Dr. Fritz Hörmann

Member of the Graduiertenkolleg Cohomological Methods in Geometry


Mathematisches Institut
Albert-Ludwigs-Universität Freiburg

Büro/Office

Anschrift/Mail address:Mathematisches Institut - Raum 433
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 (Multi-)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 (2017)Derivator six-functor-formalisms, Definition and Construction I, preprint55 pages
10 (2017)Derivator six-functor-formalisms, habilitation thesis (consist mainly of publications 5, 6 and 9 with an extended introduction)231 pages
11Derivator six-functor-formalisms, Construction II, in preparation

Events

Summer school "Degeneration of Calabi-Yau varieties and arithmetic"
with Ch. Doran, M. Kerr, R. Laza, J. Walcher, and D. Zagier
Freiburg, October 9-13, 2017

Further information...

Past events:
Summer school Derivators, Freiburg 18.8-22.8.2014
Workshop on "Homotopical approaches to categories and geometry", Freiburg June 2-3, 2016
Workshop on Derivators, Prague, Czech Republic, December 12-16, 2016


Lehrveranstaltungen

Sommer 2017Seminar zur Algebra

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
Sommer 2016 (Freiburg)Algebraische Zahlentheorie
Sommer 2016 (Freiburg)GRK Seminar on "Codimension 2"
Winter 2016/17 (Freiburg)Seminar Klassenkörpertheorie

Scripts and Documents

The following are some writings not intended for publication. They are not always carefully proofread and sometimes preliminary.
2008Compactifications of moduli spaces and mixed Hodge structures - with applications to automorphic forms
Notes
2010The arithmetic volumes of Shimura varieties of orthogonal type
Beamer slides
2011Toroidal compactifications of Hilbert modular varieties
Beamer slides
2011Divisorial rings and Cox rings
Notes
2014Homotopy limits and colimits in nature - A motivation for derivators
Notes for the summer school on derivators
64 pages
2014Kommutative Algebra und Einführung in die algebraische Geometrie
Vorlesungsskript (in German)
2015The Weil representation and Eisenstein series
Notes
2016The Tate and Weil conjetures for rational K3 surfaces
Notes
2016Lectures on Shimura varieties
Lecture notes

Links

Two body problem

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