreover, I will give an explicit description of the inertia group and Frobenius actions on the vanishing cycles. Finally, I will briefly discuss how these results provide new insights into the study of the arithmetic aspects of Airy-type differential equations with irregular singularities.

 

      Sangwon Yoon (Seoul National University)

Title : SUSY extension of universal enveloping vertex algebras

 

Abstract : In this talk, we first study the relationship between vertex algebras and supersymmetric vertex algebras using the language of SUSY vertex algebras introduced by Kac and Heluani. Based on these observations, in particular, we note that the universal enveloping vertex algebra of a linear Lie conformal algebra can be extended to a SUSY vertex algebra.

 

  Tuesday

      Futaba Sato (University of Tokyo)

Title : Sharp Sobolev embedding property of quantum automorphism groups of finite dimensional C*-algebras

 

Abstract : Quantum groups are generalizations of groups in terms of algebras (Hopf algebras). Namely the theory of operator algebras allows us to consider quantizations of compact groups called compact quantum groups. We consider a class of compact quantum groups called quantum automorphism group $\mathrm{Aut}^+(B)$ of a finite dimensional C*-algebra B. These contain essential examples, such as quantum permutation groups. We obtain noncommutative $L^p$-theoretical properties of $\mathrm{Aut}^+(B)$ by the form of heat semigroups on $\mathrm{Aut}^+(B)$: the sharpness of the Sobolev embedding property.

 

      Peng Yang (Tsinghua University)

Title : Stochastic Calculus and Hochschild Homology

 

Abstract : I will talk about the connection between stochastic calculus and topological quantum field theory, through the lens of topological quantum mechanics. The topological correlation is realized as a large-variance limit of Gaussian free fields, and the $S^1$-product leads to a quantum version of the Hochschild–Kostant–Rosenberg map.

 

      Shuang-Yen Lee (National Taiwan University)

Title : Quantum Extremal Transitions and Special L-values

 

Abstract : In this talk, I will describe the relation between the quantum cohomologies QH(X) and QH(Y ) for a Type II transition Y ↘ X and the limit of Novikov variables. I will also explain the modularity of the extremal function E := E3/〈E, E, E〉 Y and period integrals of Eisenstein series. This is a joint work with Chin-Lung Wang and Sz-Sheng Wang.

 

      Ningyuan Yang (Fudan University)

Title : The Spectrum of Growth Rates for the Number of Maximal Sum-Free Sets

 

Abstract : How many maximal sum-free sets does a finite Abelian group contain? The growth rate of this number, denoted $g_{\max}(G)$, is known to be below $3^{1/3}$. It was conjectured that $g_{\max}(G)$ only takes extreme values or is at most $2^{1/2}$. In this talk, we disprove this by constructing infinite families of Type I groups with intermediate growth, satisfying $2^{1/2+c} < g_{\max}(G) < 3^{1/3-c}$. Concurrently, we confirm a related conjecture for all even-order groups $G \neq \mathbb{Z}2^k$, proving $g_{\max}(G) \leq 2^{(1/2-c)\mu(G)}$. A key tool is a new, sharp upper bound on the number of maximal independent sets in graphs with a given matching number, which is of independent interest in graph theory.

 

      Oto Araki (Tohoku University)

Title : Singular integrals in the week subsystem of second-order arithmetic

 

Abstract : By studying theorems of ordinary mathematics within weak subsystems of second order arithmetic, it becomes clear which set existence axioms are not only sufficient but also necessary for proving those theorems. Studies on measure theory and L^p space theory from the perspective of Reverse Mathematics have shown that general results in measure theory, such as countable additivity of measures and the Vitali covering lemma, require WWKL_0, while an even stronger axiom ACA_0 is necessary when dealing with differentiation and limits. In this talk, however, we provide a framework to deal with singular integrals within a weaker subsystem RCA_0. The idea is to restrict applications of integrals and measure-theoretic arguments to compactly supported smooth functions. Properties established within RCA_0 for this subspace is then extended to general L^p functions by the subadditivity of the operator.   In this way, the L^p boundedness of the Riesz transforms is justified within RCA0, which enables us to attempt to study partial differential equations in RCA_0.

