Speaker: Andrei OkounkovVenue: Room 210, Haina Building 2, Zijingang CampusAbstract: Enumerative geometers and their colleagues in representation theory and mathematical physics are very excited about the new perspectives on old and new problems offered by the nascent field of 3-dimensional mirror symmetry. While most formulations or explanations of what 3-dimensional mirror symmetry is require a lot of prerequisites and a high level of abstraction, some of its core predictions can be easily cast in the language that people like P.L. Chebyshev, C.G. Jacobi, and I.G. Macdonald would have no problem grasping. This is what I will try to do in this talk, which I hope will be accessible to the general mathematical audience.

Speaker: Brian TomVenue: Room 210, Haina Building 2, Zijingang CampusAbstract: In precision medicine, there is growing interest in discovering disease endotypes from high-dimensional biomarkers which associate with clinically relevant outcomes or phenotypes. Motivated by an application in knee osteoarthritis (OA) using synovial fluid protein markers, we aimed to identify OA endotypes linked to disease severity (based on Kellgren–Lawrence grade). Bayesian profile regression (Molitor et al. 2010) was adopted to perform this outcome-guided clustering. However, although the clusters found were stable across training and validation sets, the prediction of disease severity from these clusters were poor in the validation set; thus, limiting its practical use. The poor out-of-sample performance can partly be attributed to the weak influence of the single binary outcome relative to the high dimensional set of biomarkers in determining the clustering structure. To address this imbalance and for more general multi-task learning problems, we propose a generalized Bayesian framework for outcome-guided clustering by reformulating the problem as a decision problem with separate loss components for the clustering and prediction tasks. This framework offers greater flexibility and admits standard Bayesian profile regression as a special case. To improve the interpretability of the weighting of the different loss components, we propose a principled standardization that places each task risk on a common scale, thereby decoupling the task weights from the learning rate. The learning rate is tuned/guided by an estimate of the expected out-of-sample risk under a user-chosen evaluation loss.

Speaker: Joy TongVenue: Room 530, Chengjun Building 7, Zijingang CampusAbstract: We use a novel text-based classification method to identify green trademarks that capture environmentally friendly products and services introduced to the market. Firms with more green products generate higher green revenues, emit less greenhouse gas, and receive higher environmental ratings. These firms also exhibit higher firm value, particularly when green products align with core businesses and prior experience and generate product synergies. The valuation effect appears to be driven by consumer environmental awareness rather than investor preferences or concerns. Finally, we provide causal evidence that firms expand their green product offerings following nearby natural disasters or peer firms’ environmental scandals.

Speaker: HAN WeiminVenue: Room 202, Haina Building 2, Zijingang CampusAbstract: In recent years, modeling, mathematical analysis, and numerical solution of hemivariational inequalities, or more generally, variational-hemivariational inequalities, have attracted much attention in the research communities.  Through the formulation of variational-hemivariational inequalities, application problems involving nonsmooth, monotone or non-monotone, multivalued constitutive laws, forces, and boundary conditions can be treated successfully. Variational-hemivariational inequalities have been successfully applied in a wide variety of subjects, ranging from nonsmooth mechanics, physics, engineering, to economics. This talk will provide an overview of the mathematical theory and numerical analysis of families of variational-hemivariational inequalities, with applications in contact mechanics.  It will begin with a brief discussion of a model boundary value problem of an elliptic PDE, and then naturally extend the discussion to sample variational inequalities and hemivariational inequalities.  The talk will be accessible to anyone with basic knowledge of PDEs.

Speaker: ZHANG QianVenue: Building 2, room 312, Haina yuan, Zijingang CampusAbstract: In the ideal limit and in the absence of external forces, the incompressible Navier–Stokes equations preserve fundamental invariants, including kinetic energy and helicity. From a numerical perspective, failure to respect these invariants may reduce the physical reliability of long-time simulations of three-dimensional flows. However, numerical methods that simultaneously preserve kinetic energy and helicity remain relatively limited; many existing approaches are computationally expensive, require nonlinear solvers, or are applicable only under restrictive boundary conditions.In this talk, I will present an efficient enriched Galerkin method that preserves both invariants. The method enriches a first-order continuous Galerkin velocity space with the lowest-order Raviart–Thomas space and uses a piecewise-constant pressure approximation. The enrichment corrects the normal component of the continuous Galerkin velocity field, yields an inf-sup stable velocity–pressure discretization, and retains the same number of global degrees of freedom as the classical Bernardi–Raugel element. Together with a carefully designed rotational-form discretization of the convective term, this formulation leads to a fully nonlinear Crank–Nicolson scheme and two linearized variants. All three schemes exactly preserve discrete kinetic energy and helicity in the inviscid limit, and each Picard iteration step of the nonlinear scheme preserves the invariants. I will also present numerical examples demonstrating the accuracy and structure-preserving performance of the proposed method.

Speaker: SHI ZhentaoVenue: Building 2, room 206, Haina yuan, Zijingang CampusAbstract: When the number of assets is larger than the sample size, the minimum variance portfolio interpolates the training data, delivering pathological zero in-sample variance. We show that if the weights of the zero variance portfolio are learned by a novel “Ridgelet” estimator, in a new test data this portfolio enjoys out-of-sample generalizability. It exhibits the double descent phenomenon and can achieve optimal risk in the overparametrized regime when the number of assets dominates the sample size. In contrast, a “Ridgeless” estimator which invokes the pseudoinverse fails in-sample interpolation and diverges away from out-of-sample optimality. Extensive simulations and empirical studies demonstrate that the Ridgelet method performs competitively in high-dimensional portfolio optimization.

Speaker: Mingchao CaiVenue: Building 2, room 204, Haina yuan, Zijingang CampusAbstract: Thermo-poroelastic models capture the interplay between elastic porous material deformation, fluid flow, and thermal effects under non-isothermal conditions. This talk presents a four-field formulation for the linear thermo-poroelastic model and introduces two novel algorithms. The first focuses on constructing parameter-robust preconditioners for the resulting linear system, proposing two approaches: one reorganizes variables into a 2-by-2 block structure, while the other directly addresses the 4-by-4 coupled operator. Both preconditioners exhibit robustness to parameter variations and mesh refinement. The second algorithm is a decoupled iterative finite element method, for which stability and optimal convergence are rigorously proven. Numerical experiments are provided to validate the effectiveness and efficiency of the proposed methods.

Speaker: HUANG XuehaiVenue: Room 101, building 2, Haina yuanAbstract: In this talk, we begin with the development of distributional finite element complexes, including the distributional div div and curl div complexes. In the main part of the talk, we discuss applications of these complexes to partial differential equations, such as the biharmonic equation, fourth-order elliptic singular perturbation problems, quad-curl problems, and the Stokes equation. We also present a distributional formulation and a corresponding discretization for strain gradient elasticity.

Speaker: YU BangxingChair: QIU YangVenue: Room A215, School of Management, Zijingang campusAbstract: This study examines how improved judicial independence affects corporate governance using the staggered establishment of circuit courts in China. By reducing local protectionism, these courts increase firms’ exposure to litigation risk. We find that independent director compensation rises following the reform. The evidence supports an efficient contracting explanation rather than rent extraction. The increase is stronger in regions with greater prior protectionism and for directors located farther from the firm. The effect persists in firms with strong external monitoring and high product market competition, where agency concerns are less pronounced. Additional analyses show that the reform leads to more active board oversight, reflected in more dissenting votes and greater director expertise. Overall, our study suggests that improvements in judicial independence reshape corporate contracting by increasing the value of effective board monitoring in response to higher legal risk