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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...

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...

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...

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...

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)...

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...

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 real Lie theory, matrices that admit a real logarithm lie in the identity component $\mathrm{GL}_n(\mathbb{R})_+$ of the general linear group $\mathrm{GL}_n(\mathbb{R})$, while their logarithms belong to the Lie algebra $\mathfrak{gl}_n(\mathbb{R}...

Abstract TBA

It is well-known that for any finite group G, there exists a closed 3-manifold M with G as a quotient of the fundamental group of M. However, we can ask more detailed questions about the possible finite quotients of 3-manifold groups, e.g. for G and...