 

      Chong-Wei Liang (National Taiwan University)

Title : Brascamp–Lieb inequalities and the related problems

 

Abstract : Brascamp and Lieb discovered a family of inequalities that unifies several classical inequalities, such as multilinear H¨older’s inequality, Young’s convolution inequality and the Loomis–Whitney inequality.

Let σj : V → Vj be linear maps between vector groups and let pj be Lebesgue exponents for all 1 ≤ j ≤ J. The Brascamp–Lieb inequality is the inequality of the form of $$\left| \int_V \prod_{j=1}^J (f_j \circ \sigma_j)(x) dx \right| \le C \cdot \prod_{j=1}^J ||f_j||_{L^{p_j}(V_j)}, \quad \forall f_j \in C_0(V_j).$$

In this talk, we will mainly discuss the history of the Brascamp–Lieb inequalities and some of its connections. If times is allowed, we will also discuss some questions left by J. Bennett and T. Tao

 

      Maoyin Lyu (Fudan University)

Title : The mathematical analysis of a nonlocal Cahn–Hilliard equation with nonlocal dynamic boundary condition and singular potentials

 

Abstract : In this talk, I will introduce a class of nonlocal Cahn-Hilliard equations in a bounded domain $\Omega \subset \mathbb{R}^d (d=2, 3)$ , subject to a nonlocal kinetic rate-dependent dynamic boundary condition. This diffuse interface model describes phase separation processes with possible long-range interactions both within the bulk material and on its boundary. The kinetic rate $1/L$, with $L \in [0, + \infty]$, distinguishes different types of bulk-boundary interactions.

The first part is devoted to the existence and uniqueness, the regularity, and the instantaneous strict separation property of global weak solutions. For the initial boundary value problem endowed with general singular potentials, including the physically relevant logarithmic potential, we first establish the existence of global weak solutions for the case $L \in (0, +\infty)$. The proof is based on a Moreau-Yosida approximation of the singular potentials and a suitable Faedo-Galerkin scheme. Subsequently, we investigate asymptotic limits as the kinetic rate approaches zero and infinity, which yield the existence of weak solutions for the limiting cases $L=0$ and $L=+\infty$, respectively. The continuous dependence on the initial data can be established by the standard energy method, which implies the uniqueness of weak solutions. Finally, we demonstrate that every global weak solution exhibits a propagation of regularity over time, and when , we establish the instantaneous strict separation property by means of a suitable De Giorgi's iteration scheme.

The second part is devoted to the long-time behavior of the system considered above. When $L \in [0, +\infty)$, we establish the existence of a global attractor in a suitable complete metric space. When $L \in (0, +\infty)$, based on the strict separation property of solutions, we prove the existence of exponential attractors through a short trajectory type technique, which also shows that the global attractor has finite fractal dimension. Finally, for this case, we show that every weak solution converges to a single equilibrium in $\mathcal{L}^\infty$ as time tends to infinity, using a generalized Lojasiewicz-Simon inequality and an Alikakos-Moser type iteration.

 

  Wednesday

      Yixiao Tao (Tsinghua University)

Title : Elliptic modular graph forms, equivariant iterated integrals and single-valued elliptic polylogarithms

 

Abstract : The low-energy expansion of genus-one string amplitudes produces infinite families of non-holomorphic modular forms after each step of integrating over a point on the torus worldsheet which are known as elliptic modular graph forms (eMGFs). We solve the differential equations of eMGFs depending on a single point $z$ and the modular parameter $\tau$ via iterated integrals over holomorphic modular forms which individually transform inhomogeneously under ${\rm SL}_2(\mathbb Z)$. Suitable generating series of these iterated integrals over $\tau$, their complex conjugates and single-valued multiple zeta values (svMZVs) are combined to attain equivariant transformations under ${\rm SL}_2(\mathbb Z)$ such that their components are modular forms. 

