Alternatively have a look at the program.

## Lie groupoids determined by their orbit spaces

he orbit space of a Lie groupoid carries a natural diffeology. More generally, we have a quotient functor from the Hilsum-Skandalis category of Lie groupoids to the category of diffeological spaces. We introduce a class of effective Lie groupoids, called "lift-complete," for which this functor restricts to an equivalence of distinguished sub-categories. In particular, the diffeomorphism class of the orbit space of a lift-complete Lie groupoid determines its Morita class.

## Higher categorical structures in symplectic geometry

We will explore higher categorical structures in symplectic geometry by taking some not entirely rigorous but everthemore instructive shortcuts to the algebraic implications of the analysis of pseudoholomorphic curves. Please come prepared to engage in collective inquiry on questions such as

- Why do pseudoholomorphic disks generate $A_\infty$ algebras?
- What is $A_\infty$ algebra anyways?
- What 2- or $\infty$-categorical structures arise from interpreting string diagrams as pseudoholomorphic curves?

## A quick proof of the étale and pro-étale exodromy theorems

Locally constant sheaves are most easily understood as representations of the fundamental group, via the monodromy correspondence. In algebraic geometry, it is often preferable to use the larger class of constructible sheaves, as these are stable under (higher) pushforward. In 2018, Barwick, Glasman, and Haine proved an exodromy correspondence for constructible étale sheaves, using ideas from higher topos theory and profinite stratified homotopy theory.

## Stability of fixed points of Dirac structures

Given a geometric structure which induces a foliation on a manifold and a leaf of this foliation, one can ask when the leaf is preserved under deformations of the geometric structure. For Poisson structures and Lie algebroids, this question was addressed by Marius Crainic and Rui Loja Fernandes, and they showed that a leaf is stable when a certain cohomology group vanishes. I will give a general approach to such questions in terms of the L-infinity-algebra governing the deformations of the geometric structure, and an L-infinity-subalgebra.

## A unified approach to different generalizations of $\infty$-category theory

The language of Joyal and Lurie’s $\infty$-categories has now become indispensable in homotopy theory. However, for some purposes, it is convenient to pass to indexed or enriched versions of $\infty$-categories. For instance, homotopy theories of mathematical objects that admit symmetries governed by some group $G$, are usually better organized in so-called $G$-equivariant $\infty$-categories. We will see some examples of this principle. There are specialized notions of categorical concepts in the equivariant context, such as adjunctions, (co)limits, and Kan extensions.

## Blow ups and (formal) Lie algebroid cohomology

Studying the blow-down map in cohomology in the context of real projective blow ups of Lie algebroids can be used to gain a better insight into, or even compute, Lie algebroid cohomologies, which we discuss in this talk. The key observation is that the pullback via the blow-down map is an isomorphism when restricted to flat Lie algebroid forms, which leads to the consideration of formal Lie algebroid cohomology.

## Logarithmic topological cyclic homology

Logarithmic ring spectra are a simultaneous generalization of logarithmic rings from algebraic geometry and structured ring spectra from homotopy theory. Working with logarithmic ring spectra allows the construction of interesting intermediate localizations of rings or structured ring spectra where one can make an element invertible without making its powers invertible. In this talk, I will outline how topological Hochschild homology and topological cyclic homology can be defined for logarithmic ring spectra.

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