Prof. Dr. Thomas Krämer

My research lies in algebraic and arithmetic geometry. Among other things, I am interested in abelian varieties and their moduli, and more generally in irregular varieties. Ideas from Hodge theory, perverse sheaves and representation theory lead to rich interactions in different directions such as the Schottky problem for compact Riemann surfaces, the topology of complex varieties, and the Shafarevich conjecture for varieties over number fields.

• The Tannaka group E6 only arises from cubic threefolds
  
  With Christian Lehn and Marco Maculan. Preprint (2024).
• Arithmetic finiteness of very irregular varieties
  
  With Marco Maculan. Preprint (2023).
• The monodromy of families of subvarieties on abelian varieties
  
  With A. Javanpeykar, C. Lehn and M. Maculan. Preprint (2023).
• Semicontinuity of Gauss maps and the Schottky problem
  
  With Giulio Codogni. Mathematische Annalen 382 (2022) 607-630.
• Characteristic cycles and the microlocal geometry of the Gauss map II
  
  Journal für die reine und angewandte Mathematik 774 (2021) 53-92.
  
• Characteristic cycles and the microlocal geometry of the Gauss map I
  
  Annales Scientifiques de l'École Normale Supérieure 55 (2022) 1475-1527.
  
• Summands of theta divisors on Jacobians
  
  Compositio Mathematica 156 (2020) 1457-1475.
  
• Characteristic classes and Hilbert-Poincaré series for perverse sheaves
  
  Selecta Mathematica 22 (2016) 1337-1356.
  
• Cubic threefolds, Fano surfaces and the monodromy of the Gauss map
  
  Manuscripta Mathematica 149 (2016) 303-314.
  
• On the Tannaka group attached to the theta divisor of a generic ppav
  With R. Weissauer. Mathematische Zeitschrift 281 (2015) 723-745.
  
• On a family of surfaces of general type attached to abelian fourfolds
  
  International Mathematics Research Notices IMRN 24 (2015) 13062-13105.
  
• Semisimple super Tannakian categories with a small tensor generator
  With R. Weissauer. Pacific Journal of Mathematics 276 (2015) 229-248.
  
• Vanishing theorems for constructible sheaves on abelian varieties
  With R. Weissauer. Journal of Algebraic Geometry 24 (2015) 531-568.
  
• Perverse sheaves on semiabelian varieties
  
  Rendiconti del Semin. Mat. della Università di Padova 132 (2014) 83-102.
  

• In the summer term 2024, I am teaching a class for computer scientists:
• Lineare Algebra und ihre Bezüge zur Informatik. Details can be found on [Moodle].

• Class Field Theory (Winter 23/24)
  [Notes] [Problems] [Moodle]
• Intersection Theory (Summer 2023)
  [Notes] [Problems] [Moodle]
• Algebraic Geometry II (Winter 22/23)
  [Notes] [Problems] [Moodle]
• Algebraic Geometry I (Summer 2022)
  [Notes] [Problems] [Moodle]
• Algebra und Funktionentheorie (Winter 2021/22)
  [Skript] [Übungen][Moodle-Kurs]
• Lineare Algebra und Analytische Geometrie I* und II* (2020/21)
  [Notes for part I and II] [Problems I] [Problems II]
• Elliptische Kurven (Winter 19/20)
  [Notes for part of the lecture] [Problems]
• Algebraische D-Moduln (Sommer 2019)
  [Notes] [Problems]
• Algebra II (Winter 18/19)
  [Notes] [Problems]
• Riemannsche Flächen (Sommer 2018)
  [Notes on the finiteness theorem] [Problems]
• Darstellungstheorie (Winter 17/18)
  [Notes] [Problems]
• Algebraische Zahlentheorie (Sommer 2017)
  [Notes] [Problems]

• Humboldt Algebraic Geometry Seminar
• Humboldt Arithmetic Geometry Seminar