Our generating series of equivariant iterated integrals for eMGFs is related to elliptic multiple polylogarithms (eMPLs) through a gauge transform of the flat Calaque-Enriquez-Etingof connection. By converting iterated $\tau$-integrals to iterated integrals over points on a torus, we arrive at an explicit construction of single-valued eMPLs where all the monodromies in the points cancel.  Each single-valued eMPL depending on a single point $z$ is found to be a finite combination of meromorphic eMPLs, their complex conjugates, svMZVs and equivariant iterated Eisenstein integrals. Our generating series determines the latter two admixtures via so-called zeta generators and Tsunogai derivations which act on the two generators $x$, $y$ of a free Lie algebra and where the coefficients of words in $x,y$ define the single-valued eMPLs. This talk is based on arXiv: 2511.15883.

 

      Dong Jun Choi (Seoul National University)

Title : Generalized finite and affine W-algebras

 

Abstract : W-algebras associated with a finite-dimensional simple Lie algebra and its nilpotent element arose in conformal field theory and have been studied extensively in both the mathematics and physics literature. Finite and affine W-algebras can be obtained via quantum Drinfeld-Sokolov reduction of the universal enveloping algebra and the universal affine vertex algebra, respectively. In 2006, De Sole and Kac showed that applying the Zhu functor to an affine W-algebra yields the corresponding finite W-algebra. In this talk, we introduce a new family of finite and affine W-algebras associated with the centralizers of nilpotent elements in the Lie algebra $\mathfrak{gl}_N$, which we call the generalized finite and affine W-algebras. This family turns out to interpolate between several classes of vertex algebras previously studied in the literature, and the application of the Zhu functor to the generalized affine W-algebra yields the corresponding generalized finite W-algebra. This is joint work with Alexander Molev and Uhi Rinn Suh.

 

  Thursday

      Jiwon Brandon Jeong (Pusan National University)

Title : Variation of the Solutions to the Dirichlet Problems for the Complex Monge–Ampère Equation on Bounded Strongly Pseudoconvex Domains

 

Abstract : Let $\pi : D \to \Delta$ be the projection from a bounded pseudoconvex domain $D \subset \mathbb{C}^{n+1}$ onto the unit disc $\Delta$. For each fiber $D_s = \pi^{-1}(s)$, assumed to be a bounded strongly pseudoconvex domain with smooth boundary, we solve the Dirichlet problem for the complex Monge–Ampère equation

$$(dd^c_z u(s, \cdot))^n = e^{u(s, \cdot)-f(s, \cdot)} \quad \mbox{ in } D_s ;$$

$$u(s, \cdot)|_{\partial D_s} = 0 \quad \mbox{on} \partial D_s$$

 obtaining a smooth family of fiberwise solutions $u(s, z)$. It is well known that each $u(s, \cdot)$ is strictly plurisubharmonic along its fiber, whereas the function $u(s, z)$ is not necessarily plurisubharmonic in the base direction. Our main result shows that, under the additional assumption that $f \in C^\infty (\overline{D})$ is plurisubharmonic, there exists a non-negative constant $m=m(D, f)$ such that the real (1, 1)-form

$$dd^c(u(s, z)+ m|s|^2)$$

 is semi-positive on the total space $D$. In particular, the constant $m$ is determined solely by boundary data; specifically, it is given by the supremum of an explicit non-negative continuous function on $\partial D$.

 

      Hui-Tzu Chang (National Cheng Kung University)

Title : Fluid-dynamical approximation to the Boltzmann equation at the level of the Navier-Stokes equation

 

Abstract : The compressible Navier-Stokes equation obtained as the approximation of the formal Chapman-Enskog expansion, which is investigated on its relations to the Boltzmann equation. In this talk, we will present that the solutions of the Boltzmann equation for small initial data are asymp-totically equivalent to the compressible NavierStokes equation for the corresponding initial data.

