Prospects in Theoretical Physics (PiTP) 2011
Prospects in Theoretical Physics is an intensive two-week summer program designed for graduate students and postdoctoral scholars considering a career in theoretical physics. The 2011 program, “Frontiers of Physics in Cosmology,” took place from July 18 to July 29.
Workshop on Sheaf-Theoretic Methods in Symplectic Topology
Elections and Strategic Voting
U.S. presidential elections often drive many citizens to vote strategically—to vote for a candidate they do not like in hope of preventing someone they dislike even more from winning. Many who favored Ralph Nader in the 2000 election ended up voting for Al Gore (though not enough to stop George W. Bush from getting elected). And a lot of those inclined toward Ross Perot in 1992 voted for George H. W. Bush instead (though Bill Clinton still won). An electoral system that induces widespread strategic voting, which is hardly unique to America, is undesirable for many reasons. Most obviously, it deprives citizens of the chance to express their views without fear that doing so will lead to the election of someone they strongly oppose. In this lecture, Eric Maskin, Albert O. Hirschman Professor in the School of Social Science and winner of the 2007 Nobel Memorial Prize in Economic Sciences, discusses how to design electoral systems that do not put voters in this bind.
Serre's Conjectures on the Number of Rational Points of Bounded Height
JOINT IAS/PU NUMBER THEORY SEMINAR
We give a survey of recent results on conjectures of Heath-Brown and Serre on the asymptotic density of rational points of bounded height. The main tool in the proofs is a new global determinant method inspired by the local real and p-adic determinant methods of Bombieri-Pila and Heath-Brown.
On the Comparison of Trace Formulas
GALOIS REPRESENTATIONS AND AUTOMORPHIC FORMS SEMINAR
We shall recall the spectral terms from the trace formula for G and its stabilaization, as well as corresponding terms from the twisted trace formula for GL(N). We shall then discuss aspects of the proof of the theorems stated in the first talk that are related to the comparison of these formulas.
Classification of Representations
GALOIS REPRESENTATIONS AND AUTOMORPHIC FORMS SEMINAR
Suppose that G is a connected, quasisplit, orthogonal or symplectic group over a field F of characteristic 0. We shall describe a classification of the irreducible representations of G(F) if F is local, and the automorphic representations of G in the discrete spectrum if F is global. The classification is by harmonic analysis and endoscopic transfer, which ultimately ties the representations of G to those of general linear groups.
Computer Science and Homotopy Theory
Quadratic Goldreich-Levin Theorems
Decompositions in theorems in classical Fourier analysis which decompose a function into large Fourier coefficients and a part that is pseudorandom
Learning and Testing k-Model Distributions
A k-modal probability distribution over the domain {1,...,N} is one whose histogram has at most k "peaks" and "valleys". Such distributions are a natural generalization of the well-studied class of monotone increasing (or monotone decreasing) probability distributions.
Pseudorandomness in Mathematics and Computer Science Mini-Workshop
In math, one often studies random aspects of deterministic systems and structures. In CS, one often tries to efficiently create structures and systems with specific random-like properties. Recent work has shown many connections between these two approaches through the concept of "pseudorandomness". This workshop highlights these connections, aimed at a joint audience of mathematicians and computer scientists.