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Higher algebraic K-theory is a powerful invariant which was originally defined for rings, but has since grown far beyond its initial scope to encompass increasingly rich and intricate settings. There are many different constructions of algebraic K...

Abstract TBA

In 1859, Bernhard Riemann published his seminal (and only) article in analytic number theory, where he showed that the distribution of prime numbers is connected to the distribution of the complex zeros of the zeta function that bears his name...

The reconfiguration of one discrete structure into another one, through a sequence small local modifications, is a wide research area. Famous topics of study range from games like the Rubik's cube or the 15-puzzle via robot motion planning to...

I will survey the state of the art on the regularity theory for multiplicity 2 integral stationary currents. The talk will be based on joint work with C. De Lellis and J. Hirsch, and will touch upon recent work of Becker Kahn, Minter and...

The Brauer–Manin obstruction provides a powerful framework for explaining failures of the Hasse principle for rational points on algebraic varieties. While many known examples arise from the algebraic part of the Brauer group, comparatively few...

For two multiplicatively independent positive integers p and q, Furstenberg (2019) conjectured that the transformations px mod 1 and qx mod1 are transverse. This means that the Hausdorff dimension of the intersection of two closed invariant sets is...

Since its inception in the early 2000s, compressive sensing has become a well-established paradigm for efficient signal recovery, with applications ranging from medical imaging to scientific computing. More recently, data-driven reconstruction...

Tensor triangular geometry associates a rich geometric structure, the spectrum, to a “nice” category where one can add, subtract and multiply objects. Examples include modules over a commutative ring and representations of a finite group. I’ll give...

Let C be a class of algebraic structures. For example, C could be a class of quadratic forms, field extensions or algebraic curves of a given genus. To measure the complexity of C, mathematicians ask a natural question: how many algebraically...