 

      Hau-Yuan Jang (National Cheng Kung University)

Title : Products of Commutators in Simple Algebras

 

Abstract : In this talk, I will present my joint work with professor MATEJ BREŠAR and LEONEL ROBERT, in which we show that every element in a finitely dimensional noncommutative central simple algebra is the product of two commutators, and this is not true in general for infinitely dimensional central simple algebras.

 

      Shunsuke Hirota (Kyoto University)

Title : Understanding Lie Superalgebras from a Purely Algebraic Perspective

 

Abstract : The idea of Lie superalgebras originally arose from physics, but today there are several motivations for understanding them in a purely algebraic way, especially from categorical and combinatorial perspectives. In this talk, we focus on  general linear Lie superalgebras as a representative example and explain the natural appearance of superalgebras from the viewpoints of symmetric tensor categories, categorification, Khovanov arc diagrams, frieze patterns, and Young tableaux.

 

      Yanhan Chen (Kyoto University)

Title : Characterizations of the weighted infinitesimal relative boundedness of Schrödinger operators

 

Abstract : Relative boundedness plays a fundamental role in the study of Schrödinger operators through perturbation method. It provides a rigorous definition of Schrödinger semigroups and extends key properties of the Laplace operator to Schrödinger operators with potentials. In this work, we employ the Carleson condition and capacity theory to characterize the infinitesimal relative boundedness of Schrödinger operators in weighted $L^{p}$ spaces. Our results generalize the classical work of Maz'ya and Verbitsky.

 

      Cheng-Pu Lin (National Yang Ming Chiao Tung University)

Title : The Korteweg–de Vries equation with an interface

 

Abstract : In this talk, I will present how to establish local well-posedness for the one-dimensional interface problem associated with the Korteweg–de Vries equation. I will begin with a brief historical overview of the development of Korteweg–de Vries equation, and then introduce an effective approach now known as the Fokas method. This method can be adapted to treat interface problems, and finally, by applying the contraction mapping theorem, we obtain a local well-posedness result.

 

      Sangmin Park (Sungkyunkwan University)

Title : Algebraic Formulas via Theta Lifts for Half-Integral Weight Harmonic Weak Maass Forms

 

Abstract : In this talk, we discuss algebraic formulas for the Fourier coefficients of certain harmonic weak Maass forms of weight $-1/2$. These coefficients can be expressed as traces of singular moduli associated with weak Maass forms, and the formulas are obtained via the Kudla-Millson theta lift. We also introduce a related construction, the Millson theta lift, and explain how it leads to analogous trace formulas. As an application, we show that the coefficients of Ramanujan's mock theta functions $f(q)$ and $\omega(q)$ admit descriptions in terms of traces of CM-values of a weakly holomorphic modular function. Finally, we illustrate these results by explicitly computing the coefficients $a_f(n)$ of $f(q)$ for $n=1,2,3$.

 

 

Parallel Session B

 

  Monday

     Minsik Kang (Seoul National University)

Title : Homomorphic Encryption with Mathematical Backgrounds

 

Abstract : We aim to introduce the mathematical background of homomorphic encryption, which is the main area of our research, and to briefly present our recent work. We will first explain what homomorphic encryption is, and describe its structure and security based on lattice theory and the (Ring-)Learning with Errors ((R)LWE) problem. Building on this, we will introduce the encoding mechanism of the Cheon–Kim–Kim–Song homomorphic encryption scheme (CKKS), its homomorphic operations, and the notion of bootstrapping. We will conclude by outlining our research contributions in this setting.  

 

      Kai-Lun Jin (National Tsing Hua University)

Title : A New Numerical Scheme Preserving Distance Function for Moving Interface Problems in Mean Curvature Flow

 

Abstract : In this talk, we will propose a new numerical scheme for moving interface problem under mean curvature flow. The scheme can maintain the numerical solution being the signed distance function of the current interface with less frequent reinitialization. We test our algorithm for some various initial interfaces and compare the results with the local level set method proposed by D. Peng et al.. Finally, we will show a case to illustrate why cannot abandon the reinitialization step.

