Joint Seminar on Complex Algebraic Geometry and Complex Analysis (Bochum - Essen - Köln - Wuppertal)
Photo by Max Greve and Timo Bobert
The "Joint Seminar on Complex Algebraic Geometry and Complex Analysis" is a research seminar, organised by the algebraic and complex geometry research groups in Bochum, Essen, Cologne, and Wuppertal. The seminar meets roughly twice per semester for a full day in Bochum, Essen, Cologne, or Wuppertal. There are three talks per meeting, both by invited guests and by speakers from the organising universities. We aim to leave ample room for discussions.
The talks are open for everyone. Contact one of the organisers if you are interested in attending the meeting. We have some funds that might help to support travel for some junior participants.
Meetings of the seminar are partially supported by the DFG via
- GRK 2553 "Symmetries and Classifying Spaces - analytic, arithmetic, and derived" (Essen)
- SFB/TR 191 "Symplectic structures in geometry, algebra and dynamics" (Bochum-Cologne)
DATE AND PLACE
The next meeting will take place on Friday, January 29th, 2021 in a virtual format, hosted by Essen.
- Robert Berman (Chalmers): An invitation to Kähler-Einstein metrics and random point processes
While the existence of a unique Kähler-Einstein metrics on a canonically polarized manifold X was established already in the seventies there are very few explicit formulas available (even in the case of complex curves!). In this talk I will give a non-technical introduction to a probabilistic approach to Kähler-Einstein metrics, which, in particular, yields canonical approximations of the Kähler-Einstein metric on X. The approximating metrics in question are expressed as explicit period integrals and the conjectural extension to the case of a Fano variety leads to some intriguing connections to zeta functions.
- Simone Diverio (Sapienza): Pointwise universal Gysin formulae and positivity of some characteristic forms
In the last few years there has been a renewed interest around an old conjecture by Griffiths characterizing which should be the positive characteristic forms for any given Griffiths positive holomorphic Hermitian vector bundle. According to this conjecture, they should be precisely the characteristic forms belonging to the positive cone spanned by the Schur forms. After recalling the various notions of positivity for holomorphic Hermitian vector bundles, and how they are (or should be) related, we shall explain a recent result obtained in collaboration with my PhD student F. Fagioli, which gives a partial confirmation of the above conjecture. Such a result is obtained as a consequence of a pointwise, differential-geometric Gysin formula for the push-forward of the curvature of the tautological line bundles over flag bundles.
- Ilaria Mondello (Université Paris-Est): Some properties of Einstein metrics and their conformal classes on stratified spaces
The Hilbert-Einstein functional on a Riemannian manifold of dimension n is defined as the integral of the scalar curvature, normalized by the volume of the manifold to the power 2/n. The Yamabe problem consists in studying critical points of such functional in a conformal class of a given metric, and a conformal minimizing metric is called Yamabe metric. It is well known that on a compact manifold, an Einstein metric g is a Yamabe metric. Moreover, Obata's theorem shows that either no other metric in the conformal class of g is minimizing, or the manifold is isometric to the sphere. In this talk, we will consider Einstein metrics in the singular setting of stratified spaces, which generalize conical singularities. After giving an introduction to these singular spaces, we explain how, depending on the angle along the codimension 2 singularities, the situation is more involved. In particular, if the angle is larger than 2\pi, we give examples in which an Einstein metric is not a Yamabe metric (and no Yamabe metrics exists in the conformal class). When the angle is less than 2\pi, we illustrate an analog of Obata's theorem. Some of the results presented in this talk are joint work with K. Akutagawa.
10:00 - 11:00 Berman
11:15 - 12:15 Mondello
afterwards Lunch break
14:00 - 15:00 Diverio
Talks will take place using ZOOM. Access data will be distributed via the usual channels. In case you don't have the information and want to participate, please write an eMail to one of the organisers in order to gain access.
Valdemar [dot] Tsanov [at] ruhr-uni-bochum [dot] de
daniel [dot] greb [at] uni-due [dot] de
Universität zu Köln
gmarines [at] math [dot] uni-koeln [dot] de
Bergische Universität Wuppertal
jean [dot] ruppenthal [at] math [dot] uni-wuppertal [dot]de
26.4.2013, Bochum: Tim Kirschner, Christian Miebach, Henrik Seppänen
28.6.2013, Wuppertal: Rafael Andrist, Immanuel Stampfli, Matei Toma
22.11.2013, Bochum: Sébastien Boucksom, Egmont Porten, Sönke Rollenske
24.1.2014, Wuppertal: Clemens Jörder, Helge Ruddat, Jörg Winkelmann
16.5.2014, Bochum: Alberto Abbondandolo, Judith Brinkschulte, Julius Ross
20.6.2014, Wuppertal: Julie Déserti, Slawomir Dinew, Slawomir Rams
24.10.2014, Bochum: Henri Guenancia, Shulim Kaliman, Adriano Tomassini
15.12.2014, Wuppertal: Richard Lärkäng, Christian Miebach, Marco Spinaci
7.5.2015, Essen: Brent Doran, Erwan Rousseau, Emanuel Scheidegger
15.6.2015, Bochum: Roya Beheshti, Daniel Greb, Hossein Raufi
27.11.2015, Wuppertal: Francesco Bei, Kai Cieliebak, Tyson Ritter
1.2.2016, Essen: Ursula Ludwig, George Marinescu, Wenhao Ou
25.4.2016, Wuppertal: Gian Maria Dall’Ara, Christian Lehn, Luca Tasin
26.6.2016, Cologne: Chin-Yu Hsiao, Stefan Nemirovski, Nikhil Savale
25.11.2016, Bochum: Ana-Maria Brecan, Antonio di Scala, Dan Popovici
27.1.2017, Essen: Tim Kirschner, Viêt Anh Nguyên, Stefan Schreieder
21.4.2017, Wuppertal: Vicente Cortés, Philipp Naumann, Markus Reineke
7.7.2017, Cologne: Roger Bielawski, Dan Coman, Martin Schwald
3.11.2017, Bochum: Junyan Cao, Sönke Rollenske, Robert Szöke
1.2.2018, Essen: Gilberto Bini, Ruadhaí Dervan, Hendrik Herrmann
27.4.2018, Wuppertal: Hugues Auvray, Bernd Stratmann, Michael Lennox Wong
6.7.2018, Cologne: Turgay Bayraktar, Jarek Buczynski, Andrew Dancer
23.11.2018, Bochum: Ben Anthes, Kevin Fritsch, Ariyan Javanpeykar
18.1.2019, Essen: André Belotto, Andreas Höring, Valdemar Tsanov
12.4.2019, Wuppertal: Ya Deng, Christian Miebach, Duc Viet Vu
5.7.2019, Cologne: Tien-Cuong Dinh, Xiaonan Ma, Nessim Sibony
21.11.2019, Bochum: Patrick Graf, Ulrike Rieß, Jonas Stelzig
16.1.2020, Essen: Anda Degeratu, Takeo Ohsawa, Mihai Paun
14.5.2020, Wuppertal (via ZOOM): Lynn Heller, Simone Marchesi, Jan Swoboda
16.7.2020, Cologne (via ZOOM): Shin-ichi Matsumura, Sönke Rollenske, Lars Martin Sektnan
17.11.2020, Bochum (via ZOOM): Rafael Andrist, Nicholas Buchdahl, Eleonora di Nezza