Award
Professor receives honorable Frontiers of Science Award
The new International Congress for Basic Science (ICBS) honors top research and emphasizes excellent and outstanding scholarly achievements from the past five years.
Professor Vivek Shende in collaboration with Tobias Ekholm (Uppsala University) and Lenhard Ng (Duke University) were honored with this award for the paper A complete knot invariant from contact homology published in Inventiones mathematicae (2018).
The inaugural ICBS was held in Beijing, July 2023 covering both mathematics, theoretical physics, and theoretical computer and information science. To receive this prestigious new award the paper’s achievement must be of highest scientific value and originality and have made an important contribution to its area.
According to ICBS, the goal of this award is “to encourage young scholars to look to the frontiers of basic science, set goals to obtain breakthrough results as early as possible, and contribute wisdom and energy to humankind's study of the mysteries of the natural world.”
Meet the researcher
Vivek Shende is Professor at the Centre for Quantum Mathematics and at Department of Mathematics and Computer Science (IMADA), University of Southern Denmark.
”I am very happy about this award and would like to thank my excellent collaborators Tobias Ekholm and Lenhard Ng
A complete knot invariant from contact homology
Abstract: We construct an enhanced version of knot contact homology and show that we can deduce from it the group ring of the knot group together with the peripheral subgroup. In particular, it completely determines a knot up to smooth isotopy. The enhancement consists of the (fully noncommutative) Legendrian contact homology associated to the union of the conormal torus of the knot and a disjoint cotangent fiber sphere, along with a product on a filtered part of this homology. As a corollary, we obtain a new, holomorphic-curve proof of a result of the third author that the Legendrian isotopy class of the conormal torus is a complete knot invariant.
