Robert Tarjan: “Binary Search Tree” Abstract: The binary search tree is one of the most fundamental data structures in computer science, with many applications. Binary search trees support binary search in a set of totally ordered items, and ideally reduce search time from linear to logarithmic. A central question is how to keep such a […] (more)


Heisuke Hironaka: “Resolution of Singularities in Algebraic Geometry” Abstract: Algebraic geometry in general has three fundamental types in terms of its base ground: (I) Q (and its fields extensions), (II) F(p) with a prime number p > 0 (and every finite field), and at last (III) Z in the case of the arithmetic geometry. In […] (more)

Sir Tony Hoare: “A finite geometric representation of computer program behaviour” Abstract: Scientists often illustrate the behaviour of a dynamic system by a geometric diagram, in which one dimension represents the passage of time, and the other(s) represent distribution of objects in space. We develop a nonmetric finite plane geometry as an intuitive representation of […] (more)

Barbara Liskov: “The power of abstraction” Abstract: Abstraction is at the center of much work in Computer Science. It encompasses finding the right interface for a system as well as finding an effective design for a system implementation. Furthermore, abstraction is the basis for program construction, allowing programs to be built in a modular fashion. […] (more)

Leslie Lamport: “The PlusCal Algorithm Language” Abstract: An algorithm is not a program, so why describe it with a programming language? PlusCal is a tiny toylike language that is infinitely more expressive than any programming language because an expression can be any mathematical formula. (more)

Vladimir Voevodsky: “UniMath” Abstract: UniMath is a library of formalized mathematics that is based on the Univalent Foundations and written in what we call the UniMath language which is a small subset of the language of the Coq proof assistant. I wrote the core of the library under the name Foundations in 201011 to try […] (more)

Richard Edwin Stearns: “Strategies for Extensive Form Games” Abstract: We want to describe sets of mixed strategies using linear equations such that 1. The number of variables is small compared to the game size. 2. Every mixed strategy has an equivalent strategy in the set. 3. Implementing the strategies is easy. It is known how […] (more)

Raj Reddy: “Too Much Information and Too Little Time” Abstract: This talk is about having to cope with too much information within human time limitations given that we are not changing at exponential rates like semiconductors. Humans make errors, tend to forget, are impatient and look for least effort solutions. Such limitations, sometimes, lead to […] (more)

Fred Brooks: “What Makes the Illusion Work? Studies in Effective Immersive Virtual Environments” Abstract: A virtual environment (VE) is a technological display to the senses that undertakes to make the user believe (to some degree) and behave as if he is present elsewhere. The vision, proposed by Sutherland in 1965, has driven a halfcentury of […] (more)

Ngô Bảo Châu: “The Riemann zeta function and its generalizations” Abstract: Since the publication of Riemann’s memoir on prime numbers less than a given magnitude, the zeta function has never ceased to fascinate mathematicians. We will discuss its many appearances and generalizations in number theory. (more)

Joseph Sifakis: “On the Nature of Computing” Abstract: Computing is a domain of knowledge. Knowledge is truthful information that embedded into the right network of conceptual interrelations can be used to understand a subject or solve a problem. According to this definition, Physics, Biology but also Mathematics, Engineering, Social Sciences and Cooking are all domains […] (more)

Sir Andrew Wiles: “Equations in arithmetic” Abstract: I will describe some of the interactions between modern number theory and the problem of solving equations in rational numbers or integers’. (more)

Brian Schmidt: “State of the Universe” Abstract: Our Universe was created in ‘The Big Bang’ and has been expanding ever since. I will describe the vital statistics of the Universe, including its size, weight, shape, age, and composition. I will also try to make sense of the Universe’s past, present, and future – and describe […] (more)

Raúl Rojas: “Konrad Zuse‘s Early Computing Machines (19351945) Abstract: The exhibition “Konrad Zuse‘s Early Computing Machines (19351945)” about the machines built by the German inventor Konrad Zuse tells a story. It covers the years 1935 to 1945, which was the most creative phase of his life. Raúl Rojas gives an overview of the life and […] (more)

