This is a reading seminar to be given Mr. Jaehong Kim (a graduate student in the department) on foundations of the intersection theory and the classification theory of complex algebraic surfaces. He will give three 2-hour long talks.

In this talk, I will discuss the expansion of the free energy of two-dimensional Coulomb gases as the size of the system increases. This expansion plays a central role in proving the law of large numbers and central limit theorems. In particular, I will explain how potential theoretic, topological, and conformal geometric information of the model arises in this expansion and present recent developments.

This is a reading seminar to be given Mr. Jaehong Kim (a graduate student in the department) on foundations of the intersection theory and the classification theory of complex algebraic surfaces. He will give three 2-hour long talks.

This is a reading seminar to be given Mr. Jaehong Kim (a graduate student in the department) on foundations of the intersection theory and the classification theory of complex algebraic surfaces. He will give three 2-hour long talks.

In this talk, we will discuss Leray-Hopf solutions to the two-dimensional Navier-Stokes equations with vanishing viscosity. We aim to demonstrate that when the initial vorticity is only integrable, the Leray-Hopf solutions in the vanishing viscosity limit do not exhibit anomalous dissipation. Moreover, we extend this result to the case where the initial vorticity is merely a Radon measure, assuming its singular part maintains a fixed sign. Our proof draws on several key observations from the work of J. Delort (1991) on constructing global weak solutions to the Euler equation. This is a joint work with Luigi De Rosa (University of Basel).