A celebrated result by Poincaré states that a compact Riemann surface ofpositive genus has a conformal metric of constant curvature, unique up torescaling. Clearly, the case of genus 0 is not so exciting: there is aunique complex structure and a…
Categoria evento: Geometry Seminar
Counting self-intersecting multi curves – Viveca Erlandsson (Aalto University)
I will describe some joint work in progress with Juan Souto studying the asymptotic growth on the number $n_k^S(L)$ of multicurves with $k$ self-intersections of length at most $L$ on a hyperbolic surface $S$. More concretely, I will show that for…
Decomposition of quantum representations into irreducible factors – Julien Korinman (Université de Grenoble)
I will define two families of representations of the mapping class group of surfaces, namely the Weil and Reshetikhin-Turaev representations. Then I will state some results concernings the (in)finiteness of their image and their decomposition into…
Instanton-Symplectic homology and integral Dehn Surgery – Guillem Cazassus (Institut de Mathématiques de Toulouse)
Motivated by the Atiyah-Floer conjecture, Manolescu and Woodward defined an invariant for closed oriented 3-manifolds called “Instanton-Symplectic homology”. I will explain how they fit into the framework of a “Floer Field Theory” developped by…
Elimination of cusps in dimension 4 and its applications – Stefan Behrens (Alfréd Rényi Institute, Budapest)
In recent years, low dimensional topologists have become interested in the study of “generic” smooth maps to surfaces. The approach is similar to Morse theory, only with two dimensional target. In this talk, I will discuss a specific problem in the…
Plane cuspidal curves and Heegaard Floer homology – Marco Golla (Unversità di Pisa)
In this talk, I will focus on applications of Heegaard Floer homology to the study of genus-g plane curves in CP^2, with one cuspidal singularity: I will discuss bounds on the semigroup counting function of the singularity and show their…
On the Dolbeault cohomological dimension of the moduli space of Riemann surfaces – Gabriele Mondello (Università di Roma)
The moduli space $M_g$ of Riemann surfaces of genus g is (up to a finite étale cover) a complex manifold and so it makes sense to speak of its Dolbeault cohomological dimension (i.e. the highest k such that $H^{0,k}(M_g,E)$ does not vanish for some…