## 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

- SFB/TR 45 "Periods, moduli spaces and arithmetic of algebraic varieties"
- SFB/TR 191 "Symplectic structures in geometry, algebra and dynamics"

## Next Meeting

### DATE AND PLACE

The next meeting will take place on **Friday, July 6th, 2018** in **Cologne**.

### TALKS

**Turgay Bayraktar (Istanbul):**Random Sparse Polynomials

Abstract:

It is well-known that Newton polytope of a Laurent polynomial has a crucial influence on its value distribution and in particular on its zero set. A classical result due to Bernstein-Kouchnirenko asserts that for systems of Laurent polynomials in general position the number of simultaneous zeros in the torus (\Bbb{C}^*)^m depends only on their Newton polytopes. In this talk, I will present a quantitative localization of Bernstein-Kouchnirenko Theorem. A basic tool is P-pluripotential theory which is a generalization of classical Lelong's theory in the complex Euclidean space. If time permits, I will also mention some applications regarding the asymptotic distribution of amoebas associated with Laurent polynomials.**Jarek Buczynski (Warsaw):**Algebraic torus actions on contact Fano manifolds

Abstract:

A complex manifold is a contact manifold if there is a distribution in the tangent bundle which is as non-integrable as possible. I will report on recent progress in classification of projective contact manifolds focusing on the case of (complex) dimension 7 and 9. Our work implies the classification of quaternion-Kaehler manifolds of (real) dimensions 12 and 16, a famous problem from Riemannian geometry. The tools we use include representation theory and actions of (complex) reductive groups on manifolds, symplectic geometry, characteristic classes, and equivariant localisation theorems. The talk is based mainly on "Algebraic torus actions on contact manifolds" by Jarosław A. Wiśniewski and myself, with an appendix by Andrzej Weber, which is available as arXiv:1802.05002.

**Andrew Dancer (Oxford):**Quivers, nonreductive quotients and symplectic duality

Abstract:

Symplectic implosion is an abelianisation construction for group actions on symplectic spaces. There is also an analogue in hyperkahler geometry, and both the symplectic and hyperkahler implosions can be viewed as quotients by nonreductive groups. We discuss current work (with Hanany and Kirwan) on identifying symplectic duals of hyperkahler implosions.

### SCHEDULE

**10:30 - 11:30 ** Dancer

**11:45 - 12:45 ** Bayraktar

**12:45 - 14:30 ** Lunch break

**14:30 - 15:30 ** Buczynski

### VENUE

Universität zu Köln

Mathematisches Institut

All talks will take place in

**Seminar Room 2 @ Mathematical Institute**.

How to find the seminar room: see the map on the following website.

## 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