Abstracts

Week of March 1, 2026

March 2, 2026
Geometric Analysis Learning Seminar Regularity of Einstein 5-manifolds via 4-dimensional gap theorems 3:45pm -
KT 906

We refine the regularity of noncollapsed limits of Einstein 5-manifolds. In particular, we prove uniqueness of tangent cones along the full top stratum of singular set and show that the entire singular set is contained in a countable union of bi-Lipschitz curves and points. Moreover, we establish that thesingular curve carries a real-analytic Einstein orbifold structure and is a geodesic in the limit space. The proofs rely on new 4-dimensional gap theorems for spherical and hyperbolic Einstein orbifolds. This is joint work with Tristan Ozuch.
Geometry, Symmetry and Physics The constant sheaf on Bun_G 4:30pm -
KT 801

Given a smooth projective curve X and a reductive group G, the geometric Langlands equivalence proved by Gaitsgory, Raskin et al. (roughly) gives an equivalence between sheaves on the stack Bun_G(X) of G-bundles on X (automorphic side) and quasi-coherent sheaves on the stack of G^-local systems on X (spectral side). To compute the image of an object under the geometric Langlands equivalence, one usually bootstraps from the Whittaker model. This method fails for the constant sheaf on Bun_G(X), which is “maximally singular.” Still, we will compute its image under the equivalence, confirming a conjecture of V. Lafforgue. As a consequence, when X is over F_q we find a spectral description for the constant function on Bun_G(X)(F_q
March 3, 2026
Geometric Analysis Learning Seminar Geometric Analysis Learning Seminar 10:30am -
KT 801

TBA
March 5, 2026
Analysis Soliton Resolution Conjecture for the energy-critical heat equation 4:00pm -
KT 201

The Soliton Resolution Conjecture predicts that finite-energy solutions to nonlinear dispersive PDEs asymptotically decouple into a sum of stationary solutions, called solitons, and free radiation, with an error that goes to zero in the energy norm. In this talk, we discuss the conjecture for the energy-critical nonlinear heat equation in dimension $d\geq 3$ and present its proof in the radial case. If time permits, we will also discuss recent progress in the non-radial setting, with potential applications to other geometric flows such as the Yang-Mills heat flow.
Quantum Topology and Field Theory Quantum algebras from generalized Poisson sigma models 4:30pm -
KT 801

Poisson sigma models sit at the intersection of deformation theory, geometry, and quantum field theory; specifically, the perturbative expansion of the two-dimensional Poisson sigma model with boundary is known to recover Kontsevich’s deformation quantization formula. In this talk, we introduce a higher-dimensional holomorphic–topological generalization of Poisson sigma models and explain their connections to the deformation quantization (or obstruction) of holomorphic–topological factorization algebras. This construction can be viewed as a field-theoretic incarnation of the higher Deligne conjecture. We also explain how these models relate to the construction of Hopf-type algebras via Koszul duality, and explore examples related to the quantization of Lie bialgebras, W-algebras, and Yangians.
March 6, 2026
Learning seminar on Groups, Geometry and Dynamics Lattices, fundamental domains and Ratner's orbit closure theorem. 4:00pm -
KT 801 or KT217