# 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 **Thursday, May 14th, 2020** in a virtual format, hosted by **Wuppertal**.

### TALKS

**Lynn Heller (Hannover):**Higher solutions of Hitchin’s self duality equations

Abstract:

Solutions of Hitchin’s self-duality equations corresponds to special real sections of the Deligne-Hitchin moduli space – twistor lines. A question posed by Simpson in 1997 asks whether all real sections give rise to global solutions of the self-duality equations. An affirmative answer would allow for complex analytic procedure to obtain all solutions of the self-duality equations. The purpose of this paper is to construct counter examples given by certain (branched) Willmore surfaces in 3-space (with monodromy) via the generalised Whitham flow. Though these sections do not give rise to global solutions of the self-duality equations on the whole Riemann surface M, they induce solutions on an open and dense subset of it. This suggest a deeper connection between Willmore surfaces, i.e., rank 4 harmonic maps theory, with the rank 2 self-duality theory.**Simone Marchesi (Barcelona):**On hypertetrahedral arrangements

Abstract:

In this talk we will introduce and study hypertetrahedral arrangements, which consist in a particular configuration of hyperplane arrangements, focusing on their associated module of derivations and the degree of its generators. In the second part we will restrict our attention to the particular case of lines in the projective plane, which we call triangular arrangements, studying the connections between their combinatorics and the freeness of the derivations module, a question related to Terao’s conjecture.**Jan Swoboda (Heidelberg):**Geometry and analysis of Higgs bundle moduli spaces

Abstract:

Moduli spaces of stable Higgs bundles are present in several different mathematical contexts: on the one hand, as generalizations of holomorphic vector bundles these are complex geometric objects. On the other hand, there are close relations to both the fields of geometric analysis and differential topology where -- due to foundational results of Hitchin, Simpson, Donaldson, Corlette and others -- they appear as solution spaces of nonlinear elliptic PDEs as well as representations of surface groups. In my talk I shall highlight some of the resulting rich geometric structures. I will finally present a number of recent results concerning the asymptotic geometry of these moduli spaces and take a glimpse of some currently open problems.

### NEW SCHEDULE

**10:30 - 11:30 ** Swoboda

**11:45 - 12:45** Marchesi

**12:45 - 13:45 ** Lunch break

**13:45 - 14:45 ** Heller

### VENUE

Talks will take place using ZOOM.

The ZOOM meeting can be accessed (with a password) here: https://uni-wuppertal.zoom.us/j/94837150409

If you don't know the password already, please write an eMail to one of the organisers. In case you got an eMail from the organisers in the last couple of days, the link contained in that mail includes the password.

# Organisers

Kevin Fritsch

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