 

      Yuto Masamura (University of Tokyo)

Title : Construction of algebraic varieties admitting small contractions

 

Abstract : Birational algebraic geometry studies the classification of algebraic varieties up to birational equivalence — that is, up to isomorphism outside lower-dimensional subsets. The Minimal Model Program (MMP) provides a framework for simplifying varieties within such birational classes. A small contraction is a birational morphism that is an isomorphism outside a locus of codimension at least two. Such contractions reflect subtle geometric phenomena in higher dimensions, and play an important role in the MMP. Constructing examples of small contractions is thus a fundamental problem. In this talk, I will present a general blow-up construction that, given any smooth projective variety, produces new varieties admitting small contractions. This talk is based on  joint work with Tomoki Yoshida.

 

      Pingxin Gu (Tsinghua University)

Title : Weinstock inequality in hyperbolic space

 

Abstract : In this talk, we establish the Weinstock inequality for the first non-zero Steklov eigenvalue on star-shaped mean convex domains in hyperbolic space $\mathbb{H}^n$ by use of inverse mean curvature flow. In particular, when the domain is convex, we give an affirmative answer to Open Question 4.27 by Colbois-Girouard-Gordon-Sher.

 

      Jihyeon Kim (Pusan National University)

Title : Generating Nurse Schedules Using Multi-Objective Mixed-Integer Linear Programming to Minimize Extra Shifts, Ensure Fairness, and Maintain Consistent Care Quality

 

 

Abstract : This study proposes a multi-objective mixed-integer linear programming (MO-MILP)-based approach for optimizing nurse scheduling in the complex operating environment of a Korean hospital. To account for the fluctuation in number of available nurses owing to various factors such as the bed utilization rate, sliding scale of nursing grades, and number of statutory holidays per month, we introduce the assumption of minimum staffing requirements for weekdays, weekends, and holidays. In addition, the MO-MILP model is configured to simultaneously consider hard constraints (e.g., legal working standards and minimum staffing levels) and soft constraints (e.g., nurses' preferences, back-to-back work restrictions, and fair work distribution) to produce an optimal schedule that minimizes unnecessary overtime and ensures continuity of work patterns. Numerical experiments conducted between January to March, 2024, demonstrate that the proposed model generated reasonable and balanced shifts under the staffing and working conditions of real-world hospitals; thus, it has the potential to improve the operational efficiency of hospitals, prevent fatigue and burnout among nurses, and ultimately contribute to patient safety and the delivery of quality healthcare. Future work should focus on enriching the MO-MILP framework by incorporating additional constraints that better reflect human factors in real hospital settings. For example, integrating nurses’ interpersonal preferences—such as avoiding certain colleagues or preferring to work with specific peers—could capture emotional and relational aspects of scheduling. Such extensions would allow the model to address not only operational efficiency but also the social dynamics and well-being of the nursing workforce.

 

 

 

      Rei Muramaki (Tohoku University)

Title : An analytic proof of Griffiths' conjecture on compact Riemann surfaces

 

Abstract : Griffiths' conjecture asserts that the ampleness of a holomorphic vector bundle is equivalent to the existence of a Hermitian metric with Griffiths positive curvature. In the case of line bundles, this is a consequence of Kodaira’s embedding theorem, and the conjecture is also settled in dimension one. Recently, J.-P. Demailly proposed an analytic approach to this conjecture based on a system of partial differential equations. In this talk, we present a new proof of the one-dimensional case of Griffiths’ conjecture using this method. The results in this talk are based on arXiv:2509.23201v2.

 

  Tuesday

      Woohyeok Jo (Seoul National University)

Title : Montgomery-Yang problem and fillings of 3-manifolds

Abstract : The Montgomery-Yang problem conjectures that a pseudofree circle action on the 5-sphere has at most three exceptional orbits. Its algebraic version concerns the case where the quotient orbifold admits the structure of a complex projective surface. In this talk, I will give a brief overview of these problems and discuss our earlier results together with some ongoing developments. This is joint work with Jongil Park and Kyungbae Park.

