In view of scheme language, we start from the beginning of the theory of elliptic curves and geometric modular forms, and further cover the topics about Jacobians and Galois representation as well as modularity problems.

In this talk, we will survey the article "Modular forms and projective invariants - J.Igusa(1967)".

In this talk, we will survey the article "Class fields over real quadratic fields and Hecke operators - G.Shimura(1972)".

In this talk, we will investigate the algebraic construction of the Jacobian of a hyperelliptic curves.

In this talk we will present a new method of providing both conductivity  and permittivity images at the MR Larmor frequency in magnetic resonance electrical property tomography (MREPT), a relatively new MR-based electrical tissue property imaging modality.

In view of scheme language, we start from the beginning of the theory of elliptic curves and geometric modular forms, and further cover the topics about Jacobians and Galois representation as well as modularity problems.

This is a working seminar so that no details will be provided.

In this talk, we will survey the article "Modular forms and projective invariants - J.Igusa(1967)".

In this talk, we will survey the article "Class fields over real quadratic fields and Hecke operators - G.Shimura(1972)".

In this talk, we will investigate the algebraic construction of the Jacobian of a hyperelliptic curves.

In view of scheme language, we start from the beginning of the theory of elliptic curves and geometric modular forms, and further cover the topics about Jacobians and Galois representation as well as modularity problems.

In this talk, we will survey the article "Modular forms and projective invariants - J.Igusa(1967)".

In this talk, we will survey the article "Class fields over real quadratic fields and Hecke operators - G.Shimura(1972)".

In this talk, we will investigate the algebraic construction of the Jacobian of a hyperelliptic curves.

This is a working seminar, so that no details will be provided.

In this talk, we revisit an auxiliary space preconditioning method proposed by Xu [Computing 56, 1996], in which low-order nite element spaces are employed as auxiliary spaces for solving linear algebraic systems arising from high-order nite element discretizations. We provide a new convergence rate estimate and parallel implementation of the proposed algorithm. We show that this method is user-friendly and can play an important role in a variety of Poisson-based solvers for more challenging problems such as the Navier-Stokes equation. We investigate the performance of the proposed algorithm using the Poisson equation and the Stokes equation on 3D unstructured grids. Numerical results demonstrate the advantages of the proposed algorithm in terms of efficiency, robustness, and parallel scalability.

 In this talk, we present how to obtain Log-Lipschitz regularity of solutions to the 3D Navier-Stokes equations with initial data in $L^{r}cap L^{3}$, $1<r<frac{3}{2}$. As a corollary, we also obtain H"{o}lder regularity of the flow map.

 I present results obtained in collaboration with J. Froehlich and W. de Roeck on quantum Brownian motion. We consider a quantum particle on the lattice weakly coupled to a spatial array of independent non-interacting reservoirs in thermal states (heat baths). We prove that the motion of the particle is diffusive at large times. If in addition the particle is driven by a weak external force field, we show that the motion of the particle is diffusive around a mean ballistic motion with constant velocity proportional to the external force field. Moreover, we prove that the Einstein relation (or Green-Kubo formula) holds, linking the mobility of the particle with the diffusion constant at vanishing external force.

In view of scheme language, we start from the beginning of the theory of elliptic curves and geometric modular forms, and further cover the topics about Jacobians and Galois representation as well as modularity problems.

In this talk, we will survey the article "Modular forms and projective invariants - J.Igusa(1967)".

In this talk, we will survey the article "Class fields over real quadratic fields and Hecke operators - G.Shimura(1972)".

This is a working seminar. No details are provided.

In this talk, we will investigate the algebraic construction of the Jacobian of a hyperelliptic curves.

I will discuss various aspects of the geometry of the extension graph.  I will discuss vertex link projections, the bounded geodesic image theorem, and a distance formula for right-angled Artin groups.  Joint with S. Kim.

I will discuss basics of extension graphs for right-angled Artin groups and the actions of right-angled Artin groups on their extension graphs.  The main result in this lecture will be a version of the Nielsen--Thurston classification for right-angled Artin groups.  Joint with S. Kim.

In the last several decades, conformal blocks have been studied by many algebraic geometers who are interested in the geometry of moduli spaces of vector bundles. Recently, people have begun to study the relation between conformal blocks and the birational geometry of the moduli space $bar{M}_{0,n}$ of stable pointed rational curves, because they give a huge family of base point free divisors on $bar{M}_{0,n}$. In this talk, I will discuss an example of interaction between three approaches to the birational geometry of $bar{M}_{0,n}$: stack theoretic viewpoint, GIT, and conformal blocks. This is based on a joint work with A. Gibney, D. Jensen and D. Swinarski.

Since Hassett and Hyeon initiated the study of birational geometry of moduli spaces of curves in a viewpoint of minimal model program, there have been a tremendous amount of results. In this talk, I will explain three different approaches toward this direction: stack theory, GIT and the minimal model program. After that, I am going to describe Mori's program for the moduli space of Deligne-Mumford pointed stable rational curves $bar{M}_{0,n}$. If the time is permitted, I will discuss some generalizations toward higher genera and relative cases.