학과 세미나 및 콜로퀴엄
The Gromov-Wasserstein (GW) distance is a generalization of the standard Wasserstein distance between two probability measures on a given ambient metric space. The GW distance assumes that these two probability measures might live on different ambient metric spaces and therefore implements an actual comparison of pairs of metric measure spaces. A metric-measure space is a triple (X,dX,muX) where (X,dX) is a metric space and muX is a fully supported Borel probability measure over X.
In Machine Learning and Data Science applications, this distance is estimated either directly via gradient based optimization approaches, or through the computation of lower bounds which arise from distributional invariants of metric-measure spaces. One particular such invariant is the so-called ‘global distance distribution’ which precisely encodes the distribution of pairwise distances between points in a given metric measure space. This invariant has been used in many applications yet its classificatory power is not yet well understood.
This talk will overview the construction of the GW distance, the stability of distributional invariants, and will also discuss some results regarding the injectivity of the global distribution of distances for smooth planar curves, hypersurfaces, and metric trees.
This is a reading seminar to be given by 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.
A perfect field is said to be Kummer-faithful if the Kummer maps for semiabelian varieties over the field are injective. This notion originates in the study of anabeian geometry. At the same time, our study is also motivated by a conjecture of Frey and Jarden on the structure of Mordell-Weil groups over large algebraic extensions of a number field.
I will begin with a review of known results in this direction, as well as a brief discussion on anabelian geometry. Then I will introduce some recent results on the construction of "large" Kummer faithful fields. This is a joint work with Takuya Asayama.
This is a reading seminar to be given by 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 by 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).