Locally conformally symplectic (LCS) manifolds are
generalisations of symplectic manifolds where the 2-form is not
closed but instead satisfies the identity dω = η ∧ ω for a closed
1-form η. The study of these manifolds is equivalent to that
of...
The past few years have seen rapid development in arithmetic
statistics over function fields over finite fields, questions
like: what is the distribution of the ell-primary part of the
class group of a random quadratic extension of F_q(t)?
(Cohen...
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...
