# 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, November 27th, 2020** in a virtual format, hosted by **Bochum**.

### TALKS

**Rafael Andrist (Beirut):**The Density Property for Calogero--Moser Spaces

Abstract:

A Calogero--Moser space describes the (completed) phase space of a system of finitely many particles in classical physics. Since the past two decades, these spaces are also an object of ongoing study in pure mathematics. In particular, a Calogero--Moser space of $n$ particles is known to be a smooth complex-affine variety, and to be diffeomorphic to the Hilbert scheme of $n$ points in the affine plane. We establish the density property for the Calogero--Moser spaces and describe their group of holomorphic automorphisms.**Nicholas Buchdahl (Adelaide):**Polystability and the Hitchin-Kobayashi correspondence

Abstract:

The classical Hitchin-Kobayashi correspondence states that a holomorphic vector bundle on a compact Kaehler manifold is stable if and only if it admits an irreducible Hermite-Einstein connection. The correspondence can be seen as an infinite-dimensional analogue of key ideas from Mumford's finite-dimensional Geometric Invariant Theory, particularly results of Kempf and Ness. In this talk I shall describe some recent results obtained together with Georg Schumacher that reveal that this analogue between the infinite-dimensional and finite-dimensional pictures is considerably deeper than it appears at first sight.**Eleonora di Nezza (Paris):**Energy & Entropy

Abstract:

One of the approaches to search for Kähler-Einstein metrics is the variational approach, which consists in minimizing a functional over the space of metrics. In this context, the set of probability measures with finite energy and the set of those with finite entropy play a crucial role. A key point is that a measure with finite entropy has finite energy as well. We actually have more regularity: the (optimal) exponent of the energy class is very explicit! The fun part of the story is that to establish such a result we prove inequalities of Moser-Trudinger type. This is a joint work with Vincent Guedj and Chinh Lu.

### PRELIMINARY SCHEDULE

**09:15 - 10:15** Buchdahl

**10:45 - 11:45** di Nezza

**afterwards** Lunch break

**14:15 - 15:15** Andrist

### 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

kevin [dot] fritsch [at] rub [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