I am an Associate Professor in the Department of Mathematics at UGA. I was born in Athens, Greece and now find myself in Athens, GA. Before this, I was in the University of Rochester, NY. I studied at the University of Cambridge, where I did my PhD under the supervision of Tim Gowers, and spent four years as a Visiting Assistant Professor at the University of Rochester.

I am a handling editor of *Combinatorial Theory*, an online journal of mathematics dedicated to open access publishing with no fees for authors or readers. Submissions are welcome!

I am a member of the Number Theory and Arithmetic Geometry group (a proud member of the additive combinatorics and discrete analysis subgroup).

## Research

**Research Interests:**

Most of my work is in arithmetic combinatorics -- the 21st century descendant of combinatorial number theory. I am also interested in combinatorial geometry, in some areas of analysis, and broader questions in discrete mathematics.

**Grants:**

**NSF DMS**Award 2054214**NSF DMS**Award 1723016 & Award 1500984, 2015 - 2021 (standard grant, one is continuation of the other).**NSF DMS**Award 1804049, 2018 (conference grant for the Georgia Discrete Analysis conference)**.****AMS-Simons**Travel Grant, 2013 - 2015.

## Selected Publications

**Selected Publications:**

My arXiv public author identifier is petridis_g_1.

My research is supported by the NSF Award 2054214**.** I gratefully acknowledge the support from the RTG in Algebraic Geometry, Algebra, and Number Theory at the University of Georgia, and from the NSF RTG grant DMS-1344994.

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Journal publications and preprints in reverse chronological order of completion. Until publication, the year given is that of submission to arXiv.

**21**. **Almost orthogonal subsets of vector spaces over finite fields** (with Ali Mohammadi), *European Journal of Combinatorics, *volume 103, article 103515, 2022. Journal | arXiv

**20**. **A question of Bukh on sums of dilates** (with Brandon Hanson), *Discrete Analysis*, 2021:Paper No. 13, 21 pp., 2021. Journal | arXiv

**19**. **Bounds of trilinear and trinomial exponential sums** (with Simon Macourt, Ilya D. Shkredov and Igor E. Shparlinski), *SIAM Journal on Discrete Mathematics*, volume 34, issue 4, pp. 2124-2136, 2020. Journal | arXiv

**18**. **On the pinned distances problem in positive characteristic** (with Brendan Murphy, Thang Pham, Misha Rudnev and Sophie Stevens), *Journal of London Mathematical Society*, volume 105, issue 1, pp. 469-499, 2022. Journal | arXiv

**17**. **An energy bound in the affine group** (with Oliver Roche-Newton, Misha Rudnev and Audie Warren), *International Mathematics Research Notices, *volume 2022, issue 2, pp. 1154-1172, 2022. Journal | arXiv

**16**. **Refined estimates concerning sumsets contained in the roots of unity** (with Brandon Hanson), *Proceedings of the L**ondon Mathematical Society*, volume 122, issue 3, pp. 353-358, 2021. Journal | arxiv

**15. An example related to the Erdős-Falconer question over arbitrary finite fields** (with Brendan Murphy), *Bulletin of the Hellenic Mathematical Society*, volume 63, pp. 38-39, 2019. Journal | arXiv

**14. Bisectors and pinned distances** (with Ben Lund), *Discrete** & Computational Geometry*, volume 64, issue 3, pp.** **995-1012, 2020. Journal | arXiv

**13. Products of differences over arbitrary finite fields** (with Brendan Murphy), *Discrete Analysis*, 2018: Paper No. 18, 42 pp., 2018. Journal | arXiv

**12. New results on sum-product type growth over fields** (with Brendan Murphy, Oliver Roche-Newton, Misha Rudnev and Ilya D. Shkredov), *Mathematika*, volume 65, issue 3, pp. 588-642, 2019. Journal | arXiv

**11. Pinned algebraic distances determined by Cartesian products in 𝔽2𝑝Fp2**, *Proceedings of the American Mathematical Society*, volume 145, issue 11, pp. 4639-4645, 2017. Journal | arXiv

**10. Bounds of trilinear and quadrilinear exponential sums** (with Igor E. Shparlinski), *Journal d'Analyse Mathematique*, volume 138, issue 2, pp. 613-641, 2019. Journal | arXiv

**9. A point-line incidence identity in finite fields, and applications** (with Brendan Murphy), *Moscow Journal of Combinatorics and Number Theory*, volume 6, issue 1, pp. 64-95, 2016. Journal | arXiv

**8. On the number of dot products determined by a large set and one of its translates in finite fields**, *Online Journal of Analytic Combinatorics*, issue 12, #4, 2017. Journal | arXiv

**7. Tiling sets and spectral sets over finite fields** (REU project run together with Alex Iosevich and Jonathan Pakianathan), *Journal of Functional Analysis*, volume 273, issue 8, pp. 2547-2577, 2017. Journal | arXiv

**6. The cardinality of sumsets: different summands **(with Brendan Murphy and Eyvi Palsson), *Acta Arithmetica*, volume 167, issue 4, pp 375-395, 2015. Journal | arXiv

**5. Matchings in random biregular bipartite graphs** (with Guillem Perarnau), *The Electronic Journal of Combinatorics*, volume 20, issue 01, p60, 2013. Journal | arXiv

**4. New proofs of Plünnecke-type estimates for product sets in groups,** *Combinatorica*, volume 32, issue 06, pp. 721-733, 2012. Journal | arXiv

**3. The 𝐿1L1-norm of exponential sums in ℤ𝑑Zd**, *Mathematical Proceedings of the Cambridge Philosophical Society*, volume 154, issue 03, pp. 381-392, 2013. Journal | arXiv

**2. Upper bounds on the cardinality of higher sumsets,** *Acta Arithmetica*, volume 158, issue 04, pp. 299-319, 2013. Journal | arXiv

**1. Plünnecke's** **inequality**, *Combinatorics, Probability and Computing*, volume 20, issue 06, pp. 921-938, 2011. Journal | arXiv

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Conference proceedings publications (all three are peer reviewed; I and II have citations).

