TBC

In this talk, I will explain how to obtain the space of local operators of a 4d N=2 gauge theory using the category of line operators in the Kapustin twist (holomorphic topological twist). This category is given a precise definition by Cautis-Williams, as the category of equivariant coherent sheaves on the space of Braverman-Finkelberg-Nakajima. We compute the derived endomorphism of the monoidal unit in this category, and show that it coincides with the vacuum module of the Poisson vertex algebra of Oh-Yagi and Butson. The Euler character of this space reproduces the Schur index. I will also explain how to obtain the space of local operators at the junction of minimal Wilson-t’Hooft line operators. Its Euler character can be compared to the index formula of Cordova-Gaiotto-Shao. This is based on arXiv: 2112.12164.

There have been several proposals of scale-separated AdS vacua in the literature. All known examples arise from the effective field theory of flux compactifications with low supersymmetry, and there are often doubts about their consistency as 10 or 11d backgrounds in string theory. These issues can often be tackled in the bulk theory, or by analysis of the dual CFT via holography. I will review the most common issues, and focus the analysis on the recently constructed family of 3d scale-separated AdS vacua, which is dual to a two-dimensional CFT, emphasizing the discrete symmetry structure of the model in comparison to DGKT. Finally, I will comment on the tantalizing observation of integer operator dimensions in DGKT-like vacua, and comment on possible places to look for consistency issues in these models.

Let X be a smooth projective curve over a finite field equipped with an action of a finite group G. I’ll first briefly introduce the corresponding Artin L-function and a certain equivariant Euler characteristic. The main result will be a precise relation between the epsilon constants appearing in the functional equations of Artin L-functions and that Euler characteristic if the projection X → X/G is at most weakly ramified. This generalises a theorem of Chinburg for the tamely ramified case. I’ll end with some speculations in the arbitrarily wildly ramified case. This is joint work with Helena Fischbacher-Weitz and with Adriano Marmora.

In this talk, we discuss existentially closed measure preserving actions of countable groups.  A classical result of Berenstein and Henson shows that the model companion for this class exists for the group of integers and their analysis readily extends to cover all amenable groups.  Outside of the class of amenable groups, relatively little was known until recently, when Berenstein, Henson, and Ibarlucía proved the existence of the model companion for the case of finitely generated free groups.  Their proof relies on techniques from stability theory and is particular to the case of free groups.  In this talk, we will discuss the existence of model companions for measure preserving actions for the much larger class of universally free groups (also known as fully residually free groups), that is, groups which model the universal theory of the free group.  We also give concrete axioms for the subclass of elementarily free groups, that is, those groups with the same first-order theory as the free group.  Our techniques are ergodic-theoretic and rely on the notion of a definable cocycle.  This talk represents ongoing work with Brandon Seward and Robin Tucker-Drob.

Lahars and huaicos are potent natural hazards that threaten lives and livelihoods. They comprise debris-laden fluid that flows rapidly down slopes, bulking up considerably as they progress. Owing to their rapid onset and the significant threat that they pose to communities and infrastructures, it is important to be able to predict their motion in order to assess quantitatively some of the impacts that they may cause. In this seminar I will present mathematical models of these flows and apply them to various natural settings, drawing on examples from Peru and the Philippines.  Along the way I will show some informative, idealised solutions, the susceptibility of these flows to roll wave instabilities, ways to prevent ill-posedness and how to include measured topography in the computation.

The presence of glaciers and ice sheets leaves a significant imprint
on Earth's surface.  We steadily improve our physical understanding of
the involved processes, from the erosion of kilometer-deep fjords in
crystalline bedrock to the broad ice-marginal deposition of sediments.
This talk will highlight observations of landforms, sedimentary deposits,
laboratory experiments, and models that aim to capture the interplay
between ice and substratum.  I show how the interplay may play a role in
the future evolution of the West Antarctic Ice Sheet in a warming climate.