Last monday we had the annual meeting of the Israeli Mathematical Union (IMU) that took place this year in Bar-Ilan University in Ramat Gan. (IMU is famously also the acronym of the International Mathematical Union but in this post IMU will stand for “Isreali Mathematical Union.”) The first IMU meeting that I participated was in 1972 and I try to participate every year. One year, Nati Linial and me were the treasurer and secretary of the IMU and were assigned (by the IMU president at the time, Yisrael Aumann) the task of organizing the meeting. The IMU meetings have different formats and usually they are very successful and this year was no exception. So I will tell you a little more about it later. Five more short items for today:
- Last Wednesday two new research centers were inaugurated. Here at the Hebrew University of Jerusalem the new Quantum Information Science Center had its kick-off workshop on Wednesday. Here are the slides of the lecture I gave devoted to my debate with Aram Harrow. (As always, remarks and corrections are most welcome.)
- In Haifa at the Technion , the newly founded Technion-Microsoft Electronic-Commerce Research Center held a one day workshop on electronic-commerce .
- There is a new research blog Windows on Theory devoted to research in theoretical computer science. It is run by theory people from Microsoft Research, most from the Silicon Valley. The last post mentioned a nice story of Ehud Friedgut about hitting a rotating sphere from a 1997 paper of mine.
- Last month, Luca Trevisan was the Erdos’ Lecturer of the center for Discrete Mathematics and Theoretical Computer Science, here at HU. Luca is one of the world leaders in theoretical computer science and also the author of a famous blog: In Theory. Luca Trevisan’s blog’s celebration of Alan Turing’s 100th birthday, spanned over several posts, will be devoted to a big part of Turing’s life – being gay.
- Starting on monday: A conference on graph limits (“Graphs and Analysis“) at IAS, Princeton. Many great talks are expected. Our blog is negotiating with Itai Benjamini for letting us post the slides of his lecture on Euclidean versus graph metrics.
The Bar-Ilan Meeting
David Kazhdan gave a talk about the classic master equation.
The abstract of his lecture read:
We formalize the construction by Batalin and Vilkovisky of a solution of the classical master equation associated with a classical action, a regular function on a nonsingular affine variety. We introduce the notion of stable equivalence of solutions and prove that a solution exists and is unique up to stable equivalence. A consequence is that the associated BRST cohomology groups are independent of choices and are uniquely determined up to unique isomorphism by the classical action.
David, however, decided to give a talk about the background to a talk described in the abstract. He gave a quick mathematical introduction to classical and quantum mechanics, leading to the Faddeev-Popov method, described in as elementary and jargon-free as possible differential geometry language. Beautiful talk!
Let’s glimpse at the lecture: Quantum mechanics is about calculating integrals of the form While classical mechanics is the study of the stationary points of . (In cases where the stationary point is unique, the derivative at a stationary point is well-defined and the Hessian is non-zero, and other pleasant things occur we can approximate the integral by a normalized value of .)
When there is a group G (gauge symmetry) acting on X then we can try to make the computation on the quotient X/G . (This computation leads to expansion in terms of Feynman diagrams.) Faddeev-Popov method is based on the idea: don’t take quotients but rather enlarge your space! So you replace X by the Cartesian product of X with the associated Lie algebra of G. (Here, a structure of a “supermanifold” emerges.) At this point a) some differential geometry enters into the picture, b) this allows to the master equation promised in the title to emerge, and c) The computation has some cohomological nature.
After David’s talk Jonathan Wahl gave a talk on Topology versus geometry of complex singularities. There is a famous book by Milnor on this topic and a lot have been learned since. Then there was a brief prize awards session. Our annual Erdos’ prize for a mathematician under 40, was awarded to Irit Dinur, and the Haim Nessiyahu prize for excellent doctoral thesis was awarded to Alexander Sodin on his work on random matrices. Ran Raz gave a talk about PCP and, in particular, on Irit’s contribution. This is the 20th anniversary of the PCP Theorem. Heartily Congratulations to Irit and Sasha.
And then we separated into ten parallel sessions: Algebra and number theory; Analysis; Discrete Math and Computer Science; Dynamics and Ergodic Theory; History and Philosophy of Mathematics; Homotopy Theory; Mathematical Education; Topology and Geometry; Probability; Nonlinear Analysis and Optimization. To avoid being torn between too many good options my policy is usually to stay with the combinatorics session. But this year since my flight was brutally delayed and I landed only at five in the morning I had to choose the option of going home to sleep.