Andreas Cap

Professor at the Faculty of Mathematics (key research area Analysis, Geometric Structures and Mathematical Physics) of the University of Vienna.
Speaker of the Vienna School of Mathematics.
DSPL (director of the doctoral study program) for the doctoral program in mathematics.

Office: Oskar-Morgenstern-Platz 1, room 10.132 (10th floor)
Phone: xx-43-1-4277-50619
FAX: xx-43-1-4277-850619
E-Mail: Andreas.Cap@univie.ac.at
Postal Address: Institut für Mathematik, Universität Wien, Oskar-Morgenstern-Platz 1, A-1090 Wien, AUSTRIA
Contact hours: (during the semester) Tue, 11-12. (This should be the default time for my role as DSPL for the doctoral program in mathematics. In urgent cases and for other issues, it is also possible to make an appointment via mail.)
New: During the Corona restrictions, there will be an online contact hour. This is accessible via the moodle page of the DSPL 51, which is open for self-inscriptions here or directly via this guest link.

Aktuelles

Teaching in spring term 2020/21: I had to change my plans on short notice and will be teaching the master course Analysis on manifolds. (The accompanying Proseminar will be taught by my PhD student Michal Wasilewicz.) For the beginning of the semester, the teaching will exclusively be done online. The main source of information for the courses will be their moodle pages, which become available once you have registered for the respective course via u:space.
Skripten und Übungsbeispiele zu meinen Lehrveranstaltungen finden sich auf meiner Skriptenseite. / Lecture notes and Exercises are available here.

Exams: I currently don't have any plans for written exams, so this concerns oral exams only. In principle, is it always possible to sit exams on courses I have taught earlier. In the current situation, only online exams are possible. This may change during the semester, but based on the rules of the University of Vienna and the good experiences from the last year, I would anyway view online exams as the preferred option. The most fundamental requirement for an online exam is that both audio and video connection must be available throughout the exam. If you are using either skype or zoom, we can use this platform for an exam, otherwise I can set up a session on BigBlueButton, which does not require registration from your side. Appointments for exams can be made on relatively short notice, usually it will be no problem to find an appropriate time within a few days after you contact me. Further information on oral online exams can be found here.

Prüfungen: Ich habe derzeit keine schriftlichen Prüungen geplant, es gibt aber grundsätzlich die Möglichkeit, mündliche Prüfungen zu meinen Vorlesungen aus früheren Semestern abzulegen. Nach den derzeitigen Regelungen sind nur online-Prüfungen gestattet. Das kann sich im Laufe des Semesters ändern, aber auf Basis der Empfehlungen der Universität Wien als auch der guten Erfahrungen aus dem letzten Jahr, sind online Prüfungen jedenfalls zu bevorzugen. Grundvoraussetzung für eine online-Prüfung ist, dass während der gesamten Prüfungszeit sowohl Audio- als auch Videoübertragung möglich sind. Wenn Sie an die Verwendung von Skype oder Zoom gewöhnt sind, können wir eine dieser Plattformen für eine Prüfung verwenden. Ansonsten kann ich eine BigBlueButton-Sitzung für die Prüfung einrichten, für die Sie keine Registrierung oder Ähnliches benötigen. Die Terminvereinbarung für Prüfungen kann normalerweise eher kurzfristig erfolgen. Weitere Inofrmationen zu Online-Prüfungen finden Sie hier, ein Blog-Eintrag der Uni Wien mit Tips zur Vorbereitung auf so eine Prüfung ist hier verfügbar.

