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We hope you are enjoying your time in our graduate programs. Check out our course offerings, information about degree completion, the PhD qualifying exams, the PhD lecturing requirement, and instructions on submitting your PhD annual activity report. If you still have some years ahead in your grad studies, you might be interested in applying for scholarships.

If you have any administrative questions, please contact us at cograd@uwaterloo.ca.

Seminars in Combinatorics and Optimization

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.

Here we show and formally prove that communication systems that need to be resilient against certain types of state loss (which can occur in practice) fundamentally cannot achieve full PCS for end-users. Whereas previous work showed that the Signal messenger did not achieve this with its current session-management layer, we isolate the exact conditions that cause this failure, and we show why this cannot be simply solved in communication systems by implementing a different session-management layer or an entirely different protocol. Moreover, we clarify the trade-off of the maximum number of sessions between two users (40 in Signal) in terms of failure-resilience versus security.
Our results have direct consequences for the design of future secure communication systems and could motivate either the simplification of redundant mechanisms or the improvement of session-management designs to provide better security trade-offs with respect to state loss/failure tolerance.
Monday, January 26, 2026 11:30 am - 12:30 pm EST (GMT -05:00)

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. 

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.