Member Seminar Speaker: Ahsan Khan Title: Formality Theorem and Webs Abstract: The “formality theorem” of Kontsevich was a key result that implies that every Poisson manifold admits a deformation quantization. I will review the ideas behind the formality theorem and discuss a potentially novel viewpoint on it involving webs and twisted masses.
Member Seminar Speaker: Vasily Krylov, CMSA Title: ADHM spaces and their quantizations Abstract: In their paper “Construction of Instantons,” Atiyah, Drinfeld, Hitchin, and Manin introduced an algebraic construction of the moduli space of instantons on R^4, now also known as the "ADHM space." This is a Poisson complex variety; it has been actively studied by both […]
Member Seminar Speaker: Uri Kol Title: Quantum Criticality in Black Hole Scattering Abstract: Perturbation theory around rotating black holes captures a few important effects in the physics of gravitational waves emitted from binary mergers. Despite a long and rich history, developing a qualitative understanding of the system remains a challenging problem. In this talk I […]
Member Seminar Speaker: Alejandro Poveda Title: Identity crises phenomena in the large cardinal hierarchy Abstract: It is well-known that certain mathematical questions cannot be answered on the grounds of the standard foundation of mathematics. Large cardinal axioms constitute a series of postulates about the higher infinite which permit to classify these undecidable problems in a coherent hierarchy way. […]
Member Seminar Speaker: Robert Moscrop Title: On the Coulomb branch scaling dimensions of 4d N=2 SCFTs Abstract: To each four dimensional N=2 superconformal field theory of rank-r, one can associate an r-tuple of numbers given by the scaling dimensions of a special set of protected operators whose VEVs parameterise the Coulomb branch. In this talk, I will demonstrate […]
Member Seminar Speaker: Iacopo Brivio Title: Smooth projective fibrations over the projective line and their sections Abstract: Suppose $f\colon X\to \mathbf{CP}^1$ is a smooth projective fibration, is it then true that $f$ has a section? This deceptively simple result was established by Seidel and McDuff using deep methods of symplectic geometry. Alex Pieloch recently generalized this to morphisms […]
Member Seminar Speaker: Houcine Ben Dali, Harvard CMSA Title: Jack polynomials and enumeration of non-orientable maps Abstract: A map is a graph embedded on a surface, which may be orientable or not. The representation theory of the symmetric group can be used to write the generating series of maps on orientable surfaces using Schur symmetric functions. Several […]
Member Seminar Speaker: Matteo Parisi Title: The Combinatorics of the Amplituhedron – Tiles, Tilings, and Cluster Algebras Abstract: The amplituhedron is the image of the positive Grassmannian—the region of the Grassmannian where all Plücker coordinates are nonnegative—under a totally positive linear map. It is a far-reaching generalization of cyclic polytopes and hyperplane arrangements, and the positive […]
Member Seminar Speaker: Charles Doran, CMSA Title: A Tetrahedral Approach to Calabi-Yau Geometry Abstract: We will open with a quick introduction to the what and why of Calabi-Yau geometry. Following this, we will consider the problem of deforming tetrahedra while preserving the areas of their faces, following our noses to discover a beautiful path to […]
Member Seminar Speaker: Tomer Ezra Title: The Competition Complexity of Dynamic Pricing Abstract: One of the most fundamental questions in mechanism design is the tradeoff between simplicity and optimality. A canonical example of this tradeoff is competition complexity in auctions, which quantifies how many additional bidders are needed for a simple mechanism to (approximately) match the revenue of the optimal mechanism. In […]
Member Seminar Speaker: Hugo Cui Title: Learning diffusion models in high-dimensions Abstract: We consider the problem of learning a generative model parametrized by a two-layer auto-encoder, and trained with online stochastic gradient descent, to sample from a high-dimensional data distribution with an underlying low-dimensional structure. We provide a tight asymptotic characterization of low-dimensional projections of […]
Member Seminar Speaker: Bowen Yang Title: Homological Invariants in Translation-Invariant Pauli Stabilizer Codes Abstract: Pauli stabilizer codes serve as foundational models in quantum error correction and the study of exotic quantum phases. In this talk, we explore the application of homological methods to translationally invariant Pauli stabilizer codes with qudits of varying dimensions. We introduce a series of invariants, […]