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SCIENTIFIC PROGRAM

Invited Lecturers : Alain Connes - Robbert Dijkgraaf - Maxime Kontsevich - Roger Penrose - Carlo Rovelli

Invited speakers

Roger Penrose :

• Sir Roger Penrose (born 8 August 1931) is an English mathematical physicist and Emeritus Rouse Ball Professor of Mathematics at the Mathematical Institute, University of Oxford and Emeritus Fellow of Wadham College. He has received a number of prizes and awards, including the 1988 Wolf Prize for physics which he shared with Stephen Hawking for their contribution to our understanding of the universe.[1] He is renowned for his work in mathematical physics, in particular his contributions to general relativity and cosmology.

• Penrose earned his Ph.D. at Cambridge (St John's College) in 1958, writing a thesis on "tensor methods in algebraic geometry" under algebraist and geometer John A. Todd. He devised and popularised the Penrose triangle in the 1950s, describing it as "impossibility in its purest form" and exchanged material with the artist M. C. Escher, whose earlier depictions of impossible objects partly inspired it. In 1965 at Cambridge, Penrose proved that singularities (such as black holes) could be formed from the gravitational collapse of immense, dying stars.
  

  In 1967, Penrose invented the twistor theory which maps geometric objects in Minkowski space into the 4-dimensional complex space with the metric signature (2,2). In 1969 he conjectured the cosmic censorship hypothesis. This proposes (rather informally) that the universe protects us from the inherent unpredictability of singularities (such as the one in the centre of a black hole) by hiding them from our view behind an event horizon. This form is now known as the "weak censorship hypothesis"; in 1979, Penrose formulated a stronger version called the "strong censorship hypothesis". Together with the BKL conjecture and issues of nonlinear stability, settling the censorship conjectures is one of the most important outstanding problems in general relativity. Also from 1979 dates Penrose's influential Weyl curvature hypothesis on the initial conditions of the observable part of the Universe and the origin of the second law of thermodynamics. Penrose and James Terrell independently realized that objects travelling near the speed of light will appear to undergo a peculiar skewing or rotation. This effect has come to be called the Terrell rotation or Penrose-Terrell rotation.

  Roger Penrose is well known for his 1974 discovery of Penrose tilings, which are formed from two tiles that can only tile the plane nonperiodically, and are the first tilings to exhibit fivefold rotational symmetry. Another noteworthy contribution is his 1971 invention of spin networks, which later came to form the geometry of spacetime in loop quantum gravity. He was influential in popularizing what are commonly known as Penrose diagrams (causal diagrams). In 2004 Penrose released The Road to Reality: A Complete Guide to the Laws of the Universe. He has proposed a novel interpretation of quantum mechanics.

Alain Connes :

• Alain Connes (born 1 April 1947) is a French mathematician, currently Professor at the Collège de France, IHÉS and Vanderbilt University.
  

  Alain Connes is one of the leading specialists on operator algebras. In his early work on von Neumann algebras in the 1970s, he succeeded in obtaining the almost complete classification of injective factors. Following this he made contributions in operator K-theory and index theory, which culminated in the Baum-Connes conjecture. He also introduced cyclic cohomology in the early 1980s as a first step in the study of noncommutative differential geometry.

  Connes has applied his work in areas of mathematics and theoretical physics, including number theory, differential geometry and particle physics.
  

• Connes was awarded the Fields Medal in 1982, the Crafoord Prize in 2001 and the gold medal of the CNRS in 2004. He is a member of the French Academy of Sciences and several foreign academies and societies, including the Danish Academy of Sciences, Norwegian Academy of Sciences, Russian Academy of Sciences, and US National Academy of Sciences.
  

Robbert Dijkgraaf :

• Robbert Dijkgraaf (born January 24, 1960) is a Dutch mathematical physicist and string theorist.

  Dijkgraaf started his education in physics at Utrecht University in 1978. After completing his Bachelor's degree equivalent in 1982 he briefly turned away from physics to pursue painting at the Gerrit Rietveld Academie. He later continued his education at Utrecht University, where he studied under Nobel laureate Gerard 't Hooft. He obtained his doctorate in 1989. Subsequently, Dijkgraaf held positions at Princeton University and the Institute for Advanced Study. In 1992, he was appointed professor at the University of Amsterdam, where he held the chair of mathematical physics.

