Daniel Herden, Ph.D.

Education

• Habilitation, University of Duisburg-Essen (Germany), 2013.
• Dr. rer. nat. (Doctorate), University of Duisburg-Essen (Germany), 2005 (Advisor: Rüdiger Göbel).
• Dipl. Math. (Diploma), University of Duisburg-Essen (Germany), 2003 (Advisor: Rüdiger Göbel).

Biography

Dr. Herden was born in Münster (Germany) and raised in Essen (Germany) where he received most of his education. His interest in mathematics got sparked at an early age and resulted in a vivid participation in various mathematical competitions throughout junior and senior high school. He finished his high school career in 1999 as the most successful participant of the German Math Olympiad (5 first, 1 second and 1 third prize) and is currently ranked #2 in the Hall of Fame of this prestigious competition. Further achievements of this early era include 3 first prizes at the German Federal Math Competition and 3 silver medals at the International Mathematical Olympiad (Argentina 1997, Taiwan 1998, Romania 1999).

Dr. Herden joined the Baylor faculty in 2014 having particularly strong affiliations to the algebra research group of the math department. Prior to this he has held various other positions including post-doctoral positions at the Hebrew University of Jerusalem, Israel (2007-2008) and at the University of Münster, Germany (2009-2010), a position as associate professor at the University of Duisburg-Essen, Germany (2013) and a visiting professor position at the Charles University in Prague, Czech Republic (2013-2014).

Academic Interests and Research

Algebra: Dr. Herden's interest focuses on the interaction between algebra and set theory. This concerns specifically the existence and construction of large algebraic structures (e.g., groups, rings, modules) under set-theoretic considerations.

Set Theory: Dr. Herden is interested in any applications of set theory and infinite combinatorics to other fields of mathematics, most notably to algebra. This research is inspired by Saharon Shelah and his proof of the undecidability of the Whitehead problem.

Combinatorics: More recently, Dr. Herden has also become interested in applications of finite combinatorics. He has contributed to incidence algebras, symplectic geometry, ergodic theory, partitions, and graph theory. This research is influenced by Richard P. Stanley.

Coding Theory: Since Spring 2021, Dr. Herden is expanding into this new research area at the boundary between algebra and combinatorics in a push towards research in applied mathematics. This is a work collaboration with Baylor postdoc Dan Bossaller.

In addition, Dr. Herden has a long-running interest in promoting mathematically talented high school students. He is a current member of the problem proposal committee of the German Mathematical Olympiad (DeMO).

Selected Publications

• P. Hagelstein, D. Herden, A. Stokolos, A theorem of Besicovitch and a generalization of the Birkhoff Ergodic Theorem, Proc. Amer. Math. Soc. Ser. B 8 (2021), 52–59.
• M. Dugas, D. Herden, S. Shelah, ℵ_k-free cogenerators, Special Issue in Honor of L. Fuchs's 95th Birthday, Rend. Semin. Mat. Univ. Padova 144 (2020), 87–104.
• J. Courtemanche, M. Dugas, D. Herden, Local automorphisms of finitary incidence algebras, Linear Algebra Appl. 541 (2018), 221–257.
• P. Hagelstein, D. Herden, D. Young, Ramsey-type theorems for sets satisfying a regularity condition, J. Math. Anal. Appl. 447 (2017), 951–956.
• H.-C. Herbig, D. Herden, C. Seaton, On compositions with x² ∕ (1 – x), Proc. Amer. Math. Soc. 143 (2015), 4583–4596.
• R. Göbel, D. Herden, S. Shelah, Prescribing endomorphism algebras of ℵ_n-free modules, J. Eur. Math. Soc. 16 (2014), 1775–1816.
• D. Herden, Constructing ℵ_k-free Structures, Habilitationsschrift, University of Duisburg-Essen (2013).
• R. Göbel, D. Herden, S. Shelah, Absolute E-rings, Adv. Math. 226 (2011), 235–253.
• R. Göbel, D. Herden, S. Shelah, Skeletons, bodies and generalized E(R)-algebras, J. Eur. Math. Soc. 11 (2009), 845–901.
• D. Herden, S. Shelah, An upper cardinal bound on absolute E-rings, Proc. Amer. Math. Soc. 137 (2009), 2843–2847.
• R. Göbel, D. Herden, E(R)-algebras that are sharply transitive modules, J. Algebra 311 (2007), 319–336.
• D. Herden, Uniquely Transitive R-modules, PhD Thesis, University of Duisburg-Essen (2005).

Current Ph.D. Students

• Indalecio Ruiz Bolaños (joint with Dan Bossaller)

Former Ph.D. students

• Jack Rebrovich (joint with Manfred Dugas), Group Automorphisms of Incidence Algebras, Baylor (June 2021)
• Lexi Pasi, Forcing ℵ₁-Free Groups to Be Free, Baylor (March 2021)
• Jordan Courtemanche (joint with Manfred Dugas), Local Automorphisms of Finitary Incidence Algebras, Baylor (June 2017)
• Katrin Leistner (joint with Rüdiger Göbel), Partial Isomorphism, Duisburg-Essen (March 2015)
• Montakarn Petapirak (joint with Rüdiger Göbel), Varieties of Groups and Cellular Covers, Duisburg-Essen (July 2014)

Honors Theses advised

• Brian King (joint with Paul Hagelstein), Inhomogeneous Diophantine Approximation, Baylor (April 2018)
• Ethan Gwaltney (joint with Paul Hagelstein), A Probabilistic Proof of the Vitali Covering Lemma, Baylor (April 2017)