Past Events

Geophysical inversion is a well-established method for conducting non-invasive surveys of underground anomalies, such as buried infrastructure. Typically, inversion is performed using numerical methods: gradient descent and physics-based simulations...

In the first part of the talk (introduction) I will recall classical and semi-classical results and conjectures. In the second part I will review the current status of PDE gluing constructions of minimal surfaces. In the last (main) part of the talk...

The special Lagrangian equation (SLE) is a fully nonlinear elliptic PDE that originates in the work of Harvey and Lawson on calibrated geometries. The question whether a viscosity solution to the SLE is smooth (or at least has minimal gradient graph)...

If X is a smooth complete variety, then the alternating sums of dimensions of sheaf cohomology groups gives an additive map from the Grothendieck group of vector bundles on X to the integers. If X is not complete, then sheaf cohomology groups are...

Pollution is a pervasive environmental stressor that affects biological systems across multiple levels of organization, from cellular processes to individual behavior and population dynamics. While numerous empirical studies document these effects...

Understanding how network structure gives rise to spatiotemporal dynamics and computation is a central challenge in computational neuroscience and artificial intelligence. Despite increasingly detailed connectomic data in neuroscience and large-scale...

A connection on a vector bundle is data which tells us how to lift a curve from the base space to the total space. In this talk, we introduce a generalization of them known as "formal connections," and explain how they offer us a way to model the...

Finitely generated groups can be treated as geometric objects by considering their Cayley graphs with respect to finite generating sets. All such graphs are quasi-isometrically equivalent. In the 80s, Gromov proposed studying finitely generated...

Infectious diseases such as tuberculosis, African swine fever virus (ASFV), and highly pathogenic influenza viruses continue to affect millions of people and animals worldwide. Developing vaccines or antiviral drugs against these pathogens...

To compute the quantum dynamics of a molecule's electrons, one tractable way to proceed is via time-dependent density functional theory (TDDFT). TDDFT gives equations of motion that, in principle, yield the same electron density as the full but...