**III. Pseudorandomness of large sets in finite fields**, in K.-U. Schmidt and A. Winterhof (eds.), *Combinatorics and finite fields: Difference sets, polynomials, pseudorandomness and applications*. Radon Series on Computational and Applied Mathematics, Berlin, Boston: de Gruyter, 199-210, 2019. Preprint | Proceedings

**II. A second wave of expanders over finite fields**, (with Brendan Murphy) in *Combinatorial and Additive Number Theory II: CANT 2015 and 2016*, 215-238, 2017. arXiv | Proceedings

**I. The Plünnecke-Ruzsa inequality: an overview**, in:* Combinatorial and Additive Number Theory: CANT 2011 and 2012*, 229-241, 2014. Author's Copy | Proceedings

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Preprints that did not make it to print (but have Google scholar citations).

## Education

**Education:**

**Doctor of Philosophy**under the supervision of W.T. Gowers, University of Cambridge, 2002 - 2011.**Certificate of Advanced Studies in Mathematics**, St John’s College, University of Cambridge, 2001 - 2002.**BA (Hons) in Mathematics**, St John’s College, University of Cambridge, 1998 - 2001

## Other Information

**Of note:**

### INVITED SPEAKER FOR WORKSHOPS

- 4th IPM Biennial Conference on Combinatorics and Computing, IPM, Teheran, Iran, May 2021.
- Additive Combinatorics in Marseille 2020, Centre International de Rencontres Mathematiques (CIRM), Marseille, France September 2020.
- Pseudo-Randomness and Finite Fields Workshop, Johann Radon Institute for Computational and Applied Mathematics (RICAM), Linz, Austria, October 2018.
- Speaker at the NSF-CBMS Conference on Additive Combinatorics from a Geometric Viewpoint, University of South Carolina, Columbia, SC USA, May 2018.
- Additive Combinatorics, Entropy, and Fractal Geometry Arbeitsgemeinschaften, Mathematisches Forschungsinstitut, Oberwolfach, Germany, 8 Oct - 13 Oct 2017.
- Week-long Block Course in Additive Combinatorics, Freie Universita ̈t Berlin, Germany, October 2014.
- Series of four talks at the New York Number Theory Seminar, CUNY Graduate Center, NY, USA, May 2011.

### SELECTED INVITED TALKS

- Copenhagen-Jerusalem Combinatorics Seminar, September 2021.
- Université de Montréal, Quebec-Vermont Number Theory Seminar, November 2020.
- Webminar in Additive Combinatorics, May 2020.
- University of Rochester, Combinatorics Seminar, April 2020.
- Universidade NOVA de Lisboa Algebra and Logic Seminar, June 2019.
- Stanford University, Number Theory Seminar, January 2019.
- The Ohio State University, Combinatorics and Probability semina, November 2018.
- 19th Atlanta Lecture Series in Graph Theory and Combinatorics, Georgia State University, April 2017.
- Universidad Autonoma de Madrid, Seminar, December 2016.
- Georgia Institute of Technology, Combinatorics Seminar, November 2016.
- MIT, Seminar and visit to Larry Guth’s group, October 2015.
- Oakridge National Laboratory, Division of Mathematics Seminar, September 2015.
- McGill University, Combinatorics Seminar, March 2014.
- Fields Institute, Number Theory Seminar, September 2013.
- University of Athens, Mathematical Analysis Seminar, January 2012.
- Universitat Politecnica de Catalunya, Combinatorics Graph Theory and Applications Seminar, December 2011.
- Newton Institute, Discrete Analysis Seminar, February 2011.

### STUDENT MENTORING

- In committee of Master's Thesis on ‘A mathematical model for RNA 3D structures’, 2021.
- Supervised Master's Thesis on ‘Compressions in extremal combinatorics and additive number theory’, 2020.
- Co-lead REU in collaboration with Neil Lyall on ‘Additive energy on the discrete cube’ and guided preparation on a public talk on ‘Investigating Additive Combinatorics Through Freiman’s Theorem and Plunnecke’s Inequality’, 2017.
- Co-lead REU with A. Iosevich and J. Pakianathan on ‘Tiling sets and spectral sets over finite fields’ with the participation of 14 students. Resulted in a publication to the Journal of Functional Analysis.
- Mentor for summer McNair program (which aims to increase graduate degree awards for students from underrepresented segments of society), 2015.

### SERVICE

**Combinatorial Theory**: Handling Editor, 2020 - present. Member of the Constitution Writing Committee (2021 - 2022).**Georgia Discrete Analysis Conference:**with E. Croot, N. Lyall and A. Magyar at The University of Georgia, May 2018 – NSF DMS Award 1804049.**Outreach:**Directed week-long group activities for high school students on Combinatorial Geometry at the UGA 2018 Math Camp, July 9–13 2018.**Public understanding of mathematics**: Quoted in Jordana Cepelewicz's article Math's `Oldest Problem Ever' Gets a New Answer that appeared in Quanta Magazine in March 2022.**Public understanding of science:**Helped edit science communication guides for the general public, one on medical screening and one on statistics.

**Courses Regularly Taught:**