November 30, 2018: Jintai Ding

Quantum-Proof Blockchain

Jintai Ding — University of Cincinnati

Blockchain technology is now going through explosive development with the aim to develop a new generation of revolutionary financial technology. The most successful example is new digital currency bitcoin. The fundamental building block in blochchain technology is actually cryptographic algorithms, which is why bistcoin is actually called a cryptocurrency. The main cryptographic algorithms used in blockchain technology are hash functions and

elliptic curve digital signatures. As we all know, quantum computers are not such a significant threat to the security of Hash functions but it can be fatal to the elliptic curve digital signatures. In this presentation, we will first show how the quantum computers can threat the security of blockchain technology, in particular, why the existing blockchain technology used in bitcoins can not fundamentally avoid such a practical attack.  Then we will explain the challenges we will face if if we just plug in existing post-quantum cryptographic solutions as a drop-in to replace the existing elliptic curve signatures, in particular, the key size problem and a few others. In the end, we will present some of the new solutions we have been developing to deal with these fundamental problems including a new type of proof of work algorithms, which, we believe, provide very viable solutions for the future long term secure blockchain technology.

November 29, 2018: Iwan Duursma

CANCELLED

Code Constructions for Distributed Storage

Iwan Duursma — University of Illinois at Urbana-Champaign

(Joint ADM/RTG Seminar)

Storage solutions for storing data on a single disk or a combination of several disks do not perform well at the scale of data centers that employ thousands of servers. Over the last decade two new families of error-correcting codes have been introduced that better address the requirements for large scale distributed storage of data. We discuss the main parameters for these families and present a variety of algebraic and graph theoretic methods that can be used to construct codes with good trade offs among the main parameters.

November 14, 2018: Yan Zhuang

Shuffle-Compatible Permutation Statistics

Yan Zhuang — Davidson College

It has been observed since the early work of Richard Stanley that several well-known permutation statistics are “compatible” with the operation of shuffling permutations. In joint work with Ira Gessel, we formalize this notion of a shuffle-compatible permutation statistic and develop a unifying framework for studying shuffle-compatibility, which has close connections to the theory of P-partitions, quasisymmetric functions, and noncommutative symmetric functions. In this talk, I will survey the main results of our work as well as several new directions of research concerning shuffle-compatibility.

November 8, 2018: Michael Cowen and James Gossell

The power edge ideal of a finite simple graph

Michael Cowen and James Gossell — Clemson University

Every electric power system can be modeled by a graph G whose vertices represent electrical buses and whose edges represent power lines. A phasor measurement unit (PMU) is a monitor that can be placed at a bus to observe the voltage at that bus as well as the current and its phase through all incident power lines. The problem of monitoring the entire electric power system using the fewest number of PMUs is closely related to vertex covering and dominating set problems in graph theory.

In this talk, we will give an overview of the PMU placement problem and its connections to commutative ring theory. By defining the power edge ideal IPG of a graph G, we will show how to use graphs of electric power grids to generate polynomial rings with desired algebraic properties. In particular, we will classify the trees G for which IPG is Cohen-Macaulay and prove that every such ideal is also a complete intersection.

This project is joint work with Alan Hahn, Frank Moore, and Sean Sather-Wagstaff.