Fred Rohrer


 

The question you raise "how can such a formulation lead to computations" doesn't bother me in the least! Throughout my whole life as a mathematician, the possibility of making explicit, elegant computations has always come out by itself, as a byproduct of a thorough conceptual understanding of what was going on. Thus I never bothered about whether what would come out would be suitable for this or that, but just tried to understand – and it always turned out that understanding was all that mattered.

Alexander Grothendieck (in a letter to Ronnie Brown, 12.04.1983)


Address:
Universität Tübingen
Fachbereich Mathematik
Auf der Morgenstelle 10
72076 Tübingen
Room:
Building C, Room 6A14
Phone:
++49 (0)7071 29 78599
E-Mail:
rohrer@mail.mathematik.uni-tuebingen.de



Research
I study toric varieties from a scheme-theoretical point of view. In some sense this means to study arbitrary base changes of toric varieties, i.e., toric schemes over arbitrary base rings. Hence, and more generally, I am interested in algebraic geometry, (graded) commutative algebra, polyhedral geometry, homological algebra... For a quick overview I suggest this text.
Motivated by the above I also study graded commutative algebra (and graded homological algebra) from the viewpoint of coarsening functors.


CV (Genealogy)
02/2012-04/2013 Postdoktorand im Fachbereich Mathematik, Eberhard Karls Universität Tübingen, Tübingen, Deutschland
09/2010-01/2012 Nhà nghiên cứu sau tiến sĩ ở Viện Toán Học, Viện Khoa học và Công nghệ Việt Nam, Hà Nội, Việt Nam
03/2004-06/2010 Doktorat am Institut für Mathematik, Universität Zürich, Zürich, Schweiz
03/2001-09/2009 Assistent am Institut für Mathematik, Universität Zürich, Zürich, Schweiz
10/1998-02/2004 Diplom am Institut für Mathematik, Universität Zürich, Zürich, Schweiz


Publications
Published articles (MathSciNet, arXiv)
[10] Quasicoherent sheaves on toric schemes. To appear in Expo. Math. PDF
[9] Graded integral closures. To appear in Beiträge Algebra Geom. PDF or PDF
[8] Coarsenings, injectives and Hom functors. Rev. Roumaine Math. Pures Appl. 57 (2012), 275-287. PDF or PDF
[7] Coarsening of graded local cohomology. To appear in Comm. Algebra. PDF
[6] The geometry of toric schemes. J. Pure Appl. Algebra 217 (2013), 700-708. PDF or PDF
[5] Torsion functors with monomial support. Acta Math. Vietnam. 38 (2013), 293-301. PDF or PDF
[4] Completions of fans. J. Geom. 100 (2011), 147-169. PDF or PDF
[3] (with M. Brodmann and S. Kurmann) An avoidance principle with an application to the asymptotic behaviour of graded local cohomology. J. Pure Appl. Algebra 210 (2007), 639-643. PDF or PDF
[2] (with M. Brodmann and R. Sazeedeh) Multiplicities of graded components of local cohomology modules. J. Pure Appl. Algebra 197 (2005), 249-278. PDF or PDF
[1] (with M. Brodmann) Hilbert-Samuel coefficients and postulation numbers of graded components of certain local cohomology modules. Proc. Amer Math. Soc.133 (2005), 987-993. PDF

Articles under review or in preparation
* (with P. H. Quy) Bad behaviour of injective modules. Submitted (2012).
* (with M. Brodmann and S. Fumasoli) First steps in local cohomology. Lecture notes, under consideration for Ramanujan Math. Soc. Lect. Notes Ser. PDF (Preliminary version)

Other writings
[7] On quasicoherent sheaves on toric schemes. Contribution to the proceedings of the 7th Japan-Vietnam Joint Seminar on Commutative Algebra (Quy Nhon, Viet Nam, 2011). PDF
[6] On toric schemes. Proceedings of the 32nd Symposium and the 6th Japan-Vietnam Joint Seminar on Commutative Algebra (Hayama, Japan, 2010). PDF
[5] Around "Around Castelnuovo-Mumford regularity". Appendix to: M. Brodmann, Around Castelnuovo-Mumford regularity. Lecture notes, Universität Zürich (2010). PDF
[4] Toric Schemes. PhD Thesis, Universität Zürich, 2010. PDF Corrigendum (15/02/2013)
[3] (with R. Boldini and M. Brodmann) Kommutative Algebra. Lecture notes, Universität Zürich (2009). PDF
[2] (with M. Brodmann) Zahlentheorie für Studierende des Lehramtes der Sekundarstufe I. Lecture notes, Universität Zürich (2003). PDF
[1] Hilbert-Samuel Koeffizienten graduierter lokaler Kohomologiemoduln. Diploma Thesis, Universität Zürich, 2003. PDF

Talks (since 09/2010)
[11] The yoga of coarsening. Arbeitsgemeinschaft Algebraische Geometrie, Fachbereich Mathematik, Universität Tübingen, Tübingen, Germany, November 2012.
[10] The geometry of toric schemes. Arbeitsgemeinschaft Algebraische Geometrie, Fachbereich Mathematik, Universität Tübingen, Tübingen, Germany, May 2012.
[9] On quasicoherent sheaves on toric schemes. 7th Japan-Vietnam Joint Seminar on Commutative Algebra, Quy Nhơn, Việt Nam, December 2011. Slides Picture
[8] Bad behaviour of injective modules. Seminar of the Department of Algebra, Institute of Mathematics, Hà Nội, Việt Nam, November 2011.
[7] On quasicoherent sheaves on toric schemes. National Conference on Algebra, Geometry and Topology "DAHITO 2011", Thái Nguyên, Việt Nam, November 2011. Slides Picture
[6] On the combinatorics of fans. Mini-Workshop on Commutative Algebra, Combinatorial & Projective Algebraic Geometry, KAIST, Daejeon, South Korea, September/October 2011 (invited).
[5] Linear representations of finite groups (Part II). Working Seminar on Tate's Thesis, Institute of Mathematics, Hà Nội, Việt Nam, March 2011.
[4] Coarsening of graded local cohomology. Seminar on Commutative Algebra, College of Science, Thai Nguyen University, Thái Nguyên, Việt Nam, January 2011 (invited).
[3] On toric schemes. 32nd Symposium and 6th Japan-Vietnam Joint Seminar on Commutative Algebra, Hayama, Japan, December 2010.
[2] Toric schemes. Series of three talks, Seminar of the Department of Algebra, Institute of Mathematics, Hà Nội, Việt Nam, September 2010.
[1] Introduction to toric geometry. Working Seminar on Toric Geometry, Institute of Mathematics, Hà Nội, Việt Nam, September 2010.

Teaching (since 09/2010)
* Schemata. Hauptseminar (4h/Woche), Universität Tübingen, Wintersemester 2012/13.
* Homologische Algebra. Spezialvorlesung (2h/Woche), Universität Tübingen, Sommersemester 2012.
* Homological Algebra. Lectures for master students (2 Lectures), College of Science, Thai Nguyen University, Thái Nguyên, Việt Nam, January 2011.
* Introduction to Homological Algebra. Course for the International Master Program (7 Lectures), Institute of Mathematics, Hà Nội, Việt Nam, December 2010 - January 2011.


Uni Tübingen | Fachbereich Mathematik | Arbeitsbereich Algebra