Akshat Mudgal

activity

20192026

most citedEnergy estimates in sum-product and convexity problems

5 citations · 9 across the 22 of their papers we have counts for

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10 papers · 1 filter

math.CO2025

On exponential Freiman dimension

Jeck Lim, Akshat Mudgal, Cosmin Pohoata +1

The exponential Freiman dimension of a finite set $A \subset R^{m}$ , introduced by Green and Tao in 2006, represents the largest positive integer $d$ for which $A$ contain…

math.CO2024

Brunn-Minkowski type estimates for certain discrete sumsets

Albert Lopez Bruch, Yifan Jing, Akshat Mudgal

Let $d, k$ be natural numbers and let $L_{1}, \dots, L_{k} \in GL_{d} (Q)$ be linear transformations such that there are no non-trivial subspaces $U,…

math.CO2023

An Elekes-Rónyai theorem for sets with few products

Akshat Mudgal

Given $d, n \in N$ , we write a polynomial $F \in C [x_{1}, \dots, x_{n}]$ to be degenerate if there exist $P \in C [y_{1}, \dots, y_{n - 1}]$ and $m_j = x_1^{v_{j,1}}\…

math.CO2023

Kemperman's inequality and Freiman's lemma via few translates

Yifan Jing, Akshat Mudgal

Let $G$ be a connected compact group equipped with the normalised Haar measure $μ$ . Our first result shows that given $α, β > 0$ , there is a constant $c = c (α, β) > 0$ such that for any…

math.CO2021

New lower bounds for cardinalities of higher dimensional difference sets and sumsets

Akshat Mudgal

Let $d \geq 4$ be a natural number and let $A$ be a finite, non-empty subset of $R^{d}$ such that $A$ is not contained in a translate of a hyperplane. In this setting, we sh…

math.CO2021★ 5 cited

Energy estimates in sum-product and convexity problems

Akshat Mudgal

We prove a new class of low-energy decompositions which, amongst other consequences, imply that any finite set $A$ of integers may be written as $A = B \cup C$ , where $B$ and $C$ a…

math.CO2020★ 3 cited

Difference sets in higher dimensions

Akshat Mudgal

Let $d \geq 3$ be a natural number. We show that for all finite, non-empty sets $A \subseteq R^{d}$ that are not contained in a translate of a hyperplane, we have \[ |A-A| \…

math.CO2020

Sum-product estimates for diagonal matrices

Akshat Mudgal

Given $d \in N$ , we establish sum-product estimates for finite, non-empty subsets of $R^{d}$ . This is equivalent to a sum-product result for sets of diagonal matric…

math.CO2020

Arithmetic Combinatorics on Vinogradov systems

Akshat Mudgal

In this paper, we present a variant of the Balog-Szemerédi-Gowers theorem for the Vinogradov system. We then use our result to deduce a higher degree analogue of the sum-product ph…

math.CO2019

Sums of linear transformations in higher dimensions

Akshat Mudgal

In this paper, we prove the following two results. Let $d$ be a natural number and $q, s$ be co-prime integers such that $1 < q s$ . Then there exists a constant $δ > 0$ depending only…