Sir Michael Atiyah: “The Soluble and the Insoluble” Abstract: What do we mean by a solution to a problem? This is both a philosophical question, and a practical one, which depends on what one is trying to achieve and the means, time and money available. The explosion in computer technology keeps changing the goal posts. […] (more)

John E. Hopcroft: “Exciting Computer Science Research Directions” Abstract: We have entered the information age and this has changed the nature of computer science and created many exciting research problems. Two of these are extracting information from large data sources and learning theory. This talk will focus on two problems: first, how to find hidden […] (more)


Leslie G. Valiant: “Holographic Algorithms” Abstract: When are two mathematical functions the same? One might think that this can be generally answered immediately from their definitions. However, functions may have numerous dissimilar alternative definitions. Fortunately, sameness can be often demonstrated systematically by certain linear mappings internal to the function definitions. These mappings, called holographic transformations, […] (more)

Srinivasa S. R. Varadhan: “Entropy and its many Avatars”” Abstract: The concept of Entropy was first introduced by Clausius in his study of the relationship between mechanical energy and heat. It was given a mathematical definition by Boltzmann in his formulation of statistical mechanics. It has since appeared as an indispensable tool in dynamical systems, […] (more)

Andrew C. Yao: “Quantum Computing: A Great Science in the Making” Abstract: In recent years, the scientific world has seen much excitement over the development of quantum computing, and the ever increasing possibility of building real quantum computers. What’s the advantage of quantum computing? What are the secrets in the atoms that could potentially unleash […] (more)

Peter Naur: “Science versus Philosophy” Abstract: Philosophy may be very harmful to science by making claims that have no empirical support, no support in the constitution of the world as it may be observed. A prominent example of philosophical confusions concerns human knowing. Immanuel Kant in his philosophical treatise Critique of pure reason from 1781, […] (more)

Endre Szemerédi: “The Shifting Method” Abstract: The shifting method is a counting technique. To understand it we are going to illustrate the method with three examples. 1) Arithmetic progressions of length 3. 2) Ramsey‐type problem in additive combinatorics. 3) Giving a tight bound for the size of a set S ⊂ [1, N] having the […] (more)

Leonard Max Adleman: “Strata in Complex Analysis” Abstract: What would happen if a bunch of computer scientists who knew (and perhaps still know) next to nothing about complex analysis studied it for a decade? This is not a talk about algorithms or complexity theory; it is pure math, and this is the first presentation of […] (more)

Butler W. Lampson: “Hints and Principles for Computer System Design” Abstract: I have many hints that can be helpful in designing computer systems, as well as a few principles. Two ways to organize them are: • Goals (what you want)—simple, timely, efficient, adaptable, dependable, yummy. • Methods (how to get it)—approximate, increment, iterate, indirect, divide […] (more)

Ivan Sutherland: “Understanding selftimed systems” Abstract: The “clocked” paradigm for hardware design insists that the state of each and every part of a system may change only upon the “tick” of a clock. Each clock tick changes the global system state atomically; between clock ticks the global state remains stable. Global state is a convenient […] (more)

Fred Brooks: “A Personal History of Computers” Abstract: I fell in love with computers at age 13, in 1944 when Aiken (architect) and IBM (engineers) unveiled the Harvard Mark I, the first American automatic computer. A halfgeneration behind the pioneers, I have known many of them. So this abbreviated history is personal in two senses: […] (more)

Vladimir Voevodsky: “UniMath” Abstract: UniMath is the name of the library of formalized mathematics and related formalization tools that Benedikt Ahrens, Daniel Grayson, Michael Warren and myself started to build a little over a year ago based in the earlier code created in 20092014. The library is written entirely in the univalent formalization style and […] (more)

Edmund Melson Clarke: “Model Checking Hybrid Systems” Abstract: Although every undergraduate in computer science learns about Turing Machines, it is not well known that they were originally proposed as a means of characterizing computable real numbers. For a long time, formal verification paid little attention to computational applications that involve the manipulation of continuous quantities, […] (more)

