Since the work of Jacobi and Siegel, it is well known that Theta
series of quadratic lattices produce modular forms. In a vast
generalization, Kudla and Millson have proved that the generating
series of special cycles in orthogonal and unitary...
Direct-product testers” are used in the design of (some)
probabilistically checkable proofs (PCPs), which, in turn, play a
fundamental role in modern complexity theory and cryptography. We
investigate the direct-product testability of certain...
The classical Rokhlin Lemma asserts that for an aperiodic
measure-preserving transformation $T$ of a probability space, one
can find a "tower" of sets on which $T$ acts by translation and
which covers almost all of the space. This result is a basic...
In 2003, Bressan proposed a conjecture on the mixing efficiency
of incompressible flows, which remains open. This talk surveys
progress toward resolving Bressan’s mixing conjecture and presents
a new result confirming its asymptotic validity for...
A line of work has shown how nontrivial uniform algorithms for
analyzing circuits can be used to derive nonuniform circuit lower
bounds. In this talk, I will show in depth how the nonexistence of
nontrivial circuit-analysis algorithms can also imply...
