Calendar

On May 6-8, 2022, the CMSA will be hosting a second NSF FRG Workshop.

This project brings together a community of researchers who develop theoretical and computational models to characterize shapes. Their combined interests span Mathematics (Geometry and Topology), Computer Science (Scientific Computing and Complexity Theory), and domain sciences, from Data Sciences to Computational Biology.

Scientific research benefits from the development of an ever-growing number of sensors that are able to capture details of the world at increasingly fine resolutions. The seemingly unlimited breadth and depth of these sources provide the means to study complex systems in a more comprehensive way. At the same time, however, these sensors are generating a huge amount of data that comes with a high level of complexity and heterogeneity, providing indirect measurements of hidden processes that provide keys to the systems under study. This has led to new challenges and opportunities in data analysis. Our focus is on image data and the shapes they represent. Advances in geometry and topology have led to powerful new tools that can be applied to geometric methods for representing, searching, simulating, analyzing, and comparing shapes. These methods and tools can be applied in a wide range of fields, including computer vision, biological imaging, brain mapping, target recognition, and satellite image analysis.

This workshop is part of the NSF FRG project: Geometric and Topological Methods for Analyzing Shapes.

The workshop will be held in room G10 of the CMSA, located at 20 Garden Street, Cambridge, MA. For a list of lodging options convenient to the Center, please visit our recommended lodgings page.

We invite junior researchers to present a short talk in the workshop. The talks are expected to be 15-20 minutes in length. It is a great opportunity to share your work and get to know others at the workshop. Depending on the number of contributed talks, the organizers will review the submissions and let you know if you have been selected. If you are interested, please send your title and abstract to FRG2022harvard@gmail.com by 5 pm, April 30, 2022.

Workshop on Discrete Shapes
May 6–8, 2022

Organizers:

• David Glickenstein (University of Arizona)
• Joel Hass (University of California, Davis)
• Patrice Koehl (University of California, Davis)
• Feng Luo (Rutgers University, New Brunswick)
• Maria Trnkova (University of California, Davis)
• Shing-Tung Yau (Harvard)

Current List of Speakers:

• Miri Ben-Chen (Technion)
• Chris Bishop (Stony Brook)
• Alexander Bobenko (TU Berlin)
• John Bowers (James Madison)
• Herbert Edelsbrunner  (IST, Austria)
• Steven Gortler (Harvard)
• Craig Gotsman (New Jersey Institute of Technology)
• David Gu (Stony Brook)
• Anil Hirani (UIUC)
• Yanwen Luo (Rutgers)
• Peter Schroeder (Caltech)
• Justin Solomon (MIT)
• Tianqi Wu (Clark University)

For more information, please see https://cmsa.fas.harvard.edu/2022-frg/

Benoist and Wittenberg recently introduced a new rationality obstruction that refines the classical the Clemens–Griffiths intermediate Jacobian obstruction to rationality, and exhibited its strength by showing that this new obstruction characterizes rationality for intersections of two quadrics.  We show that this phenomenon does not extend to all geometrically rational threefolds.  We construct examples of conic bundle threefolds over P^2 that have no refined intermediate Jacobian obstruction to rationality, yet fail to be rational. This is joint work with S. Frei, L. Ji, S. Sankar, and I. Vogt.

We are familiar with the idea that quantum gravity in AdS can holographically emerge from complex patterns of entanglement, but can the physics of big bang cosmology emerge from a quantum many-body system? In this talk I will argue that standard tools of holography can be used to describe fully non-perturbative microscopic models of cosmology in which a period of accelerated expansion may result from the positive potential energy of time-dependent scalar fields evolving towards a region with negative potential. In these models, the fundamental cosmological constant is negative, and the universe eventually recollapses in a time-reversal symmetric way. The microscopic description naturally selects a special state for the cosmology. In this framework, physics in the cosmological spacetime is dual to the vacuum physics in a static planar asymptotically AdS Lorentzian wormhole spacetime, in the sense that the background spacetimes and observables are related by analytic continuation. The dual spacetime is weakly curved everywhere, so any cosmological observables can be computed in the dual picture via effective field theory without detailed knowledge of the UV completion or the physics near the big bang. Based on 2203.11220 with S. Antonini, P. Simidzija, and M. Van Raamsdonk.

For information on how to join, please see:  https://cmsa.fas.harvard.edu/seminars-and-colloquium/

Many statistical and computational tasks boil down to comparing probability measures expressed as density functions, clouds of data points, or generative models.  In this setting, we often are unable to match individual data points but rather need to deduce relationships between entire weighted and unweighted point sets. In this talk, I will summarize our team’s recent efforts to apply geometric techniques to problems in this space, using tools from optimal transport and spectral geometry. Motivated by applications in dataset comparison, time series analysis, and robust learning, our work reveals how to apply geometric reasoning to data expressed as probability measures without sacrificing computational efficiency.

For information on how to join, please see:  https://cmsa.fas.harvard.edu/seminars-and-colloquium/

The CDF collaboration recently reported a new precise measurement of the W boson mass MW with a central value significantly larger than the SM prediction. We explore the effects of including this new measurement on a fit of the Standard Model (SM) to electroweak precision data. We characterize the tension of this new measurement with the SM and explore potential beyond the SM phenomena within the electroweak sector in terms of the oblique parameters S, T and U. We show that the large MW value can be accommodated in the fit by a large, nonzero value of U, which is difficult to construct in explicit models. Assuming U = 0, the electroweak fit strongly prefers large, positive values of T. Finally, we study how the preferred values of the oblique parameters may be generated in the context of models affecting the electroweak sector at tree- and loop-level. In particular, we demonstrate that the preferred values of T and S can be generated with a real SU(2)L triplet scalar, the humble swino, which can be heavy enough to evade current collider constraints, or by
(multiple) species of a singlet-doublet fermion pair. We highlight challenges in constructing other simple models, such as a dark photon, for explaining a large MW value, and several directions for further study.

For information on how to join, please see:  https://cmsa.fas.harvard.edu/seminars-and-colloquium/

The size Ramsey number of a graph $H$ is the minimum number of edges in a  graph $G$ with the property that no matter how we two-color the edges of  $G$, we can find a monochromatic copy of $H$. This notion was introduced  in 1978 by Erdős, Faudree, Rousseau, and Schelp, and despite more than  four decades of work, there is a lot that is still unknown; notably, of  the four questions that conclude the Erdős–Faudree–Rousseau–Schelp paper,  only one had been resolved as of last year. In this talk, I’ll discuss  recent work in which we resolve $\approx 2.5$ of the three remaining  questions, using a variety of new combinatorial and probabilistic constructions.

Based on joint work with David Conlon and Jacob Fox.