Quantum Field Theory and Physical Mathematics Seminar Speaker: Kevin Costello (Perimeter Institute) Title: Non-perturbative aspects of self-dual gauge theory Abstract: Self-dual gauge theory is conformal in perturbation theory, but has a non-trivial beta-function when instanton effects are included. I will give two computations of this beta-function, one based on the Grothendieck-Riemann-Roch formula and one using holography […]
Colloquium Speaker: Alexei Borodin, MIT Title: Geometry of dimer models Abstract: Random dimer coverings of large planar graphs are known to exhibit unusual and visually apparent asymptotic phenomena that include formation of frozen regions and various phases in the unfrozen ones. For a specific family of subgraphs of the (periodically weighted) square lattice known as the Aztec diamonds, the asymptotic behavior of dimers admits a precise description in […]
Geometry and Quantum Theory Seminar Speakers: Daniel Spiegel, Harvard Math Title: A Classifying Space for Phases of Matrix Product States Abstract: Alexei Kitaev has conjectured that there should be a loop spectrum consisting of spaces of gapped invertible quantum spin systems, indexed by spatial dimension d of the lattice. Motivated by Kitaev’s conjecture, I will […]
https://youtu.be/04E8r76TetQ New Technologies in Mathematics Seminar Speaker: Alex Damian, Harvard Title: Understanding Optimization in Deep Learning with Central Flows Abstract: Traditional theories of optimization cannot describe the dynamics of optimization in deep learning, even in the simple setting of deterministic training. The challenge is that optimizers typically operate in a complex, oscillatory regime called the "edge of […]
Algebra Seminar Speaker: David Treumann (Boston College) Title: Profinite tensor powers Abstract: I'll discuss the problem of defining a tensor product of profinitely many copies of a vector space V, and propose a definition $\bigotimes_X^{mcc} V$ in the special situation that (1) V is finite-dimensional over F_2, and (2) the profinite X indexing the tensor […]
https://youtu.be/vf3pIK9I9HI Differential Geometry and Physics Seminar Speaker: Xingyang Yu, Virginia Tech Title: Symmetries and Moduli Spaces: Baby Steps beyond Calabi-Yau Abstract: I will explore the interplay between symmetries and moduli spaces in string compactifications, starting from the familiar Calabi–Yau case and then taking some baby steps toward more general settings. A classical benchmark is the line […]
Member Seminar Speaker: Lorenzo Riva Title: The Rozansky-Witten field theory in the functorial TQFT formalism Abstract: This will be a broad talk about the topic of my PhD thesis. We will discuss a particular example of a 3D field theory from physics called Rozansky-Witten which is interesting from both a physical and a mathematical point […]
Geometry and Quantum Theory Seminar Speaker: Dylan Galt, Harvard (60 minute talk) Title: What is a "nonlinear" near-symplectic form? Abstract: In this talk, I will explain how one might understand this question and why a possible answer can be found in the geometry of coassociative 4-folds, a special class of minimal submanifolds discovered by Harvey and Lawson. […]
https://youtu.be/qVoEUFvDqWk Millennium Prize Problems Lecture Date: October 15, 2025 Time: 5:00–6:00 pm Location: Harvard Science Center Hall D, 1 Oxford St., Cambridge MA Speaker: Sourav Chatterjee, Stanford University Title: Yang-Mills and the foundations of quantum field theory Abstract: Yang-Mills theories are the building blocks of the Standard Model of quantum mechanics, which is the best […]
Algebra Seminar Speaker: Linquan Ma (Purdue University) Title: Lech's inequality and stability of local rings Abstract: We explore Lech's inequality relating the colength and multiplicity of m-primary ideals in a Noetherian local ring (R,m). We introduce a natural invariant that measures the sharpness of Lech's inequality and show its connections with singularities of asymptotically semistable varieties […]
Differential Geometry and Physics Seminar Speaker: Andy Neitzke, Yale Title: Abelianization of tau functions Abstract: The symplectic and hyperkahler geometry of moduli spaces of flat connections over Riemann surfaces is in a sense quantized by the theory of isomonodromic tau functions. These functions in turn arise as partition functions in the conformal field theory of […]
Member Seminar Speaker: Blake Bordelon Title: DMFT, Two Point Correlations of Resolvents, and Applications to Machine Learning Theory Abstract: Machine learning algorithms evolve the parameters of a model in a high dimensional and disordered loss landscape. To characterize the effects of random initialization of model parameters, randomly sampled training data, and the effect of SGD noise, it […]