TCD Analysis seminar

The meetings are on Fridays from 11-12am in the seminar room of the Hamilton Mathematics Institute.

Please contact me at if you are interested.








Hilary 2026


02.04.25   Rafael Andrist

On Stein manifolds determined by their endomorphisms
Abstract: By a result of Merenkov, two bounded domains are (anti-)biholomorphically equivalent if and only if they have isomorphic groups of holomorphic endomorphisms. In this talk, we explore the case of unbounded domains and obtain positive results for Stein manifolds that contain a punctured complex line as a retract. Then we treat the case of pseudoconvex Reinhardt domains in dimension two. Joint work with W. Zwonek.


26.03.25   Andreea Nicoara

Multitype and commutator multitype for the Bloom example.



19.03.25   Ilya Kossovskiy (SUSTECH)

The Analytic Regularizability Theory for Strictly Pseudoconvex CR Hypersurfaces.



12.03.25   Lev Birbrair

Lipschitz geometry of surface germs in R4: metric knots
Abstract: A link at the origin of an isolated singularity of a two-dimensional semialgebraic surface in R4 is a topological knot (or link) in S3 . We study the connection between the ambient Lipschitz geometry of semialgebraic surface germs in R4 and knot theory. Namely, for any knot K, we construct a surface XK in R4 such that: the link at the origin of XK is a trivial knot; the germs XK are outer bi-Lipschitz equivalent for all K; two germs XK and XK′ are ambient semialgebraic bi-Lipschitz equivalent only if the knots K and K′ are isotopic. We show that the Jones polynomial can be used to recognize ambient bi-Lipschitz non-equivalent surface germs in R4 , even when they are topologically trivial and outer bi-Lipschitz equivalent.


26.02.25   Dmitri Zaitsev

Tower Multitype VII



19.02.25   Dmitri Zaitsev

Tower Multitype VI



12.02.25   Dmitri Zaitsev

Tower Multitype V



05.02.25   Christina Neumayer

Tower Multitype - Examples
Abstract: We are going to construct the Tower Multitype on several examples, which illustrate its behavior.







Michelmas 2025


05.12.25   Christina Neumayer

Tower Multitype - A computational perspective
Abstract: After recalling the exact definition of the tower multitype, we will construct the tower multitype on some examples. Further, we will see some phenomenon of lowering the tower multiitype with terms of higher weight.


28.11.25   Dmitri Zaitsev

Introduction into the tower multitype IV



21.11.25   Dmitri Zaitsev

Introduction into the tower multitype III



07.11.25   Dmitri Zaitsev

Introduction into the tower multitype II



24.10.25   Dmitri Zaitsev

Introduction into the tower multitype.
Abstract: My plan is introduce the tower multitype following my recent paper (on arxiv) and my lecture notes available on https://www.maths.tcd.ie/~zaitsev/#research . I will discuss the relationship with other multitypes and their applications to regularity in the d-bar-Neumann problem.


17.10.25   Gian Maria Dall'Ara

The global irregularity phenomenon in the dbar-Neumann problem
Abstract: In this talk, I will discuss some work that I did in the last few years around the mysterious phenomenon of global irregularity in the dbar-Neumann problem, uncovered by M. Christ (building on the work of various others) in the 1990s. I will touch the following topics: 1) how finding a convenient setting for investigating the interaction of geometry and global regularity led us to using methods of o-minimal geometry (this is various joint works with S. Mongodi, B. Lamel, A. Berarducci, M. Mamino and S. Calamai) 2) how failure of compactness and global hypoellipticity emerges in (some) linear PDEs (this is in part joint with A. Martini) 3) what we still do not understand about the d-bar Neumann problem on worm domains (beyond Christ's work)


10.10.25 Nikhil

Bergman kernels in the semiclassical limit II

26.09.25   Nikhil

Bergman kernels in the semiclassical limit I
Abstract: Given a Hermitian holomorphic line bundle on a complex Hermitian manifold, the Bergman projector is the projector from smooth sections of the bundle onto the holomorphic ones. The Bergman kernel is the Schwartz kernel of the projector. For tensor powers of the line bundle one is interested in the asymptotics of the Bergman kernel in the semiclassical limit as the power goes to infinity. This asymptotics can be derived using the sophisticated classical work of Boutet de Monvel-Sjostrand. As well as the analytic localization technique of Bismut-Lebeau and Dai-Liu-Ma-Marinescu. This talk will be a survey of these techniques.