Week of April 5, 2026

April 6, 2026
Geometric Analysis and Application Geometry of Mean Curvature Flow near Cylindrical Singularities Ao Sun - Lehigh University 3:45pm -
KT 906
Geometry, Symmetry and Physics Elementary categorification of U_q(gl(1|1)) Alexei Oblomkov - U Mass Amherst 4:30pm -
KT 801
April 7, 2026
Geometric Analysis Learning Seminar Geometric Analysis Learning Seminar 10:30am -
KT 801
April 9, 2026
Analysis Completeness of reparametrization-invariant Sobolev metrics on the space of surfaces Martin Bauer - Florida State University 4:00pm -
Zoom
Quantum Topology and Field Theory Summing over topologies in 3d gravity Scott Collier - Syracuse University 4:30pm -
KT 801
April 10, 2026
Learning seminar on Matroids and Algebraic Cycles Learning seminar on Matroids and Algebraic Cycles 2:15pm -
KT 801
Learning seminar on Groups, Geometry and Dynamics Learning seminar on Groups Geometry and Dynamics 4:00pm -
KT 801

Abstracts

Week of April 5, 2026

April 6, 2026
Geometric Analysis and Application Geometry of Mean Curvature Flow near Cylindrical Singularities 3:45pm -
KT 906

The cylindrical singularities are prevalent but complicated in geometric flows. We discuss one of the simplest extrinsic flows, the mean curvature flow, and illustrate how the local dynamics of the singularities influence the singular set itself, and the geometry and topology of the flow. This talk is based on a series of joint work with Zhihan Wang (Cornell) and Jinxin Xue (Tsinghua).
Geometry, Symmetry and Physics Elementary categorification of U_q(gl(1|1)) 4:30pm -
KT 801

In joint work with Lev Rozansky we construct a coherent sheaf realization of the tensor powers of $U_q(gl(1|1))$ vector representation $\mathbb{C}^{1|1}$. The construction reveals the non-semisimple nature of the representation of $U_q(gl(1|1))$. I plan to explain how this
construction extends to а wider class of the representations. The origin of the construction is a boson/fremion correspondence in physics context and Legandre transformation in the mathematical context.
April 7, 2026
Geometric Analysis Learning Seminar Geometric Analysis Learning Seminar 10:30am -
KT 801

TBA
April 9, 2026
Analysis Completeness of reparametrization-invariant Sobolev metrics on the space of surfaces 4:00pm -
Zoom
The space of immersions of a closed manifold M into Euclidean space is among the most important infinite dimensional manifolds. The most natural Riemannian metrics on this space are reparametrization-invariant Sobolev metrics; these form a hierarchy of metrics, based on their order—the number of derivatives they “see”. They arise as natural extensions of right-invariant metrics on diffeomorphism groups, central to Arnold’s geometric formulation of hydrodynamical equations. Beyond their theoretical significance, they play a crucial role in mathematical shape analysis and geometric data science, where they enable meaningful and robust comparisons between shapes modeled as curves or surfaces. 
 
In 2013, David Mumford conjectured that for orders larger than dim(M)/2 + 1, these geometries are complete. Note, that by the seminal work of Ebin and Marsden a similar statement is known to be true for diffeomorphism groups. In the context of immersions this conjecture was shown to be true in the case of immersed curves in the work of Bruveris, Michor and Mumford. In this talk I will present the first construction of complete metrics on immersions of two-dimensional surfaces, discuss the context and techniques, as well as possible extensions to higher dimensions. Based on joint work with Cy Maor and Benedikt Wirth.
Quantum Topology and Field Theory Summing over topologies in 3d gravity 4:30pm -
KT 801

I will describe recent progress towards understanding the gravitational path integral in AdS_3 quantum gravity and its boundary interpretation. A central question is: which spacetime topologies should be included in the path integral, and why? To address this question, we formulate a “statistical bootstrap” that constrains the universal statistics of CFT data in the boundary theory, imposing crossing symmetry and “typicality” (a generalization of the eigenstate thermalization hypothesis). These constraints are geometrized by iterative surgery moves on bulk manifolds that we refer to as the “gravitational machine,” leading to an infinite set of non-handlebody topologies that we argue must be included in the path integral. The machine generates only on-shell (hyperbolic) 3-manifolds, whose partition functions can be computed exactly using Virasoro TQFT. But not all hyperbolic manifolds are produced by this procedure. This reveals a large landscape of consistent sums over topologies. Based on joint work with Alexandre Belin, Lorenz Eberhardt, Diego Liska, and Boris Post.
April 10, 2026
Learning seminar on Matroids and Algebraic Cycles Learning seminar on Matroids and Algebraic Cycles 2:15pm -
KT 801

TBA
Learning seminar on Groups, Geometry and Dynamics Learning seminar on Groups Geometry and Dynamics 4:00pm -
KT 801

TBA