Abstracts

Week of March 29, 2026

March 30, 2026
Geometric Analysis and Application Existence of genus 2 minimal surfaces in 3-spheres 3:45pm -
KT 906

In the past decades, we have witnessed rapid development in the construction of minimal surfaces with controlled topology by Simon-Smith min-max theory. In this talk, I’ll discuss the existence of a number of genus 2 minimal surfaces in a 3-sphere with a positive-Ricci-curved metric. This is based on the recent work joint with Adrian Chu and Yangyang Li.
Geometry & Topology Knot complements decomposing into prisms 4:00pm -
KT 203

The Menasco-Reid conjecture supposes a negative answer to the question: Is there a hyperbolic knot complement which contains a closed embedded totally geodesic surface? Another Kirby problem asks which hyperbolic knot complements admit hidden symmetries? Here a manifold $M$ admits hidden symmetries, if $M$ covers an orbifold $Q$ and  $Q$ is not the quotient of $M$ by symmetries. Historically, there were three knot complements known to have hidden symmetries, and a conjecture Neumann and Reid states these are the only such examples.  After giving some of the relevant background, we will construct examples of knot complements that are counterexamples to both conjectures. Each of these knot complements has the property that it admits a decomposition into geometric prisms.  This is joint work with Jason DeBlois and Arshia Gharazolou and has appeared on the arxiv: arXiv:2507.01263.
Geometry, Symmetry and Physics Coulomb branches of 4d N=2 gauge theories and the double affine Grassmannian. 4:30pm -
KT 801
Coulomb branches of 3d N=4 gauge theories for a gauge group
G have been rigorously defined by Braverman, Finkelberg and Nakajima.
These are affine (singular) symplectic algebraic varieties; their
algebras of functions can be defined via the equivariant Borel-Moore
homology of certain ind-schemes closely related to the affine
Grassmannian of G.

The story is significantly more complicated in 4 dimensions. In that
case from physics one expects that the corresponding Coulomb branches
are (more or less) singular hyper-kahler manifolds, which look
drastically different in different complex structures: while for
generic complex structure it is still supposed to be an affine
algebraic variety, whose coordinate ring is just given by the
equivariant K-theory of the above ind-schemes, for some special
complex structure it is not; in that case the corresponding variety
has  a structure of an integrable system with affine base and with
generic fiber being an abelian variety (examples include the total
space of the affine Toda integrable system or the so-called Dolbeault
hyper-toric varieties).

In this talk I will
1) review the above ideas
2) present a conjectural construction of the homogeneous coordinate
ring of the above (projective over affine) varieties via the
Borel-Moore homology of some spaces related this time to the affine
Grassmannian of the affine Kac-Moody group associated to G
3) Explain how to make this construction precise in the case when G is a torus.

 
March 31, 2026
Geometric Analysis Learning Seminar Geometric Analysis Learning Seminar 10:30am -
KT 801

TBA
April 2, 2026
Analysis Incompressible Euler Blowup at the $C^{1,\frac{1}{3}}$ Threshold 4:00pm -
Zoom

We prove finite-time Type–I blowup for the three-dimensional incompressible Euler equations in the
axisymmetric no-swirl class, with initial velocity in $C^{1,\alpha}(\R^3)\cap L^2(\R^3)$ and odd
symmetry in $z$, for \emph{every} $\alpha\in(0,\tfrac13)$. Since axisymmetric no-swirl solutions
with $C^{1,\alpha}$ velocity are globally regular for $\alpha >\tfrac13$,  this result is sharp up to the
endpoint: it covers the entire open interval $(0,  \tfrac{1}{3})$,  reaching the structural regularity threshold
from below.

The singularity forms at the stagnation point on the symmetry axis, with vorticity and strain
blowing up at the Type–I rate $\|\bs{\omega}(\cdot,t)\|_{L^\infty}\sim(T^*-t)^{-1}$,
$-\partial_z u_z(0,0,t)\sim(T^*-t)^{-1}$, and the meridional Jacobian collapsing as
$J(t)\sim\big(\Gamma(T^*-t)\big)^{1/(1-3\alpha)}$.

The proof introduces a Lagrangian clock-and-driver framework that replaces the Eulerian self-similar
ansatz used in prior work. The collapse dynamics are governed by a Riccati-type ODE for the axial
strain, and the decisive step is a non-perturbative bound on the strain–pressure competition,
established via a spectral decomposition of the angular pressure source, showing that the quadratic
strain term dominates the resistive pressure Hessian uniformly for all $\alpha\in(0,\tfrac13)$.

The blowup mechanism is structurally stable: it persists for an open set of admissible angular
profiles in a weighted topology.
Quantum Topology and Field Theory Some algebra behind non-semisimple TQFTs 4:30pm -
KT 801

In this talk I will give an introductory lecture on constructing Topological Quantum Field Theories (TQFTs) from non-semisimple categories. The main goal of the talk is to give a hint of what is needed to extend the Turaev-Viro and Crane-Yetter TQFTs from the useful setting of semisimple categories to the non-semisimple world.  I will do this from an algebraic and categorical point of view.  In particular, I will discuss what kind of structures are needed in non-semisimple categories to give rise to (2+1)-TQFTs.  Then I will remark that any spherical tensor category (in the sense of Etingof, Douglas et al.) has such structures.  This work is joint with Francesco Costantino, Benjamin Haïoun, Bertrand Patureau-Mirand and Alexis Virelizier and based on arXiv:2302.04509 and arXiv:2306.03225.
April 3, 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 Measures of maximal entropy. 4:00pm -
KT 801 or KT217