 

      Zhuoming Lan (Tsinghua University)

Title : Equivariant mirror symmetry for footballs

 

Abstract : In this research, we establish equivariant mirror symmetry for footballs $\cF(m,r)$. This extends the results by B. Fang, C.C. Liu and Z. Zong, where the projective line was considered [{\it Geometry \& Topology} 24:2049-2092, 2017], and the results by D. Tang of weighted projective lines, on [arXiv:1712.04836].  More precisely, we prove the equivalence of the $R$-matrices for A-model and B-model at large radius limit, and establish isomorphism for $R$-matrices for general radius. We further demonstrate that the graph sum of higher genus cases are the same for both models, hence establish equivariant mirror symmetry for footballs. We also consider the large radius limit and equivariant limit are considered, resulting a generealized Bouchard-Mari\~{n}o conjecture and Norbury-Scott conjecture respectively.  

 

      An-Tien Hsiao (National Yang Ming Chiao Tung University)

Title : Bifurcation Dynamics of an Epidemic Model with Socio-Economic Processes and Limited Medical Resources

 

Abstract : We propose an SIS epidemic model that integrates spontaneous human behavioral change, modeled by replicator dynamics from evolutionary game theory, with limited medical resources characterized by a saturating treatment rate. The interplay between behavioral feedback and medical capacity fundamentally alters the system dynamics. In particular, we demonstrate that changes in medical capacity and the basic reproduction number can induce complex bifurcation structures, including hysteresis bifurcation, degenerate Hopf bifurcation, discontinuous Hopf-like bifurcation, and saddlenode bifurcation of limit cycles. Finally, we present numerical simulations to illustrate these results.

 

      Sungsu Park (Sungkyunkwan University)

Title : Convergence of an Eulerian scheme for the Vlasov-Poisson-BGK model

 

Abstract : The Vlasov-Poisson-BGK (VPBGK) model is a kinetic model for describing the dynamics of collisional plasmas. Although various numerical schemes have been developed for it, a corresponding convergence theory has been absent. We fill this gap by presenting the first convergence analysis for a non-splitting, finite-difference Eulerian scheme discretized on the full phase-space grid. Under a truncated velocity domain with a Neumann boundary condition, we establish an error estimate for the distribution function in a weighted $L^{\infty}$ norm and for the electric field in a $L^{\infty}$ norm, respectively.

 

      Shuniciro Orikasa (Kyoto University)

Title : Quantitative Estimates of Systoles and Dilation under Positive Scalar Curvature

 

Abstract : We develop a framework for quantitative estimates linking positive scalar curvature (PSC) to both systolic invariants and analytic properties of distance-decreasing maps in high dimensions. Our first focus is on disk bundles, where, under suitable stretch-scale conditions, we derive upper bounds on two-dimensional stable relative systoles. The second focus addresses complements of embedded circles in spheres, equipped with complete metrics admitting distance-decreasing self-maps. By controlling the areas of Lipschitz 2-chains relative to spinor bundle holonomy, we obtain sharp scalar curvature bounds. The proofs combine geometric measure theory for Plateau problems with index-theoretic arguments on non-compact manifolds, carefully controlling curvature contributions via Lipschitz maps realizing the prescribed stretch scale.

 

      Chankyu Joung (Seoul National University)

Title : Bifurcations of highly inclined near halo orbits using Moser regularization

 

Abstract : Symplectic geometry provides the natural mathematical language for classical mechanics, and its connections to concrete problems in celestial mechanics are still actively being developed. In this talk, I will describe recent work that combines symplectic ideas with numerical methods to study the restricted three-body problem, a fundamental model in astrodynamics. After briefly introducing the Hamiltonian framework and the role of regularization in near-collision dynamics, I will present results on the bifurcation structure of highly inclined spatial orbits with close approaches to the light primary, including halo orbits that play a central role in mission design. Using a Hamiltonian formulation together with Moser regularization, we develop a numerical framework for continuing families of periodic orbits and computing their Floquet multipliers that remains effective near collision. These results provide a coherent global picture of polar orbit architecture near the light primary and offer groundwork for future applications, such as trajectory design for Enceladus plume sampling missions. This is based on joint work with Dayung Koh and Otto van Koert.

