|
|
|
|
MGT meeting - fourth edition The first MGT - Milan Grenoble Turin meeting in geometry and topology took place in Grenoble in january 2023. The whole project started when a bunch of people from these three cities realized that they were working in closely related field, but there were relatively few interactions and events organized between our departments (probably because of the mountains!). So, we decided to organize these meetings to bridge the gap. For the fourth edition, we are very happy to welcome you in Grenoble again! Where will the conference take place? The conference will be held at the ground floor of the "IMAG" building (Thursday morning in room "Séminaire 1", after that in the auditorium), on the campus of the University of Grenoble (here is a map: https://batiment.imag.fr/files/plan_campus_bat-IMAG-Intranet.pdf) It is ~5 min walk from the tramway B stops "Gabriel Fauré" or "Bibliothèques Universitaires" If you need to find it at some point, the math department ("Institut Fourier") is located next to the tramway B stop Bibliothèques Universitaires" (building nb 100 in the above map) Schedule THURSDAY 18/09 9:00-10:00 Laurent Bessières (Lecture 1) 10:00-10:30 Coffee Break 10:30-11:30 Asia Mainenti 11:30-12:30 Marco Pozzetta 12:30-14:00 Lunch Break 14:00-15:00 Ana Rechtman 15:00-16:00 Luciano Mari 16:00-16:30 Coffee Break 16:30-17:30 Zehao Sha 19:30 Diner at Brasserie des Antiquaires (https://www.tripadvisor.fr/Restaurant_Review-g187264-d23511508-Reviews-Brasserie_Des_Antiquaires-Grenoble_Isere_Auvergne_Rhone_Alpes.html)
FRIDAY 19/09 08:30-9:30 Pierre-Damien Thizy 9:30-10:00 Coffee Break 10:00-11:00 Damaris Meier 11:00-12:00 Laurent Bessières (Lecture 2) 12:00-13:30 Lunch Break 13:30-14:30 Stefano Pigola 14:30-15:30 Francesco Pediconi Speakers Laurent BESSIERES (Bordeaux) - minicourse Asia MAINENTI (ICMS & IMI-BAS) Luciano MARI (Università Milano Statale) Damaris MEIER (Friburg) Francesco PEDICONI (Politecnico Torino) Stefano PIGOLA (Università Bicocca) Marco POZZETTA (Politecnico Milano) Ana RECHTMAN (Grenoble) Zehao SHA (Grenoble) Pierre-Damien THIZY (Lyon) How to get there? And other practical information The train line from Milan to France is back! The best option by train for coming back to Milan/Turin after the conference is to take the train from the station "Gières Université" (not far from the University, it can be reached easily by tramway in ~10 min) to Chambéry Challes-Les-Eaux, and change train to Milan. A ticket from Gières to Chambéry is valid no matter when you travel during the day (trains run every ~1/2h in peak hour), while you will have to book in advance your trip from Chambéry to Milan, the last one on Friday afternoon leaving Chambéry at 17:44. Train schedules can be found here: https://www.sncf-connect.com/en-en/ Titles and abstracts Ana Rechtman Title: Dynamics of Reeb flows in dimension 3 Luciano Mari Title: When is $C^\infty_c$ dense in $W^{k,p}$ on a complete manifold? Abstract: If $M$ is a complete manifold, it is known that $C^\infty_c(M)$ is dense in $W^\ Damaris Meier Title: Uniformization of metric surfaces Abstract: The uniformization problem for metric surfaces asks under which condition a metric space $X$, homeomorphic to a model surface $M$, admits a parametrization $u\colon M\to X$ with good geometric and analytic properties. In this talk, we focus on the case where $X$ has locally finite Hausdorff 2-measure. After revisiting the breakthrough results of Bonk-Kleiner and Rajala, we will demonstrate that no additional assumptions are necessary for the existence of a "good" parametrization. If $X$ is locally geodesic, such parametrizations can be constructed by exploiting existence and regularity properties of energy-minimizing Sobolev mappings. Marco Pozetta Title: On the isoperimetry of noncompact manifolds with Ricci bounded below
Abstract: The isoperimetric problem on a Riemannian manifold aims at minimizing the measure of the boundary, called perimeter, among subsets having a given volume. The isoperimetric profile is the one-variable function that associates to any volume the infimum of the problem.
In this talk we will present the sharp concavity properties enjoyed by the isoperimetric profile on manifolds having Ricci curvature bounded from below.
The theory of metric measure spaces with lower Ricci bounds will naturally come into play in order to prove the result on noncompact manifolds. A further crucial tool is represented by a generalized notion of constant mean curvature for boundaries of isoperimetric sets in nonsmooth spaces with lower Ricci bounds.
Francesco Pediconi Title: On the long-time behavior of ancient homogenous Ricci flows
Abstract: Ricci flow solutions that exist for all negative times have special significance and are known as ancient solutions. In this talk, we describe the geometry of collapsed ancient solutions to the homogeneous Ricci flow on compact manifolds, and we show that they subconverge, in the Gromov-Hausdorff topology, to an Einstein metric on the base of a torus bundle. This is based on joint work with S. Sbiti and A. Krishnan.
Asia Mainenti Title: p-Kähler structures and Lie groups
Abstract: A p-Kähler structure on a complex manifold is a closed, transverse (p,p)-form. For the extremal values of p, we get the well known Kähler and balanced manifolds, however, for each other possible p, such structures have no metric meaning. The aim of the talk, after discussing similarities and differences between p-Kähler manifolds and Kähler and balanced ones, is to present some results on the existence of p-Kähler structures, with a focus on Lie groups and their compact quotients. Based on a work in progress with A. Fino and G. Grantcharov. Laurent Bessières Title : $\mu$-bubbles and PSC manifolds Abstract : The $\mu$-bubbles were introduced by Gromov to generalize the notion of minimal hypersurfaces and have been an important tool in the study of PSC manifolds, a.k.a manifolds admitting a complete Riemannian metric of positive scalar curvature. In these lectures, I will present the basic properties of these $\mu$-bubbles and some applications by Chodosh, Li and Liokumovich to the study of closed PSC manifolds in dimension 4 and 5. Zehao Sha Title: Rigidity of complete Kähler--Einstein metrics under cscK perturbations
Abstract: I will discuss when a constant scalar curvature Kähler (cscK) deformation of a complete Kähler–Einstein (KE) metric must remain KE, which is obvious on compact manifolds but remains less understood on complete non-compact manifolds. The main result gives a natural sufficient condition ensuring KE-rigidity along cscK deformations. As a model case, I will explain the Bergman metric and the metric constructed by defining functions on bounded strictly pseudoconvex domains.
Pierre-Damien Thizy TBA Stefano Pigola Title: Volume and parabolicity for the drifted Laplacian
Abstract: Shrinking Ricci solitons and properly immersed self-shrinkers of the mean curvature flow are weighted manifolds with finite weighted volumes. This, in particular, implies that they are parabolic manifolds with respect to their natural weighted Laplacians. In 2011, X. Cheng and D. Zhou detected a set of differential inequalities on the potential function under which a weighted manifold has finite weighted volume, thus giving a unified function-theoretic proof of the volume properties alluded to above. In this talk I shall discuss Cheng-Zhu type result from a different perspective that is suitable to be extended to general drifted Laplacians. Within this broader context, we are naturally led to speculate about parabolicity and to what extent it is related to volumes. It is a work in progress joint with Leandro Pessoa and Alberto G. Setti.
|
