## Philipp Hieronymi

E-mail: hieronymi@math.uni-bonn.de

Office: Room 4.005

### Research interests

- Mathematical Logic, in particular model theory, o-minimality, its generalizations and their applications.
- Theoretical Computer Science, in particular automata theory, complexity theory and computability theory.

### Teaching (SoSe24)

- Advanced Mathematical Logic I - Tame Geometry (V4A7)

Mondays 14:15-16:00, Wednesdays 12:15-14:00, We10 Kleiner Hörsaal - Graduate Seminar on Logic - O-minimal structures (S4A4)

Fridays 12.15-14:00, SemR 0.011 - Begleitseminar (S3G1)/Master thesis seminar (S5G1)

Tuesdays 10:15-12:00, N0.003 Neubau

### Publications

- 'Defining the set of integers in expansions of the real field by a closed discrete set',

*Proc. Amer. Math. Soc.*138 (2010) 2163-2168, pdf - 'The real field with the rational points of an elliptic curve', with Ayhan Günaydin,
*Fund. Math.*211 (2011) 15-40, pdf - 'Dependent pairs', with Ayhan Günaydin,
*J. Symb. Logic*(2) 76 (2011) 377-390, pdf - 'The real field with an irrational power function and a dense multiplicative subgroup',

*J. London Math. Soc.*(2) 83 (2011) 153-167, pdf, - 'Expansions of subfields of the real field by a discrete set',
*Fund. Math.*215 (2011) 167-175, pdf - 'Expansions which introduce no new open sets', with Gareth Boxall,

*J. Symb. Logic*(1) 77 (2012) 111-121, pdf - 'A dichotomy for expansions of the real field', with Antongiulio Fornasiero and Chris Miller,

*Proc. Amer. Math. Soc.*141 (2013) 697-698, pdf - 'An analogue of the Baire Category Theorem',
*J. Symb. Logic*(1) 78 (2013) 207-213, pdf - 'Interpreting the projective hierarchy in expansions of the real line', with Michael Tychonievich,

*Proc. Amer. Math. Soc.*142 (2014) 3259-3267, pdf - 'A fundamental dichotomy for definably complete expansions of
ordered fields', with Antongiulio Fornasiero,
*J. Symb. Logic*(4) 80 (2015) 1091-1115 pdf - 'Expansions of the ordered additive group of real numbers by two discrete subgroups',
*J. Symb. Logic*(3) 81 (2016) 1007–1027 pdf - 'Distal and non-distal pairs', with Travis Nell,

*J. Symb. Logic*(1) 82 (2017) 375-383 pdf - 'How to avoid a compact set' with Antongiulio Fornasiero and Erik Walsberg,

*Adv. Math.*317 (2017) 758-785 pdf - 'Wild theories with o-minimal open core' with Travis Nell and Erik Walsberg,

*Ann. Pure Appl. Logic*(2) 169 (2018) 146-163 pdf - 'Ostrowski numeration systems, addition and finite automata', with Alonza Terry Jr,
*Notre Dame J. Formal Logic*(2) 59 (2018) 215-232 pdf - 'Interpreting the monadic second order theory of one successor in expansions of the real line', with Erik Walsberg,

*Israel J. Math.*(1) 224 (2018) 39–55 pdf - 'A tame Cantor set',

*J. European Math. Soc.*(9) 20 (2018) pp. 2063–2104 pdf - 'When is scalar multiplication decidable?',

*Ann. Pure Appl. Logic*(2019) 1162-1175 pdf - 'Metric dimensions and tameness in expansions of the real field' with Chris Miller,

*Trans. Amer. Math. Soc.*(2) 373 (2020) 849-874 pdf - 'An o-minimal trace that does not eliminate imaginaries' with P. Eleftheriou,

Appendix to: 'Small sets in dense pairs' by P. Eleftheriou,*Israel J. Math.*233 (2019) 1-27 pdf - 'Structure theorems in tame expansions of o-minimal structures by a dense set' with Pantelis Eleftheriou and Ayhan Günaydin,

*Israel J. Math.*239 (2020) 435-500 pdf - 'Continuous Regular Functions' with Alexi Block Gorman, Elliot Kaplan, Ruoyu Meng, Erik Walsberg, Zihe Wang, Ziqin Xiong and Hongru Yang,

*Log. Methods Comput. Sci.*(1) 16 (2020) #17 pdf - 'The Choice Property in tame expansions of o-minimal structures' with Pantelis Eleftheriou and Ayhan Günaydin,

*Math. Logic Quart.*(2) 66 (2020) 239-246 pdf - 'Pairs of Theories Satisfying a Mordell-Lang Condition' with Alexi Block Gorman and Elliot Kaplan,

*Fund. Math.*(2) 251 (2020) 131-160 pdf - 'Expansions of the real field by discrete subgroups of Gl_n(C)' with Erik Walsberg and Samantha Xu,

*Proc. Amer. Math. Soc.*149 (2021) 2221-2233 pdf - 'Presburger Arithmetic with algebraic scalar multiplications ' with Danny Nguyen and Igor Pak,

*Log. Methods Comput. Sci.*(3) 17 (2021) #4 pdf - 'A tetrachotomy for expansions of the real ordered additive group' with Erik Walsberg,

*Sel. Math. New Ser.*27 (2021) #54 pdf,

formerly: 'On continuous functions definable in expansions of the ordered real additive group' - 'Pathological examples of structures with o-minimal open core' with Alexi Block Gorman and Erin Caulfield,

*Math. Logic Quart.*(3) 67 (2021) 382-393 pdf - 'Decidability for Sturmian words', with Dun Ma, Reed Oei, Luke Schaeffer, Chris Schulz and Jeffrey Shallit,

