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Giorgis Petridis

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Associate Professor

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 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  2021 - 2024 (standard grant).
  • 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:

My arXiv public author identifier is petridis_g_1.

My Google Scholar page.

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.

________

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

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

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

19Bounds 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

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

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

16Refined estimates concerning sumsets contained in the roots of unity (with Brandon Hanson), Proceedings of the London 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 MurphyOliver Roche-NewtonMisha 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 𝔽2𝑝Fp2Proceedings 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 fieldsOnline 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 ℤ𝑑ZdMathematical 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 inequalityCombinatorics, Probability and Computing, volume 20, issue 06, pp. 921-938, 2011. Journal | arXiv

________

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

________

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

  • Collinear triples and quadruples for Cartesian products in 𝔽2𝑝Fp2 (absorbed in [13] above). arXiv
  • Products of differences in prime order finite fields (absorbed in the second conference proceedings article above; see also [12] and [13]). arXiv
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
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 Conferencewith 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.

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