Upcoming Seminars

We consider the geo-localization task - finding the pose (position & orientation) of a camera in a large 3D scene from a single image. We aim toexperimentally explore the role of geometry in geo-localization in a convolutional neural network (CNN) solution. We do so by ignoring the often available texture of the scene. We therefore deliberately avoid using texture or rich geometric details and use images projected from a simple 3D model of a city, which we term lean images. Lean images contain solely information that relates to the geometry of the area viewed (edges, faces, or relative depth). We find that the network is capable of estimating the camera pose from the lean images, and it does so not by memorization but by some measure of geometric learning of the geographical area. The main contributions of this work are: (i) providing insight into the role of geometry in the CNN learning process; and (ii) demonstrating the power of CNNs for recovering camera pose using lean images.
 
This is a joint work with Moti Kadosh  & Ariel Shamir
 

Periods of automorphic forms have an important place in the theory of automorphic representations. They are often related to (special values of) L-functions and have applications to arithmetic geometry and analytic number theory. For an automorphic form on a group G, a period is its integral over a subgroup of G. If the automorphic form is not cuspidal such integrals are usually divergent. It is nonetheless possible in many cases to extend the definition of the period to almost all automorphic forms which has direct applications to the study of the given period. In this talk I will describe a general procedure of defining such periods in the case when the subgroup is reductive.
I will also discuss the joint work with A. Pollack and C. Wan that applies this to the study of certain periods and their relations to special values of L-functions confirming predictions of Sakellaridis and Venkatesh.