*Computer Science Logic (CSL)*(2022) #24 pdf - 'A strong version of Cobham's theorem', with Chris Schulz,

*ACM Symposium on Theory of Computing (STOC)*(2022) 1172-1179 pdf - 'Fractals and the monadic second order theory of one successor' with Erik Walsberg,

*J. Log. Anal.*15:5 (2023) 1-25 pdf - 'Decidability bounds for Presburger arithmetic extended by sine' with Eion Blanchard,

*Ann. Pure Appl. Logic*(2024) to appear pdf - DPhil Thesis, 'The real field with an irrational power function and a dense multiplicative subgroup',

ORA, Nov. 2008

Preprints

- 'Definability and decidability in expansions by generalized Cantor sets' with William Balderrama, pdf
- 'Pecan: An Automated Theorem Prover for Automatic Sequences using Büchi Automata' with Reed Oei, Dun Ma and Christian Schulz, pdf

Economics

- 'The Clean-Development Mechanism, stochastic permit prices and energy investments' with David Schüller,

*Energy Economics*47 (2015) 25–36 - 'The Influence of Permit Price Uncertainty and Lobbying on Energy Investments' with David Schüller,

in 'Emissions Trading as a Policy Instrument: Evaluation and Prospects',*CESifo Seminar Series, MIT Press*(2015) 87-120

Other

- 'Geometry Labs United: An Invitation' with Jayadev Athreya, David Dumas, William Goldman,Sergey Grigorian, Rosemary Guzman, Sean Lawton, Anton Lukyanenko, Jeremy Tyson, and Aaron Wilson,

*Notices Amer. Math. Soc.*(9) 65 (2018) 1088-1094, pdf - 'Innovating and modernizing a Linear Algebra class through teaching computational skills', with Mariana Silva, Matthew West, Sascha Hilgenfeldt, Nicolas Nytko, Akshit Deshpande, and Jer-Chin Chuang,

2022 ASEE Annual Conference & Exposition, Minneapolis, MN, peer.asee.org/40766, pdf

Work by students

- 'On expansions of the real field by complex subgroups', by Erin Caulfield,
*Ann. Pure Appl. Logic*168 (2017) 1308–1334 pdf - 'Distal and non-Distal Behavior in Pairs', by Travis Nell,

*Math. Log. Quart.*(1) 65 (2019) 23-36, pdf - 'Companionability Characterization for the Expansion of an O-minimal Theory by a Dense Subgroup', by Alexi Block Gorman,

*Ann. Pure Appl. Logic*(10) 174 (2023) 103316, pdf - 'Undefinability of multiplication in Presburger arithmetic with sets of powers', by Chris Schulz, pdf

### Advising

Postdocs

- Erik Walsberg, 2016-2019, first position: Postdoc UC Irvine
- Christian d'Elbée, 2022-2023, first position: Marie Curie Leeds
- Tingxiang Zou, since 2024

PhD students

- Erin Caulfield, graduated 2018, first position: Postdoc McMaster University
- Travis Nell, graduated 2019, first position: Data Scientist at Capital One
- Alexi Block Gorman, graduated 2021, first position: Postdoc Fields Institute
- Chris Schulz, graduated 2023, first position: Postdoc Waterloo
- Eion Blanchard, graduated 2023, first position: Postdoc MSRI
- Madie Farris, since 2020
- Leon Chini, since 2022
- Sven Manthe, since 2023
- Yilong Zhang, since 2023

Master students

- Xiaoduo Wang (2022), Quantifier elimination and decidability of the theory of additive integer group augmented by predicates of multiplicative cyclic submonoids, pdf (-> PhD student Manchester)
- Leo Gitin (2022), Decidability in expansions of local fields, pdf (-> DPhil student Oxford)
- Felix Jäger (2022), Towards a d-minimal Pila-Wilkie theorem, pdf
- Juan Sebastian Diaz Serrano (2023), Alpha-Presburger Arithmetic: Complexity and Axiomatization
- Sven Manthe (2023), An analogue of Cobham's theorem for scalar multiplication (-> PhD student Bonn)
- Yilong Zhang (2023), Green points in the real field (-> PhD student Bonn)
- Iñaki Garrido (2023), Linearity of type A expansions
- Carlos Urban Abengozar (2023), The zero set property in definably complete expansions of ordered fields
- Roman Feller (2023), A dichotomy for type A structures, pdf (-> PhD student Vienna)
- Kim Kiehn (2023), Complexity Theory in Expansions of Presburger Arithmetic (-> PhD student Stockholm)
- Frederik Gebert (2024), NIP Expansions of the Real Field

Bachelor students

- Carl Jacobsen (2022)
- Matthias Franz (2022)
- Lucas Valle Thiele (2022), The Pila-Zannier method for abelian varieties, pdf
- Simon Blasinski (2022)
- Thomas Freiherr von Campenhausen (2022)
- Antonia Westphal (2022)
- Sarah Zengl (2022)
- Johannes Dertmann (2022)
- Laura Caspers (2023), A structure with a weak pole that is not field-type, pdf
- Laura Khaze (2023)
- Fabian Schmitthenner (2023), Decidability Questions in Ostrowski Numeration Systems, pdf
- Darius Tenthoff (2023)

Graduate students (who participated in research projects)

- Pete Glaze (2010-2011)
- Nathan Rehfuss (2013-2014)
- Alonza Terry Jr. (2013-2016)
- William Balderrama (2016)
- Rocco Davino (2019-2021)
- Ran Ji (2020-2022)

### Contact

Universität BonnMathematisches Institut

Endenicher Allee 60

D-53115 Bonn

Germany