1,397 research outputs found
Relative trace formulae toward Bessel and Fourier-Jacobi periods of unitary groups
We propose a relative trace formula approach and state the corresponding
fundamental lemma toward the global restriction problem involving Bessel or
Fourier-Jacobi periods of unitary groups ,
extending the work of Jacquet-Rallis for (which is a Bessel period). In
particular, when , we recover a relative trace formula proposed by Flicker
concerning Kloosterman/Fourier integrals on quasi-split unitary groups. As
evidence for our approach, we prove the fundamental lemma for
in positive characteristics.Comment: 55 page
Enhanced adic formalism and perverse t-structures for higher Artin stacks
In this sequel of arXiv:1211.5294 and arXiv:1211.5948, we develop an adic
formalism for \'etale cohomology of Artin stacks and prove several desired
properties including the base change theorem. In addition, we define perverse
t-structures on Artin stacks for general perversity, extending Gabber's work on
schemes. Our results generalize results of Laszlo and Olsson on adic formalism
and middle perversity. We continue to work in the world of -categories
in the sense of Lurie, by enhancing all the derived categories, functors, and
natural transformations to the level of -categories.Comment: 53 pages. v2: reformulatio
Data-Driven Approach to Simulating Realistic Human Joint Constraints
Modeling realistic human joint limits is important for applications involving
physical human-robot interaction. However, setting appropriate human joint
limits is challenging because it is pose-dependent: the range of joint motion
varies depending on the positions of other bones. The paper introduces a new
technique to accurately simulate human joint limits in physics simulation. We
propose to learn an implicit equation to represent the boundary of valid human
joint configurations from real human data. The function in the implicit
equation is represented by a fully connected neural network whose gradients can
be efficiently computed via back-propagation. Using gradients, we can
efficiently enforce realistic human joint limits through constraint forces in a
physics engine or as constraints in an optimization problem.Comment: To appear at ICRA 2018; 6 pages, 9 figures; for associated video, see
https://youtu.be/wzkoE7wCbu
Relative trace formulae toward Bessel and Fourier–Jacobi periods on unitary groups
We propose an approach, via relative trace formulae, toward the global restriction problem involving Bessel or Fourier–Jacobi periods on unitary groups U[subscript n] × U[subscript m], generalizing the work of Jacquet–Rallis for m = n − 1 (which is a Bessel period). In particular, when m = 0, we recover a relative trace formula proposed by Flicker concerning Kloosterman/Fourier integrals on quasi-split unitary groups. As evidences for our approach, we prove the vanishing part of the fundamental lemmas in all cases, and the full lemma for U[subscript n] × U[subscript n].National Science Foundation (U.S.). (grant DMS–1302000
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