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The failure to calculate the vacuum energy remains a central problem in theoretical physics. In my talk I present a new understanding of the cosmological constant problem, grounded in the insight that vacuum energy density can be expressed in terms of phase space volume. Introduction of a UV-IR regularization implies a relationship between the vacuum energy and entropy. Combining this insight with the holographic bound on entropy then yields a bound on the cosmological constant consistent with observations. It follows that the universe is large, and the cosmological constant is naturally small, because the universe is filled with a large number of degrees of freedom. The talk is based on our papers Phys.Rev.D 107 (2023) 12, 126016; e-Print: 2212.00901 [hep-th] and Int.J.Mod.Phys.D 32 (2023) 14, 2342004; e-Print: 2303.17495 [hep-th].

Observations of gravitational waves from binary black-hole mergers provide a unique testbed for General Relativity in the strong-field regime. To extract the most information, many gravitational-wave signals can be used in concert to place constraints on theories beyond General Relativity. Although these hierarchical inference methods have allowed for more informative tests, careful consideration is needed when working with astrophysical observations. Assumptions about the underlying astrophysical population and the detectability of possible deviations can influence hierarchical analyses, potentially biasing the results. In this talk, I will address these key assumptions and discuss their mitigation. Finally, I will demonstrate how we can leverage the astrophysical nature of gravitational-wave observations to our advantage to empirically bound the curvature dependence of extensions to General Relativity.

Chern-Simons theory is a topological quantum field theory which leads to link invariants, such as the Jones polynomial, through the expectation values of Wilson loops. The same link invariants also appear in a mathematical construction of Reshetikhin and Turaev which uses a trace on Yang-Baxter operators. Several algebraic structures are involved in these frameworks for computing link invariants, including the braid group, quantum algebras and centralizer algebras (such as the Temperley-Lieb algebra). In this talk, I will explain how the Askey-Wilson algebra, originally introduced in the context of orthogonal polynomials, can also be understood within the Chern-Simons theory and the Reshetikhin-Turaev link invariant construction.

Carl Sagan’s iconic question, "Who speaks for Earth?" from Cosmos invites us to reflect on whose voices are heard as we contemplate humanity's place in the universe. I will explore this question from the perspective of a queer mathematician, intertwining my personal journey with the broader experiences of LGBTQ+ scientists. Our diverse identities contribute to the richness of the scientific narrative, and by embracing our queerness, we ensure that the full spectrum of experiences is represented in the pursuit of knowledge. Drawing on Sagan’s legacy, I will argue that our voices, and our kindness to each other, are not just necessary but essential in shaping the future of science and our collective understanding of the world.