Gram-Schmidt Walk algorithm and consequences for Komlós conjecture

Komlós conjecture states that minimal discrepancy of a set of vectors in R^d is bounded from above by a universal constant. I will present, by using a method called Gram-Schmidt Walk, how the best known upper bound constant can be improved. I will also present the result for a smoothed version of the problem - where initial vectors are perturbed with Gaussian noise.