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Seminars in Combinatorics and Optimization
Crypto Reading Group -Sam Jaques-Impossibility Results for Post-Compromise Security in Real-World Communication Systems
| Speaker | Sam Jaques |
| Affiliation | University of Waterloo |
| Location | MC 6029 |
Abstract: Modern secure communication systems, such as iMessage, WhatsApp, and Signal include intricate mechanisms that aim to achieve very strong security properties. These mechanisms typically involve continuously merging fresh secrets into the keying material that is used to encrypt messages during communications. In the literature, these mechanisms have been proven to achieve forms of Post-Compromise Security (PCS): the ability to provide communication security even if the full state of a party was compromised some time in the past. However, recent work has shown these proofs cannot be transferred to the end-user level, possibly because of usability concerns. This has raised the question of whether end-users can actually obtain PCS or not, and under which conditions.
Algebraic Graph Theory-Sebastian Cioabă-Spectral Moore theorems for graphs and hypergraphs
| Speaker: | Sebastian Cioabă |
| Affiliation: |
University of Delaware |
| Location: | Please contact Sabrina Lato for Zoom link. |
Abstract: The spectrum of a graph is closely related to many graph parameters. In particular, the spectral gap of a regular graph which is the difference between its valency and second eigenvalue, is widely seen an algebraic measure of connectivity and plays a key role in the theory of expander and Ramanujan graphs. In this talk, I will give an overview of recent work studying the maximum order v(k,\theta) of a regular graph (bipartite graph or hypergraph) of given valency k whose second largest eigenvalue is at most a given value \theta. This problem can be seen as a spectral Moore problem and has connections to Alon-Boppana theorems for graphs and hypergraphs and with the usual Moore or degree-diameter problem.
Algebraic and enumerative combinatorics seminar - Nathan Pagliaroli- Counting triangulations from bootstrapping tensor integrals
| Speaker: | Nathan Pagliaroli |
| Affiliation: | University of Waterloo |
| Location: | MC 5417 |
Abstract: Tensor integrals are the generating functions of triangulations of pseudo-manifolds. Such triangulations are constructed by gluing simplices along facets. These generating functions satisfy an infinite system of recursive equations called the Dyson-Schwinger equations, derived by reclusively gluing together triangulations. Such integrals also satisfy positivity constraints. By combining the Dyson-Schwinger equations and positivity constraints in a process called bootstrapping we are able to deduce known results for the generating functions of certain classes of triangulations as well as find new explicit formulae. This talk is based on joint work with Carlos I. Perez-Sanchez and Brayden Smith.
There will be a pre-seminar presenting relevant background at the beginning graduate level starting at 1:30pm.