 

      Yifan Chen (Tsinghua University)

Title : On the monodromy conjecture of determinantal varieties

 

Abstract : We presents a proof of the monodromy conjecture for determinantal varieties. Our strategy centers on an in-depth analysis of monodromy zeta functions, leveraging a generalized A'Campo formula, an examination of multiple contact loci, and the exploitation of the intrinsic symmetric structures inherent to these varieties.

 

  Wednesday

      Jin-Zhi Phoong (National Taiwan University)

Title : On Synchronization Analysis of Complex Coupled Kuramoto Oscillators

 

Abstract : In this talk, I will explore the widespread occurrence of synchronization in natural phenomena, ranging from the synchronous cortical activity to fireflies flashing in unison as well as the synchronized frequencies of different power generators. I will provide an overview of the Kuramoto model, including both first and second-order formulations. I will also discuss our research, which considers mixed scenarios, and present the established sufficient conditions for frequency synchronization.

 

      Xinyue Luo (Fudan University)

Title : Inverse Coefficient Problems for Reaction–Diffusion Systems: From Identifiability to Physics-Informed Learning

 

Abstract : We investigate inverse coefficient identification for reaction–diffusion systems from partial observations. On the theoretical side, we prove that observing a single component over a space–time cylinder can uniquely determine the unknown constant decay coefficients, provided a simple non-degeneracy condition holds. The proof yields an explicit recovery procedure by reducing the inverse problem to a low-dimensional algebraic determination, and counterexamples delineate degenerate regimes in which uniqueness fails.  On the computational side, we address the more challenging setting of steady-state Turing patterns, where temporal information is unavailable. We develop a physics-informed learning framework combining neural state estimation with symbolic basis representation to jointly infer hidden components and reaction kinetics from a single spatial snapshot. Numerical experiments on canonical models demonstrate the method's accuracy and robustness to noise.

 

  Thursday

      Fuya Hiroi (Tohoku University)

Title : Moving boundary problems of area-preserving curvature flows with general contact angles on skew lines

 

Abstract : The $(2m+2)$-order area-preserving curvature flow (ACF),  which can be regarded as the $H^{-m}$-gradient flow for the length functional of curves, has been studied in  mathematical literature. In particular, the area-preserving curve shortening flow ((ACF) with $m=0$) and the curve diffusion flow ((ACF) with $m=1$) have attracted significant mathematical interest. In this talk, we consider the moving boundary problem of (ACF) for open curves with endpoints meeting  skew lines at general contact angles. Hiroi--Okabe (2025) proved that circular arcs are stable under the moving boundary problem of the curve diffusion flow with  right contact angles, i.e., the flow converges to a circular arc if the initial curve is sufficiently close to one. The aim of this talk is to extend this stability result to any non-negative integer $m$ and non-right contact angles. One difficulty arises from the non-right contact angle condition. Indeed, (ACF) with the non-right contact angle condition is generally not a gradient flow for the length functional. However, by solving a suitable modified moving boundary problem, we can recover the gradient structure of (ACF) for the length functional and prove the stability of circular arcs. This talk will focus on how to achieve this.

 

      Pengjin Wang (Fudan University)

Title : On fibers for pluricanonical maps of varieties of general type

 

Abstract : Understanding pluricanonical systems of smooth projective varieties of general type is an important task in birational geometry. For surfaces of general type, Beauville established that the 1-canonical map has birationally bounded fibers; that is, there is a universal bound on its degree when generically finite, and on the volume of its general fiber otherwise. However, this property fails in higher dimensions due to examples by Chen, Hacon and Jiang. Chen and Jiang posed the question whether the result holds for r-canonical maps when r>1. Based on works of Chen-Jiang, Lacini, Chen-Liu and myself, we give an affirmative answer to this question in any dimension.

