[17]  J. Chapman, A. Mudgal, On commuting integer matrices, submitted, 20 pages.

[16]  A. Mudgal, On commuting pairs in arbitrary sets of 2x2 matrices, submitted, 23 pages.

[15]  A. L. Bruch, Y. Jing, A. Mudgal, Brunn-Minkowski type estimates for certain discrete sumsets, submitted, 17 pages.

[14]  Y. Jing, A. Mudgal, Kemperman's inequality and Freiman's lemma via few translates, submitted, 18 pages.

[13]  Y. Jing,  A. Mudgal, Finding large additive and multiplicative Sidon sets in sets of integers, Math. Ann. 391 (2025), no. 1, 685–715. journal

[12]  A. Mudgal, Energy estimates in sum-product and convexity problems, Amer. J. Math. 147 (2025), no. 4, 869–899.

[11]  S. Mansfield, A. Mudgal, A quadratic Vinogradov mean value theorem in finite fields, Q. J. Math. 75 (2024), no. 3, 1007–1029. journal

[10]  A. Mudgal, An Elekes-Rónyai theorem for sets with few products, Int. Math. Res. Not. IMRN (2024), no. 13, 10410–10424. journal

[9]  A. Mudgal, Unbounded expansion of polynomials and products, Math. Ann. 390 (2024), no. 1, 381–415. journal

[8]  B. Cook, K. Hughes, Z. K. Li, A. Mudgal, O. Robert, P. Yung, A decoupling interpretation of an old argument for Vinogradov's Mean Value Theorem, Mathematika, 70 (2024), no.1, Paper No. e12231, 32 pp. journal

[7]  A. Mudgal, Diameter free estimates for the quadratic Vinogradov mean value theorem,  Proc. Lond. Math. Soc. (3) 126 (2023), no. 1, 76–128. journal

[6]  A. Mudgal, New lower bounds for cardinalities of higher dimensional difference sets and sumsets, Discrete Analysis 2022, Paper No. 15, 19 pp. journal 

[5]  A. Mudgal, Additive energies on spheres,  J. Lond. Math. Soc. (2) 106 (2022), no. 4, 2927-2958. journal 

[4]  A. Mudgal, Difference sets in higher dimensions,  Math. Proc. Cambridge Philos. Soc. 171 (2021), no. 3, 467-480.  journal

[3]  A. Mudgal, Sum-product estimates for diagonal matrices, Bull. Aust. Math. Soc. 103 (2021), no. 1, 28-37.  journal

[2]  A. Mudgal,  Arithmetic combinatorics on Vinogradov systems,  Trans. Amer. Math. Soc. 373 (2020), no. 8, 5491–5516.  journal 

[1]  A. Mudgal, Sums of linear transformations in higher dimensions, Q. J. Math. 70 (2019), no. 3, 965–984.  journal 

My PhD thesis, titled "Arithmetic combinatorics on Vinogradov systems and related topics", is present here.

I wrote a short introduction to some recent work concerning the sum-product phenomenon in 2024. This can be found here.