arXiv subjects

Bryan Wang Peng Jun

Publications and source records attributed to Bryan Wang Peng Jun.

3 recordsLinked to original sources

arXiv2025

On knots that divide ribbon knotted surfaces

We define a knot to be half ribbon if it is the cross-section of a ribbon 2-knot, and observe that ribbon implies half ribbon implies slice. We introduce the half ribbon genus of a knot K, the minimum genus of a ribbon knotted surface of which K is a cross-section. We compute this genus for all prime knots up to 12 crossings, and many 13-crossing knots. The same approach yields new computations of the doubly slice genus. We also introduce the half fusion number of a knot K, that measures the complexity of ribbon 2-knots of which K is a cross-section. We show that it is bounded from below by the Levine-Tristram signatures, and differs from the standard fusion number by an arbitrarily large amount.

math.GT↗

arXiv2023

Global theta lifting and automorphic periods associated to nilpotent orbits

A systematic way to organise the interesting periods of automorphic forms on a reductive group $G$ is via the theory of nilpotent orbits of $G$. On the other hand, it is known that the theta correspondence can be used effectively to relate automorphic periods on each member of a dual pair. In this paper, we establish this relation in full generality, facilitated by a certain transfer of nilpotent orbits via moment maps. This is the analogous global result to the local result previously established by Gomez and Zhu.

math.NT↗

arXiv2023

Generalised Whittaker models as instances of relative Langlands duality

The recent proposal by Ben-Zvi, Sakellaridis and Venkatesh of a duality in the relative Langlands program, leads, via the process of quantization of Hamiltonian varieties, to a duality theory of branching problems. This often unexpectedly relates two a priori unrelated branching problems. We examine how the generalised Whittaker (or Gelfand-Graev) models serve as the prototypical example for such branching problems. We give a characterization, for the orthogonal and symplectic groups, of the generalised Whittaker models possibly contained in this duality theory. We then exhibit an infinite family of examples of this duality, which, provably at the local level via the theta correspondence, satisfy the conjectural expectations of duality.

math.RT↗