• Publications
  • Influence
Supersaturated sparse graphs and hypergraphs
A central problem in extremal graph theory is to estimate, for a given graph $H$, the number of $H$-free graphs on a given set of $n$ vertices. In the case when $H$ is not bipartite, fairly preciseExpand
  • 12
  • 1
  • PDF
C O ] 8 O ct 2 01 9 Resilience of the Rank of Random Matrices
Let M be an n × m matrix of independent Rademacher (±1) random variables. It is well known that if n ≤ m, then M is of full rank with high probability. We show that this property is resilient toExpand
Lecture 6 : Pseudorandom Generators from One Way Functions
We describe a construction of PRGs from one way permutations. Later, we discuss discuss why we need a permutation as opposed to any one way function. Here is a very natural approach to try andExpand
Maximum entropy and integer partitions
We derive asymptotic formulas for the number of integer partitions with given sums of jth powers of the parts for j belonging to a finite, non-empty set J ⊂ N. The method we use is based on theExpand
Resilience of the rank of random matrices
TLDR
An asymptotic solution to a slightly weakened version of a conjecture made by Van Vu in [17]. Expand
  • 1
  • PDF
Superlogarithmic Cliques in Dense Inhomogeneous Random Graphs
TLDR
We show that if $W$ is allowed to approach 1 at a finite number of points, and displays moderate rate of growth near these points, then the clique number of $\mathbb{G}(n,W)$ will be $\Theta(\sqrt{n})$ almost surely. Expand
  • 1
  • PDF