Talks

How did the universe evolve prior to the creation of the cosmic microwave background? There are no direct observational probes of the universe’s expansion history prior to the onset of Big Bang nucleosynthesis (BBN), and numerous theories predict deviations from radiation domination during the universe’s first second. Meanwhile, a persistent discrepancy between local and cosmological measurements of the Hubble constant has prompted us to reconsider the evolution of the universe between BBN and recombination. Since the growth of dark matter density perturbations depends on the expansion rate, deviations from the standard expansion history leave imprints on the matter power spectrum. I will discuss how adding decaying massive particles or fast-rolling scalar fields to the standard cosmological model impacts the abundance and structure of dark matter halos. Both cases illustrate how small-scale structure provides a powerful probe of the evolution of the universe prior to recombinatio

In slow-roll inflationary models, the inflaton can undergo excursions on the order of the Planck scale, leading to significant changes in the properties of fields coupled to the inflaton, referred to as spectator fields. These changes may result in transitions between weakly and strongly interacting regimes, or even alterations in mass squared within the spectator field sector during inflation. Such dynamics can induce phase transitions, which have profound implications for the early Universe. In this talk, I will explore the phenomenological consequences of these phase transitions, focusing on the production of gravitational waves, curvature perturbations, non-Gaussianities, dark matter, and baryon number. I will also demonstrate how gravitational waves generated by scalar perturbations induced by phase transitions may potentially explain the alleged gravitational wave signals observed in recent pulsar timing array studies.

Cosmological observations provide strong motivation for new physics beyond the Standard Model (SM). In addition to dark energy, and dark matter, the measured density of ordinary matter presents a further challenge to the SM. Creating enough baryons in the early universe to match what is seen today is difficult, and the SM does not appear to be able to do so. In this talk I will present some of the most promising mechanisms for baryogenesis and discuss how they will be tested by planned and proposed future experiments.

I will give a brief review of how large-language models are now being used for theoretical physics research. I will show the rapid progress of these models at the example of the TPBench benchmark, and present our recent work on improving their reliability with a symbolic verification agent and test-time scaling techniques. I will also discuss whether these models are truly reasoning and speculate how we might improve their performance in our field in the future.

Discrete minimal surfaces in the Euclidean space are central in the research field discrete differential geometry. Similarly, we can consider discrete spacelike maximal surfaces and discrete timelike minimal surfaces in Lorentz-Minkowski space. Although their formulation is analogous to discrete minimal surfaces, their behaviors are quite different.

In this talk we introduce recent progress on discrete zero mean curvature surfaces in Euclidean and Lorentz-Minkowski spaces. After briefly introducing basic results on discrete minimal surfaces, we investigate discrete zero mean curvature surfaces in Lorentz-Minkowski space and their singular behaviors. Furthermore, if time permits, we will introduce a construction of discrete zero mean curvature surfaces in Lorentz-Minkowski space that change causal characters along specific singularities.

This talk is partially based on ongoing project with Joseph Cho, Wayne Rossman, and Seong-Deog Yang.

This talk presents a study of biconservative hypersurfaces M4r(r = 0, 1, 2, 3, 4) in the pseudo-Euclidean space E5s(s = 0, 1, 2, 3, 4, 5) with constant norm of the second fundamental form. We find that every such hypersurface in E5s with a diagonal shape operator has constant mean curvature and constant scalar curvature. This is a joint work with Ram Shankar Gupta, Andreas Arvanitoyeorgos, and Marina Statha.

There is a broad body of work devoted to proving theorems of the following form: spaces with infinitely many special sub-spaces are either nonexistent or rare. Such finiteness statements are important in algebraic geometry, number theory, and the theory of moduli space and locally symmetric spaces. I will talk about joint work with Simion Filip and David Fisher proving a finiteness statement of this kind in a differential geometry setting. Our main theorem is that a closed negatively curved analytic Riemannian manifold with infinitely many closed totally geodesic hypersurfaces must be isometric to an arithmetic hyperbolic manifold. The talk will be more focused on providing background and context than details of proofs and should be accessible to a general audience.