Sir C. Antony R. Hoare: “Pioneers of Computer Science: Aristotle and Euclid” Abstract: In the fifteen years of this century, computer application has expanded dramatically from day to day, both in outreach and in sophistication. However, the origins of computer science itself date back several millennia, to the teachings of the most famous philosophers of […] (more)

Lenore Blum: “Alan Turing and the other Theory of Computation” Abstract: Most theoretical computer scientists are familiar with Alan Turing’s 1936 seminal paper setting the stage for the foundational (discrete) theory of computation. Most however remain unaware of Turing’s 1948 seminal paper, notwithstanding its many references in the modern literature of numerical analysis and computational […] (more)

Shigefumi Mori: “A compelling Desire to do Mathematics” Abstract: Mathematics is admittedly useful in the current digital world, though it is classified as a curiositydriven science, which I accept. There is thus a question frequently asked by nonmathematicians. If mathematicians do their research out of curiosity why should they be supported by tax money? It […] (more)

Leslie Lamport: “A Mathematical View of Computer Systems” Abstract: Mathematics provides what I believe to be the simplest and most powerful way to describe computer systems. (more)

Manuel Blum: “Human Computation” Abstract: A source of power for theoretical computer science has been the interplay of algorithms and complexity: given a computational problem to be solved, algorithm design is concerned with finding faster solutions than what is currently available. Complexity theory is concerned with showing that faster solutions are impossible. When a faster […] (more)

Stefan Hell (Lindau Lecture): “Optical Microscopy: the Resolution Revolution” Abstract: Throughout the 20th century it was widely accepted that a light microscope relying on conventional optical lenses cannot discern details that are much finer than about half the wavelength of light (200400 nm), due to diffraction. However, in the 1990s, the viability to overcome the […] (more)


Daniel A. Spielman: The path from Laplacian matrices to the KadisonSinger problem Abstract: Linear algebra in computer science and mathematics: The path from Laplacian matrices to the KadisonSinger problem. I will tell the story of some remarkable interactions between Mathematics and Computer Science, showing how progress in each area built on developments in the other. […] (more)

Efim Zelmanov: Infinite Groups Abstract: I will discuss the subject of Infinite Groups from the very beginning (1900 + ε ) to our time. (more)

Gerd Faltings: Diophantine Equations Abstract: Diophantine equations are a classical subject. Progress in modern times has been possible because of modern algebraic geometry. I review what is known for curves and the techniques of proof involved. In addition I explain open problems like the “abcconjecture”, a seemingly simple problem for which new attempts have been […] (more)

John E. Hopcroft: Computer Science in the Information Age Abstract: Computer science has changed significantly in the last few years. In the early years computer science was focused on making computers useful and was concerned with programing language, compilers, operating systems, and algorithms. Today the focus has shifted to what computers are used for. Several […] (more)

JeanChristophe Yoccoz: Regularity versus chaos in area preserving maps Abstract: I will present what is perhaps the most important open question in the theory of dynamical systems : do typical areapreserving maps have positive measuretheoretic entropy ? The socalled « standard map family » offers a very concrete instance of this problem. (more)

Shigefumi Mori: Algebraic geometry vs. impressionism paintings Abstract: Mathematics is beautiful as well as useful, though many people do not recognize it. The main topic of my talk is the beauty of algebraic geometry. The research in mathematics is considered to be quite unique and different from those in other academic disciplines. However a mathematician’s […] (more)

Robert Endre Tarjan: Data Structures Abstract: Algorithms are at the core of computing, and choosing a good data structure is often key in producing an efficient algorithm. This talk will review the development of data structures over the last 65 years, and how the speaker came to play a role in it. (more)

Manjul Bhargava: Rational points on elliptic and hyperelliptic curves Abstract: Understanding whether (and how often) a mathematical expression takes a square value is a problem that has fascinated mathematicians since antiquity. In this talk I will give a survey of this problem, and will then concentrate on the case where the mathematical expression in question […] (more)

