# Joint Seminar

# Joint Seminar on Complex Algebraic Geometry and Complex Analysis

(Bochum - Essen - Köln - Wuppertal)

Photo by Max Greve and Timo Bobert

# The Seminar

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)

# Next Meeting

### DATE AND PLACE

The next meeting will take place on **Friday, January 29th, 2021** in a virtual format, hosted by **Essen**.

### TALKS

**Robert Berman (Chalmers):**An invitation to Kähler-Einstein metrics and random point processes

Abstract:

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

Abstract:

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

Abstract:

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.

### SCHEDULE

**10:00 - 11:00** Berman

**11:15 - 12:15** Mondello

**afterwards** Lunch break

**14:00 - 15:00** Diverio

### VENUE

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.

# Organisers

Valdemar Tsanov

Ruhr-Universität Bochum

Valdemar [dot] Tsanov [at] ruhr-uni-bochum [dot] de

Daniel Greb

Universität Duisburg-Essen

daniel [dot] greb [at] uni-due [dot] de

George Marinescu

Universität zu Köln

gmarines [at] math [dot] uni-koeln [dot] de

Jean Ruppenthal

Bergische Universität Wuppertal

jean [dot] ruppenthal [at] math [dot] uni-wuppertal [dot]de

# Past Meetings

**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