Research

List of publications (mostly with links to full texts of articles).
Selected recent lectures (partly with links to proceedings articles or slides).

current activities

Jointly with Xavier Bekaert (Tours), Stefan Fredenhagen (Vienna), Maxim Grigoriev (Moscow), and Alexei Kotov (Hradec Kralove), I am orgainzing a thematic program "Geometry for Higher Spin Gravity: Conformal structures, PDEs, and Q-manifolds" at the ESI in Vienna from August 23 to September 17, 2021.
Jointly with Charles Frances (Universit&eactue; de Strasbourg), Karin Melnick (University of Maryland), Thomas Mettler (Goethe-Universität Frankfurt), and Katharina Neusser (Masaryk University) I am organizing a workshop Geometric Structures, Compactifications, and Group Actions at the Goethe University in Frankfurt from July 19-23, 2021.
Since October 2020, I am running the research project Applications of parabolic geometries and BGG Sequences of the Austrian Science fund (FWF).
Since July 2020, I am speaker of the Vienna School of Mathematics, a joint doctoral school with the TU Wien.
Since summer 2014, I am serving as an editor for the European Journal of Mathematics (EJM). This new journal is intended to be a followup for the "Central European Journal of Mathematics" (CEJM).
Since fall 2009, I am serving as an editor for the Journal Differential Geometry and Its Applications
Since November 2008, I am serving as an editor for the Journal Monatshefte für Mathematik.

past activities

From August 2014 to May 2018, I was running the research project "New directions in the theory of Bernstein-Gelfand-Gelfand sequences" (P27072-N25) of the Austrian Science fund (FWF).
Jointly with M. Eastwood, R. Gover, P. Hekmati, and A. Waldron, I have organized the conference "Conformal and symplectic geometry" at the University of Auckland in February 2018.
Jointly with Ilka Agricola (Marburg), I have organized the section "Differential Geometry and Topology" of the 19th ÖMG congress and Annual Meeting of the DMV, Salzburg, September 11-15, 2017.
Jointly with M. Eastwood and J. Slovak, I have organized the program session "Geometric Structures and Representation Theory" in the conference "Differential Geometry and its Applications", Brno (Czech Republic), July 11-15, 2016.
Jointly with J. Slovak, I was organizing a program session "Special Structures and Representation Theory" in the Conference "Differential Geometry and its Applications", August 19-23, 2013, Brno (Czech republic).
From September 3-14, 2012, I have organized together with A. Carey, A.R. Gover, C.R. Graham and J. Slovak a workshop under the title "The Interaction of Geometry and Representation Theory. Exploring new frontiers" at the ESI.
From July 11-22, 2011, I have organized together with C. Frances and K. Melnik a workshop Cartan Connections, Geometry of Homogeneous Spaces, and Dynamics at the ESI.
In the first half of 2004, I have organized together with Tom Branson and Jan Slovak a research program Geometric and analytic problems related to Cartan connections at the ESI in Vienna.
From January 2011 to March 2014, I was running the research project "Cartan geometries and differential equations" funded by the Austrian Science Fund (FWF).
From March 2007 to August 2010, I have been running the research project "Parabolic geometries II" funded by the Austrian Science Fund (FWF).
From October 2002 to August 2006, I have been running the research project "Parabolic Geometries" (P15747-N05) funded by the Austrian Science Fund (FWF).

partly outdated pages to be updated

Description of my current and former research interests .

Teaching

Kolloquiumstermine: Termine für mündliche Prüfungen über meine Vorlesungen der letzten Jahre können jederzeit kurzfristig vereinbart werden.
Courses: WS 18/19, SS 18, WS 17/18, WS 16/17, SS 16, WS 15/16, SS 15, WS 14/15, WS 13/14, SS 13, WS 12/13, SS 12, WS 11/12, SS 11, WS 10/11, SS 10, WS 09/10, SS 09, WS 08/09, SS 08, WS 07/08, SS 07, WS 06/07, SS 06, SS 05, WS 04/05, SS 04, WS 03/04, SS 03, WS 01/02, WS 00/01, SS 00
Lecture notes.
List of courses in the area "Geometry and Topology" of the master program (also for PhD level), including plans for the next year(s).
A list of students and Post docs that I have supervised or helped to supervise