Dr. Fritz Hörmann

Member of the Graduiertenkolleg Cohomological Methods in Geometry


Postdoc
Mathematisches Institut
Albert-Ludwigs-Universität Freiburg

Büro/Office

Anschrift/Mail address:Mathematisches Institut - Raum 421
Albert-Ludwigs-Universität Freiburg
Eckerstraße 1
D-79104 Freiburg
Sprechstunde:Dienstag, 16-18 Uhr
Tel:+49 761 203 5550
eMail: fritz.hoermann@math.uni-freiburg.de

Research interests

Shimura varieties and their compactifications and integral models, arithmetic of quadratic forms, Weil representation, Borcherds' theory, Kudla's conjectures on arithmetic theta functions

Fibered Derivators, (co)homological Descent, Grothendieck's 6-functor formalism, Algebraic stacks

Publications

1 (2005)Komplexe Multiplikation, Diploma thesis, University of Heidelberg (in German)98 pages
2 (2010)The arithmetic volume of Shimura varieties of orthogonal type, Ph.D. thesis, Humboldt-University of Berlin313 pages
3 (2012)On recursive properties of certain p-adic Whittaker functions, Journal of Number Theory 132 (2012) pp. 1438-148244 pages
4 (2014)The arithmetic and geometric volume of Shimura varieties of orthogonal type, CRM Monograph Series, Vol 35, Am. Math. Soc.151 pages
5 (2015)Fibered multiderivators and (co)homological descent, preprint (new version: Oct 20, 15)87 pages
6 (2016)Six Functor Formalisms and Fibered Multiderivators, preprint67 pages
7 (2016)Descent for coherent sheaves along formal/open coverings, preprint19 pages
8 (2016)Generalized automorphic sheaves and the proportionality principle of Hirzebruch-Mumford, preprint30 pages
9 Construction of derivator six-functor-formalisms, in preparation

Summer school "Derivators"

Derivators, Freiburg 18.8-22.8.2014

Topic: Introduction to the formalism of derivators. This is built on work of Grothendieck, Heller and others and is a powerful and elegant approach to homological algebra, and homotopy theory, encompassing triangulated categories and derived functors.

Further information...

Lecture notes:
1Homotopy limits and colimits in nature - A motivation for derivators64 pages
2Fibered derivators, (co)homological descent, and Grothendieck's six functors33 pages

Lehrveranstaltungen

Sommer 2016Algebraische Zahlentheorie
Sommer 2016GRK Seminar on "Codimension 2"

Lehrveranstaltungen vergangener Semester

Fall 2010 (McGill)Math 316 - Complex analysis
Winter 2011 (McGill)Math 571 - Higher Algebra 2
Sommer 2011 (Freiburg)Assistent Vorlesung Diskrete Algebraische Strukturen
Winter 2011/12 (Freiburg)Assistent Vorlesung Algebraische Zahlentheorie
Winter 2011/12 (Freiburg)Proseminar Elementare Zahlentheorie
Winter 2011/12 (Freiburg)Seminar on Mordell's conjecture
Sommer 2012 (Freiburg)Projektseminar Algebraische Zahlentheorie - Analysis auf Adel- und Idelgruppen
Sommer 2012 (Freiburg)Assistent Vorlesung Mathematik II für Informatiker
Sommer 2012 (Freiburg)Organisation SWAS
Winter 2012/13 (Regensburg)Lectures on Shimura varieties
Sommer 2013 (Freiburg)Proseminar Graphentheorie
Sommer 2013 (Freiburg)Assistent Vorlesung Kommutative Algebra
Winter 2013/14 (Freiburg)Seminar Algebraische Geometrie (mit Dr. M. Wendt)
Winter 2013/14 (Freiburg)Assistent Vorlesung Algebra und Zahlentheorie
Sommer 2014 (Freiburg)Vorlesung: Kommutative Algebra und Einführung in die algebraische Geometrie
Winter 2014/15 (Freiburg)Seminar: Endliche Algebraische Gruppen
Winter 2014/15 (Freiburg)Assistent Vorlesung Mathematik I für Ingenieure und Informatiker
Sommer 2015 (Freiburg)Assistent Vorlesung Mathematik II für Informatiker
Winter 2015/16 (Freiburg)Lectures on Shimura varieties

Links

Graduiertenkolleg Cohomological Methods in Geometry

Süd-West-Arithmetik-Seminar (SWAS)

Arbeitsgruppe Zahlentheorie Freiburg

The Québec-Vermont Number Theory Seminar

First Montreal-Toronto Workshop in Number Theory

Second Montreal-Toronto Workshop in Number Theory