Talks

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.

CMC (constant mean curvature) surfaces are critical with respect to area as long as we restrict to competitor surfaces which 'enclose the same volume'. The index of a CMC surface is the number of ways we can locally deform it to reduce its area whilst enclosing the same amount of volume. We will show that the index of a CMC surface is bounded linearly from above in terms of its genus and a Willmore-type energy i.e. the more unstable a surface is the more genus and/or ‘Willmore energy’ it must have. Joint work with Luca Seemungal. 

An unavoidable part of studying astrophysics based on catalogs of detected events is quantifying the probability of detecting different types of events. I will briefly discuss the types of design considerations that go into constructing such estimates and how they will scale with larger catalog sizes. I will also introduce the wide variety of uses for such data products, including uncovering unexpected features within the data caused by the fact that humans build and operate the detectors.