 

      Xingjian Ma (Tsinghua University)

Title : Random Distributionally Robust Optimization under Phi-divergence

 

Abstract : This work introduces a novel framework, Random Distributionally Robust Optimization (RDRO), which extends classical Distributionally Robust Optimization (DRO) by allowing the decision variable to be a random variable. We formulate the RDRO problem using a bivariate utility function and $\varphi$-divergence ambiguity sets, enabling a more flexible and realistic treatment of uncertainty. The RDRO framework encompasses a broad range of robust decision-making applications, including portfolio optimization, healthcare resource allocation, and reliable facility location. By optimal transport theory and convex analysis, we characterize key structural properties of the RDRO problem. Our main theoretical contributions include establishing the existence and uniqueness of optimal randomized decisions and proving a duality theorem that links the constrained RDRO formulation to its penalized counterpart.  We further propose an efficient numerical scheme that combines the scaling algorithm for unbalanced optimal transport with projected gradient descent, and demonstrate its effectiveness through numerical experiments.

 

      Wook Yoon (Seoul National University)

Title : Time-discrete consensus-based optimization algorithm for multi-objective optimization problems

 

Abstract : We study asymptotic consensus and finite-time reachability to Pareto optimal set for time-discrete multi-objective consensus-based optimization (M-CBO) algorithm in particle regime without resorting to the mean-field approximation. While the original CBO algorithm assumes that all particles share a common single objective function, the M-CBO algorithm assigns each particle to a distinct  sub-objective function obtained by the method of scalarization. In this paper, we show that for a sufficiently small noise, the expected value of the state diameter decays to zero exponentially fast. This results in almost sure asymptotic consensus. We also show that the CBO particle system approximates a Pareto optimal set in finite time. Moreover, the approximation becomes increasingly accurate, as the noise strength vanishes, while the number of particles and the inverse temperature parameter tend to infinity. These results extend  our theoretical understanding for CBO-type algorithms to the multi-objective regime by exhibiting asymptotic behaviors that are not observed in the previous mean-field analysis for M-CBO.

 

      Masaki Taho (University of Tokyo)

Title : Infinitely Many Tangent Functors on Diffeological Spaces

 

Abstract : Diffeological spaces, introduced by Souriau in the 1980s, provide a flexible framework that extends smooth manifolds while keeping a workable notion of smoothness on many spaces that arise naturally from constructions in geometry and topology. This flexibility makes them a convenient setting for asking how classical differential notions behave beyond the manifold world. In this talk, we study tangent spaces on diffeological spaces. While tangent spaces are canonical on smooth manifolds, extensions of the tangent functor to diffeological spaces are not unique. Besides the existing internal and external tangent spaces, we construct infinitely many pairwise non-isomorphic tangent functors on diffeological spaces, all extending the usual tangent functor on smooth manifolds. We compare these constructions with known models and explain how different choices encode genuinely different tangent information outside manifolds.

 

      Qianshun Cui (Tsinghua University)

Title : Hypersurfaces of $\mathbb{S}^2\times\mathbb{S}^2$ and $\mathbb{H}^2\times\mathbb{H}^2$ with recurrent Ricci tensor

 

Abstract : In the study of submanifolds geometry, the parallelism of some tensor fields like the second fundamental form, the Ricci tensor, etc attracts much attention. We prove that a hypersurface in $\mathbb{S}^2\times\mathbb{S}^2$ (resp. $\mathbb{H}^2\times\mathbb{H}^2$) with recurrent Ricci tensor is either an open part of $\Gamma\times\mathbb{S}^2$ (resp. $\Gamma\times\mathbb{H}^2$) for a curve $\Gamma$ in $\mathbb{S}^2$ (resp. $\mathbb{H}^2$), or a hypersurface with constant sectional curvature.

 

      Rixin Fang (Fudan University)