Previous Conferences & Workshops

A cohomology class of the group GL_n(Q_p) gives rise to a characteristic class of Q_p-local systems on algebraic varieties or topological spaces. It turns out that all rational primitive cohomology classes (in degrees >1) give vanishing...

The compressible Euler equation can lead to the emergence of shock discontinuities in finite time, notably observed behind supersonic planes. A very natural way to justify these singularities involves studying solutions as inviscid limits of Navier...

Riemannian metrics are the simplest generalizations of Euclidean geometry to smooth manifolds. The Ricci curvature of a metric measures, in an averaged sense, how the geometry deviates from being flat. The tensor $-2\,\mathrm{Ric}$ can be viewed as...

Large language models (LLMs) sometimes generate statements that are plausible but factually incorrect—a phenomenon commonly called "hallucination." We argue that these errors are not mysterious failures of architecture or reasoning, but rather...

The theory of Euler systems, first developed by Thaine and Kolyvagin, has become a central tool for proving cases of the Birch–Swinnerton-Dyer and Bloch–Kato conjectures. Many of the known examples are inspired from automorphic period integrals that...

The goal of these lectures is to present the fundamentals of Simpson’s correspondence, generalizing classical Hodge theory, between complex local systems and semistable Higgs bundles with vanishing Chern classes on smooth projective varieties.

The goal of these lectures is to present the fundamentals of Simpson’s correspondence, generalizing classical Hodge theory, between complex local systems and semistable Higgs bundles with vanishing Chern classes on smooth projective varieties.

In the 1930s, Einstein, Podolsky and Rosen devised the "EPR paradox", which shed light on a peculiar phenomenon in the mathematical modeling of quantum mechanics:  Very far apart particles can exhibit correlated behaviour, which seemed to suggest a...

Let $q,Q$ be two integral quadratic forms in $m n$
variables. One can ask when $q$ can be represented by $Q$ - that is,
whether there exists an $n \times m$-integer matrix $T$ such that $ Q \circ T = q $.  Naturally, a necessary condition is that...