## Dr. Philipp Hieronymi

Associate Professor

Director, Illinois Geometry Lab

Curriculum Vitae

Office: Room 332, Illini Hall

E-mail: phierony@illinois.edu

Phone: 217-300-4994

### 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.

### 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.*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.*to appear pdf - 'Expansions of the real field by discrete subgroups of Gl_n(C)' with Erik Walsberg and Samantha Xu,

*Proc. Amer. Math.*to appear pdf - 'Structure theorems in tame expansions of o-minimal structures by a dense set' with Pantelis Eleftheriou and Ayhan Günaydin,

*Israel J. Math.*to appear 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) 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.*251(2) (2020) 131-160 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
- 'On continuous functions definable in expansions of the ordered real additive group' with Erik Walsberg, pdf
- 'Presburger Arithmetic with algebraic scalar multiplications ' with Danny Nguyen and Igor Pak, pdf
- 'Fractals and the monadic second order theory of one successor' with Erik Walsberg, 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

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, pdf

### Advising

Postdocs

- Erik Walsberg, 2016-2019, first position: Postdoc UC Irvine

PhD students

- Erin Caulfield, graduated 2018, first position: Postdoc McMaster University
- Travis Nell, graduated 2019
- Alexi Block Gorman, since 2017
- Christian Schulz, since 2018
- Rocco Davino, since 2019
- Eion Blanchard, since 2019

Graduate students (who participated in research projects)

- Pete Glaze (2010-2011)
- Nathan Rehfuss (2013-2014)
- Alonza Terry Jr. (2013-2016)
- William Balderrama (2016)

### Mailing Address:

Department of Mathematics

University of Illinois at Urbana-Champaign

1409 W. Green Street (MC-382)

Urbana, IL 61801

### Outreach

## A Math Carnival at IllinoisHundreds of local adults and children converged on Altgeld Hall on Saturday, January 28th 2017 for Math Carnival: Gathering for Gardner. As they participated in the numerous puzzles, games, riddles, magic tricks, and other hands-on activities, they discovered that math is more than just figures and formulas. According to Melinda Lanius, a math Ph.D. student who, along with Assistant Professor Philipp Hieronymi, organized this year’s event, “Math is play!” So numerous volunteers from Illinois’ Department of Mathematics, Illinois Geometry Lab, and Association for Women in Mathematics spent the afternoon showing members of the community that play can indeed be math—and that it’s fun. For more details, see the ISTEM report. | |

## A Math Carnival at IllinoisYou love mathematics? Fantastic! You don't like mathematics? Well, then give us a chance to change that! The Department of Mathematics at the University of Illinois at Urbana-Champaign would like to invite you and your family to our winter math carnival! The Gathering for Gardner 2017 will be held on Saturday, January 28, 2017 from 2 - 5 pm in Altgeld Hall. This fun filled day will be packed with hands on activities, demonstrations, games and puzzles, refreshments, and mathematical prizes for participants! All activities are free and open to the public and there is no math training required to enjoy! Our puzzles are particularly designed for kindergarten, elementary school, and middle school students. Please come visit us and bring the whole family!For more details, see https://faculty.math.illinois.edu/~lanius2/G4G.html or join us on Facebook. | |

## Impressions from the Gathering for Gardner 2014At the occasion of Gardner's 100th birthday the Illinois Geometry Lab and Department of Mathematics at the University of Illinois at Urbana-Champaign hosted a celebration of recreational mathematics and fun math puzzles on Saturday October 11th of this year. This event, a Gathering for Gardner 2014, was to honor the achievements of popular mathematics writer Martin Gardner who, for over 50 years, entertained general audiences with a rich variety of mathematical puzzles. Local mathematicians and computer scientists provided demonstrations of magic tricks, visual paradoxes and much more! At our math fair children of all ages (and adults as well!) were able to attempt and solve a large variety of Gardner's puzzles. For pictures of the event, click here. For more information about the event, click here. | |

## Gathering for Gardner 2014 - Oct 11, 1-4pm, Altgeld HallCome join Champaign-Urbana's celebration of the spirit of recreational mathematics and fun math puzzles, and the life of math and science writer Martin Gardner! At the occasion of Gardner's 100th birthday the University of Illinois will host a dozen local mathematicians and computer scientists who will present math puzzles, logic puzzles, hexaflexagons, magic tricks, visual paradoxes and much more! It is free and open to members of the public of all ages - no math training required to enjoy the puzzles and the mathematics! For more information, click here. |

### Teaching

Spring 2019 - Math 415 - Applied Linear Algebra

Fall 2018 - Math 595 - Definability Theory

Fall 2017 - Math 415 - Applied Linear Algebra

Fall 2016 - Math 415 - Applied Linear Algebra

Fall 2015 - Math 415 - Applied Linear Algebra

Fall 2014 - Math 415 - Applied Linear Algebra

Spring 2014 - Math 415 - Applied Linear Algebra

Fall 2013 - Math 415 - Applied Linear Algebra

Fall 2013 - Math 595 - O-minimal structures

Spring 2013 - Math 414 - Mathematical Logic

Fall 2012 - Math 570 - Mathematical Logic

Spring 2012 - Math 225 - Section P1 - Intro Matrix Theory

Spring 2012 - Math 414 - Mathematical Logic

Fall 2011 - Math 347 - Section G1 - Fundamental Mathematics

Spring 2011 - Math 225 - Section P1 - Intro Matrix Theory

Spring 2011 - Math 414 - Mathematical Logic

Fall 2010 - Math 285 - Section L1 - Intro Differential Equations