Colloquium

Digital geometry processing (DGP) is one of the core topics of computer graphics, and has been an active line of research for over two decades. On one hand, the field introduces theoretical studies in topics such as vector-field design, preservative maps and deformation theory. On the other hand, the tools and algorithms developed by this community are applicable in fields ranging from computer-aided design, to multimedia, to computational biology and medical imaging.

Even if what you do is rocket science, technical and logical faculties are only part of the skills you need for your job. Your success has always been dependent on your soft skills—your understanding of and your ability to collaborate with fellow humans. However, major developments in technology and economy are making soft skills even more vital.

Inspired by the astonishing success of cryptocurrencies, most notably the Bitcoin system, several recent works have focused on the design of robust blockchain-style protocols that work in a peer-to-peer setting such as the Internet. In contrast to the setting traditionally considered in multiparty computation (MPC), in these systems, honesty is measured by computing power instead of requiring that only a certain fraction of parties is controlled by the adversary.

Consider the following scenario: A 911 dispatcher receives a call about a fire and needs to dispatch the closest fire truck. There are two difficulties with locating the appropriate vehicle to dispatch. First, the vehicles are constantly on the move. Second, there are different types of emergency vehicles, whereas the dispatcher specifically needs a fire truck.

Voting is one of the most recognized symbols of democracy. Having been around for over two millennia, we might expect voting mechanisms to be a solved problem. However, it turns out that this is not the case. The reason is a "contradiction" in our security requirements from voting. We want voting to be resistant to vote buying and coercion—implying ballots must be secret—but at the same time verifiably resistant to tampering—implying that the ballot counting must be public.

Intel's Software Guard Extensions (SGX) is a recent processor-based security technology that was introduced in the 6^th Generation Intel Core processor (microarchitecture codename Skylake). It provides a trusted execution environment for software modules, in the presence of malicious software, operating systems, hypervisors, and some hardware attacks. SGX enables developers to provide, with relative ease and flexibility, a high level of security for their applications.

In the lecture I will talk about some mathematical puzzles that have preoccupied me over the years, and I will also reveal to you some of the secrets of our trade.
I will first discuss trees, their numbers, and how to extend the notion of trees to two dimensional objects, next, I will talk about high dimensional geometric bodies,
and the last topic will be about election rules that are immune to errors in counting the votes.

Meshcash is a new framework for cryptocurrency protocols. It combines a novel, proof-of-work based, permissionless byzantine consensus protocol (the tortoise) that guarantees eventual consensus and irreversibility, with a possibly-faulty but quick consensus protocol (the hare). The construction is modular, allowing any suitable "hare" protocol to be plugged in. The combined protocol enjoys best of both worlds properties: consensus is quick if the hare protocol succeeds, but guaranteed even if it is faulty.

In this talk, I will briefly introduce myself and mainly focus on my doctoral dissertation, which addresses realistic facial animation. Realistic facial synthesis is one of the most fundamental problems in computer graphics, and is desired in a wide variety of fields, such as film and advertising, computer games, teleconferencing, user-interface agents and avatars, and facial surgery planning. In the dissertation, we present the most commonly practiced facial content creation process, and contribute to the quality of each of its three steps.

A clean model for designing algorithms for processing strings is to assume a read-only random access to the input and measure the working space. This is particularly attractive when we consider big data, where even a linear time complexity might be not enough if the algorithm uses substantial amount of additional space on top of the input (the streaming model is another possibility, but it appears too restrictive for some natural problems). We consider three basic questions in such a model: