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Seminars in Combinatorics and Optimization

Thursday, February 13, 2025 2:00 pm - 3:00 pm EST (GMT -05:00)

Algebraic and enumerative combinatorics seminar-Yasaman Yazdi

Title: Statistical Fluctuations in the Causal Set-Continuum Correspondence

Speaker Yasaman Yazdi
Affiliation Dublin Institute for Advanced Studies and Perimeter Institute
Location MC 5479

 Abstract: Causal set theory is an approach to quantum gravity that proposes that spacetime is fundamentally discrete and the causal relations among the discrete elements play a prominent role in the physics. Progress has been made in recognizing and understanding how some continuumlike features can emerge from causal sets at macroscopic scales, i.e., when the number of elements is large. An important result in this context is that a causal set is well approximated by a continuum spacetime if there is a number-volume correspondence between the causal set and spacetime.

This occurs when the number of elements within an arbitrary spacetime region is proportional to its volume. Such a correspondence is known to be best achieved when the number of causal set elements is randomly distributed according to the Poisson distribution. I will discuss the Poisson distribution and the statistical fluctuations it induces in the causal set-continuum correspondence, highlighting why it is important and interesting. I will also discuss new tools and techniques that facilitate such analyses.

There will be a pre-seminar presenting relevant background at the beginning graduate level starting at 1pm,

Friday, February 14, 2025 3:30 pm - 4:30 pm EST (GMT -05:00)

Tutte colloquium-Xi He

Title:Accuracy Aware Minimally Invasive Data Exploration For Decision Support

Speaker: Xi He
Affiliation: University of Waterloo
Location: MC 5501

Abstract: Decision-support (DS) applications, crucial for timely and informed decision-making, often analyze sensitive data, raising significant privacy concerns. While privacy-preserving randomized mechanisms can mitigate these concerns, they introduce the risk of both false positives and false negatives. Critically, in DS applications, the number of false negatives often needs to be strictly controlled. Existing privacy-preserving techniques like differential privacy, even when adapted, struggle to meet this requirement without substantial privacy leakage, particularly when data distributions are skewed. This talk introduces a novel approach to minimally invasive data exploration for decision support. Our method minimizes privacy loss while guaranteeing a bound on false negatives by dynamically adapting privacy levels based on the underlying data distribution. We further extend this approach to handle complex DS queries, which may involve multiple conditions on diverse aggregate statistics combined through logical disjunction and conjunction. Specifically, we define complex DS queries and their associated accuracy requirements, and present algorithms that strategically allocate a privacy budget to minimize overall privacy loss while satisfying the bounded accuracy guarantee.