  His research focuses on string theory and the interface of mathematics and physics in general. He is most well-known for his work on topological string theory and matrix models, and has given name to the Dijkgraaf-Witten invariants and the Witten-Dijkgraaf-Verlinde-Verlinde formula.

   

• In 2003, Dijkgraaf was awarded the Spinozapremie. In doing so he became the first recipient of the award whose advisor also was a recipient ('t Hooft received the first spinozapremie in 1995).

  In the Netherlands, Dijkgraaf is also a promotor of hard sciences. He frequently appears on Dutch national television and has a (monthly) column in the Dutch newspaper NRC Handelsblad. He also used part of his Spinozapremie grant to set up a website targeted at children to promote science: Proefjes.nl.

  Dijkgraaf is a member of the Royal Netherlands Academy of Arts and Sciences and the Royal Holland Society of Sciences and Humanities. Since May 1, 2008 he is president of the Royal Netherlands Academy of Arts and Sciences. He is also elected as one of the two co-chairs of the InterAcademy Council for the period 2009-2013.

   

Carlo Rovelli :

• Carlo Rovelli is an Italian physicist and cosmologist who has worked in Italy, the USA, and France. He was born in Verona, Italy in 1956. In 1986 he obtained his PhD at the University of Padova, Italy. He is currently at the Université de la Méditerranée, in the Centre de Physique Théorique, in Marseille, France. He is also affiliated Professor in the Department of History and Philosophy of Science of the University of Pittsburgh, USA. His work is mainly in the field of quantum gravity.

  In 1988 Carlo Rovelli, Lee Smolin and Abhay Ashtekar introduced a theory of quantum gravity denoted loop quantum gravity. In 1995 Rovelli and Smolin obtained an explicit basis of states of quantum gravity, labelled by Penrose's spin networks, and using this basis they were able to show that the theory predicts that area and volume are quantized. This result indicates the existence of a discrete structure of space at the very small scale. The theory is today considered a leading candidate for a quantum theory of gravity. In 1994 Rovelli introduced the relational interpretation of quantum mechanics, based on the idea that all quantum states are relative to an observer. With Alain Connes he formulated a covariant model of Quantum field theory, based on the thermal time hypothesis. According to this hypothesis time does not exist in the fundamental theory and emerges only in a thermodynamical or statistical context. If this were correct the flow of time would be an illusion, deriving from the incompleteness of knowledge. Rovelli has also worked in the history and philosophy of science. He has written a book on the Greek philosopher Anaximander which was published in France in June 2009.

• In 1995 Rovelli has received the International Xanthopoulos Award for his contributions to theoretical physics. In 2009 is has obtained the first 'community' prize of the FQXi contest on the 'nature of time'. He is senior member of the Institut Universitaire de France (IUF), member of the Académie Internationale de Philosophie des Sciences and honorary Professor of the Beijing Normal University, in China.

Maxim Kontsevich :

• Maxim Lvovich Konsevitch (Russian: Максим Львович Концевич) (born 25 August 1964) is a Russian mathematician. He received a Fields Medal in 1998, at the 23rd International Congress of Mathematicians in Berlin. He also received the Henri Poincaré Prize in 1997 and a Crafoord Prize in 2008.
  

  Born into the family of Lev Rafailovich Kontsevich – Soviet orientalist and author of the Kontsevich system. After ranking second in the All-Union Mathematics Olympiads, he attended Moscow State University but left without a degree in 1985 to become a researcher at the Institute for Problems of Information Transmission in Moscow. In 1992 he received his Ph.D. at the University of Bonn under Don Bernard Zagier. His thesis proves a conjecture by Edward Witten that two quantum gravitational models are equivalent. Currently he is a Professor at the Institut des Hautes Études Scientifiques (IHÉS) in Bures-sur-Yvette, France and Distinguished Professor at University of Miami in Coral Gables, Florida, U.S..

  His work concentrates on geometric aspects of mathematical physics, most notably on knot theory, quantization, and mirror symmetry. His most famous result is a formal deformation quantization that holds for any Poisson manifold. He also introduced knot invariants defined by complicated integrals analogous to Feynman integrals. In topological field theory, he introduced the moduli space of stable maps, which may be considered a mathematically rigorous formulation of the Feynman integral for topological string theory. These results are a part of his "contributions to four problems of geometry" for which he was awarded the Fields Medal in 1998.

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