Unsurprisingly, a fundamental draw of the Heidelberg Laureate Forum (HLF) is the laureate lectures. Monday, September 25, 2017, the Scientific Program of the 5th HLF got underway with five gripping lectures. ACM A.M Turing laureate Martin Hellman opened up the scientific program and he was followed by the Lindau Lecture of the 5th HLF, given by Aaron Ciechanover who received the Nobel Prize in Chemistry 2004. After a short break, the next round of lectures began with Nevanlinna Prize laureate, Daniel Spielman, and continued with Fields Medalist, Martin Hairer. The lectures came to a close with the renowned mathematician, Piergiorgio Odifreddi. After the lectures, the Scientific Program continued with a double session of postdoc workshops. Below, you can find brief abstracts of the lectures, which are also available to stream online on the HLF video archive.
“The Evolution of Public Key Cryptography”
While I love that public key cryptography is seen as revolutionary, after this talk you might wonder why it took Whit Diffie, Ralph Merkle and me so long to discover it. For example, Whit and I had been talking about trap door cryptosystems and it is a small step from that concept to public key cryptography. This talk will also high¬light the contributions of some unsung (or “under-sung”) heroes: Ralph Merkle, John Gill, Stephen Pohlig, Richard Schroeppel, Loren Kohnfelder, and researchers at GCHQ (Ellis, Cocks, and Williamson).
Lindau Lecture at the 5th HLF
“The Personalized Medicine Revolution: Are We Going to Cure all Diseases and at What Price?”
Many important drugs such as penicillin were discovered by serendipity. Other major drugs like the cholesterol-reducing statins were discovered using more ad¬vanced technologies, such as screening of large chemical libraries. In all these cases, the mechanism of action of the drug were largely unknown at the time of their dis¬covery and was unraveled later. With the realization that patients with apparently similar diseases – breast or prostate cancer, for example – respond differently to similar treatments, we have begun to understand that the molecular bases of what we thought is the same disease entity, are different. (Abbreviated abstract)
We provide context for and explain the recent Approximate Gaussian Elimination algorithm of Kyng and Sachdeva. Gaussian Elimination is the first algorithm most of us learn for solving systems of linear equations. While it is simple and elegant, it can also be impractically slow. Kyng and Sachdeva show that, after carefully modifying elimination to randomly drop and rescale entries, it can provide very fast approximate solutions to systems of equations in Laplacian matrices. Our implementation of a refinement of this algorithm is now among the best Laplacian solvers in practice. We will explain what Laplacian matrices are, what it means to approximately solve a system of linear equations over the reals, and how one analyzes this algorithm using recent results in Random Matrix Theory. We will also discuss what it means for an algorithm to be the “best in practice.”
“The mathematics of randomness”
From the gambling machines in a casino to the predictions of next week’s weather, the world that surrounds us is governed by seemingly random events. How do mathematicians make sense of this and what does it even mean to “predict” some¬thing inherently random? We will explore these questions and see what are the main guiding principles of our modern understanding of randomness. Along the way, we will see how the works of an 18th century egyptologist and a 19th century biologist allow today’s banks to model the stock market.
“Ménage à trois: art, math and computer science”
On the occasion of the Computer Art Exhibition organized for this meeting, I will give a short general overview of the relationships between art, mathematics and computer science, to place into a wider context the specific works exhibited. I will tell a story in three acts, illustrated by many pictures. The first act deals with a superficial level of interaction beween art and mathematics, in which mathemat-ical objects (solids, knots, surfaces …) are used as subjects of the works of art. The second act deals with a deeper level of penetration, in which mathematical con¬cepts (tessellations, perspective, hyperbolic geometry …) are used as structures for the works of art. And the third act deals with an even deeper level of integration, in which computers and programs are used as tools by the artist, to achieve infinitary extensions of the finitary procedures used in the previous two acts.
Running parallel to each workshop session were separate ‘Heidelberg City Tours’ which revealed some of the sights that Heidelberg has to offer. The participants were shuttled to the Halle 02 for the Welcome Dinner and had some time to enjoy the venue’s park before the heading inside to enjoy the food.
Photos from Monday are available on the HLF flickr gallery.