Martin Hairer: Taming infinities Abstract: Some physical and mathematical theories have the unfortunate feature that if one takes them at face value, many quantities of interest appear to be infinite! Various techniques, usually going under the common name of “renormalization” have been developed over the years to address this, allowing mathematicians and physicists to tame […] (more)

Joseph Sifakis: Is Computing a Science? Abstract: Initially considered rather as applied technology, over the years computing resisted absorption back into the fields of its roots and developed an impressive body of knowledge. We discuss how computing is related to other domains of scientific knowledge and draw conclusions about the very nature of the discipline. […] (more)

Leslie Lamport: How to write a 21st Century Proof Abstract: Mathematicians have made a lot of progress in the last 350 years, but not in writing proofs. The proofs they write today are just like the ones written by Newton. This makes it all too easy to prove things that aren’t true. I’ll describe a […] (more)

Ngô Bảo Châu: Number theory and the Langlands program Abstract: My talk would depict in impressionistic manner the deep transformation that number theory has been undergoing under the influences of ideas of Robert Langlands. (more)

Vinton Gray Cerf: On Digital Preservation Abstract: We are creating and depending upon digital content and processing to an unprecedented degree. How will we assure that this massive amount of information will be accessible in the distant future? Digital preservation has many facets but among them will be the discovery and resolution of references to […] (more)

Wendelin Werner: Randomness, continuum and complex analysis. Abstract: The fact that space and time can be continuous is rather intuitive. But when one thinks of random phenomena, the natural examples that first come to mind are of discrete nature, such as coin tossing. The conceptual question on how randomness can be split up into and […] (more)

William Morton Kahan: Desperately Needed Remedies for the Undebuggability of Large FloatingPoint Computations in Science and Engineering Abstract: How long does it take to either allay or confirm suspicions, should they arise, about the accuracy of a computed result? Often diagnosis has been overtaken by the end of a computing platform’s service life. Diagnosis could […] (more)

Manuel Blum: Toward a Theory of Humanly Computable Protocols Abstract: ALGORITHMS are instructions for single agents. PROTOCOLS are instructions for multiple agents. Agents may be specified to be humans or computers. Our GOAL is to know which cryptographic problems can be solved by protocols that specify certain agents to be human. We are especially interested […] (more)

Sir Michael Atiyah: Beauty in Mathematics Abstract: Many famous mathematicians have highlighted the importance of beauty in mathematics. I will discuss what we mean by beauty and why it is so important. I will compare beauty in mathematics with beauty in the arts and report on recent experiments that show the underlying neurological similarities. (more)



John Hopcroft: Future Directions in Computer Science Research Abstract: Over the last 40 years, computer science research was focused on making computers useful. Areas included programming languages, compilers, operating systems, data structures and algorithms. These are still important topics but with the merging of computing and communication, the emergence of social networks, and the large […] (more)

Butler Lampson: Hints and Principles for Computer System Design Abstract: I have many hints that are often helpful in designing computer systems, and I also know a few principles. There are several ways to organize them: · Goals (What you want) — simple, timely, efficient, adaptable, dependable, yummy. · Methods (How to get it) — […] (more)

Alan Kay: Putting Turing to Work Abstract: Many computer programs today are enormously large — 10s and 100s of millions of lines of code — and distressingly messy and buggy — many to the point that programmers are afraid to make major revisions, but must resort to adding still more code “around the outside”. Though […] (more)

Srinivasa Varadhan: Scaling Limits Abstract: We often model the evolution of a complex system at the lowest or micro level because that is what makes the most physical sense. But if the system is large, we invariably want answers to questions posed on the larger macro or global scale. This then involves the study of […] (more)

Michael O. Rabin: Miracles of Cryptography, Preventing Collusion in Auctions Abstract: We present novel algorithms enabling an auctioneer in a sealed bid auction to prove to bidders who won without revealing any bid values. These methods were extended together with Silvio Micali to enable bidders to submit bids in a deniable uncontrollable manner. One application […] (more)

