Hiram H. Lopez, Clemson University
“Linear codes using basic tools of commutative algebra” – video
In this talk we are going to give an introduction to linear codes and we will see how they are applied. Then we introduce the linear codes known as evaluation codes. We are interested in this sort of codes because its parameters can be computed using basic tools of commutative algebra, and we will see how to do it.
The family of evaluation codes mainly depends on an affine or a projective set, thus we are going present some examples using different families of affine and projective points.
Finally, we are going to use the ideas of evaluation codes to define purely algebraic concepts.
Jintai Ding, University of Cincinnati – Joint with ADM Seminar
“The LWE-based key exchange” – video
Public key cryptosystems (PKC) are a critical part of the foundation of modern communication systems, in particular, the Internet. However Shor’s algorithm shows that the existing PKC like Diffie-Hellmann key exchange, RSA and ECC can be broken by a quantum computer. To prepare for the coming age of quantum computing, we need to build new public key cryptosystems that can resist quantum computer attacks. In this lecture, we present a practical and provably secure (authenticated) key exchange protocol based on the learning with errors problems, which is conceptually simple and has strong provable security properties. This new construction was established in 2011-2012. These protocols are indeed practical. We will explain that all the existing LWE based key exchanges are variants of this fundamental design. In addition, we will explain how to use the signal function invented for KE for authentication schemes.
Winnie Li – Pennsylvania State University
“Modular forms for noncongruence subgroups: an introduction” – video – slides
“Modular forms for noncongruence subgroups: recent progress and open problems” – video – slides
Abstract: Modular forms for congruence subgroups have been studied for over one century.
There are fabulous results and remarkable applications. On the other hand, the
arithmetic of modular forms for noncongruence subgroups is much less understood.
Nonetheless there are very interesting questions in this area waiting to be explored.
In this two-part talk we shall compare the developments in both areas, and discuss
important open problems and review recent progress on noncongruence forms.