## Loop group action on symplectic cohomology

For a compact Lie group G, its massless Coulomb branch algebra is the G-equivariant

## Examples of adic spaces

## tba

## Non-abelian Lubin-Tate theory over R

## The stack of G-bundles on the twistor-$P^1$

## Variations of Hodge/twistor structures

## The Witten Genus

## Fun with 4D fundamental groups

Any finitely presented group can be the fundamental of a smooth 4-manifold. So, generally, the study of 4-manifolds has been restricted to simply connected cases or, thanks to Freedman and Teichner's profound results, to groups with subexponential growth (where surgery theoretical results still hold). In this talk, we'll explore this a bit further.

## The universal property of bordism rings of manifolds with commuting involutions

My talk concerns bordism rings of compact smooth manifolds equipped with a smooth action by a finite group. I will start by recalling classical results on the subject from the 60's and 70's, mostly due to Conner-Floyd, Boardman, Stong and Alexander. Afterwards I will discuss joint work with Stefan Schwede in which we prove an algebraic universal property for the collection of all bordism rings of manifolds with commuting involutions.

## Intertwining Fourier-Mukai and Wehrheim-Woodward functors via mirror symmetry of tori (master's talk 1)

After a brief motivation for mirror symmetry, we will discuss how to sistematically produce the mirror symmetry functor for the product, following the paper of Abouzaid and Smith. The technology presented will help us relate Wehrheim-Woodward functors to Fourier-Mukai ones.

For the most part of the talk we will handle symplectic 2-tori, but we will ask ourselves whether what we performed holds in greater generality. Does this point towards a 2-categorical framework for mirror symmetry?

## Problems in Fourier restriction theory

This talk will provide an overview of recent developments in Fourier restriction theory, which one could describe as the study of exponential sums over restricted frequency sets with geometric structure, typically arising in PDE or number theory. Decoupling inequalities measure the square root cancellation behavior of these exponential sums.

## Oscillatory integrals and stationary phase estimates in analytic number theory

I will give an overview of how oscillatory integrals arise in analytic number theory, especially the theory of L-functions and automorphic forms. Usually the integrals we are faced with are multiple-yet-low dimensional, so that they are approachable by repeated one-dimensional stationary phase estimates.

## Hodge theory, unlikely intersections and o-minimal geometry

## Arithmetic jet spaces and the Zilber—Pink conjecture

The Zilber—Pink conjecture is a simultaneous generalisation of the Mordell—Lang conjecture and the Andre

## Oscillatory integrals in number theory. Number Theory Lunch Seminar jointly with the Hausdorff School

## -- CANCELLED -- Intertwining Fourier-Mukai and Wehrheim-Woodward functors via mirror symmetry of tori (master's talk 1)

After a brief motivation for mirror symmetry, we will discuss how to sistematically produce the mirror symmetry functor for the product, following the paper of Abouzaid and Smith. The technology presented will help us relate Wehrheim-Woodward functors to Fourier-Mukai ones.

For the most part of the talk we will handle symplectic 2-tori, but we will ask ourselves whether what we performed holds in greater generality. Does this point towards a 2-categorical framework for mirror symmetry?

## Λ-algebras and the algebraic EHP sequence

## The restricted lower central series spectral sequence

## Adic spaces

## tba

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