William Morton Kahan: Desperately Needed Remedies for the Undebuggability of LargeScale FloatingPoint Computations in Science and Engineering Abstract: How long does it take to either allay or confirm suspicions, should they arise, about the accuracy of a computed result? Often diagnosis has been overtaken by the end of a computing platform’s service life. Diagnosis could […] (more)

Vladimir Voevodsky: Univalent Foundations of Mathematics Abstract: Settheoretic approach to foundations of mathematics work well until one starts to think about categories since categories cannot be properly considered as sets with structures due to the required invariance of categorical constructions with respect to equivalences rather than isomorphisms of categories. On the other hand the underlying […] (more)

Joseph Sifakis: System Design Science Abstract: Design is the process that leads to artifacts meeting given requirements. We propose a decomposition of a design process into three main steps each one addressing a corresponding characteristic problem. We identify principles and associated scientific challenges for moving design from an art to a science. Endowing design with […] (more)

Sir Michael Atiyah: Advice to a Young Mathematician Abstract: Having spent a long life in mathematics I thought it would be useful to give some general advice to the younger generation based on my experience. I will discuss many aspects of a life in research, both personal and scientific. Motivation, psychology, curiosity will be some […] (more)

Richard Manning Karp: The Computational Lens on the Sciences Abstract: The computational lens is a metaphor for a relationship that is emerging between the theory of computation and the physical, biological, engineering and social sciences. Viewing natural or engineered systems in therms of their computational requirements or capabilities provides new insights and ways of thinking. […] (more)

Madhu Sudan: Reliable Meaningful Communication Abstract: Around 1940, engineers working on communication systems encountered a new challenge: How can one preserve the integrity of digital data, where minor errors in transmission can have catastrophic effects? The resulting theories of information (Shannon 1948) and error – correcting codes (Hamming 1950) created a ”marriage made in heaven” […] (more)

Silvio Micali: Rational Proofs Abstract: We unify the treatment of asymmetry of information in theoretical computer science and economics. We put forward a new type of proof system, where an unbounded Prover and a bounded Verifier interact, on inputs a string x and a function f, so that the Verifier may learn f(x). In our […] (more)

Avi Wigderson: Randomness Abstract: Is the universe inherently deterministic or probabilistic? Perhaps more importantly – can we tell the difference between the two? Humanity has pondered the meaning and utility of randomness for millennia. There is a remarkable variety of ways in which we utilize perfect coin tosses to our advantage: in statistics, cryptography, game […] (more)

Leslie Valiant: Learning as the Source of Life’s Phenomena Abstract: The assertion that all aspects of living organisms are determined by some combination of learning during an individual life and evolution beforehand is close to tautologous. Recent work that unifies within a computational framework Darwinian evolution on the one hand with learning on the other, […] (more)

Edmund Melson Clarke: Model Checking and the Curse of Dimensionality Abstract: Model Checking is an automatic verification technique for large state transition systems. It was originally developed for reasoning about finitestate concurrent systems. The technique has been used successfully to debug complex computer hardware and communication protocols. Now, it is beginning to be used for […] (more)

Stephen Smale: Protein Folding Abstract: The National Research Council Report on Mathematics to 2025 has drawn attention to 5 areas in science for mathematicians; Protein Folding is one. Here I will give some mathematical setting of this problem addressed to scientists without background in biology. We will lead up to our new results on this […] (more)

Curtis T. McMullen: Billiards and Moduli Spaces Abstracts: The motion of a billiard ball on a rectangular table is related to complex analysis on a torus. Billiards in more general polygons can be studied using surfaces of higher genus. We will present this connection as a gateway to current research on Riemann surfaces and their […] (more)

Raj Reddy: Who invented the Computer: Babbage, Atanasoff, Zuse, Turing or von Neumann? Abstract: In this talk we examine the evolution of automation of computation and the events that are central to the advancement of computers. We will examine the concepts and technologies that were seminal, the necessary conditions, to the development of computers and […] (more)
