Maths seminars at HÍ
Mathematical seminars and Mathematical Colloquia at the University of Iceland 🇮🇸.
Announcements are sent on the mailing-list math-seminars 📬.
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The Mathematical Colloquium is usually on Thursday, 13:20 - 14:50.
To suggest a speaker, get in touch.
Forthcoming
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Past
20-5-2025, 14:00 (note the unusual day and time!) in room 157, VR-IIFinnur Lárusson
Reconciling dichotomies in holomorphic dynamics.
I will describe recent joint work with Leandro Arosio (University of Rome, Tor Vergata) in holomorphic dynamics. We study the iteration of endomorphisms of complex manifolds of a fairly general kind, as well as the iteration of automorphisms for a class that is somewhat smaller, but still includes almost all linear algebraic groups. The main goal of our work is to reconcile two fundamental dynamical dichotomies in these settings, “attracted vs. recurrent” and “calm vs. wild”.
15-5-2025, 13:20 in room 157, VR-II
Joseph Stanley Smith (RU)
Interactive theorem provers and mathematics.
Interactive theorem provers are gaining popularity and becoming increasingly powerful. In this talk, I will introduce what interactive theorem provers are and explain how they are being used in mathematics. I will also discuss the future of interactive theorem provers and the potential role artificial intelligence may play in their story.
10-4-2025, 13:20 in room 157, VR-II
Daniel Amankwah - HÍ
Scaling Limits of Random Series-Parallel Maps.
A finite graph embedded in the plane is called a series-parallel map if it can be constructed from a tree by iteratively subdividing and doubling edges. In this talk, we investigate the scaling limits of weighted random two-connected series-parallel maps with $n$ edges. Under suitable integrability conditions on the weights, we show that when distances are rescaled by a factor of $n^{-1/2}$, these maps converge in the Gromov–Hausdorff sense to a constant multiple of Aldous’ continuum random tree (CRT). The proof relies on a bijection between certain families of trees and series-parallel maps, allowing us to analyze geodesics using a Markov chain argument introduced by Curien, Haas, and Kortchemski (2015).
3-4-2025, 13:20 in room 157, VR-II
Eggert Briem - HÍ
Homomorphisms and isomorphisms of real commutative Banach algebras into C(X).
We give conditions, either on the dual space of an algebra A or on the norm of the algebra, which garantee the existence of homomorphism or isomorphism into C(X).
20-3-2025, 13:20 in room 158, VR-II
Pierre-Louis Curien
General coherence theorems on CW-complexes and polyhedral complexes.
We formulate and prove a coherence theorem on regular CW-complexes: 1-cells determine so-called cellular paths, and the theorem states that, if each path component of the complex is simply connected, any two such parallel paths (i.e. with the same end 0-cells) are provably equivalent by repeated transformations along 2-cell (this is in fact an « if and only if »). in other words, continuous homotopy agrees with a discrete and cellular version of homotopy.
A number of coherence theorems of the literature of category theory follow as a corollary, via a geometrical reading of the relevant data. For example, for monoidal categories (introduced by Mac Lane), the associated polytopes are called associahedra.
But most of those theorems were originally proved in a quite different way, using techniques now well-established in computer science under the name of rewriting systems.
We give a second strictly less general proof of geometrical coherence, applying to polyhedral complexes satisfying a certain condition (which is in particular satisfied by all polytopes), that relies on an orientation given by some generic vector, and that retains most of the features of Mac Lane’s original proof.
Finally, if we further restrict our attention to a class of polytopes called nestohedra, that have a nice combinatorial description, and to a certain subclass of those, we show that we get even closer to Mac Lane’s original proof. (Joint work with Guillaume Laplante-Anfossi).