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Since the work by Caffarelli-Chan-Silvestre-Vasseur, integro-differential equations naturally arise from models in physics, engineering, and finance, attracting an increasing level of interest. They a...
Since the work by Caffarelli-Chan-Silvestre-Vasseur, integro-differential equations naturally arise from models in physics, engineering, and finance, attracting an increasing level of interest. They a...
With noisy and asynchronous high-frequency data collected for an ultra-large number of assets, we estimate high-dimensional spot volatility matrices satisfying a low-rank plus sparse structure. A loca...
Since the work of Sela, and Kharlampovich & Myasnikov on Tarski’s problem for non-abelian free groups, the model theoretic analysis of classes of groups arising from combinatorial and geometric group ...
We first consider the basic theory of algebraic curves, including the compact Riemann surface, Riemann-Hurwitz formula, Baker-Akhiezer function, three kinds of Abelian differentials, the construction ...
In this talk, I will breifly introduce the p-aidc number, p-aidc manifolds, p-adic algebraic groups and p-aidc definable groups. Using an elementary method, I will show that every open subgroup of a c...
In this talk we will develop a framework for enriching various classical invariants of homological algebra and algebraic topology with additional descriptive set-theoretic information. The resulting "...
KPZ limit for one-dimensional weakly asymmetric Ginzburg-Landau model was studied by Diehl-Gubinelli-Perkowski in a setting of martingale (energy) solution. Our goal is to apply a path-wise approach b...
O'Grady's generalized Franchetta conjecture is concerned with algebraic cycles of codimension 2 on the universal polarized K3 surface of genus g. This conjecture has been confirmed only for certain sm...
Legendrian knots and their exact Lagrangian fillings are central objects to study in low dimensional contact and symplectic topology. In recent developments, cluster algebras have proven to be powerfu...
In this talk, we mainly show some eigenvalue properties of second order Sturm-Liouville problems and third-order boundary value problems with both transmission conditions and eigenparameter-dependent ...
We will introduce the polynomial partitioning method which has wide applications in incidence geometry, geometric measure theory, and harmonic analysis. In the first course, we will present some basic...

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