Inspired by recent work on the quantile-randomized Kaczmarz method (qRK) for solving a linear system of equations, we propose an acceleration of the randomized Kaczmarz method using quantile information. We show that the method converges faster than the randomized Kaczmarz algorithm when the linear system is consistent. In addition, we demonstrate how this new acceleration may be used in conjunction with qRK, without additional computational complexity, to produce both a fast and robust iterative method for solving large, sparsely corrupted linear systems. Finally, we provide new error horizon bounds for qRK in the setting where the corruption may not be sparse.

SoCalDM is a friendly, day-long research conference designed for discrete mathematicians in Southern California. For more details please visit the conference website:

https://sites.google.com/view/socaldm2025/home

Here is the schedule for the event: 

9:00-9:30 Welcome coffee

9:30-10:00 Jonathan Davidson (Cal State LA), A Combinatorial Design Approach to a Multicolor Bipartite Ramsey Problem

10:10-10:40 Lenny Fukshansky (Claremont McKenna College), On a new absolute version of Siegel’s lemma

10:40-11:00 Coffee Break

11:00-11:30 Mason Shurman (UCI), Covering Random Digraphs with Hamilton Cycles

11:40-12:10 Claire Levaillant (USC), Solutions to the Diophantine equation $\sum_{i=1}^n\frac{1}{x_i}=1$ in integers of the form p^a*q^b with p and q two distinct primes. 

12:10-2:00 Lunch

2:00-2:30 Sehun Jeong (Claremont Graduate University), Integral quadratic forms and lattice angles

2:40-3:10 Justin Troyka (Cal State LA), Growth rates of permutations with given descent or peak set

3:20-3:50 Yizhe Zhu (USC), CLTs for linear spectral statistics of inhomogeneous random graphs

There is an infinite pool of balls and an infinite number of boxes. Let's randomly drop n balls into the boxes and study the number of occupied boxes. Classical limit theorems, the law of large numbers and the central limit theorem, are non-trivial, but known. Can we now prove the law of the iterated logarithm? I will show how to do this using tools that have much wider applicability. The talk is based on joint work with Dariusz Buraczewski (Wroclaw, Poland) and Alexander Iksanov (Kyiv, Ukraine).

In joint work with Chi-Fang Chen, Joel Tropp, and Ramon van Handel, we developed a new method for establishing strong convergence. In this talk I will explain what strong convergence is, and, as an application of our results I will discuss a simple way of generating nearly optimal expanders using very little randomness.