Abstract: We discuss the algebraic geometry of maximum likelihood estimation from the perspective of scattering amplitudes in particle physics. A guiding examples the moduli space of n-pointed rational curves. The scattering potential plays the role of the log-likelihood function, and its critical points are solutions to rational function equations. Their number is an Euler characteristic. Soft […]
Abstract: In “Mirror symmetry for log Calabi–Yau surfaces I,” given a smooth log Calabi–Yau surface pair (Y,D), Gross–Hacking–Keel constructed its mirror family as the spectrum of an explicit algebra whose structure coefficients are determined by the enumerative geometry of (Y,D). As a follow-up of the work of Gross–Hacking–Keel, when (Y,D) is positive, we prove the […]
On April 27–29, 2022, the CMSA hosted a workshop on Nonlinear Algebra and Combinatorics. Organizers: Bernd Sturmfels (MPI Leipzig) and Lauren Williams (Harvard). In recent years, ideas from integrable systems and scattering amplitudes have led to advances in nonlinear algebra and combinatorics. In this short workshop, aimed at younger participants in the field, we will […]
Speaker: Venkatesan Guruswami, UC Berkeley Title: Long common subsequences between bit-strings and the zero-rate threshold of deletion-correcting codes Abstract: Suppose we transmit n bits on a noisy channel that deletes some fraction of the bits arbitrarily. What’s the supremum p* of deletion fractions that can be corrected with a binary code of non-vanishing rate? Evidently p* is at […]
https://www.youtube.com/watch?v=c6_RbJS8CoM&list=PL0NRmB0fnLJQAnYwkpt9PN2PBKx4rvdup&index=14&t=2s Abstract: We will overview the program of geometrically engineering four dimensional supersymmetric QFTs as compactifications of six dimensional SCFTs. In particular we will discuss how strong coupling phenomena in four dimensions, such as duality and emergence of symmetry, can be better understood in such geometric constructions.
Speaker: Guillaume Duclos (Brandeis) Title: Building active nematic and active polar liquids out of biological machines Abstract: Active matter describes out-of-equilibrium materials composed of motile building blocks that convert free energy into mechanical work. The continuous input of energy at the particle scale liberates these systems from the constraints of thermodynamic equilibrium, leading to emergent collective behaviors not found in passive materials. In this talk, I […]
Abstract: Let X be a compact hyperbolic surface. We can see that there is a constant C(X) such that the intersection number of the closed geodesics is \leq C(X) times the product of their lengths. Consider the optimum constant C(X). In this talk, we describe its asymptotic behavior in terms of systole, length of the shortest […]
Abstract: The nonlinear stability of the slowly-rotating Kerr-de Sitter family was first proven by Hintz and Vasy in 2016 using microlocal techniques. In my talk, I will present a novel proof of the nonlinear stability of slowly-rotating Kerr-de Sitter spacetimes that avoids frequency-space techniques outside of a neighborhood of the trapped set. The proof uses […]
Member Seminar Speaker: Sergiy Verstyuk Title: Machine Learning the Gravity Equation for International Trade Abstract: We will go through modern deep learning methods and existing approaches to their interpretation. Next, I will describe a graph neural network framework. You will also be introduced to an economic analog of gravity. Finally, we will see how these […]
General Relativity Workshop on scalar curvature, minimal surfaces, and initial data sets Dates: May 2–5, 2022 Location: Room G10, CMSA, 20 Garden Street, Cambridge MA 02138 and via Zoom webinar. Advanced registration for in-person components is required. Organizers: Dan Lee (CMSA/CUNY), Martin Lesourd (CMSA/BHI), and Lan-Hsuan Huang (University of Connecticut). Speakers: Zhongshan An, University of Connecticut […]
Abstract: Consider a bootstrap percolation process that starts with a set of `infected’ triangles $Y \subseteq \binom{}3$, and a new triangle f gets infected if there is a copy of K_4^3 (= the boundary of a tetrahedron) in which f is the only not-yet infected triangle. Suppose that every triangle is initially infected independently with […]
Abstract: Although everyone talks about AI + healthcare, many people were unaware of the fact that there are two possible outcomes of the collaboration, due to the inherent dissimilarity between the two giant subjects. The first possibility is healthcare-leads, and AI is for building new tools to make steps in healthcare easier, better, more effective or […]