**George Shakan**

I am a postdoc at CRM working in the research group of Andrew Granville and Dimitris Koukoulopoulos. Until August 2021, I was a postdoct at the University of Oxford working in the research group of Ben Green. Until May of 2019, I was a PhD student at the University of Illinois at Urbana-Champaign under Kevin Ford. My primary research interests are additive combinatorics, analytic number theory and the intersection of the two. Research has lead me to incidence geometry, exponential sums, probability, harmonic analysis, sieve theory, combinatorics, and elsewhere.

## Papers and Preprints

Please see my CV for the formal references.

**Additive Combinatorics**

Explicit RIP matrices: An update with K. Ford and D. Kutzarova; **Preprint**

Effective results on the size and structure of sumsets with A. Granville and A. Walker; **Preprint**

A large gap in a dilate of a set; **SIAM J. Discrete Math.**

An analytic approach to cardinalities of sumsets with Dávid Matolcsi, Imre Ruzsa and Dmitrii Zhelezov; **Combinatorica**

A weighted Prékopa-Leindler inequality and sumsets with quasi-cubes with Ben Green Dávid Matolcsi, Imre Ruzsa and Dmitrii Zhelezov; **Submitted**

The Frobenius Postage Stamp Problem, and beyond with Andrew Granville; **Acta. Math. Hung.**

On distinct consecutive differences with Imre Ruzsa, József Solymosi and Endre Szemerédi; **Springer Volume: Combinatorial and Additive Number Theory IV**

Stronger sum-product inequalities for small sets with Misha Rudnev and Ilya Shkredov; **Proc. Amer. Math Soc.**

Monochromatic Hilbert cubes and arithmetic progressions with József Balogh, Misha Lavrov, and Adam Wagner; **Electron. J. Comb**

On higher energy decompositions and the sum-product phenomenon; **Math. Proc. Cambridge Philos. Soc. **(Quanta Article)

On distinct consecutive r-differences with Junxian Li; **J. Number Theory**

Sum of dilates in vector spaces with Antal Balog; **North-West. Eur. J. Math.**

Sum of many dilates in **Comb. Prob. Comput.**

On the Sum of Dilations of a Set with Antal Balog; **Acta. Arith.**

**Number Theory**

Quantitative Hilbert irreducibility and almost prime values of polynomial discriminants with T. Anderson, A. Gafnie, R. Lemke Oliver, D. Lowry-Duda, R. Zhang; **IMRN**

On generating functions in additive number theory II: Lower order terms with applications to PDEs with Julia Brandes, Scott Parsell, Konstantinos Poulias, and Robert Vaughan; **Math. Ann.**

Fractal solutions to dispersive partial dispersive equations on the torus with Burak Erdoğan; **Selecta Math.**

A lower bound for the least prime in an arithmetic progression with Junxian Li and Kyle Pratt; **Q. J. Math.**

A Generalization of the Schur-Siegel-Smyth Trace Problem with Kyle Pratt and Alexandru Zaharescu; **J. Math. Anal. Appl.**

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## Contact Information

You can contact me at the domain gmail.com and local part george.shakan

## Undergraduate Research (As Mentor)

Singular Value Decomposition (2015)

## Undergraduate Thesis

Q-Polynomial Association Schemes with Irrational Eigenvalues (2012)