| Geometric Analysis and Application [3] | Index and nullity of minimal surfaces |
3:45pm -
KT 906
|
We discuss the strategies and results on the determination of index and nullity of minimal surfaces. In particular, we prove that for any large enough $m$, the genus $\gamma=m+1$ equator-poles minimal surface doubling of the equatorial two-sphere in the round three-sphere, which has two catenoidal bridges at the poles and $m$ bridges equidistributed along the equatorial circle and was discovered in earlier work of Kapouleas, has index $2g+5=2m+7$ and nullity $6$. We also discuss the progress in the study of indices of minimal surfaces from similar constructions. https://yale.zoom.us/j/92334178441?pwd=FmjkR0LeihzxyR7AaNzsvTIPa11tmK.1 [4] |
| Geometry, Symmetry and Physics [5] | Tate-Shafarevich twists of Lagrangian fibrations |
4:30pm -
KT 801
|
A Tate-Shafarevich twist of a (proper) fibration modifies it by a 1-cocycle of automorphisms given by flows of (holomorphic) vector fields relative to the base, locally in the analytic topology. In general, the total space of a twist does not even have to be homeomorphic to that of the original fibration. Nevertheless, it was conjectured by Saccà that if one started with a Lagrangian fibration of an irreducible hyper-Kähler variety, then the total space of the resulting twist should always be deformation-equivalent to that of the original fibration, provided that it is also algebraic. I will introduce evidence towards this conjecture, including coincidences of certain cohomological invariants, as well as a proof under further topological constraints. |
| Analysis [6] | Lattice packing of spheres in high dimensions using a stochastically evolving ellipsoid | 4:00pm - |
We prove that in any dimension n there exists an origin-symmetric ellipsoid of volume c n^2 that contains no points of Z^n other than the origin. Here c > 0 is a universal constant. Equivalently, there exists a lattice sphere packing in R^n whose density is at least c n^2 / 2^n. Previously known constructions of sphere packings in R^n had densities of the order of magnitude of at most n log n / 2^n. Our proof utilizes a stochastically evolving ellipsoid that accumulates at least c n^2 lattice points on its boundary, while containing no lattice points in its interior except for the origin. |
| Quantum Topology and Field Theory [8] | A whittled complex for the Khovanov homology of torus braids |
4:30pm -
KT 801
|
We give an algorithm to reduce the number of generators of the Khovanov chain complex of torus braids $(\sigma_1\sigma_2 \dots\sigma_{n−1})^k$ on $n$ strands. I will begin the talk with context on the stable Khovanov homology of torus links leading to the open question of the structure of their homology theory, as well as potential applications to open questions concerning the colored Jones polynomial. Next I will discuss our work, joint with Carmen Caprau, Nicolle Gonzalez, and Radmila Sazdanovic, using Bar-Natan Gaussian elimination, that gives our whittled complex $\mathcal{FT}_n^k$. The whittled complex is homotopy-equivalent to the original Khovanov chain complex but with a reduced number of generators. After sketching the proof, I will end the talk discussing related future projects. |
| Learning seminar on Matroids and Algebraic Cycles [9] | Learning seminar on Matroids and Algebraic Cycles |
2:15pm -
KT 801
|
We will have our first introductory and organizational meeting to study the recent advances where matroids are used to show the failure of the integral Hodge conjecture. |
| Learning seminar on Groups, Geometry and Dynamics [10] | (Infinite) approximate groups. | 4:00pm - |
In this talk I will give a brief introduction to approximate groups, with a focus on infinite approximate groups. We will discuss known results in the abelian setting, and a few results about approximate lattices in Lie groups.
|
Links
[1] https://calendar.math.yale.edu/list/calendar/grid/week/abstract/2026-W04
[2] https://calendar.math.yale.edu/list/calendar/grid/week/abstract/2026-W06
[3] https://calendar.math.yale.edu/seminars/geometric-analysis-and-application
[4] https://yale.zoom.us/j/92334178441?pwd=FmjkR0LeihzxyR7AaNzsvTIPa11tmK.1
[5] https://calendar.math.yale.edu/seminars/geometry-symmetry-and-physics
[6] https://calendar.math.yale.edu/seminars/analysis
[7] https://yale.zoom.us/j/99948057179
[8] https://calendar.math.yale.edu/seminars/quantum-topology-and-field-theory
[9] https://calendar.math.yale.edu/seminars/learning-seminar-matroids-and-algebraic-cycles
[10] https://calendar.math.yale.edu/seminars/learning-seminar-groups-geometry-and-dynamics