Office: S2|15-203
Phone: +49-6151-16-2860
Fax: +49-6151-16-3317
safarik [at] mathematik.tu-darmstadt.de

Research

• Publications

  • A functional interpretation for nonstandard arithmetic (with Benno van den Berg and Eyvind Briseid), submitted in September 2011
  • A Quantitative Nonlinear Strong Ergodic Theorem for Hilbert Spaces, submitted in March 2011
  • On the Interpretation of the Bolzano-Weierstrass Principle (with Ulrich Kohlenbach), final version in Math. Log. Q. 56 (2010), no. 5, 508–532

• Current topics

  paper on a finitization of another generalization of von Neumann's mean ergodic theorem,
  a pattern for obtaining uniform primitive recursive bounds for strong nonlinear ergodic theorems (with Ulrich Kohlenbach),
  finitization of Helly's theorem and its application,
  connection between the Weihrauch-lattice (see e.g. Brattka, Gherardi 2011) and proof mining

• Interests

  Logic (mainly proof mining as a specific field of proof theory) with applications to mathematics and, to some extent, computer science. Currently, my primary goal is to analyze all the different aspects of the usage of sequential compactness in its various forms in formal proofs in classical analysis. Recently, I developed some interest in Ergodic theory. There are many open questions concerning bounds in this field and the investigation of majorants in general is a crucial point in proof mining.

• Supervisor

  Prof. Dr. Ulrich Kohlenbach

• Thesises

  • Diploma (corresponds to Master): The Interpretation of the Bolzano-Weierstrass Principle Using Bar Recursion (pdf) (ps)
  • Bachelor: In the field of planar routing strategies in Ad Hoc Networks

Teaching

SS 2011: Assistent for the Analysis I course of professor Streicher.
WS 2010: Assistent for the Mathematik II f. Inf course of professor Streicher.
WS 2008/09: Assistent for the LA I course of professor Otto.

Other

My curicculum vitae is available in pdf format .